Levels 3 to 6 eBook - Jebel Ali Secondary School...

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Levels 3 to 7eBook Answers

Level 3 Contents ................. (i)

Level 4 Contents ................. (ii)

Level 5 Contents ................. (iii)

Level 6 Contents ................. (iv)

Level 7 Contents ................. (v)

APP Record Sheet .............. (vi)

Level 3 Certificate ............... (vii)

Level 4 Certificate ............... (viii)

Level 5 Certificate ............... (ix)

Level 6 Certificate ............... (x)

Level 7 Certificate ............... (xi)

Worksheets ......................... 1A to 134

Extras - Weights .................. 135A to 135E

Extras - Balances ................ 136A to 136E

Extras - Congruent Halves .. 137A to 137E

Extras - Circles .................... 138A to 138E

M atchathsWM atchathsW

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Number

N1..... Place Value .......................................................1A, 1BN2..... Negative Numbers.............................................2A, 2BN3..... Introduction to Fractions ....................................3A, 3BN4..... Money ...............................................................4A, 4B

Calculating

C1..... Mental Addition ..................................................5A, 5BC2..... Mental Subtraction ............................................6A, 6BC3..... Addition of Integers ...........................................7A, 7BC4..... Subtraction of Integers ......................................8A, 8BC5..... Multiplication by 2, 3, 4, 5 and 10 ......................9A, 9BC6..... Division by 2, 3, 4, 5 and 10 ..............................10A, 10B

Shape, Space and Measure

S1 ..... Reflective Symmetry of 2D Shapes ...................11A, 11BS2 ..... Recognising Nets ..............................................12A, 12BS3 ..... Reflecting Shapes .............................................13A, 13BS4 ..... Metric Units .......................................................14A, 14BS5 ..... Time ..................................................................15A, 15B

Handling Data

D1..... Reading Bar Charts and Pictograms .................16A, 16B, 16CD2..... Drawing Bar Charts and Pictograms .................17A, 17B

Level 3

N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2

LEVEL 3

Page

Page (i)

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Number

N5..... Number Patterns ...............................................18A, 18BN6..... Square Numbers ...............................................19A, 19BN7..... Multiples ............................................................20A, 20BN8..... Factors ..............................................................21A, 21BN9..... Multiplication and Division by 10 and 100 .........22A, 22BN10... Fractions and Percentages................................23A, 23BN11 ... Ordering Decimals .............................................24A, 24BN12... Basic Ratio ........................................................25A, 25B

Calculating

C7..... Addition .............................................................26A, 26BC8..... Subtraction ........................................................27A, 27BC9..... Short Multiplication ............................................28A, 28BC10... Short Division ....................................................29A, 29BC11 ... Multiplication of Decimals ..................................30A, 30BC12... Problems, Without a Calculator .........................31A, 31BC13... Problems, With a Calculator ..............................32A, 32B

Algebra

A1 ..... Formulae Expressed in Words ..........................33A, 33BA2 ..... Coordinates in First Quadrant ...........................34A, 34B


S6 ..... Making 3D Models .............................................35A, 35B, 35C, 35DS7 ..... Reflection in Diagonal Lines ..............................36A, 36B, 36C, 36D, 36ES8 ..... Translation .........................................................37A, 37BS9 ..... Rotation .............................................................38A, 38BS10 ... Reading Scales .................................................39A, 39BS11 ... Perimeter ...........................................................40A, 40BS12 ... Areas .................................................................41A, 41B

Handling Data

D3..... Discrete Data.....................................................42A, 42BD4..... Grouping Data ...................................................43A, 43BD5..... Mode, Median and Range .................................44A, 44B

LEVEL 4

Level 4

N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5

Page

Page (ii)

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Number

N13... Mult. and Div. of Decimals by 10 and 100 .........45A, 45BN14... Rounding ...........................................................46A, 46BN15... Ordering Negative Numbers ..............................47A, 47BN16... Ordering Fractions.............................................48A, 48BN17... Simplification of Fractions .................................49A, 49BN18... Understanding Ratios ........................................50A, 50B

Calculating

C14... Long Multiplication .............................................51A, 51BC15... Long Division .....................................................52A, 52BC16... BODMAS...........................................................53A, 53BC17... Fraction of an Amount .......................................54A, 54BC18... Directed Numbers .............................................55A, 55BC19... Ratio Questions in Context ................................56A, 56BC20... Direct Proportion ...............................................57A, 57BC21... Real Life Tables .................................................58A, 58B

Algebra

A3 ..... Algebraic Expressions .......................................59A, 59BA4 ..... Coordinates in Four Quadrants .........................60A, 60BA5 ..... Horizontal and Vertical Lines .............................61A, 61BA6 ..... Function Machines ............................................62A, 62B


S13 ... Symmetries of 2D Shapes.................................63A, 63BS14 ... Measuring and Drawing Angles .........................64A, 64B, 64C, 64D, 64E, 64FS15 ... Angle Facts .......................................................65A, 65BS16 ... Area of Rectangles ............................................66A, 66B

Handling Data

D6..... Probability..........................................................67A, 67BD7..... The Mean Average ............................................68A, 68B

LEVEL 5

Level 5

N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7

Page

Page (iii)

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Number

N19... Fractions, Decimals and Percentages ................... 69N20... Improper Fractions and Mixed Numbers ............... 70N21... Prime Numbers, HCF and LCM ............................ 71

Calculating

C22... Percentage of an Amount ...................................... 72C23... Percentage Increase and Decrease ...................... 73C24... Addition and Subtraction of Fractions.................... 74C25... Multiplication & Division of Integers by Fractions .. 75

Algebra

A7 ..... Substitution............................................................ 76A8 ..... Trial and Improvement........................................... 77A9 ..... Algebraic Simplification ......................................... 78A10 ... Linear Equations ................................................... 79A11 ... Generate a Number Sequence ............................. 80A12 ... Finding the nth Term.............................................. 81A13 ... Straight Line Graphs.............................................. 82A14 ... Distance - Time Graphs ......................................... 83A15 ... Real Life Graphs ................................................... 84


S17 ... Properties of Quadrilaterals ................................... 85S18 ... Nets of 3D Shapes ................................................ 86A, 86BS19 ... Constructions ........................................................ 87S20 ... Geometric Problems.............................................. 88S21 ... Corresponding and Alternate Angles ..................... 89S22 ... Enlargement .......................................................... 90A, 90BS23 ... Similar Shapes ...................................................... 91S24 ... Area of a Triangle .................................................. 92A, 92BS25 ... Area of a Parallelogram......................................... 93S26 ... Volume of a Cuboid ............................................... 94S27 ... Surface Area of a Cuboid ...................................... 95S28 ... Circumference of a Circle ...................................... 96S29 ... Area of a Circle...................................................... 97A, 97B

Handling Data

D8..... Bar Charts and Frequency Diagrams .................... 98D9..... Scatter Graphs ...................................................... 99D10... Pie Charts.............................................................. 100D11 ... Two-Way Tables .................................................... 101D12... Surveys ................................................................. 102D13... Further Probability ................................................. 103

LEVEL 6

Level 6

N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28

A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page

Page (iv)

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Number

N22... Rounding to 1 Significant Figure ........................... 104

Calculating

C26... Percentage Increase and Decrease ...................... 105C27... Addition and Subtraction of Fractions.................... 106C28... Multiplication and Division of Fractions ................. 107C29... Numbers Between 0 and 1 (Mult. & Div.) .............. 108C30... Estimating Answers ............................................... 109C31... Using a Calculator ................................................. 110

Algebra

A16 ... Further Algebraic Simplification ............................. 111A17 ... Expanding Brackets .............................................. 112A18 ... Factorisation .......................................................... 113A19 ... Solving Difficult Equations ..................................... 114A20 ... Rearranging a Formula ......................................... 115A21 ... Trial and Improvement........................................... 116A, 116BA22 ... Inequalities ............................................................ 117A23 ... Solving Inequalities ............................................... 118A24 ... Understanding Straight Line Graphs ..................... 119A25 ... Regions ................................................................. 120A26 ... Simultaneous Equations Graphically ..................... 121A27 ... Simultaneous Equations Algebraically ................... 122A28 ... nth Term of Quadratic Sequences ......................... 123A29 ... Graphs of Quadratic and Cubic Functions ............ 124A, 124B, 124C


S30 ... Pythagoras’ Theorem ............................................ 125A, 125B, 125CS31 ... Areas of Compound Shapes ................................. 126A, 126B, 126CS32 ... Volumes of Prisms................................................. 127S33 ... Surface Area of Triangular Prisms ......................... 128S34 ... Loci ........................................................................ 129S35 ... Enlargement by a Negative Scale Factor .............. 130S36 ... Bounds .................................................................. 131S37 ... Compound Measures ............................................ 132

Handling Data

D14... Averages from Tables ............................................ 133A, 133BD15... Relative Frequency ............................................... 134

LEVEL 7

Page

C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26

Level 7

Page (v)

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Secure Level 3

Secure Level 3 withsome Level 4 features

Secure Level 4


Secure Level 5


Secure Level 6

Name: _________________________

Year: ______ Class: ______

Teacher: ________________

APP Record Card

Date

Page (vi)

Level 3


Level 4


Level 5


Level 6


A14 A15S29S17 S18

D8 D9 D10 D11 D12 D13

Level 7



Secure Level 7

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LEVEL 7

LEVEL 6

LEVEL 5

LEVEL 4

LEVEL 3

MathematicsLevel 3

Certificate

This is to certify that _______________________

has successfully achieved Level 3 in Mathematics.

Class: ____________________

Date: ___________ Signed: ____________

Page (vii)

Level 3


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MathematicsLevel 4

Certificate



Class: ____________________

Date: ___________ Signed: ____________

Level 4


LEVEL 7

LEVEL 6

LEVEL 5

LEVEL 4

LEVEL 3

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MathematicsLevel 5

Certificate



Class: ____________________

Date: ___________ Signed: ____________

Level 5


LEVEL 7

LEVEL 6

LEVEL 5

LEVEL 4

LEVEL 3

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MathematicsLevel 6

Certificate



Class: ____________________

Date: ___________ Signed: ____________

Level 6


A14 A15S29S17 S18

D8 D9 D10 D11 D12 D13

LEVEL 7

LEVEL 6

LEVEL 5

LEVEL 4

LEVEL 3

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MathematicsLevel 7

Certificate



Class: ____________________

Date: ___________ Signed: ____________

LEVEL 7

LEVEL 6

LEVEL 5

LEVEL 4

LEVEL 3


Level 7

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Level 3


Answers

Put the following numbers in the place value table.

a) 2415

b) 607

c) 9380

d) 2004

N1Place Value

2 4 1 56 0 7

9 3 8 02 0 0 4

667

2156

914

4071

five thousand four hundred and thirty two

eight hundred and eleveneight hundred and eleven

three thousand six hundred and twenty

nine thousand and ninety

200

6000

1)

2) Write the following numbers in figures.

a) six hundred and sixty seven

b) two thousand one hundred and fifty six

c) nine hundred and fourteen

d) four thousand and seventy one

3) Write the following numbers in words.

a) 5432

b) 811

c) 3620

d) 9090

4) a) What is the value of the 2 in thenumber 1250?

b) What is the value of the 6 in thenumber 6924?

Page 1A

1000Thousands

100Hundreds

10Tens

1Units

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Level 3


AnswersN1Just For Fun

1) Match the words with the correct numbers.

2) Here are four number cards.

a) What is the biggest three digit numberyou can make with these cards?

b) What is the biggest even number youcan make with all four cards?

3) a) Write a whole number that is bigger thanone thousand but smaller than onethousand one hundred.

b) Write the number eleven thousand elevenhundred and eleven.

6 4 3

6 3 1 4

anything from 1001 to 1099

12 111

Page 1B

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Level 3


AnswersN2Negative Numbers

-5-4-3-2-10123456789

101112C

-5-4-3-2-10123456789101112C

-5-4-3-2-10123456789

101112C

-5-4-3-2-10123456789101112C

-5-4-3-2-10123456789101112C

-5-4-3-2-10123456789

101112C

A B C D E F

A

B

C

D

E

F

-3 °C rises 8 °C 5 °C

5 °C falls 6 °C -1 °C

-5 °C rises 3 °C -2 °C

11 °C falls 15 °C -4 °C

-1 °C rises 8.5 °C 7.5 °C

2 °C falls 6.5 °C -4.5 °C

Thermometer Temperatureat 3.00 A.M

Temperaturechange over

next five hours

Temperature at8.00 A.M.

The thermometers A to F show the temperature at 3:00 A.M.in six different cities.Use them to fill in the table below.The first one has been done for you.

Page 2A

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Level 3


AnswersN2Just For Fun

1) Place these numbers in order of size, smallest to largest.

a) -1, 2, 5, 6

b) -5, -2, 3, 4, 7

c) -4, -2, -1, 0, 3, 9

d) -9, -6, -4, -3, 1, 4, 8

e) -12, -10, -8, -7, -6, -4, -3

f) -5.5, -4, -3.5, -3, -2.5, 6, 7.5, 8.5

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Player A Player B

Start point

3) Place a counter on 0.Player A and B take turns in rolling a dice.Whatever scores player A gets, he/she alwaysmoves this many squares to the left.Whatever scores player B gets, he/she alwaysmoves this many squares to the right.Player A wins if he/she needs to move to asquare which is less than -8.Player B wins if he/she needs to move to asquare which is more than 8.

2) a) What is special about the temperature 100 °C?

b) What is special about the temperature 0 °C?

Water boils

Water freezes

Page 2B

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Level 3


Answers

Introduction to Fractions

1) Find three equivalent fractions to each of thefollowing:

a) b) c)

d) e) f)

2) Fill in the missing number in each of theseequivalent fractions.

a) = b) = c) =

d) = e) = f) =

g) = h) = i) =

13

3) Complete the following equivalent fraction series.

a) = = = = =

b) = = = = =

14

15

25

34

58

23

15

3119 20 22

13

5 27

10 49

8

25

57

910

814250

12

26

520

615

1250

30035

28

312

416

26

39

412

210

315

420

68

1216

2432

410

820

1640

5080

500800

50008000

6 4 6

15 35 18

20 30

90

4

3

10

10

100

10

9

20

30

500

50

These are a selectionof possible answers.

As long as you multipliedthe top and bottom

by the same numberyour answer is fine.

N3

Page 3A

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Level 3


Answers

Just For Fun

Use the diagram below to help you fill in themissing numbers.

a)

b)

c)

d)

1) Here are six number cards.

a) Choose two of these six cards

to make a fraction that is

equivalent to .

b) Choose two of these six cards


equivalent to .

2)

2 4 6 8 10 12

16

14

13

= +

1216

16

= –

212

16

+ =

16

13

+ =14

+

2

12

6

8

1

12

1

4

1

3

3

12

112

16

112

112

13 1

4

112

N3

Page 3B

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Level 3


Answers

Money

1) Write the following amounts of money usinga £ sign and numbers.

a) Three pounds and thirty seven pence.

b) Twenty four pounds and fifty pence.

c) Two hundred and five pounds.

d) Nine pounds and sixty pence.

e) Nine pounds and six pence.

f) Forty eight pence.

2) Write the following amounts of money in words.

a) £2.78

b) £6.07

c) £5.40

d) £0.24

3) Work out the following on a calculator and write theanswers correctly:

a) £115.23 ÷ 23

b) £100.80 ÷ 14

c) 71p × 10

d) £6.40 – £3.83 + £2.10

e) £14.83 + £6.17

£3.37

£24.50

£205

£9.60

£9.06

£0.48

Two pounds and seventy eight pence

Six pounds and seven pence

Five pounds and forty pence

Twenty four pence

£5.01

£7.20

£7.10

£4.67

£21

N4

Page 4A

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Level 3


Answers

Three men went into a second-hand shop to buy atelevision.

It was priced in the window at £30.

Each of them handed over £10 to the shop assistant.

As the assistant opened the till, the manager had a quietword with him, “that TV is in the sale and is only £25now, you will have to give them £5 back.”

The assistant was very lazy and couldn’t be bothered tocount out the right change for each man.

Instead, he took 5 £1 coins out of the till.

He put two of them in his own pocket and gave eachman £1 back.

Here’s the problem:

The men have now paid £9 each for the TV.

The assistant has kept £2 for himself.

3 × £9 = £27.

£27 + £2 = £29.

But £30 was handed over in the first place.

WHERE IS THE MISSING £1?

This is a very famous question and has puzzledmany generations of children.

The missing £1 is . . . . . please ask your teacher,your parents and/or your friends.

We’re just not allowed to tell you.

N4Just For Fun

Page 4B

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Level 3


AnswersC1Mental Addition

For each set of questions, time how long it takes to getthe answers.You must work out the answers in your head - you can’tdo any working on paper.

1) 23 + 35

2) 17 + 13

3) 45 + 46

4) 38 + 44

5) 71 + 54

6) 38 + 46

7) 27 + 68

8) 64 + 77

9) 64 + 99

10) 87 + 96

Set A

1) 42 + 56

2) 23 + 56

3) 37 + 25

4) 68 + 26

5) 83 + 65

6) 59 + 37

7) 42 + 39

8) 57 + 68

9) 99 + 48

10) 68 + 94

Set B

1) 62 + 24

2) 38 + 22

3) 17 + 34

4) 52 + 29

5) 82 + 63

6) 28 + 36

7) 88 + 17

8) 67 + 56

9) 42 + 98

10) 78 + 93

Set C

= 58

= 30

= 91

= 82

= 125

= 84

= 95

= 141

= 163

= 183

= 98

= 79

= 62

= 94

= 148

= 96

= 81

= 125

= 147

= 162

= 86

= 60

= 51

= 81

= 145

= 64

= 105

= 123

= 140

= 171

For any set of questions:45 seconds or less: Maths teacher standard46 to 89 seconds: Extremely fast90 to 149 seconds: Fast150 to 209 seconds: Reasonable210 seconds or more: A bit more practise needed

Page 5A

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Level 3


AnswersC1

How do you win every time?

You probably noticed that if you can get to 18 youdefinitely win.

But, if you get to 15 you can definitely get to 18and so 15 is a step on the way to victory.

And if you get to 12 you can get to 15.

To cut a long story short, just stick to the 3 timestable (or get on to it as soon as you can if you gofirst.)

So, if you go second, your numbers will always be:

3, 6, 9, 12, 15, 18, 21.

If you go first, start with a 1 or 2 and keep playinguntil you can say, 6, 9, 12, etc.

Just For Fun

Page 5B

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Level 3


AnswersC2Mental Subtraction

For each set of questions, time how long it takes to getthe answers.You must work out the answers in your head - you can’tdo any working on paper.

1) 75 – 71

2) 98 – 93

3) 84 – 32

4) 68 – 24

5) 79 – 47

6) 38 – 29

7) 67 – 48

8) 54 – 39

9) 94 – 36

10) 72 – 25

Set A

1) 57 – 52

2) 78 – 71

3) 56 – 13

4) 78 – 27

5) 66 – 31

6) 84 – 38

7) 76 – 29

8) 43 – 17

9) 62 – 26

10) 51 – 24

Set B

1) 39 – 34

2) 67 – 62

3) 83 – 42

4) 88 – 34

5) 76 – 25

6) 63 – 39

7) 46 – 28

8) 54 – 48

9) 72 – 27

10) 72 – 38

Set C

= 4

= 5

= 52

= 44

= 32

= 9

= 19

= 15

= 58

= 47

= 5

= 7

= 43

= 51

= 35

= 46

= 47

= 26

= 36

= 27

= 5

= 5

= 41

= 54

= 51

= 24

= 18

= 6

= 45

= 34

For any set of questions:45 seconds or less: Maths teacher standard46 to 89 seconds: Extremely fast90 to 149 seconds: Fast150 to 209 seconds: Reasonable210 seconds or more: A bit more practise needed

Page 6A

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Level 3


AnswersC2Just For Fun

This trick works by itself.On the piece of paper you must alwayswrite the number 1089.This number will always be the answer.Here are some examples to show you.

412214198891

–

+1089

913319594495

–

+1089

784487297792

–

+1089

543345198891

–

+1089

978879099990

–

+1089

310013297792

–

+1089

Page 6B

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Level 3


Answers

1) 51 + 36

2) 41 + 27

3) 231 + 25

4) 446 + 38

5) 569 + 84

6) 316 + 262

7) 596 + 472

8) 657 + 847

9) 62 + 38 + 517

10) 216 + 32 + 518 + 74

=

=

=

=

=

=

=

=

=

=

87

68

256

484

653

578

1068

1504

617

840

C3Addition of Integers

Page 7A

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Level 3


Answers

2 3

4

6 8

1) 5 8

2

8 4

2)

7 9

4

3) 3

8

4)

1 2 7 1 6 0

5) 2 6

3 5

6)

4

6 4

7) 6

4 6

8)

7 5 1 1 3 6 3

8

1 9 2

+ +

+ +

+ +

+ +

5 6

8 7

7

49

9

6

2

6 1 8

8 7

2

8 7

9

Work out whatthe must be.*

C3Just For Fun

Page 7B

© Mathswatch Ltd

Level 3


Answers

1) 35 – 12

2) 58 – 27

3) 93 – 46

4) 258 – 37

5) 681 – 79

6) 420 – 68

7) 743 – 471

8) 361 – 278

9) 800 – 692

10) 1450 – 785

C4

23

31

47

221

602

352

272

83

108

665

=

=

=

=

=

=

=

=

=

=

Page 8A

Subtraction of Integers

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Level 3


Answers

8)

5 9 6

9

6 3

7)

5) 6) 3 5

2 6

6 1

4)6 73)

7 9

5

3

2)4 5

2

2

1)

3 4

6

68

74

4

3

2 8

3

7 38

C4Just For Fun

4 1 2 5

5 6 5 1 8 7

6 3

– –

– –

– –

– –

8 21 6

2 4

2

Page 8B

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Level 3


AnswersC5

× 5 4 2

2

4 12

20

3

× 10 4 5 3

3

2 8

1 3

5 25

2) Work out

a) 2 × 17 = ____ b) 24 × 5 = ____

c) 10 × 9 = ____ d) 4 × 62 = ____

e) 37 × 3 = ____ f) 2 × 81 = ____

g) 5 × 32 = ____ h) 3 × 19 = ____

i) 26 × 4 = ____ j) 11 × 10 = ____

30 12 15 920 10 610 4 550 20 15

10 6 8 420 16 850 30 4015 9 12 6

3

10

34 120

90 248

111 162

160 57

104 110

Page 9A

1) Fill in the missing numbers in theminitables below.

a) b)

Multiplication by 2, 3, 4,5, and 10

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Level 3



1) a) Use the table to fill in the gaps below.

21 × 14 = ____

12 × ____ = 228

____ × 15 = 315

286 ÷ 22 = ____

b) Give two different pairs of numbers.

____ × ____ = 252

____ × ____ = 252

× 11 12 13 14 15

18 198 216 234 252 270

19 209 228 247 266 285

20 220 240 260 280 300

21 231 252 273 294 315

22 242 264 286 308 330

2) Julia says:

“Multiply any number by five. The answer must be an odd number.”

Is she correct?Circle Yes or No

Explain how you know.

_______________________________________

Yes / No

294

19

21

13

12 21

14 18

2 × 5 = 10 and 10 is an even number.Any example which shows this is wrong such as:

Page 9B

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Level 3


AnswersC6

2) Work out

a) 46 ÷ 2 = ____ b) 39 ÷ 3 = ____

c) 65 ÷ 5 = ____ d) 62 ÷ 4 = ____

e) 47 ÷ 3 = ____ f) 11 ÷ 10 = ____

g) 92 ÷ 4 = ____ h) 57 ÷ 3 = ____

i) 90 ÷ 5 = ____ j) 83 ÷ 10 = ____

1) Work out

a) 16 ÷ 2 = ____ b) 30 ÷ 5 = ____

c) 21 ÷ 3 = ____ d) 40 ÷ 4 = ____

e) 35 ÷ ____ = 7 f) 24 ÷ ____ = 8

23 13

13 15 r2

15 r2 1 r1

23 19

18 8 r3

8 6

7 10

5 3

Page 10A

Division by 2, 3, 4,5, and 10

© Mathswatch Ltd

Level 3



1) Here is part of the 45 times table.Use the table to help you fill inthe missing numbers.

a) 315 ÷ 7 = ____

b) 135 ÷ 45 = ____

c) 270 ÷ ____ = 45

d) ____ × 45 = 405

e) 495 ÷ 45 = ____

f) ____ × 45 = 900

g) 450 ÷ 30 = ____

2) Joe says:

“Divide any number by three. The answer must be an even number.”

Is he correct?Circle Yes or No

Explain how you know.

_______________________________________

Yes / No

45

3

6

9

20

11

15

15 ÷ 3 = 5 and 5 is an odd number.

1 × 45 = 45

2 × 45 = 90

3 × 45 = 135

4 × 45 = 180

5 × 45 = 225

6 × 45 = 270

7 × 45 = 315

8 × 45 = 360

9 × 45 = 405

10 × 45 = 450

Page 10B

© Mathswatch Ltd

Level 3


Answers

Look at each shape, read the descriptionand then draw in all the lines of symmetry.

S1Reflective Symmetry

of 2D Shapes

1) RectangleTwo lines of symmetry

2) SquareFour lines of symmetry

3) Isosceles triangleOne line of symmetry

4) Equilateral triangleThree lines of symmetry

5) Regular pentagonFive lines of symmetry

6) Regular hexagonSix lines of symmetry

Page 11A

© Mathswatch Ltd

Level 3


AnswersS1Just For Fun

1) Shade in five more littletriangles so that the figurehas one line of symmetry.

2) Shade in just three morelittle triangles so that thefigure has one line ofsymmetry.

Page 11B

© Mathswatch Ltd

Level 3


AnswersS2Recognising Nets

Cuboid

Triangle-basedpyramid

Square-basedpyramid

Cube

Draw two lines from each label.One line should go to the correct 3-Dshape.The other one should go to the net ofthe 3-D shape.

Page 12A

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Level 3


Answers

There are exactly eleven different nets of a cube.

Below, you can see two of them.

See how many of the other nine you can find.

1) 2)

3) 4)

6) 7)

9) 10)

5)

8)

11)

S2Just For Fun

Page 12B

© Mathswatch Ltd

Level 3


Answers

In all four questions, reflect the shadedshape in the dotted mirror line.

1)

3)

2)

4)

S3Reflecting Shapes

Page 13A

© Mathswatch Ltd

Level 3


Answers

3)

2)1) Reflect every line in the dottedmirror line.

Use the grid to help you reflectRobbie Rabbit in the dotted mirrorline.

Reflect the shape in the verticalmirror line.Then, reflect both shapes in thehorizontal mirror line.

4) Reflect the shape in the verticalmirror line.Then, reflect both shapes in thehorizontal mirror line.

S3Just For Fun

Page 13B

© Mathswatch Ltd

Level 3


AnswersS4

1) a) How many millimetres are in a centimetre?

b) How many centimetres are in a metre?

c) How many metres are in a kilometre?

d) Work out how many millimetres are in a metre.

2) How many grams are in three kilograms?

3) How many millilitres are in a five litres?

4) In the table, work out what each item should bemeasured in.

Your choices are mm, cm, m, km, g, kg, ml or l.

Amount of lemonade in a bottle

Mass of a lemonade bottle

Width of a lemonade bottle

Distance to the moon

Mass of a wasp

Length of a wasp

Amount of blood in a human body

10

1000

1000

100

3000

5000

ml or l

g or kg

mm or cm

km

g

mm

l

Metric Units

Page 14A

© Mathswatch Ltd

Level 3



Average capacity ofair breathed in a day

Blood vessels in a humanbody laid end-to-end

Mass of MountEverest

Length of airways in thelungs laid end-to-end

Mass ofthe Earth

Capacity of allwater on Earth

5 980 000 000 000 000 000 000 000 kg

1460 000 000 000 000 000 000 litres

2 400 km

11 000 litres

3 041 409 000 000 000 kg

100 000 km

A

B

C

D

E

F

U

V

W

X

Y

Z

Try to match up A to F with U to Z1)

The ship is in a harbour.

There are ten rungs visible on theship’s ladder and they are 30 cm apart.

The tide is coming in and the water isrising at the rate of 20 cm per minute.

How many rungs will be visible after 9minutes?

2)

All ten rungs will still be visiblebecause the ship floats.Try this question with your parents.

Page 14B

© Mathswatch Ltd

Level 3


AnswersS5 Time

121

2

3

4

567

8

9

1011

121

2

3

4

567

8

9

1011

121

2

3

4

567

8

9

1011

121

2

3

4

567

8

9

1011

1) Write these times as 24 hour clock times

a) b) c) d)

a.m. p.m. p.m. p.m.04:00 14:50 16:35 21:20

a) b) c) d)09:40 18:10 13:35 23:55

121

2

3

4

567

8

9

1011

121

2

3

4

567

8

9

1011

121

2

3

4

567

8

9

1011

2) Draw these times on the clock faces.Underneath the clocks write whether the time is a.m. or p.m.

a.m. p.m. p.m. p.m.

3) Peter wants to watch a programme which begins at 8.00 p.m.

It is now 4.30 p.m.

How much time will Peter have to wait?

4) Susie is going to watch a programme which begins at 20:30and lasts for one hour and forty five minutes.

What time will it finish?

Three and a half hours(3 hours 30 minutes)

22:15

121

2

3

4

567

8

9

1011

Page 15A

© Mathswatch Ltd

Level 3



1) Here is a train timetable for trains going fromLondon Euston to Crewe.

a) How many trains stop at Tamworth?

b) If Tom gets to London Euston at 15:30 howlong will he have to wait for a train to take himto Crewe?

c) How many minutes does the 09:38London Euston train take to get to Northampton?

d) How many minutes does the 14:23 Lichfield traintake to get to Crewe?

e) How long does the 17:48 London Euston traintake to get to Crewe in hours and minutes?

2) This is the easiest way but you need 22 minutes:

4

16 mins

47 mins

46 mins

1 hour and 46 mins

Put the egg in theboiling water andset both timers off

11

0

7

0

after 7 mins

4

7

0

7

turn the 7 minutetimer over straight

away

4

7

7

0

after another 4mins

0

11

3

4

turn the 7 minute timer overand wait for it to finish.

You now have 15 minutes.

11

0

4

3

set them offtogether

11

0

7

0

after 7 mins put theegg in the boiling

water

0

7

4

7

11

0

after 4 mins turnthe 11 minute timer

over again

0

11

11 minutes lateryour egg will haveboiled for exactly

15 mins

This is a harder way but it only takes 15 minutes:

Page 15B

© Mathswatch Ltd

Level 3


AnswersD1Reading Bar Charts

and Pictograms

Red

Blue

Yellow

Green

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1

2

3

4

5

6

0

Favourite colour

Numberof

children

Bar chart to show favouritecolour of all pupils in class 5A

a) How many children chose green as their favourite colour?

b) Which was the least favourite colour in the class?

c) How many more children chose blue than red?

d) How many children are in class 5A?

5

Yellow

2

18

Page 16A

© Mathswatch Ltd

Level 3


AnswersD1

An art gallery uses a pictogram to show the numberof paintings sold over a 5 week period.

1234512345123451234512345

1234512345123451234512345

1234512345123451234512345

1234512345123451234512345

Week 1123451234512345123451234512345

12345123451234512345123451234512345

12345123451234512345

1234512345123451234512345

Week 2

1234512345123451234512345

123451234512345123451234512345

12345123451234512345

1234512345123451234512345

Week 3

1234512345123451234512345

1234512345123451234512345

1234512345123451234512345

1234512345123451234512345

Week 4123451234512345123451234512345

12345123451234512345123451234512345

12345123451234512345

1234512345123451234512345

Week 5

1234512345123451234512345

1234512345123451234512345

1234512345123451234512345

1234512345123451234512345

123451234512345123451234512345

12345123451234512345123451234512345

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1234512345123451234512345

1234512345123451234512345

123451234512345123451234512345

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123456123456123456123456123456123456

123451234512345123451234512345123456

123456123456123456123456

1234512345123451234512345

123456123456123456123456123456123456123456123456123456123456

123451234512345123451234512345

12345612345612345612345612345612345612345

12345123451234512345

123456123456123456123456123456

123456123456123456123456123456

1234512345123451234512345

123456123456123456123456123456

1234512345123451234512345

1234512345123451234512345

123451234512345123451234512345

12345123451234512345

1234512345123451234512345

Key: = 4 paintings

a) How many paintings were sold in week 1?

b) In which week was the least number ofpaintings sold?

c) How many paintings were sold in week 3?

d) How many paintings were sold in week 4?

e) How many more paintings were sold in week 2compared with week 5?

f) How many paintings were sold altogether in thefive weeks?

12

Week 5

10

7

12

49

Page 16B

Reading Bar Chartsand Pictograms

© Mathswatch Ltd

Level 3


AnswersD1Just For Fun

300

250

200

150

100

50

123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789

12345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890

123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890

123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890

12345678901234567890123456789012345678901234567890123456789012345678901234567890

123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789

Ann Ben Jane Cara Dave Carl

Ma

rks

Science123456123456123456123456123456123456

Maths English

Six students sat exams in English, Maths and Science.Each exam was marked out of 100.Their teacher made a bar chart of their results.

a) Which student got the highest total mark?

b) Who got the highest English mark?

c) One student got the same mark for all threesubjects. Write down the name of this student.

d) What mark did Ann get for Maths?

e) One student had their lowest mark for English.Who was it?

Ben

Dave

Carl

75

Ann

Page 16C

© Mathswatch Ltd

Level 3


AnswersD2

White Yellow Orange Green Blueo

1

2

3

4

5

6

7

8

9

Number of different colour belts in a Judo club

Colour of belt

Fre

quen

cy

1)

Red

Green

Black

Yellow

Blue

Number of different colour pencil cases

Key:

represents 4 pencilcases

2)

Page 17A

Drawing Bar Chartsand Pictograms

© Mathswatch Ltd

Level 3


AnswersD2Just For Fun

1234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567

123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678

1234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567

1234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567

Fish Curry Pizza Stewo

1

2

3

4

5

6

7

8

9

Meals bought by Class A and Class B

Meals bought

Fre

quen

cy

1234512345123451234512345

Class A Class BKey:

2)

1) a) Geography had the most grade A results.

b) Geography had 4 more grade D results comparedwith History.

Page 17B

© Mathswatch Ltd

Level 4

Answers


N5

Page 18A

1) For each number pattern:

a) Describe the pattern

b) Work out what the next three terms are

(i) 2, 4, 6, 8, 10, 12, 14, 16, 18

(ii) 1, 4, 7, 10, 13, 16, 19, 22, 25

(iii) 5, 12, 19, 26, 33, 40, 47, 54, 61

(iv) -2, 3, 8, 13, 18, 23, 28, 33, 38

(v) 36, 33, 30, 27, 24, 21, 18, 15, 12

(vi) -12, -8, -4, 0, 4, 8, 12, 16, 20

(vii) 100, 91, 82, 73, 64, 55, 46, 37, 28

(viii) 7, 8.5, 10, 11.5, 13, 14.5, 16, 17.5, 19

goes up in 2s

goes up in 3s

goes up in 7s

goes up in 5s

goes down in 3s

goes up in 4s

goes down in 9s

goes up in 1.5s

goes up by 3 then 5 then 7 etc ORsquare numbers (1 × 1), (2 × 2), (3 × 3), etc

goes up by 2 then 3 then 4 etc ORtriangle numbers

Number Patterns

2) For both of the following number patterns:

a) Describe the pattern

b) Work out what the next three terms are

(i) 1, 4, 9, 16, 25, 36, 49, 64, 81

(ii) 1, 3, 6, 10, 15, 21, 28, 36, 45

© Mathswatch Ltd

Level 4

Answers


N5

Page 18B

1) Work out the next two terms for each ofthe following number patterns:

a) 3, 8, 15, 24, 35, 48, 63

b) 4, 14, 36, 76, 140, 234, 364


a) 1, 2, 4, 8, 16, 32, 64, 128

b) 2, 7, 22, 67, 202, 607, 1822


a) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55

b) 1, 2, 3, 6, 11, 20, 37, 68, 125, 230

4) Work out the next two terms for each ofthe following :

a) O, T, T, F, F, S, S, E, N

b) J, F, M, A, M, J, J, A, S

Each row describes the row above.In the first row we have one 1.The second row says this (1 1)The third row describes the secondrow.We have two 1s and it says this (2 1)We now have one 2 and one 1.The fourth row is therefore 1 2 1 1If you got this right you are one of aselect few.

6)

First letters of 1, 2, 3, 4, etc

First letters of Jan, Feb, Mar, etc

Yes, mathematiciansthink so.

It does eventually if you make no mistakes.

11 12 1

1 2 1 11 1 1 2 2 13 1 2 2 1 1

1 3 1 1 2 2 2 11 1 1 3 2 1 3 2 1 1

3 1 1 3 1 2 1 1 1 3 1 2 2 11 3 2 1 1 3 1 1 1 2 3 1 1 3 1 1 2 2 1 1

Just For Fun

5) Choose any number between 1 and 20.

If your number is even, halve it andwrite down the answer.If your number is odd, multiply it bythree and add one. Write down theanswer.

Look at your answer and follow thesame rules:If it is even you halve it and write downthe answer.If it is odd you multiply by three andadd one and write down the answer.

Only stop when you get to one.

Try more starting numbers (of any size).

Do they all go to one?

What about if you use 27 as thenumber to start with?

© Mathswatch Ltd

Level 4

Answers


N6

Page 19A

1 2 3 4 5 6 7 8 9 10 11 12

13 14 15 16 17 18 19 20 21 22 23 24

25 26 27 28 29 30 31 32 33 34 35 36

37 38 39 40 41 42 43 44 45 46 47 48

49 50 51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70 71 72

73 74 75 76 77 78 79 80 81 82 83 84

85 86 87 88 89 90 91 92 93 94 95 96

97 98 99 100 101 102 103 104 105 106 107 108

109 110 111 112 113 114 115 116 117 118 119 120

121 122 123 124 125 126 127 128 129 130 131 132

133 134 135 136 137 138 139 140 141 142 143 144

Square Numbers

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Level 4

Answers


Just For FunN6

Page 19B

a) The numbers1, 3, 6, 10, 15, . . . arecalled triangular numbers.You can see why, below.

1 3 6 10 15

b) The triangular numbers are1, 3, 6, 10, 15, . . . etc.If you choose any two of them which are next to eachother you will always get a square number.eg 1 + 3 = 4, 3 + 6 = 9, 6 + 10 = 16

If you look carefully at the shapes of the dots you cansee they fit together to make a square. Here’s anexample:

6 10

+ =

16

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Level 4

Answers


N7

Page 20A

Multiples

1) a) Write down the first five multiples of 3.

b) Write down the first five multiples of 7.

c) Write down the first five multiples of 4.

2) 6, 12, 18, 24, 30 are the first five multiplesof which number?

3) What are the eighth, ninth and tenth multiples of 11?

4) Put the correct numbers in these circles.Be careful of the overlaps.

First eight multiplesof 3 in this circle

First eight multiplesof 4 in this circle

3, 6, 9, 12, 15

7, 14, 21, 28, 35

4, 8, 12, 16, 20

6

88, 99, 110

12

24

3 6

9 15

1821

4

8

1620

2832

© Mathswatch Ltd

Level 4

Answers


Just For FunN7

Page 20B

×××× ×× ××××× × ×× ×× ×

××× ×× ×× × ×× ×× ××× × ×× ××

××

×× × ×× ×

×

× × ×× ××× × ×× ×× ×

××× ×× ××××

× × ××××

×× × ×××1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

The sieve of Eratosthenes

Just follow these steps:

a) Cross out 1.

b) Shade in the square with 2 in it.Now cross out all other multiples of 2.

c) Shade in the 3 square.Cross out all other multiples of 3(some will already be crossed out).

d) Shade in the 5 square.Cross out all other multiples of 5.

e) Shade in the 7 square.There should be just threeother multiples of 7 whichhaven’t already been crossed out.Cross them out.

f) Shade in every square that hasn’tbeen crossed out.

g) Write out the numbers in everyshaded square.

h) Prime numbers

© Mathswatch Ltd

Level 4

Answers


N8

Page 21A

Factors

1) Write down all the factors of:

a) 6

b) 8

c) 10

d) 12

e) 20

f) 21

2) 100 has nine factors.

What are they?

3) The numbers 2, 3, 5 and 7all have exactly two factors.

Find the next four numberswith only two factors.

4) The numbers 1, 4, 9 and 16 allhave an odd number of factors.

Find the next three numberswhich have an odd number offactors.

Factors of 24 inthis circle

Factors of 40 inthis circle

5) Put the correct numbers in the circles.Be careful of the overlaps.

1 2 3 6

1 2 4 8

1 2 5 10

1 2 3 4 6 12

1 2 4 5 10 20

1 3 7 21

1 2 4 5 10 20 25 50 100

11 13 17 19

25 36 49

1

2

4

3

6

12

24

5

810

2040

© Mathswatch Ltd

Level 4

Answers


Just For FunN8

Page 21B

A

B

C

Place all the whole numbers from 1 to 60 in thediagram below.However, you must stick to these four rules:

1) In the rectangle you must have every wholenumber from 1 to 60

2) In circle A you must have all the factors of 60

3) In circle B you must have all the factors of 45

4) In circle C you must have all the factors of 36

13

515

9

2 46 12

10

20

30

60

45

18

36

Factors of 60

Factors of 45

Factors of 36

Numbers from 1 to 60

7 8

11 13

14 16

17 19

21

22 23

24

25

26

27

28

29

31 32 33

34

35

37

38

39

40

4142

43

4446

47 4849

50

51

52

53

54

5556

5758

59

© Mathswatch Ltd

Level 4

Answers


N9

Page 22A

1) 75 × 100

2) 102 × 10

3) 9 × 1000

4) 450 ÷ 10

5) 3800 ÷ 10

6) 9700 ÷ 100

7) 60 × 1000

8) 7000 ÷ 100

9) 210 × 1000

10) 1050000 ÷ 1000

7500

1020

9000

45

380

97

60000

70

210000

1050

=

=

=

=

=

=

=

=

=

Multiplication and Divisionby 10 and 100 (and 1000)

=

© Mathswatch Ltd

Level 4

Answers


Just For FunN9

Page 22B

7 000 000

700 000

70 000

7 000

700

Place Approximate population

London

Glasgow

Barnsley

Penkbridge

High Bickington

Penkbridge

London

100

Glasgow

High Bickington

10

The table shows the approximatepopulations of five different places.

Complete these sentences:The population of Barnsley is about 10 times

bigger than the population of .............................

The population of ............................. is about 100times bigger than the population of Barnsley.

The population of Glasgow is about ........ times

bigger than the population of Penkbridge.

The population of Barnsley is about 10 timessmaller than the population of .............................

The population of ............................. is about 100times smaller than the population of Barnsley.

The population of High Bickington is about ........times smaller than the population of Penkbridge.

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Level 4

Answers


1) What fractions of the following shapes are shaded?

a) b) c)

d) e) f)

2) Shade the shapes according to the given fractions.

a) b) c)57

13

25100

3) What percentage of the shapes below are shaded?

a) b) c)

24

12

or 56

39or

13

28

14

or 49

510or

12

1% 60% 75%

N10

Page 23A

Fractions and Percentages

© Mathswatch Ltd

Level 4

Answers


Just For FunN10

Page 23B

13

16

of this shape is shaded.

a) What fraction of this diagram is shaded?

b) What fraction of this diagram is shaded?

13

These are a selection of possible answers.As long as each of your four sections is comprised offour little squares, your answer is correct.

1)

2)

© Mathswatch Ltd

Level 4

Answers


N11

Page 24A

1) a) 0.47 b) 0.407 c) 7.04 d) 47.4 ____ ____ ____ ____

From the following list, match the correct way ofreading each of the above numbers.

A- seven point four F- seven zero fourB- zero point forty seven G- forty seven point fourC- zero point four zero seven H- four seven fourD- four seven point four I- four seven point zeroE- seven point zero four J- zero point four seven

2) Arrange the numbers in order of size, starting withthe smallest.

a) 1.8 0.8 8 8.1___ ___ ___ ___

b) 0.08 1.16 0.12 1.09___ ___ ___ ___

c) £4.04 £4.40 £4.14 £0.41___ ___ ___ ___

d) 3.11 3.1 3 3.011 3.001___ ___ ___ ___ ___

e) 0.2 0.022 0.202 0.222 0.22___ ___ ___ ___ ___

f) 6.06 60.06 6.606 66.06 6.066___ ___ ___ ___ ___

Ordering Decimals

J

0.8 1.8 8 8.1

C E G

0.08 0.12 1.09 1.16

£0.41 £4.04 £4.14 £4.40

3 3.001 3.011 3.1 3.11

0.022 0.2 0.202 0.22 0.222

6.06 6.066 6.606 60.06 66.06

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N11

Page 24B

Just For Fun

I am a decimal number.I have two figures before the decimal point andtwo figures after the decimal point.I read the same forwards as backwards.I have no zeros.My first digit is bigger than my second digit.The sum of my digits is 8.

What number am I?

4 7 3 1 .

1 . 3 4 7

7 4 3 . 1

9.92

31.13

1)

2)

3)

Here are some number cards.

a) What is the smallest number you canmake?

b) What is the largest number you canmake?

Each card can be used once, all cards must be used,the decimal point card cannot be at the end of a number.

The times, in seconds, for the seven runnersin a 100m race were:

9.96 10.03 9.92 10.26 10.37 9.99 10.00

What was the time of the winner?

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N12

Page 25A

1) For each of the three grids below, write down theratio of shaded squares to unshaded squares.

Simplify the ratios if possible.

a) b) c)

2) Shade in squares for each grid to give the correct ratios.

Shaded Unshaded

5 : 7

Shaded Unshaded

1 : 2

Shaded Unshaded

5 : 1

a) b) c)

2 : 13 5 : 10 1 : 2 6 : 9 2 : 3

80 ml

50 ml

100 ml squash400 ml water

3) The instructions on a lemonsquash bottle are as follows:

a) If you put 20 ml of squash in a glass, how muchwater would you need?

b) If you had used 200 ml of water, how muchsquash should be in the drink?

c) If you want to make 500 ml of squash drink,how much squash should be used and howmuch water?

1 part squash to4 parts water

Basic Ratio

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Just For FunN12

Page 25B

DragianVesuvian

1) Here we have a fine exampleof a Vesuvian and a Dragian.

If you count carefully you cansee that the ratio of teeth is 5 : 7

a) What is the ratio of feet?

b) What is the ratio of eyes?

c) What is the ratio of fingers?

Check that you have given allratios in the simplest form.

2) Look at this picture ofVesuvians and Dragians andwork out the following:

a) The ratio of Vesuvians toDragians.

b) The ratio of Vesuvian feet inthe picture to Dragian feet inthe picture.

c) The ratio of Vesuvian eyes inthe picture to Dragian eyes inthe picture.

3) In another picture of Vesuvians and Dragians we onlyknow two things:

Firstly, there are more Vesuvians than Dragians.Secondly, there are 46 teeth altogether in the picture.

Work out how many Vesuvians and Dragians there arein the picture.

6 : 2, 3 : 1

4 : 1

6 : 6, 1 : 1

12 : 8, 3 : 2

72 : 16, 9 : 2

48 : 8, 6 : 1

5 Vesuvians3 Dragians

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C7

Page 26A

1) 1524 + 4273

2) 7452 + 216

3) 24578 + 1215

4) 591 + 372 + 85

5) 9876 + 55 + 1039

6) 59.1 + 37.2

7) 24.75 + 9.98

8) 94.78 + 104.9

9) 309 + 12.5 + 631.4

10) 105 + 7.32 + 51.8 + 2804

5797

7668

25793

1048

10970

96.3

34.73

199.68

952.9

2968.12

=

=

=

=

=

=

=

=

=

=

Addition

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Just For FunC7

Page 26B

a)

1)

2)

+ = 4.6

3.61

3.2

2.975

7.65

2.35

1.006

1.3

3.58

6.72

2.25

+ = 11.26b)

1 1 10 2 23 3 34 4 05 0 5 +

0 1 12 2 03 3 34 4 45 0 5 +

1 1 12 2 23 0 34 4 05 5 0 +

1 1 12 2 03 0 34 4 45 0 5 +

1141 3151 6261 3851

Choose a number from a box and a number from a

loop to make the totals in a) and b).

2.35 2.25

3.61 7.65

a) b) c) d)

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C8

Page 27A

1) 14562 – 1251

2) 6652 – 716

3) 42160 – 39215

4) 2300 – 934

5) 475.83 – 81.6

6) 68.1 – 27.3

7) 24.75 – 0.098

8) 94.78 – 36

9) 3564 – 1971.6

10) 800 – 237.62

13311

5936

2945

1366

394.23

40.8

24.652

58.78

1592.4

562.38

=

=

=

=

=

=

=

=

=

=

Subtraction

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Just For Fun

Page 27B

C8

Complete the boxes and the circles:

2010

– 135

– 1962

– 750

– 1179

– 806.5

– 216.2

– 21.65

– 26.261

– 1002– 347

– 38.1

1875

26.35

0.0891658.8

48

453.5

81

1260

661

1008969.9

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C9

Page 28A

=

=

=

=

=

=

=

=

=

=

39

220

576

460

609

2736

1248

2980

2023

1017

1) 3 × 13

2) 55 × 4

3) 9 × 64

4) 92 × 5

5) 7 × 87

6) 342 × 8

7) 6 × 208

8) 745 × 4

9) 289 × 7

10) 113 × 9

Short Multiplication

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Just For Fun

Page 28B

C9

20 3×27

1) Here are some items available from a

local shop:

Work out the cost of:

a) 5 jackets

b) 6 MP3 players

c) 4 pairs of trainers

d) 7 televisons

Jacket: £17 Trainers: £56 MP3 player: £32 Television: £499

2) Work out what the must be.

a) b)

*5

72

×

answer:

£85£192£224£3493

9 180

20793

6

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C10

Page 29A

1) 786 ÷ 2

2) 465 ÷ 5

3) 448 ÷ 8

4) 552 ÷ 6

5) 801 ÷ 9

6) 5976 ÷ 8

7) 9080 ÷ 5

8) 17801 ÷ 7

9) 18054 ÷ 6

10) 374877 ÷ 9

393

93

56

92

89

747

1816

2543

3009

41653

=

=

=

=

=

=

=

=

=

=

Short Division

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Just For Fun

Page 29B

C10

1) Here are some items available from a local

shop:

Work out the unit price of each item knowingthat:

7 watches cost £336,

5 cameras cost £380,

4 camcorders cost £1260,

6 laptops cost £7794.

2) a) If 3 chairs cost £17.40,

how much would one of them cost?

£_____

b) If 7 shirts cost £34.93,

how much would one of them cost?

£_____

Watch: £ ____ Camera: £ ____ Camcorder: £ ____ Laptop: £ _______48 76 315 1299

5.80

4.99

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C11

Page 30A

=

=

=

=

=

=

=

=

=

=

4.8

19.5

168.3

18

57.4

8.34

73.6

33.4

25.34

227.7

1) 4 × 1.2

2) 6.5 × 3

3) 9 × 18.7

4) 3.6 × 5

5) 7 × 8.2

6) 6 × 1.39

7) 9.2 × 8

8) 8.35 × 4

9) 3.62 × 7

10) 25.3 × 9

Multiplication of Decimals

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Just For FunC11

Page 30B

1) Here are some items available from alocal shop:

Work out the cost of:

a) 7 lollies,

b) 3 bottles of milk,

c) 2 loaves of bread,

d) 5 boxes of chocolates.

Milk: £1.20 Bread: £0.65 Lollies: £0.30 Chocolates: £3.99

2)

£2.10£3.60£1.30£19.95

Rulers cost £0.25 each.Pens cost £0.45 each.Kelly buys 3 rulers and 5 pens.

Work out how much she pays.

£3.00

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C12

Page 31A

1) Which four coins make a total of 77p?

2) Six bars of metal each weigh 2.75 kg.How much do they weigh altogether?

3) At a party for 171 people, 9 guestssat at each table.How many tables were there?

4) Coke cans cost 43p each.How many cans you buy with £6?

5) Olivia went to a cafe.She ordered:

2 sausagesBaked beans3 coffee1 juice

She paid with a £5 note.Work out how much change she got.

19 tables

MenuFried eggs 30pBaked beans 45pSausages 38p

Coffee 65pTea 72pJuice 50p

50p 20p 5p 2p

16.5 kg

13 cans

£1.34 change

Problems Withouta Calculator

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C12

Page 31B

Just For Fun

21

1.59 m

£1.25

£8.37

A bus starts at Birmingham and makes three stopsbefore reaching London.At Birmingham, 37 people get on.At Rugby, 13 people get off and 6 get on.At Willen, 9 people get off and 15 get on.At Luton, 24 people get off and 8 get on.How many people are on the bus when itreaches London?

A mug and a plate together cost £2.90.The mug cost 40p more than the plate.

How much does the plate cost?

1)

2)

3)

4)

(I hope you remembered tocount the driver)

Cheese is on offer at £3.26 per kilogram.Emma buys half a kilogram.

How much change does she receive froma £10 note?

A man is 27 cm taller than his son, who is8 cm shorter than his mother. The man was born42 years ago and is 1.78 m tall.

How tall is his wife?

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C13

Page 32A

£30.94

18 teams

£19.06

£6.00

7 Mars Bars

1) There are 7 people in a team.How many teams can you make from131 people?

2) A motorist bought 26 litres of petrol at£1.19 per litre.a) How much did it cost?b) What change did he get from £50?

3) A museum trip is organised for 57members of a youth club. They go inminibuses that can each seat up to15 people.It costs £42.50 for each minibus and £172for the group to access the museum.How much will the trip cost per person?

4) Mars Bars cost 35p. Skittles cost 45p.Gillian bought 5 bags of Skittles andsome Mars Bars.She paid with a £5 note and received30p change.How many Mars Bars did she buy?

Problems With a Calculator

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C13

Page 32B

Just For Fun

34 35 36

81

8

1.1

18

6625

1) Three consecutive integers have a sum of 105.What are they?

2) Using the brackets keys of your calculator,

work out the following.

a) 164 – (27 + 56) =

b) 44.8 ÷ (15.4 – 9.8) =

c) (19.8 – 3.3) ÷ (31.2 – 16.2) =

d) (8 × 14.4) ÷ (11.1 – 4.7) =

3) If you start with 16 and press the square root key ofyour calculator ( ) twice, the answer given is 2.

If you start with 81 and press the square root key ofyour calculator ( ) twice, the answer given is 3.

Complete the following sentences:a) If you start with 1296 and press the square root

key of your calculator twice,the answer given is_____ .

b) If you start with _____ and press the square rootkey of your calculator twice, the answer given is 5 .

16

16

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A1

Page 33A

Multiply by 2 Add 3Input Output

3) a) If Simon puts 7 into the number machine, what numbercomes out?

b) If 100 goes in, what comes out?

c) If 5½ goes in, what comes out?

d) If 2.25 goes in, what comes out?

e) If 25 comes out, what number was put in?

f) If 8 comes out, what number was put in?

g) If x goes in, what comes out?

17203147.5

112.5

x × 2 + 3 or 2 × x + 3 or 2x + 3

preferred

60p

48p

55 copies

£125£510

6 days

2) It costs 4p per copy on the school photocopier.

a) How much would it cost to make 15 single-sidedcopies?

b) Jane has to make 6 copies of a documentwhich is double-sided (writing on both sides).

How much will it cost?

c) Ted copies a single-sided document but forgetshow many copies he has made.

Rather than counting them he simply looks atthe bill and works it out from there.

The bill was for £2.20.

How many copies had he made?

Single-sidedcopies

4p each

1) A vintage car hire firm charges £70 for the first day’shire followed by £55 per day for all other days.

a) How much would it cost to hire a car for 2 days?

b) How much would it cost to hire a car for 9 days?

c) When Sue hires a car it costs her £345.

How many days did she hire the car for?

Formulae Expressed in Words

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Just For FunA1

Page 33B

1) Choose any number.

Add three to it.

Multiply your result by two.

Add six to it.

Halve your answer.

Subtract your original number.

You should be left with six.Try to find out why you are always left with six.

Input Output

1 __

4 __

10 __

2.5 __

-3 __

__ 30

__ 48

__ -18

x __

Input Output

3 __

10 __

-4 __

__ or __ 54

x __

4) Copy the table on the right.

Use this function machine to complete thetable.

Multiply byitself

Add 5Input Output

xx + 3

2x + 6

2x + 12x + 6

6

Input Output

1 __

4 __

10 __

2.5 __

-3 __

__ 30

__ 48

__ -18

x __

2) 3)

2

14

38

8

-14

8

12.5

-4

4x – 2

-4

8

32

2

-20

9.5

14

-2.5

4(x – 2)

14

105

21

-7 7

x2 + 5

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A2

Page 34A

Coordinates in First Quadrant

×

×

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8

×

×

×

×

×

×

××

A

B

C

D

E

F

G

H

I

J

x

y1) Write down the

coordinates of thecrosses labelledA to J.

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8

x

y

2) Put crosses at the followingpoints and label them with thecorrect letters.

A (3, 7)

B (8, 4)

C (2, 5)

D (6, 0)

E (2.5, 3)

F (0, 6.5)

G (5.5, 7.5)

H (8, 8)

A (1, 6)

B (3, 4)

C (7, 3)

D (5, 0)

E (6, 7)

F (8, 1.5)

G (0, 3)

H (2, 7.5)

I (4, 5.5)

J (1.5, 2.5)

××

×

×

×

××

×A

B

C

D

E

F

G H

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Just For FunA2

Page 34B

a) From (2, 3) you have to go 4 squares to theright and 2 squares up to get to the ostrich.

4 + 2 = 6

b) From (4, 6) it is 2 to the right and 1 down.

2 + 1 = 3

c) From (8, 8) it is 2 to the left and 3 down.

2 + 3 = 5

d) (6, 4) is 1 away.

e) The guess which would be furthestaway is (0, 0). It is 11 away.

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8

x

y

×O

×

1)

×

×

×

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Page 35A

Making 3D Models

Tetrahedron

S6

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Page 35B

Making 3D Models

Cube

S6

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Page 35C

Making 3D Models

Octahedron

S6

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Page 35D

Making 3D Models

Shapes put together tomake a tetrahedron

S6

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S7

Page 36A

Reflecting in Diagonal Lines

In all four questions, reflect the shadedshape in the dotted mirror line.

1)

3)

2)

4)

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Page 36B

Just For FunS7

Six Rangoli Patterns Placed Together

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Page 36C

Just For FunS7

Six Rangoli patterns put together for you to colour

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Page 36D

Just For FunS7


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Page 36E

Just For FunS7


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S8

Page 37A

Translate the shape 5 squaresto the right and 2 squares up.

1) Translate the shape 3 squaresto the left and 2 squares down.

2)

Translate the shape with vector3) -43

Translate the shape with vector4) 4-5

Translation

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Page 37B

A

C

D

E

F

GB

HI

Just For FunS8

A with vector

B with vector

C with vector

D with vector

E with vector

F with vector

G with vector

H with vector

I with vector

03

-20

5-1

20

-1-3

4-2

-3-2

23

1-4

Use tracing paper and translate the following shapes.

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S9

Page 38A

Rotate the shape 90° about thecross.

1) 2)

3) 4)

Rotate the shape 90° about thecross.

Rotate the shape 180° aboutthe cross.

Rotate the shape 90° clockwiseabout the cross.

Rotation

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Just For FunS9

Page 38B

1

2

AC

B

180°

a) Rotate triangle A 90° clockwise about cross 1.Label your new triangle B.

b) Rotate triangle B 90° clockwise about cross 2.Label your new triangle C.

c) How many degrees would you need to rotate triangle A toget to triangle C?

d) Mark with a cross the centre of rotation to get from A to C.

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S10

Page 39A

Reading Scales

ml.50

100

150

A

B

1)

2)

Miles

Kilometres0

0 10 20 30

10 20 30 40 50

Use the scale to convert

a) 10 miles to km.

b) 40 km to miles.

c) 16 miles to km.

d) 8 km to miles.

3)

1.25 L

About 3.8 L

125 ml

85 ml

C

16 km25 milesabout 25.6 km5 miles

a) If water comes up to arrow A, howmuch will there be in thecontainer?

b) About how much water will therebe if it comes up to arrow B?

a) If milk comes up to arrow A, howmuch milk will there be in thecontainer?

b) How much milk will there be ifit comes up to arrow B?

c) Draw arrow C to show 140ml ofliquid.

0.5L1L1.5L2L2.5L3L3.5L4L

A

B

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Just For FunS10

Page 39B

You have a 3 pint jug and a 5 pint jug and asmuch water from a tap as you like.How can you use the two jugs to measure outexactly 4 pints of water?

1)

2)

A

B

C

Split the coins into threesets of three.

Put set A into one panand B into the other.

If they balance, the fakeis in C.

If A is heavier than Bthen the fake is in B.

If B is heaviest, thefake is in A.

Take the set of three coinswith the fake in it and putone coin in one pan andanother coin in the otherpan.

If they balance, the othercoin is the fake.

If they don’t balance, theone that goes up is thefake.

Fill the 5 pint jug and pour it intothe 3 pint jug. This leaves 2 pints inthe 5 pint jug.

Empty the 3 pint jug and pour the 2pints from the 5 pint jug into the 3pint jug.

Fill the five pint jug and pour intothe 3 pint jug until it is full.

This will leave you exactly 4 pints inthe 5 pint jug.

5 Pints 3 Pints

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S11

Page 40A

Perimeters

1) Find the perimeter of thisrectangle on the cm grid.

2) Find the perimeter of thisshape on the cm grid.



P = 20cm P = 22cm

P = 26cm P = 20cm

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Just For FunS11

Page 40B

A

Perimeter = 16Area = 7 squares

There is more than one answer for some of the shapes.

Here are some possible answers.

Area of8cm2

Area of9cm2

Area of10cm2

Area of11cm2

Area of12cm2

Area of13cm2

Area of14cm2

Area of15cm2

Area of16cm2

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S12

Page 41A

Areas

1) Find the area of the rectangleon this centimetre grid.



Area = 20cm2

Area = 34cm2

Area = 61.75cm2

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Just For FunS12

Page 41B

1) Draw three different-shapedrectangles with an area of 12cm2

on the centimetre grid.

2) Find the area of thesquare on thiscentimetre grid.

3) Find the area of thesquare on thiscentimetre grid.

This is a difficult question

Area = 18cm2

Area = 20cm2

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D3

Page 42A

Discrete Data

Blue

Green

Red

Yellow

Tally Total1)

1234

Tally Total2)

56

7

9

11

3

712

6411

DogCatHamsterGoldfish

Tally Total3)

Snake

11101382

Colour

No. of children

Pets

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Just For Fun

Page 42B

D3

MANY YEARS AGO IN A FAR-OFF LAND THERE LIVED AN

OGRE OF HUGE PROPORTIONS.

HIS FAVOURITE OCCUPATION WAS TO CAPTURE POOR

PEASANTS AND MAKE THEM WORK FOR FREE ON HIS LAND.

HE WASN’T VERY NICE.

THE NAME OF THE OGRE WAS LANCE.

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D4

Page 43A

1) Here are the Maths test marks for two mixedability Year 7 classes.

Complete the frequency table to show all the results.

Mark Tally Frequency

20 and under

21 - 30

31 - 40

41 - 50

51 - 60

61 - 70

over 70

43 16 68 49 31 24 83 61 55 40 72 44 45 23 48 33 2081 63 58 41 50 59 46 35 24 13 66 99 53 47 66 48 5133 35 40 64 50 31 37 42 35 54 97 24 33 48 53 42

3

4

11

14

7

6

5

Class interval Tally Frequency

14 s < 16

16 s < 18

18 s < 20

20 s < 22

<

<

<

<

3

6

8

4

2) A group of students measured their hand span (s) inin centimetres. Here are their results:

Complete the frequency table to show all the results.

14.720.016.721.618.217.918.1

19.019.916.014.419.121.816.4

17.915.918.019.116.521.118.9

Grouping Data

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Just For FunD4

Page 43B

Sally, the organiser of a slimming club, keeps data on howmuch weight (w), in kg, her 60 members have lost over theprevious twelve months.

She organises the data in a two-way table.

a) Complete the two-way table.

b) How many members of the club were women?

c) How many women lost between 5 and 10 kg?

d) How many men lost less than 20 kg?

e) How many men lost 5 kg or more?

f) How many men and women lost 15 kg or more?

Men Women Total

0 < w < 5 2 4 6

5 < w < 10 4 10 14

10 < w < 15 7 9 16

15 < w < 20 2 8 10

20 < w < 25 3 11 14

Total 18 42 60

4210

1516

24

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D5

Page 44A

Mode, Medianand Range

Tim Sue Ben Tom Dev Ned Kim

1) a) In this group of seven people, which one hasthe median average height?

b) What are the names of the people who arebelow the median average height?

c) To find the range of the heights you wouldneed to measure the height of two people.Which two?

2) A class of students were asked how many petsthey own.

The answers were as follows:

1, 0, 1, 2, 1, 5, 2, 0, 1, 2, 3, 1, 4

2, 3, 1, 2, 2, 0, 1, 1, 2, 1, 3, 2

a) Find the median average number of pets per student.

b) Which number of pets is the mode?

c) What is the range of the answers?

3) Twenty children were asked what their favourite colour was.

Their answers were:

Blue, Red, Yellow, Red, Green, Red, Green, Blue, Red, Blue

Green, Blue, Red, Blue, Yellow, Red, Blue, Orange, Red, Red

a) Which colour is the modal average?

b) Why can’t we find the median colour?

Tom

Tim, Sue and Ben

Kim and Tim

2

1

5 (5 – 0)

Red

The median can only be usedwith numerical values.

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Just For FunD5

Page 44B

1) The heights of 18 plants, to the nearest cm, are as follows:

15, 19, 16, 12, 13, 15, 20, 18, 16, 14, 12, 18, 16, 16, 17, 15, 15, 15

a) Find the modal height of the plants.

b) Find the median height of the plants.

c) Find the range of the heights.

87815

2) You are told that the median score onthese four cards is 9.5

Work out what the number is on thebottom card.

9123) We have six cards with numbers on

them and we know the following:

the modal average is 3

the median average is 5

the range is 11

Work out the numbers on the other four cards.

Score Frequency

1 2

2 3

3 3

4 4

5 4

6 7

4) Sue rolls a dice 23 times and puts herscores into a table.

a) What is Sue’s modal score?

b) What is Sue’s median score?

c) What is the range of Sue’s scores?

15 cm

15.5 cm

8 cm

11

1 3 3 7

6

4

5

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N13

Page 45A

1) 3.6 × 10

2) 82.9 × 100

3) 0.5 × 1000

4) 47 ÷ 10

5) 106.4 ÷ 10

6) 9.9 ÷ 100

7) 6.2 × 1000

8) 70 ÷ 1000

9) 0.035 × 10000

10) 0.01 ÷ 100

36

8290

500

4.7

10.64

0.099

6200

0.07

350

0.0001

=

=

=

=

=

=

=

=

=

=

Multiplication and Divisionby 10 and 100

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Just For Fun

Page 45B

N13

1)

2) Using the fact below:

365 × 17 = 6205

Work out the following

a) 36.5 × 17 = ____ d) 3650 × 1.7 = ____

b) 36.5 × 1.7 = ____ e) 62.05 ÷ 17 = ____

c) 365 × 170 = _____ f) 6.205 ÷ 36.5 = ____

1200

0.75

×100

×1000

÷10

÷100

÷100

7370

0.018

0.104

620.5

62.05

62050

6205

3.65

0.17

Fill in the missing box in each case.

a) f)

b) g)

c) h)

d) i)

e) j)

1)

12 540 5.4

7.5 0.6 0.006

83.1 8310 73.7

0.9 900 ×10 0.18

662 66.2 ×1000 104

×100

÷10

÷100

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N14

Page 46A

Rounding

4.2

53.4

31.6

8.8

0.7

578.5

79.0

3443.8

27.0

100.0

2) Round the following numbers to 1 decimal place.

a) 4.21 f) 578.48

b) 53.43 g) 79.035

c) 31.59 h) 3443.77052

d) 8.827 i) 26.9999

e) 0.653 j) 99.961

1) Using a calculator, work out the following.Give your answers to the nearest 10.

a) 24 × 14

b) 383 × 43

c) 4088 ÷ 56

d) 265364 ÷ 326

e) (42000 + 768) ÷ 54

340 to the nearest 10





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Just For Fun

Page 46B

N14

Round each of the numbers on the calculators to(i) 1 d.p.(ii) 2 d.p.(iii) the nearest whole number.

4.762181)

(i) ___

(ii) ___

(iii) ___

0.5239872)

(i) ___

(ii) ___

(iii) ___

4870.10553)

(i) ___

(ii) ___

(iii) ___

4)(i) ___

(ii) ___

(iii) ___

1.6371285)

(i) ___

(ii) ___

(iii) ___

17.490386

6)(i) ___

(ii) ___

(iii) ___

4.8

4.76

5

0.5

0.52

1

4870.1

4870.11

4870

19800.0

19799.99

19800

1.6

1.64

2

17.5

17.49

17

19799.992

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N15

Page 47A

Ordering Negative Numbers

1) Work out the value of each card and then place the cards inorder from lowest to highest.

2) Work out the value of each card and then place the cards inorder from lowest to highest.

C-3

D-2

B-1

A4.5

J-£5

G-£4.50

E-£4

I-£2.75

F-£2

H-£1.50

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Just For FunN15

Page 47B

5 21)

2)

3)

4)

1 4

12 83 10

5 9-2 4

12 7-5 8

2 + 1 = 34 + 1 = 55 + 2 = 75 + 4 = 9

8 + 3 = 1110 + 3 = 1312 + 8 = 2012 + 10 = 22

4 + (-2) = 29 + (-2) = 75 + 4 = 99 + 5 = 14

7 + (-5) = 28 + (-5) = 312 + 7 = 1912 + 8 = 20

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N16

Page 48A

123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456

123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012

123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012

123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678

123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234

123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012

123456123456123456123456123456123456

123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678

123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012

123456789012123456789012123456789012123456789012123456789012

123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234

1234567890123456712345678901234567123456789012345671234567890123456712345678901234567123456789012345671234567890123456712345678901234567123456789012345671234567890123456712345678901234567123456789012345671234567890123456712345678901234567123456789012345671234567890123456712345678901234567

Ordering Fractions

1)

34

56

23

712

1320

35

34

710

9 squares 10 squares 8 squares 7 squares

34

56

23

712

The correct answer

The working

2) 710

34

1320

35

The correct answer

The working

13 squares 12 squares 15 squares 14 squares

3) 712

58

1324

12

The correct answer

4) 13

25

310

16

The correct answer

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Just For FunN16

Page 48B

1730 2

5

4760

1524

38

712

129

20

23

715

34

13

Smallest

Largest

Place the fractions on thecards in order of size fromsmallest to largest.

13

40120

38

45120

25

48120

920

54120

715

56120

12

60120

1730

68120

712

70120

1524

75120

23

80120

34

90120

4760

94120

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N17

Page 49A

Simplification of Fractions

1) Cancel each of these fractions to theirsimplest form:

a) b) c)

d) e) f)

26

510

312

216

927

2080

2) Cancel each of these fractions to theirsimplest form:

a) b) c)

d) e) f)

414

3070

1634

2442

2745

2836

3) Cancel down fully each of these fractions:

a) b) c)

d) e) f)

3355

7296

4590

13

=12

=14

=

18

=13

=14

=

27

=37

=817

=

47

=35

=79

=

35

=34

=12

=

34

=29

=1729

=75100

40180

68116

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Just For FunN17

Page 49B

Here are six number cards.

a) Choose two of these six cards


equal to .

b) Choose two of these six cards


equal to .

c) Choose three of these six cards


equal to .

d) Choose three of these six cards

to make the smallest

possible fraction.

11

7

9

2 5 9 7 4 11

4599

112144

28175

5

4

2 5

2

9 11

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N18

Page 50A

Shaded : Unshaded

1 3

1 2

1 5

5 7

1 1

1 11

2 4

0.5 2.5

0.2 1

9 15

a

b

c

d

e

f

g

h

i

j

b

3) Find the missing numbers inthese ratios:

a) 1 : 4 = 2 :

b) 1 : 5 = 6 :

c) 2 : 7 = 8 :

d) 5 : 4 = 15 :

e) 2 : 3 = : 12

f) 9 : 5 = : 35

g) 3 : = 18 : 30

c d

e f g

h i j

2) Write the following ratios intheir simplest form:

a) 8 : 12

b) 6 : 10

c) 15 : 10

d) 16 : 4

e) 18 : 16

f) 25 : 15

g) 45 : 15

h) 18 : 27

i) 24 : 30

j) 36 : 48

2 : 3

3 : 5

3 : 2

4 : 1

9 : 8

5 : 3

3 : 1

2 : 3

4 : 5

3 : 4

8

30

28

12

8

63

5

1)

Understanding Ratios

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Just For FunN18

Page 50B

A

1

2

3

4

5

6

7

B

A B

A B

BA

A B

BA

A B

= water= orangeWhich is orangier: A or B?

You must give convincingreasons for each of youranswers

A is 1:1, B is 1:3A is orangier.

A is 2:1, B is 3:2A is 6:3, B is 6:4A is orangier.

A is 1:3, B is 2:5A is 2:6, B is 2:5B is orangier.

A is 1:2, B is 2:4A is 1:2, B is 1:2They are both the same



A is 6:3, B is 4:2A is 2:1, B is 2:1They are the same.

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C14

Page 51A

1) 17 × 32

2) 24 × 62

3) 13 × 156

4) 1.5 × 22

5) 7.6 × 2.1

6) 4.5 × 9.99

7) 528 × 16

8) 19.7 × 6.3

9) 34 × 466

10) 0.35 × 0.12

=

=

=

=

=

=

=

=

=

=

544

1488

2028

33

15.96

44.955

8448

124.11

15844

0.042

Long Multiplication

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Just For FunC14

Page 51B

2)

312£374.40

A school organises a trip to a museum.

They set off in 13 minibuses, each minibus containing24 pupils who will each pay to go into the museum.

Entrance to the museum costs £1.20 per person.

a) How many people made the trip?

b) What was the total cost?

1) Work out what the must be.*a) 3

2

1 6 2

11 5

27 0

1 3 5 00

×3

4800

6120

80

answer:

×b) 60

240

5166

2

47

3 39 0

3

×c)

384

41

9 0

25450

40

answer: 13775

×

00

d)

36 200500

5

900010059

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C15

Page 52A

24

19

17

14

3.6

0.31

23.5

0.21

25.4

383.25

Long Division

=

=

=

=

=

=

=

=

=

=

1) 288 ÷ 12

2) 285 ÷ 15

3) 425 ÷ 25

4) 784 ÷ 56

5) 79.2 ÷ 22

6) 5.89 ÷ 19

7) 893 ÷ 38

8) 9.87 ÷ 47

9) 330.2 ÷ 13

10) 35259 ÷ 92

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Just For FunC15

Page 52B

1)

2)

a) If 48 luxurious pens cost £768,how much would one of them cost?

b) If 25 tee shirts cost £77.50,how much would one of them cost?

c) If 53 mobile phones cost £2 119.47,how much would one of them cost?

Cans of juice cost 24p each.

Wendy has £8.65 to spend.

a) What is the maximum number of cans Wendycan buy?

b) How much change does she get?

3) Find the missing digits.

a) b)

£16

£3.10

£39.99

36

£0.01 or 1p

3 6514 0 4 2 2 2

21

15

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C16

Page 53A

BODMAS

1) Work out the following:

a) 3 × 6 – 2

b) 7 + 2 × 3

c) 5 + 3 × 4 – 1

d) (7 + 1) × 3

e) 5 – 3 × 2

f) 9 – 35 ÷ 5

g) 3 × 2 + 7 + 5 × 4

h) 20 – 9 ÷ 3 + 1

i) 2 × (15 – 10) ÷ 5

j) 7 + 2 – 3 × 4

k) 10 ÷ (2 + 3)

l) 10 ÷ 5 – 8 ÷ 2

m) 7 × (5 – 2) + 10

n) 48 ÷ (2 + 3 × 2)

o) 4 × 12 ÷ 8 – 6


a) 32 – 23

b) 25 – (3 – 1)2

c) 8 × 7 – 16

d) 36 ÷ 22 – 3 × 3

e) 53 – (3 × 15 – 25)

f) ((9 + 1) × 4) ÷ 2

3) Place brackets in thefollowing questions tomake the answers correct.

a) 3 × 5 – 1 = 12

b) 10 + 2 × 3 = 36

c) 7 × 5 – 2 × 2 = 42

d) 24 ÷ 6 – 2 = 6

e) 3 + 2 × 6 ÷ 10 = 3

f) 5 × 5 – 3 ÷ 4 + 1 = 2

4) If x = 3 and y = 7, work out the following:

a) 2x – y

b) 3y + x2

c) y2 – x2

d) (x + y)2 – x3

e) 5(y – x) + (y + x) ÷ 2

f) 10xy – (2y – x)2

= 16

= 13

= 16

= 24

= -1

= 2

= 33

= 18

= 2

= -3

= 2

= -2

= 31

= 6

= 0

= 1

= 21

= 52

= 0

= 112

= 20

( )

( )

( )

( )

( )

( ) ( )

= -1

= 30

= 40

= 73

= 25

= 89

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Just For FunC16

Page 53B

2) Use four 4s plus the operations +, –, ×, ÷ to make thenumbers 0 to 9.

All four 4s must be used. 4s cannot be put together as in 44.

Signs can be used as many times as you like. Brackets canbe used.

A possible answer for 0 could be 4 ÷ 4 – 4 ÷ 4

0 = 4 + 4 – 4 – 4 5 = (4 × 4 + 4) ÷ 4

1 = (4 + 4) ÷ (4 + 4) 6 = (4 + 4) ÷ 4 + 4

2 = 4 ÷ 4 + 4 ÷ 4 7 = (4 + 4) – (4 ÷ 4)

3 = (4 + 4 + 4) ÷ 4 8 = 4 × 4 – 4 – 4

4 = (4 – 4) × 4 + 4 9 = (4 + 4) + (4 ÷ 4)

These are just examples ofhow to get the answers.You may well havedifferent correct answers.

1) Use the numbers 6, 3, 2 and 1 plus the operations +, –, ×, ÷to make the numbers 0 to 9.

The numbers must be used in the specified order (6, 3, 2, 1).

They cannot be put together as in 63 for example.

Signs can be used as many times as you like. Brackets canalso be used.

0 = 6 – 3 – 2 – 1 5 = 6 ÷ 3 + 2 + 1

1 = 6 – 3 × 2 + 1 6 = 6 + 3 – 2 – 1

2 = 6 – 3 – 2 + 1 7 = 6 + 3 ÷ 2 + 1

3 = 6 + 3 ÷ 2 + 1 8 = 6 + 3 – 2 + 1

4 = 6 – 3 + 2 – 1 9 = 6 – 3 × 2 + 1

( ) ( )

( )

( ) ( )

These are just examples ofhow to get the answers.You may well havedifferent correct answers.

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C17

Page 54A

1) Find the following:

a) 13

of 24 b) 23

of 24

c) 15

of 30 d) 35

of 30

e) 18

of 40 f) 58

of 40

2) Work out:

a) 710

of £30 b) 37

of £84

c) 45

of £1.50 d) 1120

of £19

e) 29

of £10.98 f) 813

of £31.85

3) Julie has £4.50 pocket money every week.

If she spends of it on a magazine and ofit on a dance lesson, how much of the pocketmoney does she have left?

25

13

4) Paul has £7.80 pocket money each week.

He always saves of it.

With the remaining money he spends oncomics and the rest on sweets.

(i) How much does he save?

(ii) How much is spent on comics?

(iii) How much does he spend on sweets?

58

13

= 8

= 6

= 5

= 16

= 18

= 25

= £21

= £1.20

= £2.44

= £36

= £10.45

= £19.60

£1.20

£2.60

£3.25

£1.95

Fraction of an Amount

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Just For FunC17

Page 54B

12

a)1) of 23( )of 60

34

b) of 12( )of 80

12

c) of 49

of 42of 34

2) If 34

a) of a number is 60, what is the number?

If 37

b) of a number is 21, what is the number?

If 49

c) of a number is 12.3, what is the number?

3) If 12

of 15

of a number is 6, what is the number?

4) If 12

of 13

of 14

of 15

of a number is 2.5, what is the number?

5) If 35

of 12

of 23

of a number is 3.8, what is the number?

= 20

= 30

= 7

80

49

27.675

60

300

19

Find

Find

Find

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C18

Page 55A

Directed Numbers

1) The temperature is 3°C at midnightand then falls 8 degrees by 6 a.m.

What is the temperature at 6 a.m?

2) Tim has only £8 in his bank accountbut writes a cheque for £15.

If the cheque is cashed, how muchwill Tim have in his account?

3) Sue owes £7 to one friend and £6 toanother friend.

She writes this in her diary as (-7) + (-6)

a) How much does she owe altogether?

b) What is (-7) + (-6)?

4) Sue still owes £7 to one friend and £6to another friend but her motherdecides to take away the £6 debt bypaying it off.

Sue writes this as (-7) + (-6) – (-6)

a) How much does Sue owe now?

b) What is (-7) + (-6) – (-6)?

5) Work out the answers to

a) 6 – 14

b) 2 – 12

c) -1 – 6

d) -3 – 5

e) -7 – 15


a) 2 – (-3)

b) 6 – (-5)

c) -3 – (-6)

d) -7 – (-2)

e) -20 – (-18)


a) 5 + (-2)

b) 8 + (-6)

c) 3 + (-8)

d) -4 + (-3)

e) -8 + (-4)

-5°C

-£7

£13-13

£7

-7

-8

-10

-7

-8

-22

5

11

3

-5

-2

3

2

-5

-7

-12

-1 0 1 2 3 4 5 6 7 8-2-3-4-5-6-7-8


a) 4 – (+1)

b) 7 – (+5)

c) 1 – (+3)

d) -6 – (+1)

e) -1 – (+6)

3

2

-2

-7

-7

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Just For FunC18

Page 55B

1) Each magic square below has a magic number writtenabove it.

You must fill in the blank squares so that the rows,columns and diagonals add up to the magic number.

10-1 3

48 0

-25 9

12 12

515 -5

9-2 8

3-8 -22

-9-23 5

-214 -10

Magic Number is

12Magic Number is

15Magic Number is

-27

2) Work out which numbers should go in the squares tomake the sums correct.

a) 7 + = 9

b) 7 + = 5

c) 2 – = -6

d) 4 – = 7

e) -5 – = 4

f) + 6 = 4

g) – 9 = -12

h) – 14 = -30

a) b) c)

2

-2

8

-3

-9

-2

-3

-16

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C19

Page 56A

Ratio Questionsin Context

1) Share out £20 between Bill and Suein the ratio 3 : 2.

2) Divide £60 between Jack and Jillin the ratio 7 : 3.

3) Debbie and Dave share 200 Smartiesin the ratio 1 : 4. How many Smartiesdo they each get?

4) Alec, Tony and Sara share £720 inthe ratio 1 : 2 : 3. How much do theyeach get?

5) If Dave and Sue share £30 in theratio 2 : 3, how much more thanDave does Sue get?

6) Divide £12 between Mick andSharon in the ratio 5 : 3.

7) Pete and Sandra work part-time in arestaurant. They share the tips in theratio 3 : 5.If Pete gets £30 at the end of theweek, how much will Sandra get?

8) Vicky and John share some sweetsin the ratio 2 : 7.If Vicky ends up with 12 sweets, howmany will John have?

9) Len makes some concrete bymixing cement, sand and gravel in theratio 1 : 4 : 3.If he uses 8 bags of sand, how manybags of cement and gravel will he use?

10) An old television has a width and heightin the ratio 4 : 3. If the width is 48 cm,what is the height?

Bill gets £12, Suegets £8

Jack gets £42, Jillgets £18

Debbie gets 40,Dave gets 160

Alec £120, Tony £240Sara £360

£6 more

Mick £7.50,Sharon £4.50

£50

42 sweets

2 of cement and 6 of gravel

36 cm

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Just For FunC19

Page 56B

1) Which one of these regularpolygons has the number ofdiagonals and the number ofsides in the ratio 2 : 1?

A B C D

2) Two numbers are in the ratio 7 : 3.If you take one of the numbers away from theother one you get an answer of 24.What are the two numbers?

3) In a class of 30 pupils the ratio of boys to girlsis 2 : 3.If 6 girls (but no boys) join the class what isthe new ratio of boys to girls?

C Heptagon has 14diagonals and 7 sides.

42 and 18

1 : 2

4) Sue, Ted and Ben all have theirbirthday on the 1st January.

In 2010, Sue, Ted and Ben haveages in the ratio 2 : 3 : 4.

a) If Ted is 15 years old, how oldare Sue and Ben?

b) When Sue, Ted and Ben are allfive years older, what will be theratio of their ages? Write theanswer in its simplest form.

c) In which year was the ratio ofSue, Ted and Ben’s age 1 : 2 : 3?

d) How old was Ben when the ratioof the three ages was 1 : 3 : 5?

e) On what date was the ratio ofSue and Ben’s age 1 : 41?

Sue is 10,Ben is 20

3 : 4 : 5

2005

12.5

1st April 2000

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C20

Page 57A

Direct Proportion

1) 4 litres of orange juice cost £3.20.

a) What is the cost of 8 litres?

b) How much would 20 litres cost?

c) How much would you pay for 6 litres?

d) What is the cost of 5 litres?

2) 15 voice minutes cost 45p.

What is the cost ofa) 30 voice minutes?

b) 150 voice minutes?

3) If £1 is worth 1.12 euros, how many euroswould you get for £150?

4) Use direct proportion to solve the followingproblems:

a) 5 litres of water cost £3.00.How much would 9 litres cost?

b) A recipe for two people uses 90 g of flour.How much flour is needed for 5 people?

c) 20 blank CD-Roms cost £3.20.How much do 75 CD-Roms cost?

d) A litre of water costs 62p.What is the cost of 2.5 litres of water?

e) 3 kg of cheese costs £7.50What is the cost of 6.5 kg of cheese?

f) 2 litres of smoothie contains 900 ml oforange juice.How much orange juice is in 8.5 litres ofsmoothie?

g) A 120 ml carton of yoghurt contains12 g of sugar.How much sugar would be in a 200 mlcarton of yoghurt?

£6.40

£16£4.80

£4

90p

£4.50

168 euros

£5.40

225 g

£12

£1.55

£16.25

3.825 litres

20 g

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Just For FunC20

Page 57B

Miles Kilometres

5 8

10 16

15 24

20 32

50 80

1)a) Use direct proportion to complete

this conversion table.

b) The distance between London andBirmingham is 120 miles.Use the table to work out thisdistance in kilometres.

c) The distance between London andParis is 460 kilometres.Use the table to work out thisdistance in miles.

3) A jar has 200 sleeping flies in it and the lid is firmly on.

The weight of the jar, when empty is 1 kg.

The weight of the jar and sleeping flies is 1.9 kg (1900 g).

a) If all the flies are the same weight, what is the weightof one fly?

b) Tina shakes the jar so that all the flies are now awakeand flying around.What will the weight of the jar of flies be, now?

2) Here are three offers for voice minutes on a mobile phone.

In which of the offers are the numbers in direct proportion?In each case, explain your answer.

Minutes Cost

1 £0.04

5 £0.20

40 £1.60

A

Minutes Cost

2 £0.24

10 £1.00

100 £7.00

B

Minutes Cost

10 £0.70

50 £3.50

60 £4.20

C

A and C are in direct proportion.

For A the cost of 1 minute is 4p. 5minutes is 5 x 4p = 20p40 minutes is 40 x 4p = £1.60

For C the cost of 1 minute is 7p.50 minutes is 50 x 7p = £3.5060 minutes is 60 x 7p = £4.20

4.5 g

Still 1.9 kgTo stay in the air, each fly must flap its wings whichcreates a downthrust equal in size to its weight.

192 km

287.5 miles

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C21

Page 58A

Real Life Tables

London

195300

330

Nottingham100

159

Manchester

56 Liverpool

All distances are in miles.

1)

a) Write down the distance between London and Nottingham.

b) Write down the names of the two cities which are(i) The furthest apart.

(ii) The least distance apart.

c) Peter travels from London to Manchester where he collects a parcel.He then delivers the Parcel in Nottingham before returning to London.Work out the total distance travelled by Peter.

Stockport 05:26 06:16 06:55 07:15 07:55

Stoke 05:55 06:45 07:24 - -

Stafford 06:12 - 07:41 - 08:41

Euston 08:09 08:26 - 09:11 10:06

2) Here is part of a railway timetable

a) Rosie wants to travel from Stockport to Euston. She mustarrive in Euston before 09:00.

(i) What is the latest time she could depart from Stockport?

(ii) How long will her journey last?

b) James gets to Stockport station at 07:00.How long will he have to wait for the next train to Stafford?

c) Alex travels to Euston.She gets on the 07:24 train from Stoke.How long will her journey take?

195 miles

London and LiverpoolManchester and Liverpool

595 miles

06:162 hours and 10 minutes

55 minutes

2 hours and 42 minutes

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Just For FunC21

Page 58B

1)

Emma lives in Doncaster.She has to drive to Peterborough to pick up her friend, David, and then continue on toLondon to attend a graduation ceremony which begins at 11 am.The ceremony will last two hours and she will then return to Doncaster with David.

a) How far does Emma travel in order to get to London with David?

b) If Emma averages 50 mph on the return trip, at what time would she be backin Doncaster?

Stevenage48

165

Peterborough

130 Doncaster

All distances are in miles.

210 170 45 York

London

2275

195

235

Chester

Wrexham16 minutes

Gobowen35 minutes

Shrewsbury55 minutes

Welshpool76 minutes

Wellington69 minutes

Newtown90 minutes

Telford75 minutes

Wolverhampton90 minutes

2) The train route diagram show the times it takesto travel from Chester to other major stationson the line.

Use the information in the diagram to completethe following

timetables.

Wolverhampton 16:42

Wellington

Shrewsbury

Gobowen

Wrexham

Chester

Telford

Chester 04:22

Gobowen

Shrewsbury

Welshpool

Newtown

Wrexham

205 miles

4.54 pm

16:57

17:03

17:17

17:37

17:56

18:12

04:38

04:57

05:17

05:38

05:52

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A3

Page 59A

Algebraic Expressions

1) Write down the expression you will have ifyou think of a number (let x be the number)and then:

a) add three to it

b) double it

c) multiply it by three and then subtract four

d) multiply it by itself

e) divide it by two

f) divide it by two and then add one

g) add three to it and multiply the resultby two

h) multiply it by five, add four, divide theresult by two

2) Say what the following expressionsmean in words.

a) x + 6

b) x – 7

c) 8x

d) 4x + 2

e)

f) 6(x + 7)

g) 4(3x – 1)

x5

3) If s = 2v, work out the value of swhen v = 7

4) If y = 3t + 4, work out the value of ywhen t = 5

5) If g = 2t – 1, work out the value ofg when t = 9

6) If f = 2(t + 8) and t = 3, find thevalue of f

7) If d = 3(2e – 3) and e = 5, findthe value of d

8) If c = 4 and d = 3, find thevalue of:

a) 2c

b) 2c – d

c) cd

d) 5c + 2d

e) 10cd

f) 2(c + d)

g) 5(3c – 2d)

What expression do I have ifI think of a number, double itand then add three?

Answer: 2x + 3

Say what the expression 4x + 17means in words.

Answer: Take a number, multiplyit by four and then add seventeen.

x + 3

2x

3x – 4

x2 x

2+ 1

2(x + 3)

5x + 42

Take a number and add six to it

Take a number andsubtract seven

Take a number andmultiply it by eight

Take a number, multiply it byfour and then add 2

Take a number and divide it by five

Take a number, add seven toit and multiply the result by six

Take a number, multiply it bythree, subtract 1 and thenmultiply the result by four

s = 14

y = 19

g = 17

f = 22

d = 21

8

5

12

26

120

14

30

x × x or x2

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Just For FunA3

Page 59B

The body mass index (BMI) is a measure used to show if an adult isat a healthy weight. It doesn’t apply to children, only adults.

Here is a formula for calculating BMI

A person with BMI between 18.5 and 25 is at a healthy weight.

A person with BMI less than 18.5 is underweight.

A person with BMI between 25 and 30 is overweight.

A person with BMI over 30 is obese.

BMI = (weight in kg) ÷ (height in m) ÷ (height in m)

1.82m57kg

BMI 17Underweight

1.62m74kg

BMI 28Overweight

1.74m70kg

BMI 23Healthy

1.62m55kg

BMI 21Healthy

No, she has a BMI of 16.7 and is underweight

Here are the heights and weights of the four people above.They are in no particular order.

a) Work out the BMI for each height and weight and put them in the table.Give your answers to the nearest whole number.

b) Match each height, weight and BMI with the correct person.

c) For each person, decide whether he/she is underweight, healthy,overweight or obese - write the answer next to each person.

d) A woman is 1.65 m tall and weighs 45.6 kg.She worries that she is overweight.Is she right?

Height (m) 1.74 1.82 1.62 1.62

Weight (kg) 70 57 55 74

BMI 23 17 21 28

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A4

Page 60A

1) Write down thecoordinates of thecrosses labelledA to J.

B

E

H

AF

J

I

C

D

×

×

×

× ×

×

××

×10-1-2-3-4-5-6 2 3 4 5 6

1

-1

-2

-3

-4

-5

-6

2

3

4

5

6

x

y

×

G

2) Put crosses at the followingpoints and label them with thecorrect letters.

A (-5, 3)

B (2, -4)

C (-2, -6)

D (5.5, 3)

E (0, 0)

F (-3, 0)

G (-6, -5)

H (0, -5)

A (2, 5)

B (-4, 2)

C (-2, -5)

D (6, -4)

E (3, -2)

F (-2.5, 5)

G (-5, 0)

H (0, -3)

I (4, 1)

J (-4.5, -3.5)

10-1-2-3-4-5-6 2 3 4 5 6

1

-1

-2

-3

-4

-5

-6

2

3

4

5

6

x

y

××

× ×

×

×

×

×

G

F E

D

C

B

A

H

Coordinates in FourQuadrants

y

y

x

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Just For FunA4

Page 60B

10-1-2-3-4-5-6 2 3 4 5 6

1

-1

-2

-3

-4

-5

-6

2

3

4

5

6

x

y

×

×

×

×

×

×

y = 2x + 1

(2, 5)

(1, 3)

(0, 1)

(-1, -1)

(-2, -3)

(-3, -5)

2) Plot the following points on thegrid, draw a line through thepoints and try and work out thename of the line.

a) y = x (because y always equals x)

b) y = ½x (because the y coordinateis always half the xcoordinate)

c) y = 2x – 3 (multiply the xcoordinate by 2 andthen take away 3 andyou always get the ycoordinate)

d) x = 5 (because x always equals 5on this line)

WEARCLEAN

POTOOOOOOOO

O _ E R _ T _ O _ XMASCARA

must get heremust get heremust get here

HOROBODDR doo

(a)(b) (c) (d)

(e) (f)

(g)

Clean underwear

Potatoes(POT followed by 8 O’s) Dr Doolittle

Robin Hood(Rob in Hood)

Painless operation

P A I N

Kiss and make up

The three musketeers

y = x

y = ½x

y = 2x – 3 x = 5

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A5

Page 61A

Horizontal & Vertical Lines

-8 -7 -6 -5 -4 -3 -2 -1 O 1 2 3 4 5 6 7 8

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

x

y

1) Draw the following lines on theaxes to the right:

a) x = 3

b) x = -4

c) y = 1

d) x = 7.5

e) y = -3

f) y = 4.5

-8 -7 -6 -5 -4 -3 -2 -1 O 1 2 3 4 5 6 7 8

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

x

y

2) Name all the lines drawn on theaxes on the left.

Line a is: ______________

Line b is: ______________

Line c is: ______________

Line d is: ______________

Line e is: ______________

Line f is: ______________

a

bc

d

e

f

x = 3x = -4 x = 7.5

y = 1

y = -3

y = 4.5

y = -1

x = 2

x = -8

y = 5

y = 6.5

x = -2.5

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Just For FunA5

Page 61B

O 1 2 3 4 5 6 7 8 9 10 11 12

1

2

3

4

5

6

7

8

9

10

11

12

x

y

1) (i) Plot the points(0, 1)(1, 2)(2, 3)(3, 4)(4, 5)(5, 6)

(ii) Draw a line throughthese coordinates.

(iii) Name the line.

2) (i) Plot the points(0, 0)(1, 2)(2, 4)(3, 6)(4, 8)(5, 10)



3) (i) Plot the points(0, 1)(1, 3)(2, 5)(3, 7)(4, 9)(5, 11)



x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

y = x + 1 y = 2x y = 2x + 1

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A6

Page 62A

Function Machines

1) Find the output for each of these function machines.

× 53a)

+ 57b)

× 2 – 36c)

+ 5 ÷ 313d)

÷ 2 – 710e)

– 4 × 2.57f)

2) Find the input for each of these function machines.

– 5 8a)

÷ 4 25b)

× 2 – 1 19c)

÷ 5 + 8 18d)

– 7 ÷ 2 3.5e)

× 19 – 4 -4f)

9

6

-2

7.5

15

12

13

100

10

50

14

0

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Just For FunA6

Page 62B

x

× 2– 7

× 5

– 7

– 2 10x - - - - - -

÷ 2– 5

- - -

- - -

- - -

x5 + 6

× 3

+ 1

× 2- - -

- - - - - + 3

- - -

- - -

4x + 1

- - - - - - - - - -

5x – 7- - - - - - - - - -

- - - - - - - - - -

- - - - - - - - - -

Complete the diagram below. Every time you see dashes like thisyou need to write the correct number or expression.

One of them (5x – 7) has already been done for you.

- - - - - - - - - -,

2xx – 7

x2

– 5

3x + 1

2x

– 2

× 4

+ 1

× 10

÷ 5

+ 6

+ 3

- - - - - - - - - -,

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S13

Page 63A

a) b)c) d)

e) f) g)

h)

Rotationalsymmetryorder 4

4 lines ofsymmetry


2 lines ofsymmetry


2 lines ofsymmetry


0 lines ofsymmetry


0 lines ofsymmetry

No rotationalsymmetry

1 line ofsymmetry


3 lines ofsymmetry

No rotationalsymmetry

1 line ofsymmetry

1) For figures a to h, work out

i) The order of rotational symmetry.

ii) How many lines of symmetry it has.

2) Shade in six more triangles sothat this figure has rotationalsymmetry order 3

Symmetries of 2D Shapes

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Just For FunS13

Page 63B

a) Shade in one squareso that this shape hasrotational symmetry oforder 2.

1)

CHLOEBAXTER

3) Seven

b) Shade in a differentsquare so that thisshape has rotationalsymmetry of order 2.

CHLOEBAXTER

upside down in the mirror

B, X, E, C, H, O, E can all be read the same

2) Shade three more squaresso that the grid has rotationalsymmetry of order 4.

These are thetwo differentanswers

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S14

Page 64A

Measuring and Drawing Angles

a

e fg

d

c

b

1) Each of the angles below can be described as an acuteangle, an obtuse angle, a reflex angle or a right angle.

Decide which each of them are.

2) a) Draw a triangle which has three acute angles.

b) Draw a triangle which has one obtuse angleand two acute angles.

c) Draw a quadrilateral (4-sided shape) whichhas one reflex angle and three acute angles.

d) Draw a quadrilateral which has one rightangle, one acute angle and two obtuse angles.

e) Draw a quadrilateral which has two obtuseangles and two acute angles.

Obtuseangle Acute

angle

Reflex angle

Rightangle Obtuse Acute

Reflex

this isjust oneexample

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S14

Page 64B

a

b

c

d

e

65°

160°

38° 112°

39°

Use a protractor to measure theangles below.


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S14

Page 64C

a

c

d

e

Use a protractor to measure theangles below.

b310° 245°

324°

248°

294°


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S14

Page 64D

Draw the angle where you see the dot.Here is an example:

40° 40°

70°a) 135°b)

28°c)

171°d)


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S14

Page 64E

340°a) 305°b)

245°c)

193°d)

Draw the angle where you see the dot.


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Just For FunS14

Page 64F

a) Measure, very carefully, angles A, B and C.

b) Add the angles together.

c) What do they add up to?

d) Tear or cut along the wavy lines.

e) Fit the angles together to form a straight line.

1)

a) Draw some more triangles.Don’t forget ones like these

b) For each triangle, label the angles A, B and C.It doesn’t matter which is which.

Fill in the table below.

2)

Triangle 1

Angle A Angle B Angle CAll three anglesadded together

Triangle 2

Triangle 3

Triangle 4

123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234

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Tear or cut here

A

B C

75°72° 33°

180°

180°

180°

180°

180°

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S15

Page 65A

Angle Facts

50°35°

a

42° b

c

65°

70°

70°80°

85°

d

55°

e

120°

58°f

g

h

95°138°

45°

125°

65°

58°

122°122°

1) Work out the size of angles a to h.

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Just For FunS15

Page 65B

C

68°

a 34°

b

123°c

68°

68 + 68 = 136180 – 136 = 44

= 44°

180 – 34 = 146146 ÷ 2 = 73

73°= 73°180 – 123 = 57

57°

57°

= 66°180 – 57 – 57 = 66

110°

xA

D

E70°

70°

40°

40°

= 30°

This becomes easier if you turn the rhombus so thatyou can see the diamond shape easily.Put dashes on all the equal sides.

1)

2)

Angle x

B

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S16

Page 66A

Areas of Rectangles

1) Find the areas of the following four rectangles.

9 cm

4 cm

5 m

3 m

9.6 cm

2.8 cm

12 m

3.5 m

a) b)

c)

d)

2) Find the lengths of the missing sides.

Area = 24 cm26 cm

?

Area = 96 cm2

12 cm

?Area =

253.44 cm2

13.2 cm

?

Area = 36 cm2

Area = 15 m2

Area = 26.88 cm2

Area = 42 m2

4 cm

8 cm 19.2 cm

b)a) c)

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Just For FunS16

Page 66B

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10 cm

14 cm

8 cm

6 cm

1) Find the area of the shaded section.

2) Find the area of the shape below.

15 cm

6 cm

10 cm

7 cm

Area of largerectangle = 140 cm2

Area of smallrectangle = 48 cm2

Area of shadedsection = 92 cm2

3 cmArea of thisrectangle = 45 cm2

Area of thisrectangle =

42 cm2

Area of theshape = 87 cm2

© Mathswatch Ltd

Level 5

Answers


D6

Page 67A

1) Estimate a probability (decimal) to go with these:

a) You will be on time for school on the nextschool day.

b) It will snow sometime this week.

c) Your teacher will smile at least once tomorrow.

d) You will have a disagreement with one of your friends.

e) England will win the World Cup in 2018.

f) England or France will win the World Cup in 2018.

2) Work out an exact probability (as a fraction)for these events:

a) If you flip a coin you will get a ‘head’.

b) If you flip two coins you will get two ‘heads’.

c) If you roll a dice you will get a 6.

d) If you roll two dice you will get two 6’s.

e) If you flip a coin and roll a dice you will geta ‘head’ and a 6.

f) If you flip three coins you will get three ‘heads’.

g) If you flip three coins you will get two ‘heads’and a tail in any order.

h) If you flip three coins you will get at leastone ‘head’.

i) If you roll two dice and add the scorestogether you will get a total of 4.

Your teacher will need tocheck this answer.

This depends on what monthit is and where you live.

It might be better not to showyour teacher this answer.

Only you and yourfriends can check this.

This is your opinion.

To be correct, this answermust be bigger than theanswer to question e).

12

14

16

112

18

38

78

336

136

Probability

© Mathswatch Ltd

Level 5

Answers


Just For FunD6

Page 67B

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12

R I V E R

The key to winning this game is to realise that not all totalscores are equally likely.

A total of 1 will never happen, of course.

The probabilities for each total are as follows:

1 0

2 136

3 236

4 336

5 436

6 536

7 636

8 536

9 436

10 336

11 236

12 136

Score

ProbabilityScore

Probability

This would be a very good line-upfor the horses.There are other similar ones whichare just as good.

© Mathswatch Ltd

Level 5

Answers


D7

Page 68A

The Mean Average

1) a) Move blocks around so thatthe heights of the five towersare the same.

b) What is the mean averagenumber of blocks in eachtower?

2) a) Move blocks around so thatthe heights of the five towersare the same (you may haveto cut some blocks).

b) What is the mean averagenumber of blocks in eachtower?

3) In a spelling test, the results for the class (out of 10) are:

3, 6, 8, 8, 4, 1, 7, 6, 2, 9, 3, 8, 4, 1, 1, 3, 5 and 2

a) Work out the mean average score for the class.

b) How many children had a score below the mean average?

4) Two Year 6 classes had a ‘times table test’ which wasmarked out of 20.

The marks in David’s class were:

14, 12, 19, 20, 20, 15, 14, 12, 13, 3, 18, 19, 16, 14, 12, 6

Harry was in the other class and the marks were:

9, 12, 17, 17, 16, 14, 18, 20, 8, 13, 16, 14, 18, 8

Use the mean average to work out which class didbetter in the test.

43.5

Mean average for David’s class: 14.1875Mean average for Harry’s class: 14.28571Harry’s class did best.

4.5

10

© Mathswatch Ltd

Level 5

Answers


Just For FunD7

Page 68B

878

52

1) If the mean average number on thesefive cards is 6, what is the number on thebottom card?

2) If the mean average number on theseeight cards is 4.25, what is the numberon the bottom card?

845

26

4

7 3

3) John rolled a dice thirty times andput the results into this table.

Work out his mean average score.

Score Frequency

1 4

2 3

3 5

4 6

5 4

6 8

4) What is the mean averagenumber of arms per personin Britain?

5) Can you find out the meannumber of children perfamily in the UK?

8

3

3.9

1.999....Very close to 2 butdefinitely not quite 2

Widely reportedas 1.8

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

N19

Page 69

Fraction Decimal Percentage

50%

40%

0.25

0.7

11013

Fraction Decimal Percentage

35%

5%

0.6

0.6

68100

1350

1) Complete the tables.

a) b)

2) Put these fractions, decimals and percentagesin order, smallest to largest.

a) , 49%, , 0.55

b) 27%, 0.2, ,

c) , 95%, 0.99,

d) , 0.6, , 30%

e) 0.125, 10%, , 0.09

12

3514

310

910

97100

13

23

11100

3) Chris says that is halfway between 0.5 and 100%.

Is Chris correct? You must explain your answer.

34

4) Emily says that 0.2 is halfway between 10% and .

Is Emily correct? You must explain your answer.

35

0.5

0.1

0.3

0.4

25%

10%

33.3%

70%

1214

71025

60%

66.6%

68%

26%

0.05

0.26

0.68

0.35

23120

72035

49%12 0.55

35

0.214 27%

310

0.9997

10095%9

10

30% 0.623

13

0.0911

10010% 0.125

Yes. 0.5 is and 100% is and is halfway between them.24

44

34

No. 10% is 0.1 and is 0.6 and 0.2 is not halfway between them.35

Fractions, Decimalsand Percentages

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 70

N20Improper Fractions and

Mixed Numbers

54

127

165

83

209

4712

307

253

758

1009

2) Convert the following mixed numbers to improper fractions.

a) f)

b) g)

c) h)

d) i)

e) j)

35

23

27

14

35

311

58

19

45

34

1

2

5

3

11

10

7

9

6

12

3) Put these numbers in order, lowest to highest.

a) 3.5, 3 ,

b) 7 , 7.14,

c) 1 , 98%, , 1

15

113

14

345

54

110

141

232

571

292

153

138

274

389

11123

1911

85

94

173

185

797

919

618

495

6911

514

3 3.515

113

345

7.14 7 14

98% 1 1 110

54

1) Convert the following improper fractions to mixed numbers.

a) f)

b) g)

c) h)

d) i)

e) j)

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 71

N21Prime Numbers,HCF and LCM

1) Split up the following numbers into the product of their prime factors.

a) 12 d) 120

b) 45 e) 550

c) 72 f) 1296

2) Find the Highest Common Factor (HCF) of the following numbers.

a) 4 and 6 d) 300 and 525

b) 8 and 16 e) 374 and 918

c) 36 and 48 f) 45, 90 and 105

3) Find the Lowest Common Multiple (LCM) of the following numbers.

a) 8 and 12 d) 4, 6 and 8

b) 30 and 45 e) 24 and 84

c) 15 and 18 f) 72 and 96

4) The bells at Kings School ring every 6 minutes.

At Queens School the bells ring every 5 minutes.

At Princess School the bells ring every 9 minutes.

All three bells ring together at 8.30 am.

When is the next time the bells of the three schools will ring together?

2 × 2 × 2 × 2 × 3 × 3 × 3 × 3

2 × 5 × 5 × 11

2 × 2 × 2 × 3 × 5

2 × 2 × 2 × 3 × 3

3 × 3 × 5

2 × 2 × 3

2

8

12

75

34

15

24

90

90

24

168

288

10 am

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 72

C22Percentage

of an Amount


a) 50% of 80

b) 50% of 48

c) 50% of 15

d) 25% of 120

e) 25% of 90


a) 10% of 150

b) 10% of 26

c) 50% of 12

d) 25% of 12

e) 75% of 12


a) 10% of £40

b) 5% of £40

c) 15% of £40

d) 5% of £70

e) 15% of £380


a) 20% of £50

b) 45% of £9

c) 80% of £11

d) 35% of £6

e) 65% of £824

5) Jamie received £26 pocket money last week.

He spent it as follows: 10% on sweets,

25% on magazines

15% on games

How much did Jamie have left?Show your working.

6) Tony had £40 saved up and gave 35% of it to his younger sister, Ella.

Ella gave 20% of what she was given to her younger brother, Ben.

Ben gave 30% of what he was given to his younger brother, Tim.

Tim spent 75% of what he was given on buying a toy for his hamster, Hammy.

How much was the toy for Hammy?

= 40

= 24

= 7.5

= 30

= 22.5

= 15

= 2.6

= 6

= 3

= 9

= £4

= £2

= £6

= £3.50

= £57

= £10

= £4.05

= £8.80

= £2.10

= £535.60

10% + 25% + 15% = 50%Therefore he had 50%left which is £13

£0.63

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 73

C23

3) Increase the following numbers by 10%

a) 40 e) 75

b) 140 f) 505

c) 810 g) 12

d) 320 h) 123

4) Decrease the following numbers by 10%

a) 20 e) 25

b) 160 f) 445

c) 80 g) 13

d) 190 h) 7


a) Increase £400 by 5% e) Increase 250 m by 50%

b) Decrease £120 by 15% f) Decrease £820 by 75%

c) Decrease 500 km by 20% g) Increase 60 kg by 60%

d) Increase 96 kg by 10% h) Decrease £26 by 35%

6) A shop is having a sale and all prices are reduced by 25%.

a) Work out the sale price of an item normally priced at £18.40

b) Work out the sale price of an item normally priced at £99

Find 10% of the number and add it on.

Find 10% of the number and take it away.

44 82.5

154 555.5

891 13.2

352 135.3

18 22.5

144 400.5

72 11.7

171 6.3

£420 375 m

£102 £205

400 km 96 kg

105.6 kg £16.9

£13.80

£74.25

2) Describe how you would decrease a number by 10%.

Percentage Increaseand Decrease

1) Describe how you would increase a number by 10%.

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 74

C24Addition and Subtraction

of Fractions

1) Work out the following, simplifying youranswers where possible.

a) e)

b) f)

c) g)

d) h)

27

37+ =

38

18+ =

79

29 =

16

23+ =

16

23+ =

45

12 =

1415

35 =

7

9

18 18+ =

6 6+ =

15 15 =

2) Work out the following, simplifying youranswers where possible.

a) f)

b) g)

c) h)

d) i)

e) j)

38

48+ =

12

13+ =

12

25+ =

510

110 =

911

511 =

57

35 = 3

812+ =

512

16+ =

56

14 =

45

110 =

89

56 =

2) Write the missing numbers in each of these fraction sums.

a)

b)

c)

d)

13 6+ =

85 15 =

37

12 =

15 14 =

+

1

1

1

1

5

5

12

25

56

56

310

13

3 12

14 9

1 4

78

411

56

435

910

712

712

710

78

118

4

21

9

12

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 75

C25Multiplication and Division of

Integers by Fractions

1) Work out the following, giving your answers in their simplest forms

a) 3 × e) 4 ×

b) 7 × f) 10 ×

c) 2 × g) × 6

d) 9 × h) × 3

14

17

45

13

49

38

89

215


a) of £40 e) of 30 cm

b) of 20 km f) of £16

c) of 120 kg g) of 7000 g

d) of £99 h) of £500

12


a) 3 ÷ e) 10 ÷

b) 7 ÷ f) 8 ÷

c) 12 ÷ g) 3 ÷

d) 9 ÷ h) 15 ÷

14

12

13

15

23

45

57

23

15

14

19

25

78

47

34

4) An industrial machine takes of an hour to produce a very special tool.

How long would it take the machine to produce 12 of the tools?

34

5) A road is 20 km long. Road signs are to be installed every ofa kilometre. How many signs will be needed?

23

34

1

85

3

169

154

163

25

£20

4 km

30 kg

£11

12 cm

£14

4000 g

£375

12

14

36

45

15

10

215

452

9 hours

30 signs, assuming that there isn’t asign at the beginning of the road.

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 76

A7 Substitution

1) Using a = 3, work out

a) a + 5 d) 2a + 1

b) 7 – a e) 13 –

c) 6a f) a2 + 2a – 20

a3

2) Using x = 5 and y = 2, work out

a) x – y d) 5y – 5x

b) y – x e) x2 + 3y

c) 3x + 2y f) – xy4xy

3) Using a = 3, b = 1 and c = -2, work out

a) a + b + c d) ab – c

b) 2b + c e) ac + 5b

c) c – a + b f) c2 – 2ab

4) Using x = 3, work out

a) x2 – 2x

b) 2x2 + x + 1

c) x3 – 2x2 – 5

5) If = 3.142 and r = 9, work out

a) 2 r

b) r 2

8

4

18

7

12

-5

3

-3

19

-15

31

0

2

0

-4

5

-1

-2

3

22

4

56.556

254.502

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 77

A8 Trial and Improvement

1) Using a trial and improvement method,solve the equation x2 – x = 56

You must show ALL your working.

2) Using a trial and improvement method,solve the equation x3 + 2x = 72


x = 6 36 – 6 = 30 Lowx = 7 49 – 7 = 42 Lowx = 8 64 – 8 = 56Therefore, x = 8

x = 2 8 + 4 = 12 Lowx = 5 125 + 10 = 135 Highx = 4 64 + 8 = 72Therefore, x = 4

3) The equation x2 + 3x = 37has a solution between 4 and 5.

Use a trial and improvement method to find this solution.Give your answer to one decimal place.


4) The equation x3 – 2x = 9has a solution between 2 and 3.



x = 4 42 + 3 × 4 = 28 Lowx = 5 52 + 3 × 5 = 40 Highx = 4.9 4.92 + 3 × 4.9 = 38.71 High

x = 4.8 4.82 + 3 × 4.8 = 37.44 High

x = 4.7 4.72 + 3 × 4.7 = 36.19 Lowx = 4.75 4.752 + 3 × 4.75 = 36.8125 LowTherefore, x = 4.8 to one decimal place.

x = 2 23 – 2 × 2 = 4 Lowx = 3 33 – 2 × 3 = 21 Highx = 2.1 2.13 – 2 × 2.1 = 5.061 Low

x = 2.2 2.23 – 2 × 2.2 = 6.248 Low

x = 2.3 2.33 – 2 × 2.3 = 7.567 Low

x = 2.35 2.353 – 2 × 2.35 = 8.277875 LowTherefore, x = 2.4 to one decimal place.

x = 2.4 2.43 – 2 × 2.4 = 9.024 High

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 78

A9Algebraic Simplification

1) Simplify these expressions

a) 3a + 4a = f) 3r – 2r + 4r =

b) b + 4b = g) 5t – 3t + t + 2t =

c) 5x – x = h) 7p – p + 2p – 5p =

d) 6d + 3d – 2d = i) -4y + 2y – y + 4y =

e) 2k + k + k – 3k = j) -2c + c – 3c – c =


a) a + b + a + b = f) 6x – 4y + 7y – 2x =

b) 3a + 2a + 4b + b = g) 2k – 3l – k + 10l =

c) 7x + 2y + x + 3y = h) 3m + 5n + 7m – 7n =

d) 5r + 6p – 2r – 3p = i) v – 4w – 5v – 2w =

e) 4c + 8d – 3c + d = j) -3x – y – 3y – x =


a) 7xy – 2xy = f) 6m + 2pr – m + 3rp =

b) 5cd + 3dc = g) 10a2d + 2y – 3da2 + y2 =

c) x2 + 4x2 + 2x2 = h) bz2 + 4t3 – 3t3 – 5zb2 =

d) 9y3 + y – 2y3 = i) 2r2b + 5r2 – r + 6br2 =

e) 3ab + 7ab – 2a = j) 8x3y + 2w – 5w – 3yx3 =

7a

5b

4x

7d

k

5r

5t

3p

y

-5c

2a + 2b

5xy

5a + 5b

8x + 5y

3r + 3p

c + 9d

4x + 3y

k + 7l

10m – 2n

-5v – 6w

-4x – 4y

8cd

7x2

7y3 + y

10ab – 2a

5m – 5pr

7a2d + 2y + y2

bz2 + t3 – 5zb2

8br2 + 5r2 – r

5x3y – 3w

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 79

A10Linear Equations

1) Solve

a) x + 5 = 8 f) 2x = 14

b) x + 7 = 9 g) 3x = 30

c) x – 3 = 12 h) = 8

d) x – 6 = 10 i) = 7

e) 2 + x = 5 j) = 8

x = 3

x = 2

x = 15

x = 16

x = 3

x = 7

x = 10

x = 16

x = 35

x = 6

2) Solve

a) 5x + 2 = 17 f) + 3 = 7

b) 3x – 1 = 17 g) – 2 = 4

c) 2x + 10 = 20 h) – 1 = 9

d) 4x – 7 = 29 i) + 5 = 11

e) 4 + 2x = 14 j) + 6 = 8

x2x5

2x53x2

4x5

x = 3

x = 6

x = 5

x = 9

x = 8

x = 30

x = 25

x = 4

x = 2.5x = 5

3) Using the statement: “I think of a number, double it,and subtract 1. I get 7.”

a) Form an equation.

b) Solve the equation to find the number that was thought of.

4) Using the statement: “I think of a number, multiply it by 7,and add 3. I get 80.”



5) Using the statement: “I think of a number, multiply it by 2,divide the result by 3 and then subtract 5.I get 5.”



2x – 1 = 7

x = 4

7x + 3 = 80

x = 11

x = 15

– 5 = 52x3

x2x5

4x3

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 80

A11Generate a Number

Sequence

1) Write the first five terms of each sequence

a) Start at 1 and add 5 d) Start at 8 and subtract 4

b) Start at 30 and subtract 4 e) Start at -10 and add 6

c) Start at 11 and add 9 f) Start at 4 and subtract 3

2) For each sequence, describe the rule and find the next two terms

a) 5, 7, 9, 11, ___, ___ d) -1, 2, 5, 8, ___, ___

b) 11, 16, 21, 26, ___, ___ e) 6, 2, -2, -6, ___, ___

c) 22, 19, 16, 13, ___, ___ f) -42, -35, -28, -21, ___, ___

3) Here is a pattern made up of sticks

a) Write the pattern as a number sequence.

b) Describe the rule.

c) Find the next five terms of the sequence.

4) For each sequence, find the first 5 terms and the 10th term.

a) 3n – 1

b) n + 2

c) 5n + 2

d) 4n – 7

e) 10n + 9

1, 6, 11, 16, 21

30, 26, 22, 18, 14

11, 20, 29, 38, 47

8, 4, 0, -4, -8

-10, -4, 2, 8, 14

4, 1, -2, -5, -8

13 15

31 36

10 7

11 14

-10 -14

-14 -7

Add 2

Add 5

Subtract 3

Add 3

Subtract 4

Add 7

5, 9, 13

Add 4

17, 21, 25, 29, 33

2, 5, 8, 11, 14, . . . . . . . , 29

3, 4, 5, 6, 7, . . . . . . . , 12

7, 12, 17, 22, 27, . . . . . . . , 52

-3, 1, 5, 9, 13, . . . . . . . , 33

19, 29, 39, 49, 59, . . . . . . . , 109

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Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 81

A12

Pattern 1 Pattern 2 Pattern 3

1)

a) Draw pattern 4

b) How many lines would be in Pattern 6?

c) How many lines would be in Pattern n?

2) Work out the nth term of the following number patterns.

a) 2, 4, 6, 8, . . . .

b) 3, 5, 7, 9, . . . .

c) 5, 8, 11, 14, . . . .

d) 1, 5, 9, 13, . . . .

e) 12, 22, 32, 42, . . . .

f) 2, 8, 14, 20, . . . .

g) 3, 4.5, 6, 7.5, . . . .

3) Write down the first four terms and the 10th term of the followingnumber patterns.

a)

b)

c)

d)

e)

f)

g)

n 3n

n 3n + 2

n n – 3

n 2n + 5

n 3n – 7

n 5n + 3

n 4n – 1

5n + 1n

31

2nn

2n + 1n

3n + 2n

4n – 1n

10n + 2n

6n – 4n

1.5n + 1.5n

3, 6, 9, 12, . . . . . 30

5, 8, 11, 14, . . . . . 32

-2, -1, 0, 1, . . . . . 7

7, 9, 11, 13, . . . . . 25

-4, -1, 2, 5, . . . . . 23

8, 13, 18, 23, . . . . . 53

3, 7, 11, 15, . . . . . 39

Finding the nth Term

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Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 82

A13Straight Line Graphs

-5 -4 -3 -2 -1 O 1 2 3 4 5

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

11

12

13

x

y

x -2 -1 0 1 2 3 4 5y

1) a) Complete the table of values for y = 3x – 2

b) Plot the graph of y = 3x – 2

c) Use your graph to estimate the value of xwhen y = 2

d) Use the graph to estimate the value of xwhen y = -4

-3 -2 -1 O 1 2 3 4

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

y

x

2) a) Plot the graphof y = 2x – 4

b) Plot the graphof x + y = 1

1310741-2-5-8

Approximately 1.3

Approximately -0.7

y = 2x – 4x + y = 1

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A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 83

A14

The graph, above, shows Jade’s journey by scooter from herhouse to university with some stops along the way.

a) How long did the journey take?

b) How many breaks did Jade take throughout her journey?

c) At what time did Jade take her first break?

d) How long did the first break last?

e) What was Jade’s average speed between 3 pm and 4 pm?

f) What was Jade’s average speed between 4.30 pm and 5 pm?

g) What was Jade’s average speed between 5.30 pm and 7 pm?

4 hours

2

4 pm

30 minutes

20 mph

40 mph

20 mph

Distancein miles

3 4 5 6 7 80

10

20

30

40

50

60

70

80

pm pm pm pm pm pmTime

Distance - Time Graphs

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Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

2) The graph below shows three different mobile phone tariffs.

Tariff 1Pay as you go50p per minute.

Tariff 2£15 per month and30p per minute

Tariff 3£40 per month,100 free minutes then10p per minute

a) Match each tariffwith its graph, A, B or C

b) Every month, Jamesneeds about 90 minstalk time.Work out which tariff wouldbe best for him. Explain your answer.

c) Tariff 4 is announced. This is £10 per month, 40 free minutes then 30p per minute.Draw a line on the graph to show this tariff.

Page 84

A15 Real Life Graphs

1) Use the conversion graph below to convert :

a) 80 km to miles

b) 35 miles to km

c) 40 km to miles

d) 60 miles to km

e) 100 miles to km

f) 140 km to miles

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

0Kilometres

Miles

0 20 40 60 80 100 120 140 1600

10

20

30

40

50

60

Costin £

Monthly used minutes

A

BC

50

56

25

96

160

86

T1 is C T2 is B T3 is A

T3 is best because it costs £40.

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Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 85

S17

a) b) c)

d) e) f) g)

1) Write down the names of the quadrilaterals a) to g)

8 cm

14 cm

9 cm

A

12 cm

8 cm

9 cm

B

16 cm

10 cm

C

Number of linesof symmetry

Order of rotationalsymmetry AreaShape

A

B

C

2) Fill in the table for quadrilaterals A, B and C.

Rhombus Trapezium Irregularquadrilateral

SquareKite

Rectangle Parallelogram

None

None

2

2

None

2

112 cm2

90 cm2

80 cm2

Properties of Quadrilaterals

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Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 86A

S18 Nets of 3D Shapes

a) Draw a net of this cube. b) Draw a net of this cuboid.

3 squares

3 squares

3 squares

2 squares1 square

4 squares

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Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 86B

S18 Nets of 3D Shapes

Draw a net of this triangular prism.

12 squares

5 squares13 squares

4 squares

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Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 87

S19

7 cm

40° 65°A B

C

AC = 6.6 cm

6 cm

25°120°

A B

C

AC = 9.1 cm

110°

80°

A B

C

D

4 cm

3.5 cm

CD = 5 cm

3 cm

3 cm3 cm

3 cm

3 cm

A B

C

DE

F

CD = 3 cm

BA

C

6 cm

7 cm4.5 cm

r = 58°s = 37°

8 cm

5 cm 5 cm

A B

C

3 cm

7.5 cm

5 cmt = 138°

A B

C

D

E

7 cm

80° 70°

4 cm

5 cmu = 81°

1)

2)

a)

b)

c)

d)

a)

b)

c)

d)

Constructions

A B

C

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Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 88

S20 Geometric Problems

In every question below, calculate the missing angles indicated by theletters. None of the diagrams are drawn accurately.

46° 78°

a

29°

35°

b

41°

c 57°

d

50°

e

235°

f50°

g

74°85°

40°

h

24°

64° e

f 35° g

h

40°

ji 55°

l

k

44°a 115°

b53°

c

38°

d

72°

115°e

125° 72°f 143° 45°

g

20°

32°

h36°

148°

65°

a

145°

73°

b 68° 54°

c32°

d

1)

2)

3)

56°

116° 49°

33°

52°

64°110°

35°

70° 70° 62.5°

62.5°

136°

65° 70°

310°

125°

146° 211°

37°

80° 141°

126°

106°

60° 109°

83°

80°

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Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 89

S21

a

bc

e

fg

d58°

28°b

d

105°f

153°

79°

h

i

jk

l

mn

o64° 70°

p q

r s

t

a

61°

72°

64°

71°

a

bc

d

e

80°

24°

37°

a

In every question below, calculate the missing angles indicated by theletters. None of the diagrams are drawn accurately.

1)

124°c

2)

e

137°

3)

4)

45°

40°

b

c

de

37°28°

124°

105°

137° 153°

58°58°

122°

122°58°

122°

122°

101° 79°79°

79°

79°

101°

101°

101°64° 70°

46°

64° 70°

47°

40° 45°95°

45°

45°

64°

24°

71°

100°

Corresponding andAlternate Angles

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Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 90A

S22 Enlargement

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Enlarge the following shapes with scale factor 2, using the dot as the centre of enlargement.

a) b)

c) d)

e) f)

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Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 90B

Enlargement

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Scale factor 3 Scale factor 3

Scale factor 4 Scale factor 0.5

a) b)

c) d)

A

B

C

D

2) Use dots to mark on the grids the positions of the centres of enlargement.

a) b)

1) Enlarge the following shapes using the dots as the centres of enlargement.

S22

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A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 91

S23Similar Shapes

1) In each of the following questions, the two shapes aremathematically similar.

Work out the lengths of the missing sides.

a) b)

c) d)

12 cm

?

4 cm

7 cm

4 cm

?

8 cm

10 cm

8.2 cm

7 cm

?

9.8 cm

4.2 cm

?10 cm

2 cm16.6 cm

?

2) a) Work out the length of CD.

b) Work out the length of AE.

A

B

CD

E

5 cm

3 cm

10 cm

4 .5 cm

21 cm

5 cm

83 cm 11.48 cm

3 cm

7.2 cm

6.25 cm

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A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 92A

S24Area of a Triangle

1) Find the areas of the following triangles

a) b) c) d)

8 cm 5 cm

6 cm 7 cm 1 cm

0.6 cm

13 cm 15 cm


a) b)

c)

12 cm

5 cm

13cm

2.8 cm

1.3 cm2.5 cm

30 cm

40 cm

50 cm


a) b)

13 cm

8 cm 8.6 cm6.4 cm

26.4 cm

18.2 cm

c)

d)

14 cm

20 cm

e) 36 cm

28 cm

24 cm2

17.5 cm2

0.3 cm2

97.5 cm2

30 cm21.625 cm2

600 cm2

52 cm2

27.52 cm2

240.24 cm2

140 cm2

504 cm2

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Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 92B

S24Area of a Triangle

16 cm

20 c

m

5 cm

3 cm

7 cm

6 cm

14 cm

22 c

m

20 cm

26 c

m

4 cm

5 cm

9 cm 6 cm

5 cm 8 cm

7 cm

7 cm

2) Find the areas of the following shaded parts of rectangles

a) b) c)

6 cm

wArea = 12 cm2

8 cm

x

Area =18 cm2

Area =12.5 cm2

y

4 cm

1) Find the lengths w, x, y and z

Area = 40.5 cm2

z z

3) The two squares are drawn on 1 cm square grids.Find the areas of the squares.

a) b)

a) b)

c)

d)

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w = 4 cmx = 4.5 cm

y = 6.25 cm

z = 9 cm

154 cm2

163.5 cm2

384.5 cm2

17 cm2 13 cm2

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Level 6

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A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 93

S25

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1) Find the areas of the five parallelograms on this cm square grid.

a) b)

c)

d)

e)

2) Find the areas of these four parallelograms

8.4 cm

3.6 cm

19 cm

19.8 cm

13 cm

12.3 cm 20 cm

18 cm

22 cm

40 cm2 9 cm2 4 cm2

15 cm2 1 cm2

360 cm2

30.24 cm2 376.2 cm2

159.9 cm2

a) b)

c)

d)

Area of aParallelogram

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 94

S26

20 cm10 cm

15 cm

19 cm

7 cm

11 cm

30 cm

22 cm

14 cm

15 cm6 cm8 cm

4.2 cm1.6 cm

2.1 cm

19 cm8 cm

?

20 cm

7 cm

9 cm

6 cm

3 cm1) Find the volume of the following:

a) b)

c) d)

2) Find the height of this cuboid

Volume = 1140 cm3

3) The cuboid below is made out ofsteel and has a rectangular hole allthe way through it.

If 1 cm3 of steel has a mass of 8 g,what is the mass of the cuboid?

Vol = 3000 cm3 Vol = 1463 cm3

Vol = 9960 cm3

Vol = 14.112 cm3

Ht = 7.5 cm

mass = 8784 g

Volume of a Cuboid

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 95

S27

20 cm10 cm

15 cm

19 cm

7 cm

11 cm

4.2 cm1.6 cm

2.1 cm

23 cm8 cm

9.5 cm

1) Find the surface area of the following:

a) b)

c) d)

Surface area = 1300 cm2 Surface area = 838 cm2

Surface area = 957 cm2 Surface area = 37.8 cm2

30 cm

22 cm

14 cm

15 cm6 cm8 cm

20 cm

7 cm

9 cm

6 cm

3 cm

3) The shape below consists of acuboid glued onto another cuboid.

If the whole shape - including thebase - is painted, work out thearea which will be painted.

2) The cuboid below is made out ofsteel and has a rectangular hole allthe way through it.

All the surfaces are paintedincluding the base and the sides ofthe rectangular hole.Work out the area which will bepainted.

Surface area = 892 cm2

Surface area = 3112 cm2

Surface Area of a Cuboid

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 96

S28

8 cm6.5 cm

9.4 cm

14 cm 9.6 cm16.7 cm

1) Find the circumference of the following circles

a) b) c)

d) e) f)

60°

The circumference of the earth isapproximately 40000 km.

If you had a piece of string which was 6.3 mlonger than 40000 km and put it around theearth, how far away from the earth, all the wayround, would the extra 6.3 m allow it to be?

a) 0.1 mm b) 1 mm c) 1 cm d) 1 m

2) Find the perimeter of the following

10 cm

11 cm

12 cm18 cma) b) c)

d) 3)

C = 50.272 cmC = 40.846 cm

C = 59.0696 cm

C = 43.988 cmC = 52.4714 cm

C = 30.1632 cm

P = 46.278 cmP = 39.281 cm

P = 80.556

P = 30.473 cm.

In all questions, take to be 3.142π

Circumference of a Circle

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 97A

S29 Area of a Circle


8 cm6.5 cm

9.4 cm

14 cm 9.6 cm16.7 cm

1) Find the areas of the following circles

a) b) c)

d) e) f)

60°

2) Find the areas of the following

10 cm

11 cm

12 cm18 cma) b) c)

d)

130°

e)

A = 201.088 cm2

A = 132.7495 cm2

A = 277.62712 cm2

A = 153.958 cm2

A = 218.068095 cm2

A = 72.39168 cm2

A = 127.251 cm2 A = 95.0455 cm2

A = 339.336 cm2

A = 52.36 cm2

A = 50.18472 cm2

.

5 cm

.

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 97B

S29 Area of a Circle

32 cm16 cm

= 2 cm

24 cm

A square touching acircle at four points

14 cm

14 cm

18 cm

In each question, find the area of the shaded section.

a) b)

c) d)

e)f)

A = 54.912 cm2 A = 164.736 cm2

A =42.042 cm2

A = 763.506 cm2

A =351.904 cm2

A = 657.792 cm2


© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

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Page 98

D8Bar Charts and

Frequency Diagrams

1) A group of pupils were askedfor their favourite colour.Here are the results.

Draw a suitable chart toshow this information.

Colour Frequency

Red 8

Blue 10

Purple 9

Green 4

Yellow 7

Time in mins Frequency

5

6

12

11

10

0 < t < 10

10 < t < 20

20 < t < 30

30 < t < 40

40 < t < 50

2) A group of people were given a puzzle to solve.The time taken by each individual to complete the puzzlewas recorded in the table below.

Draw a suitable chart to showthis information.

1

2

3

4

5

6

7

8

9

10

11

0Red Blue Purple Green Yellow

Fre

quen

cy

Favourite colour

0 10 20 30 40 500

1

2

3

4

5

6

7

8

9

10

11

12

13

Time in minutes

Favourite Colours

Time to Solve a Puzzle

Fre

quen

cy

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 99

D91) The heights and weights of some children are shown in the table, below.

a) Plot the informationfrom the table.

b) Describe the correlationbetween height and weight.

c) Draw a line of best fit.

d) Estimate the weight of achild of similar age to thegroup above with a heightof 155 cm.

Height(cm)

Weight(kg)

132

34

145

40

150

43

140

35

175

60

168

54

177

62

162

51 57

162

51

165

58

149

40

150

41

135

33

159

44

160

50

170

2) The scatter graph below relates car engine sizes to their fuel consumption in mpg.

a) Describe the correlationshown by the data.

b) A car has an mpg of 25.Estimate the engine size.

0 1 2 3 40

10

20

30

40

50

60mpg

Engine size (litres)

130 140 150 160 170 18030

40

50

60

70

Height (cm)

Positive correlation

46 kg

Negative correlation

2 litres

Your answer will depend onyour line of best fit which youmust have drawn.

Scatter Graphs

Your answer will dependon your line of best fit.

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 100

D10Pie Charts

1) The table on the right shows how far 90 visitorsto a museum have travelled.

Draw a pie chart to show this information.

Distance

Within the city

Within 30 milesof the city

Over 30 milesfrom the city

Overseas

Frequency

13

9

20

48

.

2) The table shows the land usage of a farm.

Draw a pie chart to show this information.

Land usage Area(hectares)

Arable

Pasture

Woodland

Waste

80

70

50

40.

90

360° ÷ 90 = 4°

× 4 = 52°

× 4 = 36°

× 4 = 80°

× 4 = 192°

240

360° ÷ 240 = 1.5°

× 1.5 = 120°

× 1.5 = 105°

× 1.5 = 75°

× 1.5 = 60°

Within thecity

Within 30miles of the

city

Over 30miles from

the city

Overseas

Arable

Pasture

Woodland

Waste

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

2) A survey was done by a school to find out how people travel to the school.

Altogether, 100 people were asked and the results can be seen below.

a) Complete the two-way table.

b) How many people cycle to school?

c) How many female pupils go to school by taxi?

Page 101

D11 Two-Way Tables

1) 160 pupils in a school are asked to choose a new colour for theschool tie. They can only choose from Blue, Green or Red.

Some of the results are shown in this two-way table.

Complete the two-way table.

Blue Green Red Total

30 27 28 85

35 26 14 75

65 53 42 160

Male

Female

Total

Walk Car Cycle Taxi Bus Total

12 3 6 1 3 25

2 1 5 6 6 20

7 12 6 6 1 32

4 8 2 7 2 23

25 24 19 20 12 100

Male pupils

Female pupils

Male teachers

Female teachers

Total

19

6

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 102

D12Surveys

2) Beth wants to find out two things:the types of books people prefer to readhow much time, on average, they spend reading books

a) Design two suitable questions for Beth to use in her questionnaire.

b) She decides to ask her questions to the first ten people going into thepublic library on a Saturday morning.

Give one reason why this might not be a good way to carry out the survey.

Italian Food

French Food

Indian Food

Chinese Food

Tally Frequency

Which is your favourite type of book?

Romance Thriller Comedy Other

How much time do you spend reading books per week?

Less than 3 hours Between 3 and 5 hours More than 5 hours

This would be a biased sample because people who go to thelibrary might read more, in general, than others.

Types of Food

1) Lesley wants to find out the types of food people like best.She is going to ask people to choose between Italian Food,French Food, Indian Food and Chinese Food.

Design a suitable table for a data collection sheet she coulduse to collect this information.

Please specify

© Mathswatch Ltd

Level 6

Answers


A14 A15S29 D8 D9 D10 D11 D12 D13

S17 S18

Page 103

D131) A counter is taken at random from set 1 followed by another counter

at random from set 2.

a) Write down all the possible pairs of counters that may be chosen.

b) What is the probability that 3B will be picked?

c) What is the probability that any pair of counters will be chosenexcept 3B?

d) What is the probability that the pair of counters chosen willinclude an odd number?

Further Probability

1 2

3

A

B

C

D

Set 1 Set 2

2) The two spinners on the right are spun and theirscores added together to give a total.

a) Draw a possibility space to show all the totals.

b) What is the probability of scoring a total whichis bigger than 5?

1

2 34 3

4 5

6

3) Every Tuesday the main school dinner is eitherSausages, Chicken, Pizza or Tuna.

Use the table below to work out the probability thatthe main dinner will be Pizza next Tuesday.

School dinner Sausages Chicken Pizza Tuna

Probability 0.24 0.18 ? 0.47

1A 1B 1C 1D2A 2B 2C 2D3A 3B 3C 3D1

12

812

1 2 3 4

3

4

5

6

4

5

6

7

5

6

7

8

6

7

8

9

7

8

9

10

1316

0.240.180.470.89

1 0.89 = 0.11

0.11

1112

© Mathswatch Ltd

Level 7

Answers


N22Rounding to

1 Significant Figure

1) Round the following to 1 significant figure.

a) 478 cm

b) 450 cm

c) 449 cm

d) 12761 m

e) 28481 km


a) 673.8 cm

b) 4017.9 kg

c) 246.83 m

d) £45.38

e) 20482.1 kg


a) 0.26 ml

b) 0.043 g

c) 0.0671 m

d) 0.000256 km

e) 0.3822 m


a) 962 m

b) 0.923 cm

c) 0.971 cm

d) 0.096 km

e) 0.00985 km


a) £631428

b) 0.00573 g

c) £3614.68

d) 0.493 ml

e) £968

500 cm

500 cm

400 cm

10000 m

30000 km

700 cm

4000 kg

200 m

£50

20000 kg

0.3 ml

0.04 g

0.07 m

0.0003 km

0.4 m

1000 m

0.9 cm

1 cm

0.1 km

0.01 km

£600000

0.006 g

£4000

0.5 ml

£1000

Page 104

© Mathswatch Ltd

Level 7

Answers


C26

Page 105

Percentage Increaseand Decrease

1) a) Increase £400 by 16%

b) Increase £750 by 24%

c) Increase £2000 by 38%

d) Increase £14500 by 19%

e) Increase £16.50 by 30%

2) a) Decrease £700 by 32%

b) Decrease £36 by 14%

c) Decrease £1970 by 40%

d) Decrease £3000 by 12.5%

e) Decrease £3124 by 16.25%

3) A sports shop reduces the price of all its trainersby 15% in the Spring sale.Before the sale, one pair of trainers cost £74.How much are they after the reduction?

4) Tim took up weightlifting.In his first session he could bench-press 45 kg.Four weeks later he could bench-press 22% more.How much could he now lift to the nearest kg?

5) If a manager of a shop reduces the price of a£1500 piano by 15% and then, four weeks later,increases the reduced price by 15%, how muchdoes it now cost?

£464

£930

£2760

£17255

£21.45

£476

£30.96

£1182

£2625

£2616.35

£62.90

55 kg

£1466.25

© Mathswatch Ltd

Level 7

Answers


C27Addition and Subtraction

of Fractions

1) Work out

a)

b)

c)

d)

e)

13

+ 12

35

+ 14

27

+ 35

12

+ 29

310

+ 37

2) Work out

a)

b)

c)

d)

e)

23

+ 16

35

+ 310

12

+ 45

56

+ 35

712

+ 34

3) Work out

a)

b)

c)

d)

e)

23

+ 34

12

+ 57

25

+ 12

710

+ 15

34

+ 56

4) Work out

a)

b)

c)

d)

e)

12

+ 15

34

+ 23

16

+ 13

29

+ 23

12

+ 310

1

2

3

1

2

2

1

3

2

4

1

1

1

1

2

5) Work out

a)

b)

c)

d)

e)

23

12

34

23

45

34

56

23

34

38

6) Work out

a)

b)

c)

d)

e)

34

45

16

23

29

56

12

78

7) Work out

a)

b)

c)

d)

e)

12

12

25

110

23

1115

34

58

23

49

8) Work out

a)

b)

c)

d)

e)

4

1

1

2

5

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

1

2

3

2

6

2

1

1

1

3

cm

34

2 cm

9) Find the perimeter of the rectangle below.Give your answer as a mixed number.

cm

cm

10) Find the perimeter of the triangle below. Give your answer as a mixed number.

11) If a length of copper tubing is 20 cm long and Jim

cuts off a piece that is 17 cm long, what is the length

of the copper tubing left over?

14

3 13

2 512

3 314

3 712

56

1720

3135

1318

5170

16

112

120

16

310

11415

1 18

4 29

3 710

3 89

6 45

56

910

310

1330

13

14

120

2 12

1 718

310

718

4

38

67

12 16

cm 3 34

cm

1

1

1

910

3

910

1

3 512

4 12

38

12

34

1

2

5 58

2

45

12

29

56

38

56

5

17

3

4

1

2

5

+

–

+

–

–

1

1

2

2

5

3

524

8

2

12

1

58

cm58

1

35

2 1320

cm

Page 106

© Mathswatch Ltd

Level 7

Answers


C28Multiplication and Division

of Fractions

1) Work out

a)

b)

c)

d)

e)

12

× 34

23

× 45

1011

× 23

49

× 25

47

× 19

2) Work out

a)

b)

c)

d)

e)

23

× 35

37

× 56

89

× 610

12

× 89

710

× 521

3) Work out

a)

b)

c)

d)

e)

12

× 89

23

× 67

611

× 18

25

× 1011

34

× 89

4) Work out

a)

b)

c)

d)

e)

12

× 15

34

× 23

16

× 25

29

× 15

47

× 1315

1

2

1

4

3

2

3

4

2

3

2

2

2

1

1

5) Work out

a)

b)

c)

d)

e)

23

12

34

23

25

34

37

611

34

38

6) Work out

a)

b)

c)

d)

e)

34

15

47

79

14

67

35

910

12

38

7) Work out

a)

b)

c)

d)

e)

12

12

25

110

13

1115

34

58

23

49

8) Work out

a)

b)

c)

d)

e)

23

34

25

12

2

3

1

2

5

1

4

5

3

2

14

4

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

÷

1

1

2

2

1

3

1

1

1

4

cm

34

2 cm

9) Find the area of the rectangle below.Give your answer as a mixed number.

12

1 cm

12

2 cm

10) Find the area of the triangle below. Give your answer as a mixed number.

11) Jim has a length of copper tubing which is 85 cm long.

He wants to cut it into pieces which are 4 cm long.

If there is no wastage, how many pieces will Jim get?

34

14

3 13

1 13

2 27

2744

4

3 13

38

815

2033

845

463

1 13

1 18

815

1114

2

57

3 111

2 12

1 913

31213

5 12

10

10

2 23

6 23

25

514

815

49

16

58

928

2 58

2 89

4

13

18

10

6 23

78

9 16

cm2 1 78

cm2

20

Page 107

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Page 108

C29Numbers Between 0 and 1(Multiplication and Division)

1) Work out the answers to the following:

a) 24 × 0.2

b) 13 × 0.4

c) 60 × 0.7

d) 243 × 0.2

e) 0.6 × 700


a) 314 × 0.02

b) 836 × 0.001

c) 800 × 0.006

d) 418 × 0.003

e) 411 × 0.09


a) 0.2 × 0.4

b) 0.1 × 0.03

c) 0.02 × 0.06

d) 0.08 × 0.003

e) 0.05 × 0.08


a) 62 × 0.14

b) 2.7 × 2.5

c) 613 × 0.042

d) 42.3 × 1.8

e) 228 × 0.063


a) 6 ÷ 0.2

b) 8 ÷ 0.1

c) 9 ÷ 0.3

d) 4 ÷ 0.02

e) 7 ÷ 0.002


a) 62 ÷ 0.2

b) 51 ÷ 0.3

c) 4.56 ÷ 0.04

d) 22.5 ÷ 0.05

e) 14.7 ÷ 0.007


a) 7.24 ÷ 0.2

b) 8.13 ÷ 0.3

c) 1.512 ÷ 0.07

d) 0.16 ÷ 0.008

e) 0.0732 ÷ 0.04


a) 0.718 ÷ 0.2

b) 0.0141 ÷ 0.003

c) 0.24 ÷ 0.012

d) 1.625 ÷ 0.0013

e) 47.1 ÷ 0.15

4.8

5.2

42

48.6

420

6.28

0.836

4.8

1.254

36.99

0.08

0.003

0.0012

0.00024

0.004

8.68

6.75

25.746

76.14

14.364

30

80

30

200

3500

310

170

114

450

2100

36.2

27.1

21.6

20

1.83

3.59

4.7

20

1250

314

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Page 109

C30EstimatingAnswers

1) Estimate the value of:

a) 21 × 34

b) 42 × 56

c) 17 × 62

d) 29 × 78

e) 66 × 96


a) 510 × 724

b) 86 × 2146

c) 753 × 184

d) 48 × 6315

e) 3642 × 1356


a)

b)

c)

d)

e)

6119

7643

36278

73896

416781


a)

b)

c)

d)

e)

35712 × 23

92434 × 13

172 × 411430

625 × 4316 × 38

972 × 36817 × 23 × 18


a) 8 ÷ 0.12

b) 6 ÷ 0.24

c) 5 ÷ 0.49

d) 7 ÷ 0.012

e) 23 ÷ 0.18


a)

b)

c)

d)

e)

215 × 380.183

18.3 × 31.20.017

405 × 2740.488

46 × 6.20.135

24 × 5100.53

600

2400

1200

2400

7000

350000

180000

160000

300000

4000000

3

2

5

7

0.5

2

3

200

30

50

80

30

10

700

115

20000

3000

40000

30000

240000

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Page 110

C31Using a Calculator

1) Using a calculator, work out the value of:

a) 24 + 16 ÷ 4

b) 3 + 8 ÷ 2 × 3

c) 60 × 2 – 20 ÷ 4

d) (2 + 7 × 8) × 4

e) (3 + 7) × (8 – 2)


a) 63 – (24 + 35)

b) (37 – 26) ÷ 104

c) 28 ÷ 23 × 52

d) 53 × 35

e) 220 – 38


a) 256 × 24 – 169

b) 365 × 365

c) 550 – 21

d) 28 + 34 – 13

e) 46 × 28 ÷ (32 – 1)


a)

b)

c)

7 + 4 × 818 – 5

63 – 23

(32 + 7) ÷ 2

d)

e)

62 × 24 + 23

43 + 32 + 33

284 – 29 – 112(3 + 17) × 100

729 + 2164

28

15

115

232

60

-43

0.2123

800

30375

1042015

243

365

23

18

128

3 100

26 1.32

6

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Page 111

A16Further Algebraic

Simplification

1) Simplify the following

a) 6 × x

b) 2 × x × y

c) 6 × x × 3 × y

d) s × t × u

e) 7 × s × 2 × t × u


a) x × x × x × x

b) t × t × t × t × t × t × t

c) g × g

d) x × x × x × y × y × y × y

e) x × y × x × y × y


a) x × x2

b) y3 × y4

c) x2 × x3 × x

d) g × g × g2 × g4

e) x2 × x3 × x4 × x5


a) 3x2 × 2x3

b) 5x × 4x2

c) 6y3 × 2y4

d) 9x2 × x3

e) 4x3 × 2x × 3x2


a) 3x2y3 × 2x3y4

b) 2xy4 × 3x2y

c) 5x3y4 × 2x2y2

d) 2x2y × x4y2

e) 3x3y × 2xy2 × 3x2y2


a) x8 ÷ x2

b) 9y6 ÷ 3y2

c) 14y3 ÷ 2y2

d) 20x5 ÷ 4x

e) 16x8 ÷ 8x2


a)

b)

c)

d)

e)

12x6

3x2

20x3

2x

5x4

x2

6x5

3x3

300x9

10x2


a)

b)

c)

d)

e)

12x3y4x

15x4y3

3xy

20x3y5

4x2y3

14x2y2

7xy

30x2y3z6

3xy2z4

9) Find the value of

a) 40

b) 60

c) 120

d) z0

e) x0

6x

2xy

18xy

stu

14stu

x4

t7

g2

x3y4

x2y3

x3

y7

x6

g8

x14

6x5

20x3

12y7

9x5

24x6

6x5y7

6x3y5

10x5y6

2x6y3

18x6y5

x6

3y4

7y

5x4

2x6

4x4

10x2

5x2

2x2

30x7

3x2y

5x3y2

5xy2

2xy

10xyz2

1

1

1

1

1

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Page 112

A17Expanding and

Simplifying Brackets

1) Expand

a) 2(x + 3)

b) 2(x – 4)

c) 5(2x + 1)

d) 7(3x – 1)

e) 4(2a + 7)

2) Expand

a) 2x(3x + 1)

b) 3x(4x – 2)

c) 2x(x + 1)

d) 3x(2x – y)

e) 5x(3x + 2y)

3) Expand and simplify

a) 2(x + 3) + 4(x + 1)

b) 3(2x + 1) + 2(5x + 2)

c) 4(x + 1) + 3(3x + 4)

d) 6(2x + 3) + 5(x + 2)

e) 4(3x + 2) + 5(2x + 1)


a) 2(5x + 3) + 3(x – 1)

b) 3(4x + 5) + 2(3x – 4)

c) 5(2x – 1) + 3(2x + 5)

d) 2(3x – 4) + 3(x + 2)

e) 3(2x – 1) + 4(3x – 2)


a) 3(x + 2) – 2(x + 3)

b) 4(2x + 3) – 3(2x + 1)

c) 5(3x – 2) – 2(x – 2)

d) 2(5x – 1) – 4(2x – 3)

e) 3(2x + 7) – 2(3x + 2)


a) (x + 2)(x + 2)

b) (x + 3)(x + 5)

c) (x + 7)(x + 1)

d) (x + 4)(x + 3)

e) (x + 7)(x + 2)


a) (2x + 1)(3x + 2)

b) (4x + 3)(2x + 1)

c) (3x + 4)(3x + 2)

d) (5x + 2)(5x + 7)

e) (2x + 10)(2x + 4)


a) (x + 5)(x – 3)

b) (x – 2)(x + 4)

c) (x – 6)(x – 2)

d) (x + 7)(x + 3)

e) (x – 8)(x – 2)


a) (2x – 1)(3x + 4)

b) (5x – 2)(3x – 1)

c) (3x + 4)(2x – 3)

d) (5x – 1)(5x – 2)

e) (4x + 2)(3x – 5)

Expand and simplify

a) (x + 5)2

b) (x – 2)2

c) (2x + 3)2

d) (3x – 1)2

e) (4x + 3)2

10)

2x + 6

2x – 8

10x + 5

21x – 7

8a + 28

6x2 + 2x

12x2 – 6x

2x2 + 2x

6x2 – 3xy

15x2 + 10xy

6x + 10

16x + 7

13x + 16

17x + 28

22x + 13

13x + 3

18x + 7

16x + 10

9x – 2

18x – 11

x

2x + 9

13x – 6

2x + 10

17

x2 + 4x + 4

x2 + 8x + 15

x2 + 8x + 7

x2 + 7x + 12

x2 + 9x + 14

6x2 + 7x + 2

8x2 + 10x + 3

9x2 + 18x + 8

25x2 + 45x + 14

4x2 + 28x + 40

x2 + 2x – 15

x2 + 2x – 8

x2 – 8x + 12

x2 + 10x + 21

x2 – 10x + 16

6x2 + 5x – 4

15x2 – 11x + 2

6x2 – x – 12

25x2 – 15x + 2

12x2 – 14x – 10

x2 + 10x + 25

x2 – 4x + 4

4x2 + 12x + 9

9x2 – 6x + 1

16x2 + 24x + 9

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Page 113

A18Factorisation

1) Factorise the following

a) 6x – 2

b) 8x + 14

c) 6x + 9

d) 10x – 5

e) 12x + 18


a) x2 + x

b) t2 – t

c) x3 + x

d) x5 – x2

e) a7 + a4


a) 3x2 + 6x

b) 8x3 – 2x

c) 12a2 + 4a3

d) 20x4 – 6x2

e) 7x3 + 8x


a) 6x2y4 + 4xy3

b) 4x3y4 + 2x2y2

c) 10x4y3z – 5xy5z

d) 16a2b3c4 + 3ab2c3

e) 9x2y4z – 6xy2z


a) 10x + 4

b) x4 – x2

c) 9x5 – 12x2

d) 12x2y3 + 4xy2

e) 24x3yz4 – 10xz2

2(3x – 1)

2(4x + 7)

3(2x + 3)

5(2x – 1)

6(2x + 3)

x(x + 1)

t(t – 1)

x(x2 + 1)

x2(x3 – 1)

a4(a3 + 1)

3x(x + 2)

2x(4x2 – 1)

4a2(3 + a)

2x2(10x2 – 3)

x(7x2 + 8)

2xy3(3xy + 2)

2x2y2(2xy2 + 1)

5xy3z(2x3 – y2)

ab2c3(16abc + 3)

3xy2z(3xy2 – 2)

2(5x + 2)

x2(x2 – 1)

3x2(3x3 – 4)

4xy2(3xy + 1)

2xz2(12x2yz2 – 5)

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Page 114

A19Solving Difficult Equations

1) Solve the following

a) 2x + 3 = 19

b) 3x – 2 = 13

c) 5x – 1 = 9

d) 3 + 2x = 23

e) 12 – 3x = 9


a) 2(3x – 1) = 22

b) 3(x + 7) = 18

c) 4(5x – 2) = 12

d) 66 = 6(2x + 3)

e) 20 = 5(x – 6)


a)

b)

c)

d)

e)

x – 62 = 3

x + 83 = 5

2x – 13 = 5

6x + 12 = 8

7x – 35 = 5


a) 2x + 7 = x + 12

b) 4x – 5 = 2x + 3

c) 7x + 2 = 3x + 26

d) 6x – 7 = 4x – 5

e) 3x + 4 = x – 7


a) x – 6 = 2x – 13

b) 3x + 4 = 5x – 8

c) 4x + 17 = x – 4

d) 5 – 2x = x – 7

e) 2x – 1 = 14 – 3x


a) 2(3x – 1) = 4x + 7

b) 3(x + 4) = 2(x – 5)

c) 5(2x – 3) = 3(3x + 4)

d) 2(2x – 1) = 5(2x – 4)

e) 2(2x + 3) = 5(x + 3)


a)

b)

c)

d)

e)

2(x + 1)3

= 6

4(2x – 3)5

= 4

2(4x – 5)3

= x + 10

3(5x + 4)2

= 7x – 8

2(x + 7)34 – x =

x = 8

x = 5

x = 2

x = 10

x = 1

x = 4

x = -1

x = 1

x = 4

x = 10

x = 12

x = 7

x = 8

x = 2.5

x = 4

x = 5

x = 4

x = 6

x = 1

x = -5.5

x = 7

x = 6

x = -7

x = 4

x = 3

x = 4.5

x = -22

x = 27

x = 3

x = -9

x = 8

x = 4

x = 8

x = -28

x = 25

-

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Answers


Page 115

A20Rearranging a Formula

1) Rearrange to make x the subjectof the formula

a) y = x – 2

b) y = x + 7

c) y = x + t

d) y = 5x + 3

e) y = 2x – 4


a) 3x + 2 = y

b) 4x – 1 = y

c) ax – 3 = y

d) ax + m = t

e) x + y = t


a) y = x + t – v

b) ax – c = y

c) y = ax – tv + c

d) y + x = ct

e) c + ax + t = y + m


a)

b)

c)

d)

e)

5x – 24 = y

ax + cm = y

x – 45

y =

t + mxyk =


a)

b)

c)

d)

e)

y = 3x42x5y = – 8

cxty = + m

y = abx + c

mxt + c = y


a) y = 4(x + t)

b) y = a(x – m)

c) at(c + x) = y

d) y + m = a(c + x)

e) t – v = m(x – y)


a)

b)

c)

d)

e)x + 2

3 = y

x – u4 = y

x + ab = c

3(x + 2)c = y

a(x + b)c = d

t(x + c)d = e + f

x = y + 2

x = y – 7

x = y – t

x = y – 35

x = y + 42

x = y – 23

x = y + 14

x = y + 3a

x = t – ma

x = t – y

x = y – t + v

x = y + ca

x = y + tv – ca

x = ct – y

x = y + m – c – ta

x = 3y – 2

x = 5y + 4

4y + 25

my – ca

x =

x =

yk – tmx =

4y3x =

5(y + 8)2x =

t(y – m)cx =

y – cx =

t(y – c)mx =

ab

x =y4

– t

x =ya

+ m

x =yat

– cy + m

a – cx =t – vm + yx =

x = 4y + u

x = bc – a

cy3

– 2x =

cda

– bx =

d(e + f)t

– cx =

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Page 116A

A21Trial and Improvement







x = 4 42 + 3 × 4 = 28 Lowx = 5 52 + 3 × 5 = 40 Highx = 4.9 4.92 + 3 × 4.9 = 38.71 High

x = 4.8 4.82 + 3 × 4.8 = 37.44 High

x = 4.7 4.72 + 3 × 4.7 = 36.19 Lowx = 4.75 4.752 + 3 × 4.75 = 36.8125 Low

Therefore, x = 4.8 to one decimal place.

x = 5 52 – 4 × 5 = 5 Lowx = 6 62 – 4 × 6 = 12 Highx = 5.1 5.12 – 4 × 5.1 = 5.61 Low

x = 5.2 5.22 – 4 × 5.2 = 6.24 High

x = 5.15 5.152 – 4 × 5.15 = 5.9225 Low


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Page 116B

A21Trial and Improvement




x = 2 23 – 2 × 2 = 4 Lowx = 3 33 – 2 × 3 = 21 Highx = 2.1 2.13 – 2 × 2.1 = 5.061 Low

x = 2.2 2.23 – 2 × 2.2 = 6.248 Low

x = 2.3 2.33 – 2 × 2.3 = 7.567 Low

x = 2.35 2.353 – 2 × 2.35 = 8.277875 Low


x = 2.4 2.43 – 2 × 2.4 = 9.024 High




x = 4 43 + 3 × 4 = 76 Lowx = 5 53 + 3 × 5 = 140 Highx = 4.6 4.63 + 3 × 4.6 = 111.136 Low

x = 4.7 4.73 + 3 × 4.7 = 117.923 High

x = 4.65 4.653 + 3 × 4.65 = 114.494625 High


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Page 117

A22Inequalities

-5 -4 -3 -2 -1 0 1 2 3 4 5

1) Represent the inequalities on the number lines.

a) x < 3

b) -1 < x < 4

c) -3 < x < 3

-5 -4 -3 -2 -1 0 1 2 3 4 5

-5 -4 -3 -2 -1 0 1 2 3 4 5

-5 -4 -3 -2 -1 0 1 2 3 4 5

2) Write down the inequalities shown below

a)

b)

c)

-5 -4 -3 -2 -1 0 1 2 3 4 5

-5 -4 -3 -2 -1 0 1 2 3 4 5

3) If x is an integer, what are thepossible values of x?

a) -4 < x < 2

b) -3 < x < 1

c) 1 < x < 5

d) -3 < x < 4

e) -7 < x < -4

<

-5 < x < 2

-1 < x < 3

-3 < x < 5

-4, -3, -2, -1, 0, 1, 2

-3, -2, -1, 0

2, 3, 4, 5

-2, -1, 0, 1, 2, 3, 4

-7, -6, -5, -4

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Page 118

A23Solving Inequalities

1) Solve

a) 2x – 1 > 7

b) 3x + 4 < 19

c) 5x – 7 < 18

d) 2x + 9 > 5

e) 4x + 11 < 14

2) Solve

a)

b)

c)

d) 12 > 2x – 1

e) 20 < 5 + 5x

x3 < 7

x5 – 1 > 3

2x3 + 4 < 9

3) Solve

a) 2(5x – 1) < 18

b) 3(4x + 2) > 60

c) 42 > 2(6x + 15)

d) 4(1 + x) < 12

e) 8(2x – 1) >12

4) Solve

a) 2x + 7 < x + 9

b) x – 6 > 3x – 18

c) 4x + 3 < 2x – 9

d) 2x – 4 > 7x – 34

e) 2(x + 3) < x – 1

x > 4

x < 5

x < 5

x > -2

x < 0.75

x < 21

x > 20

x < 7.5

x < 6.5

x > 3

x < 2

x > 4.5

x < 1

x < 2

x > 1.25

x < 2

x < 6

x < -6

x < 6

x < -7

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Page 119

A24Understanding

Straight Line Graphs

O 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

x

y

1) Find the gradients ofthe lines A to F.

A

BC

D

E

F

O 1 2 3 4 5

2

4

6

8

10

12

14

16

18

20

x

y

2) Find the gradients ofthe lines G to K.

G

HI

J

K

-4 -3 -2 -1 O 1 2 3 4 5 6

-4

-3

-2

-1

1

2

3

4

5

6

x

y

3) Find the equations oflines A and B.

-4 -3 -2 -1 O 1 2 3 4 5 6

-4

-3

-2

-1

1

2

3

4

5

6

x

y

4) Find the equations oflines C, D and E.

A

B

C

D

E

0

5

3

-0.25

-1

-4

-88

-10

41

y = 3x + 2

y = x – 3

y = -2x + 4

y = 0.5x

y = 0.25x – 2

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Level 7

Answers


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A25Regions

Page 120

1) a) Shade the region represented by x < -1

b) Shade the region represented by x > 3

-5 -4 -3 -2 -1 O 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

2) a) Shade the region represented by y < -1

b) Shade the region represented by y > 2

-5 -4 -3 -2 -1 O 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

3) Shade the region represented by -3 < x < 2

-5 -4 -3 -2 -1 O 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

4) Shade the region represented by 1 < y < 4

-5 -4 -3 -2 -1 O 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

5) Shade the region where -1 < x < 3and -4 < y < -2

-5 -4 -3 -2 -1 O 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

6) Shade the region where -3 < x < 2and -1 < y < 4

-5 -4 -3 -2 -1 O 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5

x

y

© Mathswatch Ltd

Level 7

Answers


A26Simultaneous Equations

Graphically

Page 121

1) a) Complete the table of values for y = x + 2

b) Draw the graph of y = x + 2

c) Complete the table of values for x + y = 7

d) Draw the graph of x + y = 7

e) Use your graph to solve the simultaneousequations y = x + 2 and x + y = 7

O 1 2 3 4 5 6 7 8

1

2

3

4

5

6

7

8

x 0 1 2 3 4

y

y

x

-6 -5 -4 -3 -2 -1 O 1 2 3 4 5 6

-6

-5

-4

-3

-2

-1

1

2

3

4

5

62) Using a graphical method, solve the

simultaneous equations

y = 2x – 3 and y = 6 – x

y

x

3) Solve the simultaneous equations y = x + 6 and y = 3 – x

4) Solve the simultaneous equations y = x – 14 and y = 2 – 3x

7 6 5 4 3

x = 2.5, y = 4.5

x = 3, y = 3

x = -1.5, y =4.5

x = 4, y = -10

x 0 1 2 3 4

y 2 3 4 5 6

© Mathswatch Ltd

Level 7

Answers


A27Simultaneous Equations

Algebraically

Page 122

1) Solve 3x + y = 11

4x – y = 3

2) Solve 2x – 5y = 3

4x + 5y = 21

3) Solve x – 2y = 3

3x + 2y = 5

4) Solve x + 3y = 10

x + y = 6

5) Solve 3x + 2y = 3

2x + 2y = 5

6) Solve 5x – 3y = 23

2x – 3y = 11

7) Solve 3x – 2y = 6

x + y = 7

8) Solve 6x + y = 10

2x – 3y = 10

9) Solve 2x + 7y = 11

3x – 2y = 4

10) Solve 4x + 3y = 9

5x + 2y = 13

11) Solve 2x + 3y = -7

7x – 2y = -12

12) Solve 3x – 2y = 5

9x + 5y = -7

13) In the first week of opening, a zoo sold200 adult tickets and 300 child tickets. Thetakings for that week were £2600.

In the second week, 500 adult tickets weresold and 400 child tickets were sold. Thetakings for the second week were £5100.

Form two equations and solve them tofind the price of an adult ticket and theprice of a child ticket.

14) If you multiply Sid’s age by four and Tony’sage by five and add the answers togetherit comes to 259 years.

However, if you multiply Sid’s age byseven and then take away two timesTony’s age the answer is 120 years.

Form two equations and solve them to findthe ages of Sid and Tony.

15) If nine rats and seven ferrets cost £116.75and four rats and six ferrets cost £88, howmuch would five rats and four ferrets cost?

16) If a mouse and a goldfish cost £1.10 andthe mouse costs £1 more than the goldfish,how much does the goldfish cost?

x = 2, y = 5

x = 4, y = 1

x = 2, y = -0.5

x = 4, y = 2

x = -2, y = 4.5

x = 4, y = -1

x = 4, y = 3

x = 2, y = -2

x = 2, y = 1

x = 3, y = -1

x = -2, y = -1

x = , y = -213

Adult ticket is £7

Child ticket is £4

Sid is 26

Tony is 31

£66.25

5p

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Level 7

Answers


A28nth Term of Quadratic

Sequences

Page 123

1) Find the nth term of

a) 1, 4, 9, 16, 25, . . . .

b) 2, 5, 10, 17, 26, . . . .

c) 0, 3, 8, 15, 24, . . . .


a) 1, 4, 9, 16, 25, . . . .

b) 2, 8, 18, 32, 50, . . . .

c) 0.5, 2, 4.5, 8, 12.5, . . . .


a) 3, 9, 19, 33, 51, . . . .

b) 1, 7, 17, 31, 49, . . . .

c) 11, 41, 91, 161, 251, . . . .

4) For the following nth terms,find the first three terms and the tenth term

a) n2 + 4

b) n2 – 3

c) n2 + 10

d) n2 + 2n

e) n2 – n

5) For the following nth terms,find the first three terms and the tenth term

a) 4n2

b) 2n2 + 3n

c) 3n2 – 2n

d) n2 + n + 1

e) 2n2 + 4n – 3

n2

n2 + 1

n2 – 1

n2

2n2

0.5n2

2n2 + 1

2n2 – 1

10n2 + 1

5, 8, 13, . . . . . 104

-2, 1, 6, . . . . . 97

11, 14, 19, . . . . . 110

3, 8, 15, . . . . . 120

0, 2, 6, . . . . . 90

4, 16, 36, . . . . . 400

5, 14, 27, . . . . . 230

1, 8, 21, . . . . . 280

3, 7, 13, . . . . . 111

3, 13, 27, . . . . . 237

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Level 7

Answers


A29Graphs of Quadratic and

Cubic Functions

Page 124A

x -2 -1 0 1 2

y 2 -1 -2 -1 2

3

7

1) a) Complete the table of values for y = x2 – 2

b) Draw the graph of y = x2 – 2

-2 -1 O 1 2 3

-3

-2

-1

1

2

3

4

5

6

7

c) Use the graph to estimate thevalues of x when y = 1

2) a) Complete the table of values for y = 4x2

b) Draw the graph of y = 4x2

c) Use the graph to estimate thevalue of y when x = 1.5

-2 -1 O 1 2-2

2

4

6

8

10

12

14

16

y

x

x

y

x -2 -1 0 1 2

y 16 4 0 4 16

×

×

×

×

×

×

×

×

×

×

×

x = -1.7, 1.7

y = 9

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Level 7

Answers



Cubic Functions

Page 124B

x -2 -1 0 1 2

y 0 -1 0 3 8

3

15

1) a) Complete the table of values for y = x2 + 2x

b) Draw the graph of y = x2 + 2x

c) Use the graph to estimate thevalues of x when y = -0.5

2) a) Complete the table of values for y = x2 – 2x + 1

b) Draw the graph of y = x2 – 2x + 1

c) Use the graph to estimate thevalue of y when x = 2.5

y

x

x

y

x -2 -1 0 1 2

y 9 4 1 0 1

-2 -1 O 1 2 3-1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

3

4

-2 -1 O 1 2 3

1

2

3

4

5

6

7

8

9

10

11

12

13

×

×

××

×

×

×

× ×

×

×

×

x = -0.4, -1.7

y = 2.2

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Level 7

Answers



Cubic Functions

Page 124C

x -2 -1 0 1 2

y 1 -3 -3 1 9

1) a) Complete the table of values for y = 2x2 + 2x – 3

b) Draw the graph of y = 2x2 + 2x – 3

c) Use the graph to estimate thevalues of x when y = -2

2) a) Complete the table of values for y = x3 + x

b) Draw the graph of y = x3 + x

y

x

x

y

x -2 -1 0 1 2

y -10 -2 0 2 10

-2 -1 O 1 2

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

-2 -1 O 1 2

-10

-8

-6

-4

-2

2

4

6

8

10

×

×

××

×

×

×

×

×

×

x = 0.4, -1.3

© Mathswatch Ltd

Level 7

Answers


S30Pythagoras’ Theorem

Page 125A

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1) Use Pythagoras’ theorem to work out the areas of squares A and B.

AB

2) Use Pythagoras’ theorem to work out the areas of squares C and D.

Area25 cm2

Area100 cm2

CArea

841 cm2

Area441 cm2

D

10squares

13squares

125 cm2

400 cm2

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Level 7

Answers


S30Pythagoras’ Theorem

Page 125B

1) Find the lengths of the sides of these three squares.

a) b) c)

Area529 cm2 Area

210.25 cm2

Area152.7696 cm2

2) Find the lengths of the sides labelled a to d.

8 cm

15 cm

a

12 cm

35 cmb

29 cm

21 cm

c25 cm

24 cm

d

23 cm 14.5 cm 12.36 cm

17 cm 37 cm

20 cm

7 cm

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Level 7

Answers


Pythagoras’ Theorem

Page 125C

1) Calculate the lengths of the sides a to f, giving each answer to 1 decimal place.

12 cm

7 cm 18 cm 13 cm

6.4 cm

12 cm

a

b

c

13.8 cm3.7 cm

9.6 cm

4.5 cm

15.8 cm

18.3 cm

d

ef

2) Calculate the lengths of the sides a and b, giving each answer to 1 decimal place.

17 cm

10 cm13 cm

15 cm

a

b

3) Find the height of this isosceles triangle.Give your answer to 1 decimal place.

13 cm

16 cm

4) Find the area of this isosceles triangle.

25 cm

14 cm

13.9 cm

12.4 cm

10.2 cm

13.3 cm

10.6 cm

9.2 cm

13.7 cm

19.8 cm

8 cm

13 cm

10.2 cm

7 cm

24 cm

168 cm2

S30

© Mathswatch Ltd

Level 7

Answers


Page 126A

S31Areas of

Compound Shapes

1) Find the areas of the following shapes:

7 cm

4 cm

12 cm

6 cm

8 cm

9 cm

a) b) c)

d) e)

16 cm10 cm


14 cm

13 cm

5 cm

9 cm

20 cm17 cm

18 cm

6 cm

12 cm

7 cm 7 cm

5 cm 3 cm4 cm

a) b)

c)

Take to be 3.142

28 cm2

36 cm2 36 cm2

314.2 cm2201.088 cm2

142 cm2

174 cm2

100 cm2

© Mathswatch Ltd

Level 7

Answers


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Page 126B

S31Areas of

Compound Shapes


7 cm

9 cm

4 cm

5 cm

12 cm

5 cm9 cm

13 cm

11 cm

9 cm6 cm

6 cm

2) Find the areas of the shaded parts of the following:

a) b) c)

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14 cm

8 cm

11 cm

5 cm15 cm

11 cm

7 cm

8 cm

15 cm

6 cm

24 cm

Take to be 3.142 when needed.a) b)

c)d)

40.5 cm2

109 cm2

57 cm2

137 cm2

111.888 cm2

123.552 cm2

84 cm2

15 cm

© Mathswatch Ltd

Level 7

Answers


Page 126C

S31Areas of

Compound Shapes

Find the areas of the shapes below:

Take to be 3.142

16 cm

22 cm12 cm

20 cm

20 cm

23 cm

a)

b)

c)

452.544 cm2

224.556 cm2

67.0695 cm2

© Mathswatch Ltd

Level 7

Answers


Page 127

S32Volumesof Prisms

Find the volumes of the prisms, below.Take to be 3.142 for questions c and d.

5 cm

6 cm

8 cm

3 cm

8 cm

10 cm

4 cm

5 cm19 cm

23 cm

12 cm

13 cm

2 cm

9 cm

10 cm

6.4 cm

25.7 cm

30 cm

a) b)

c) d)

e) f)

Volume = 240 cm3

Volume = 120 cm3

Volume = 251.36 cm3

Volume = 6522.0065 cm3

Volume = 1380 cm3

Volume = 2448 cm3

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Level 7

Answers


Page 128

S33Surface Area

of Triangular Prisms

1) Find the total surface area of this triangular prism.

10 cm

12 cm 13 cm

20 cm

2) Find the total surface area of this triangular prism.

7.2 cm

6.5 cm9.7 cm

3) Find the total surface area of this triangular prism.You will need to use Pythagoras’ theorem at somestage to get the answer.

10.2 cm

14 cm

24 cm

840 cm2

23 cm

585 cm2

1102.8 cm2

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Level 7

Answers


Page 129

S34Loci

1) Draw the locus of all the points that are 1.2 cm away from the line AB.

A B

2) Draw the locus of all the points that are 1.5 cm away from the rectangle ABCD.

3) Radio signals can be heard within a 4.5 km radius of transmitter A and a 5.5 km radiusof transmitter B. Show, by shading, the area where radio signals can be heard from bothtransmitters at the same time. Use a scale of 1 cm represents 1 km.

A B

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Answers


Page 130

S35Enlargement by a

Negative Scale Factor

O 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

x

y

1) Enlarge line AB with scale factor -2 andpoint (7, 6) as the centre of enlargement.

A

B

O 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

x

y

2) Enlarge line AB with scale factor -3 andpoint (3, 4) as the centre of enlargement.

A

B

O 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

x

y

3) Enlarge triangle ABC with scale factor -2and point (7, 6) as the centre of enlargement.

A

B

O 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

x

y

A

B

4) Enlarge triangle ABC with scale factor -1.5and point (4, 5) as the centre of enlargement.

C

C

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Level 7

Answers


Page 131

S36Bounds

1) The length of a bracelet is 24 cm measured tothe nearest centimetre.

a) Work out the lower bound of the length ofthe bracelet.

b) Work out the upper bound of the length ofthe bracelet.

2) The length of a snake is 80 cm measured tothe nearest 10 centimetres.

a) Work out the lower bound of the length ofthe snake.

b) Work out the upper bound of the length ofthe snake.

3) The weight of a necklace is 145 g measured tothe nearest 5 grams.

a) Work out the lower bound of the weight ofthe necklace.

b) Work out the upper bound of the weight ofthe necklace.

4) The length of a line is given as 17.2 cmmeasured to the nearest tenth of a centimetre.

a) Work out the lower bound of the length ofthe line.

b) Work out the upper bound of the length ofthe line.

5) A rectangle has a length of 80 cm and a width of60 cm, both measured to the nearest 10 cm.

a) Work out the lower bound of the area ofthe rectangle.

b) Work out the upper bound of the perimeterof the rectangle.

6) A right-angled triangle has lengths as shown, allmeasured to the nearest centimetre.

a) Work out the lower bound of the area ofthe triangle.

b) Work out the upper bound of the area ofthe triangle.

80 cm

60 cm

12 cm

5 cm

23.5 cm

24.5 cm

75 cm

85 cm

142.5 g

147.5 g

17.15 cm

17.25 cm

4125 cm2

300 cm

25.875 cm2

34.375 cm2

© Mathswatch Ltd

Level 7

Answers


Page 132

S37Compound Measures

1) A car travels at 60 mph for 3 hours.How far does the car travel?

2) A cyclist cycles for 4 hours and covers a distance of 48 miles.What was her average speed in miles per hour?

3) How long would it take a train which travels at an average speedof 80 mph to cover a distance of 400 miles?

4) A runner runs at a speed of 12 km/h for 3 hours and 15 minutes.How far does he run?

5) An aeroplane flies at an average speed of 510 mph.How long would it take to fly a distance of 2720 miles?

6) If a worm travels a distance of 8.25 m in 2 hours and 45 minutes, work outhis average speed in metres per hour.

7) 12.5 cm3 of mercury has a mass of 170 g.Work out the density of mercury.

8) Platinum has a density of 21.4 g/cm3.What is the mass of 35 cm3 of platinum?

9) A quantity of ice had a mass of 62.56 g.Knowing that ice has a density of 0.92 g/cm3, work out how muchice there was, in cm3.

15000 cm3 of nitrogen has a mass of 18.765 g.Work out the density of nitrogen in g/cm3.

15000 cm3 of gold has a mass of 289.5 kg.Work out the density of gold in g/cm3.

10)

11)

180 miles

12 mph

5 hours

39 km

5 hours and 20 minutes

3 metres per hour

13.6 g/cm3

749 g

68 cm3

0.001251 g/cm3

19.3 g/cm3

© Mathswatch Ltd

Level 7

Answers


Page 133A

D14Averages from Tables

1) Sally conducted a survey to see how many sandwiches each pupilbrought to school in her class per day.The results can be seen in the table.

a) What is the modal number of sandwiches brought to school?

b) What is the median number of sandwiches brought to school?

c) Work out the mean number of sandwiches brought to school.Give your answer to 1 decimal place.

24

2) 50 hippos were captured over the course of a year and weighed.The results can be seen in the table, below.

Work out an estimate for the mean weight of a hippo.Give your answer to 1 decimal place.

22.9 w < 3.2<

Weight of hippoin tonnes

Frequency

5

9

15

12

7

1.4 w < 1.7<

1.7 w < 2.0<

2.0 w < 2.3<

2.3 w < 2.6<

2.6 w < 2.9<

3 sandwiches

3 sandwiches

2.3 sandwiches

2.2 tonnes

No. ofsandwiches

Frequency

1

5

6

12

0

1

2

3

© Mathswatch Ltd

Level 7

Answers


Page 133B

D14Averages from Tables

Jenny had a theory that if asked to guess the length of a line, childrenunder the age of 10 would overestimate the length but adults wouldunderestimate the length.

To help her decide if she was correct she asked 100 under-10s and100 adults to guess the length of a 34 cm line.

The results can be seen in the two tables, below.

Use the results in the tables to see if Jenny was correct.Show all your workings.

Estimate oflength in cm

Frequency

4

11

24

39

22

20 l < 24<

24 l < 28<

28 l < 32<

32 l < 36<

36 l < 40<

Children under the ageof 10 estimates

Estimate oflength in cm

Frequency

2

6

16

62

14

20 l < 24<

24 l < 28<

28 l < 32<

32 l < 36<

36 l < 40<

Adult estimates

Estimate for the meanlength is 32.56 cm

Estimate for the meanlength is 33.2 cm

The estimate for the mean for under-10s showthat, on average, they underestimated the lengthby 1.44 cm.On average, the adults underestimated by 0.8 cm.Therefore, Jenny is not correct because bothgroups underestimated the length of the line.

© Mathswatch Ltd

Level 7

Answers


Page 134

D15Relative Frequency

1) Peter bought an unfair dice from a Joke Shop.He didn’t know how the dice was biased and so he rolled it100 times and noted down which numbers came up.

He found that the number 6 occurred 8 times.

a) What is the relative frequency of getting a six?

b) If Peter rolls the dice 400 times, estimate how many6s he will roll.

2) Mary had a bag containing four different colour marbles.She chose a marble, noted its colour and then replaced it,80 times.

The results can be seen in this table.

a) Estimate the probability that a blue marble will bechosen on the next pick.

b) If a marble is chosen and replaced 280 times,estimate how many times you would expect tochoose a red marble.

ColourNo. of times

chosen

12

24

18

26

Red

Blue

Green

Yellow

3) Benford’s law says that if you look at real-life sources ofdata (heights of mountains, populations of countries, etc)the number 1 will be the first digit with relative frequency 0.3

If you go through any newspaper and write down the first 20numbers you come across, about how many of the numberswould you expect to begin with a ‘1’.

0.08 or 8100

32

or 0.32480

42 times

6

© Mathswatch Ltd

1) Total weight Weights to use

1 1

2 2

3 3

4 1 + 3

5 2 + 3

6 1 + 2 + 3

7 7

8 1 + 7

9 2 + 7

10 3 + 7

11 1 + 3 + 7

12 2 + 3 + 7

13 1 + 2 + 3 + 7

Answers to question 1which takes a pupil toLevel 3 and allows U3to be shaded.

All the weights from 1 kg to 13 kgcan be made

Using and Applying Maths

Weights QuestionsLevel 3

Page 135A

© Mathswatch Ltd

2)

Total weight Weights to use

1 1

2 2

3 1 + 2

4 4

5 1 + 4

6 2 + 4

7 1 + 2 + 4

8 8

9 1 + 8

10 2 + 8

11 1 + 2 + 8

12 4 + 8

13 1 + 4 + 8

14 2 + 4 + 8

15 1 + 2 + 4 + 8

1kg 2kg 4kg8kg



Answers to question 2.

Page 135B

© Mathswatch Ltd

3)


1 12 23 1 + 24 45 1 + 46 2 + 47 1 + 2 + 48 89 1 + 810 2 + 811 1 + 2 + 812 4 + 813 1 + 4 + 814 2 + 4 + 815 1 + 2 + 4 + 816 1617 1 + 1618 2 + 1619 1 + 2 + 1620 4 + 1621 1 + 4 + 1622 2 + 4 + 1623 1 + 2 + 4 + 1624 8 + 1625 1 + 8 + 1626 2 + 8 + 1627 1 + 2 + 8 + 1628 4 + 8 + 1629 1 + 4 + 8 + 1630 2 + 4 + 8 + 1631 1 + 2 + 4 + 8 + 16

1kg 2kg4kg

8kg

16kg

a)b) If you had six

weights, the bestones to have wouldbe:

1kg

2kg

4kg

8kg

16kg

32kg

With seven weightsit would be best tohave:

1kg

2kg

4kg

8kg

16kg

32kg

64kg

You can see thatevery extra weightshould be doublethe highest weightso far.

For n weights, you shouldhave

1, 2, 4, 8, . . . 2n-1

Definitely not necessaryfor level 4



Answers to question 3which, along with ques-tion 2, takes a pupil toLevel 4 and allows U4to be shaded.

Page 135C

© Mathswatch Ltd

4)


1 12 3 - 13 34 3 + 15 9 - 3 - 16 9 - 37 9 + 1 - 38 9 - 19 910 9 + 111 9 + 3 - 112 9 + 313 9 + 3 + 114 27 - 9 - 3 - 115 27 - 9 - 316 27 + 1 - 9 - 317 27 - 9 - 118 27 - 919 27 + 1 - 920 27 + 3 - 9 - 121 27 + 3 - 922 27 + 3 + 1 - 923 27 - 3 - 124 27 - 325 27 - 3 + 126 27 - 127 2728 27 + 129 27 + 3 - 130 27 + 331 27 + 3 + 132 27 + 9 - 3 - 133 27 + 9 - 334 27 + 9 + 1 - 335 27 + 9 - 136 27 + 937 27 + 9 + 138 27 + 9 + 3 - 139 27 + 9 + 340 27 + 9 + 3 + 1

1kg 3kg 9kg27kg

Weights needed to give allweights from 1 kg to 40kgwith no gaps.

For two weights we need theweights 1 and 3.

For three weights we need1, 3 and 9

For four weights we need1, 3, 9 and 27

To get the next weight in aset we multiply the highestweight in the previous setby 3.

For n weights, you should have

1, 3, 9, 27, . . . 3n-1

Definitely not necessaryfor level 5



Answers to question 4which takes a pupil toLevel 5 and allows U5to be shaded.

Page 135D

© Mathswatch Ltd

LEVEL 3 leading to U3 being shaded

Try different approaches to overcomedifficulties.

Organise work and check results.

Understand a general statement byfinding particular examples.

Review work and reasoning.

EVIDENCE

Question 1 is answered with all 13 weightseventually being found. Some help by theteacher can be given.

Work is organised, possibly in table form.It may not be ordered (ie the weights from 1to 13 will be seen but may not be in order).

Reasoning is clearly seen with the ways ofgetting the weights being shown.ie to get a weight of 7 we use 1 + 2 + 4

A general statement might be made such as“All the weights from 1 kg to 13 kg can befound”. This statement might be implied byseeing the ways of making these weights.The teacher may have to prompt the pupil tomake the statement.


Develop own strategies for solvingproblems.

Use own strategies in a practicalcontext.

Present information in a clear andorganised way.

Search for a solution by trying out ideasof their own.

EVIDENCE

Questions 2 and 3 are answered.

Work is organised in ordered tables.

Pupils can answer the question “what do younotice?” by explaining that if you add aweight to the set it should be double the lastbiggest weight. Or, they may say the weightsare 1, 2, 4, 8, 16, etc where you get the nextweight by doubling the previous one.


Check results considering whether theyare reasonable.

Solve word problems.

Show understanding of situations bydescribing them mathematically usingsymbols, words and diagrams.

Draw simple conclusions of their ownand give an explanation of theirreasoning.

EVIDENCE

Question 4 is answered.

Clear evidence can be seen of the pupilbreaking down the problem, probablyconsidering the case of having just twoweights. He/she will try having weights of 1, 2and 1, 3, and 1, 4. 1, 3 will be seen to givethe most possibilities.

Three weights will then be looked at and1, 3, 9 will finally be found.

Conjectures will probably be made and aprediction for the next weight will be seen.This will then be tested.

A general rule will be given (each extraweight should be three times the largestweight of the previous set).

Using and Applying MathsTeacher Markscheme

Page 135E

These worksheets should be usedtogether with the Balances video clip.

Extras

Balances 1 Answers

1) 2)

3) 4)

5) 6)

510

5

14

7

7

77

7

6 6

2020

Page 136A


Extras

Balances 2 Answers

1) 2)

3) 4)

6)5)

10

4 1 5

9 91818

10

40

5 5

6

1026 26

6 6

17 17

Page 136B


Extras

Balances 3 Answers

1) 2)

3) 4)

3

7

2

8

5

10

5

3

6

6

22

12

2121

17

6

4824

12

5

Page 136C


Extras

Balances 4 Answers

1) 2)

6)

1 1

13

6

1

101

12

5

20

32

11

262

3

1 2

1

24

4)

1

42 2

4

2

1

163)

4 4

3

2

1

11

16

5)

2

48

2

814

1

32

The 1, 1 and 2 canbe in any of thesethree circles.

2

Page 136D


Extras

Balances 5 Answers

1)

2)

Smallest possible

Highest possible

2

33

1

41

2

99

52

1

6

5

16

37

Page 136E

© Mathswatch Ltd

These worksheets should be usedtogether with the Congruent Halvesvideo clip.

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1)2)

3) 4)

5)

Extras

Congruent Halves Answers

6)

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7) 8)

9)

10)

Extras


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11)

12)13)

Extras


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14) 15)

16)

17)

Extras


Page 137D

© Mathswatch Ltd


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18)

19)20)

Extras


Page 137E

© Mathswatch LtdThese worksheets should be usedtogether with the Circles video clip.

Extras

Circles Answers

13cm 9cm

15.6cm

1) 2)

3)

C = 40.846 cm C = 28.278 cm

C = 49.0152 cm

Find the circumference ofthe circles below

(138A)

Page 2


Extras

Circles Answers

2cm

5cm

1.8cm

7.5c

m

1)

2)

3)

4)

C = 12.568 cm

C = 31.42 cm

C = 11.3112 cm

C = 47.13 cm

Find the circumference ofthe circles below

(138B)

Page 3


Extras

Circles Answers

4cm

11cm

1.3cm

9.6c

m

1)

2)

3)

4)

A = 50.272 cm2

A = 380.182 cm2

A = 5.30998 cm2

A = 289.56672 cm2

Find the area of the circlesbelow

(138C)

Page 6


Extras

Circles Answers

24cm 17cm

16.9cm

1) 2)

3)

A = 452.448 cm2

A = 227.0095 cm2

A = 224.346655 cm2

Find the area of the circlesbelow

(138D)

Page 7


Extras

Circles Answers

13cm

30cm

30cm 11cm

12cm 15.6cm 19.2cm

53cm

23cm

1)

2)

3)

A = 369.002 cm2

11cm

A = 25.9545 cm2

A = 625.162 cm2

Find the area of the shadedsections

(138E)

Page 8

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