THOMAS WHITHAM SIXTH FORM

Year 9

Number

Levels 5 - 8

T H O M A S W H I T H A M . P B W O R K S . C O M

S J Cooper

Number(1) Basic Number work

1. List the first 5 multiples of

a) 3 b) 9 c) 15 d) 25

2. Find the lowest common multiple of

a) 2 and 3 b) 3 and 8 c) 2, 3 and 9

d) 3, 5 and 6 e) 3, 4 and 5

3. List the factors of

a) 15 b) 18 c) 32 d) 24 e) 72

4. Write down the fist twelve prime numbers

5. List all the prime numbers between 30 and 40

6. Express the following numbers as products of their prime factors.

a) 32 b) 24 c) 50 d) 70 e) 270

f) 210 g) 180 h) 336

7. a) Express 45 as a product of its prime factors

b) Hence find the highest common factor of 450 and 60

8. a) Express 200 as a product of its prime factors

b) Hence find the highest common factor of 200 and 540

9. Find the highest common factor of

a) 30 and 54

b) 60 and 84

c) 18, 36 and 45

d) 56, 64 and 96

e) 42, 105 and 126.

S J Cooper

Number (2) Ratios & Fractions

1. Express the following in their simplest form:

a 24

6 b

27

15 c

45

20 d

36

27 e

60

45

f 63

18 g

65

55 h

52

12 i

108

64 j

120

32

2. Express each of the following ratios in their simplest form:

a) 8 : 20 b) 18 : 54 c) 25 : 40 d) 42 : 64 e) 22 : 77

f) 24 : 8 g) 105 : 65 h) 49 : 21 i) 36 : 60 j) 120 : 80

3. Alison spent £350 on Saturday, of which £150 went on food, £50 on a CD and the rest on

clothes.

What fraction of her money did she spend on (a) food (b) clothes?

4. On a plane to Spain there are 480 men, 360 women and 120 children.

What is the ratio of men to women to children?

5. On a journey to Alton Towers, a distance of 140 miles, 105 miles is by motorway and the rest

is by ordinary roads. What ratio of motorways to ordinary roads?

6. In a recent mathematics test out of 72 questions , Ben obtained 54 correct answers

(a) What fraction of the marks did Ben score correctly?

(b) Express as a ratio the number of correct answers to number of incorrect answers

7. The time Asif spent on his homework for SATS last week was as follows:

1 12

h on science 3 12

h on English 2h on Maths

What is the ratio of the time spent on his homework for SATS?

8. The length of a model car is 15cm compared to the actual

length of the car which is 3.6m. What is the ratio of the

model to the actual object in its simplest form?

9. On a recent holiday Colleen and Ume had their bags weighed at

the airport and found that whilst Colleen’s weighed 24kg Ume’s

weighed only 9.6kg. Express these weights as a ratio in its

simplest form.

S J Cooper

Number (3) Addition & subtraction of fractions

1. Workout each of the following

a) 18

5

6

1

b) 4

3

8

3

c) 8

7

24

5

d) 15

7

5

2

e) 5

3

3

2

f) 9

4

36

7

g) 3

22

2

11

h) 6

5

4

13

i) 4

12

6

53

j) 5

22

8

32

k) 4

11

9

22

l) 7

21

28

5

m) 7

32

3

24

n) 16

11

8

31

o) 4

32

12

51

p) 3

22

9

7

q) 5

12

15

41

r) 21

17

7

6

s) 5

42

2

18

t) 6

1

2

1

5

2

2. Work out the perimeters for each of the following shapes.

(a) (b)

3. On a recent shopping trip Mrs Durkin bought 4

34 kg of potatoes,

3

21 kg of carrots and

2

12 kg of

cabbage. What is the total weight of these items ?

4. Alan worked out that on any given school day 12

5 of the day was in class,

8

1 of the day was

dinner or breaks and 6

1 of the day was taken up by leisure time. What fraction of that was

taken up by sleeping?

7

23

2

11

10

71

3

13

6

54

S J Cooper

5. Workout each of the following

a) 15

3

3

2

b) 8

3

4

3

c) 18

7

6

5

d) 7

41

2

13

e) 9

4

12

7

f) 3

21

8

52

g) 12

7

4

11

h) 5

31

6

13

i) 6

52

10

74

j) 5

31

7

22

k) 24

9

6

5

l) 12

5

8

7

m) 24

171

2

12

n) 16

73

4

14

o) 16

7

12

13

p) 9

5

11

52

q) 5

21

7

33

r) 6

5

10

32

s) 12

11

8

33

t) 24

71

6

54

6. A piece of rope has an initial length of 4

18 m long. Sharon cuts a length of

12

53 m away. Work

out the length of rope remaining.

7. A piece of ribbon has a length of 4

35 metre. If two lengths of

7

21 metres is cut off, what is the

length of ribbon left over ?

8. A garden has an area of 15

712 square metres. If

6

53 square metres is to be used for border

plants, what area is left for a lawn?

S J Cooper

Number (4) Multiplication & Division 1. Work out each of the following:

a) 5

4

3

2

b) 8

5

4

1

c) 5

3

7

3

d) 2

1

8

5

e) 10

3

9

7

f) 20

3

12

5

g) 20

11

55

10

h) 9

6

8

3

i) 2

11

6

51

j) 9

44

5

33

k) 4

15

7

31

l) 6

41

5

31

m) 8

52

7

5

n) 15

11

3

21

o) 15

71

4

3

p) 11

51

6

51

q) 9

51

5

33

r) 8

21

10

7

s) 16

51

3

23

t) 9

4

9

4

2. Simplify each of the following:

a) 8

5

7

5

b) 5

3

9

7

c) 12

5

8

3

d) 5

3

15

7

e) 25

9

10

3

f) 21

20

9

8

g) 7

4

21

14

h) 5

11

2

11

i) 9

5

3

21

j) 14

13

8

51

k) 7

31

4

31

l) 3

11

15

8

m) 16

7

6

33

n) 28

9

7

21

o) 5

14

2

13

p) 9

21

4

32

q) 7

33

5

22

r) 5

36

10

12

3. Joan needs 7 lengths of wood each with length 8

12 m long. How much ribbon will she

have left from a roll of length 15m?

4. Alison has a length of ribbon of length 5

27 metres. If she cuts

3

11 metres off what fraction

has she taken from removed?

S J Cooper

Number (5) Fraction of a quantity

Answer questions 1 to 5 without the use of a calculator

1. Work out each of the following

a) 4

1 of £80 f)

5

3 of £135

b) 3

2 of 36 cm g)

9

7 of 108 square metres

c) 5

4 of 180° h)

12

7 of 300 mm

d) 7

3 of $63 i)

4

3 of £2800

e) 6

5 of 240 miles j)

3

2 of 225m

2. Harriet spends 8

1 of the day practicing on the piano.

How many hours does Harriet practice on the piano?

3. In a recent Science test Graham Obtain 5

3 of the marks. If the test paper was out of 95,

how many marks did Graham obtain?

4. In the past 72 days it has rained on no less than 8

7 of the days. How many

days of rain have we seen in the past 72 days?

5. In the construction of schools for the future 7

2 of the

workforce are skilled engineers. If the workforce consist of

147 people, how many are skilled engineers.

S J Cooper

6. Work out each of the following

a) 3

2 of £14.34 d)

5

2 of one billion (1 billion = 1000 000

000)

b) 6

5 of 46.8 cm e)

12

7 of 2940 students

c) 4

3 of 102 kg f)

9

4 of €28350

7. James earns £250 each. If he is given a pay rise of 8

1. What is his new weekly wage

packet?

8. Of some 17500 Post Offices left in this country it is estimated that some 7

3 could close

over the next ten years. How many post office are likely to be open in ten

years time?

9. In Burnley last year some 12 800 babies were born of which 16

7 were

girls. How many babies born in Burnley were boys?

10. Of all the mobile phones sold in the UK some40

27 are

sold for Children. If 32 million mobile phones were sold

last year how many were for children?

S J Cooper

Number (6) Decimals 1. Work out each of the following:

a) 5.07 + 2.3 + 4.19

b) 16 + 7.34 + 1.88 + 10.374

c) 0.575 + 0.74 + 1.314

d) 102 + 78.8 + 12.45 +

25.56

e) 27.54 – 9.82

f) 13.72 – 8.47

g) 3.14 – 1.57

h) 78.2 – 46.82

2. What is the difference between 512.6 and 348.22?

3. Subtract 98.62 from 104.9

4. What is the sum of the numbers 12.23, 13.8 and 36.49?

5. Work out each of the following:

a. 0.3 0.4

b. 0.4 0.9

c. 0.02 0.3

d. 0.5 0.06

e. 1.2 0.4

f. 1.5 0.04

g. 1.1 0.7

h. 1.5 0.2

i. 0.06 0.08

j. 1.01 0.05

6. Using long multiplication work out each of the following:

a. 3.2 1.4

b. 0.62 1.8

c. 0.32 1.5

d. 2.7 0.53

e. 1.8 0.62

f. 3.2 0.21

7. Work out each of the following:

a. 2.8 0.4

b. 0.038 0.02

c. 0.105 0.07

d. 0.048 0.12

e. 6.3 0.7

f. 0.44 0.04

g. 0.084 0.007

h. 0.276 0.06

i. 624 0.8

j. 0.27 0.0009

8. Work out 008.0

03.02.3

S J Cooper

Number (7) Conversions

1. Express each of the following fractions as decimals:

a) 100

41 b)

10

9 c)

4

3 d)

25

3 e)

5

3 f)

50

7

g) 20

13 h)

7

1 i)

6

5 j)

9

4

2. Express the following decimals as fraction in their simplest form:

a) 0.2

b) 0.08

c) 0.15

d) 0.48

e) 0.105

3. Express the following decimals as percentages:

a) 0.45

b) 0.37

c) 0.03

d) 0.4

e) 0.175

4. Express each of the following fractions as percentages:

a) 10

7 b)

50

17 c)

20

13 d)

25

6 e)

2

1 f)

8

3

5. Express each of the following percentages as (a) fractions (b) decimals

a) 60% b) 55% c) 64% d) 24% e) 8% f) 17½%

6. Express each of the following recurring decimals as fractions

a) 5.0 b) 63.0 c) 24.0 d) 213.0

7. Which of the following is closest to 3

1

a) 5

2 b)

7

2 c) 30% d) 34% e) 0.29 f) 0.32?

S J Cooper

Number (8) Percentages

1. Work out each of the following percentages:

a) 20% of 180

b) 30% of 130

c) 15% of 90

d) 15% of 36

e) 20% of 45

f) 40% of 160

g) 21% of 30

h) 33% of 50

i) 25% of 620

j) 17½% of 60

2. In a school of 1500 students 20% attend the sixth from. How many members

of the sixth form are there?

3. The price of a telephone call is to reduce by 30%. If the cost

per minute for a particular operator was 40 pence what will

be the new cost?

4. The prices of houses are said to rise by 15% over the

next three years. If the price of a house on Harvey

Street is £74 000 this year, what will it be worth in

three years time?

5. H&M are having a sale with 25% of everything. If a coat

usually costs £145 what will be its cost in the sale?

6. Comet is having a sale on its Laptops with 15% off

Whilst Currys sale has 5

1 of all laptops. Which

Laptop is cheaper if the laptop usually costs £435 in

comet and £455 in Currys?

S J Cooper

Number (9) Dividing a quantity into a given ratio

1. Divide £360 in the ratio 1:8

2. Divide 4500 kg in the ratio 3:2

3. Divide €280 in the ratio 5:2

4. Divide $1320 in the ratio 5:6

5. Divide 12000 metres in the ratio 3:7

6. In a class of 24 students the ratio of boys to girls is 3:5. How many boys are

there in this class?

7. A box contains screws of length ''

4

3 and

''

2

11 in the ratio of 2:3. If the bag

contains at total of 745 screws how many are ''

2

11 in length?

8. A line is divided in the ratio 3:4. If the shortest length is 21cm what is the

length of the longest length?

9. The price of a DVD is divided between the manufacturer and

the shop keeper in the ratio 2:7. How much does the supplier

receive on a DVD costing £11.07?

10. The winning horse at Newmarket this Thursday took

home a price of £90 000. However this price had to be

divided between the owner and the stables in the ratio

7:2. How much did the owner receive?

11. A farmer uses his land for crops and cattle in the ratio 5:6. If

7.8 hectares is used for cattle to graze on, how much land has

the farmer in total?

12. Alfred and Becky share a Bingo win of £1100 between them in the ratio 1:3.

How much does each receive?

S J Cooper

Number (11) Percentage of a quantity

1. A bank account earns interest at 6.25% per annum. What interest is earned if there is

£250 in the account?

2. Next have launched their sale with 35% off all items in store.

a) If a Dress was priced at £120, what is the new price for

the dress?

b) If a pair of jeans has a price tag of £40, what is the

sale price for the jeans?

3. The sale price for a prosche as from summer is £36220.

However in America you can expect to pay an extra 6%. What

is the cost of a porsche in America?

4. Because of a recent outbreak of foot and mouth you

could expect to pay and additional 12% for your

Christmas dinner this year. Given that the average family

spent £150 on their Christmas meal last year, what is the

cost likely to be this Christmas?

5. Due to downloading, the average price of a CD is said to fall by 7%

this year. If the price in January was on average £10.49, what is the

price likely to be at the end of the year?

6. The Interest rates at a local building society have been static at 4% in recent years. If

John has £1000 invested in this building society at the beginning of the year, how

much is he likely to have in the account

a) at the end of the year

b) at the end of three years?

7. The number of students studying mathematics at A level is said to rise by 2.4% each

year. If there are 2500 students currently studying mathematics at A level how many

are their likely to be in 10 years time?

S J Cooper

Number(12) Compound Measures

1. A house is bought for £70 000 and appreciates at 3% each year what will it be worth after 4

years?

2. Mr Smith invests £800 into his building society which pays interest at a rate of 4% per

annum. If he leaves his £800 in this account for 5 years how much will he have in the

account at the end of five years?

3. A motor car bought new for £6 000 depreciates in value by 10% each year. Find its value

after two years.

4. Share prices are said to be on the increase at a rate of 2% a week. If Alison invests £1000

in shares, what is its likely value after

a) 2 weeks

b) 10 weeks

5. Mr Ahmed borrows £7000 from a bank for 5 years at 7% p.a. How much will he have to

repay at the end of the 4 years?

6. Mrs Worthless invested £100 in an ISA which is said to increase in value at a rate of 6%

per annum. What is the total value of this ISA at the end of three years?

7. At a recession house prices are on the decrease at 5% per year. A house is valued at £74

000. If this rate of decrease continues, what will be the value of the house in 10 years time?

8. The population of a small town is decreasing at a rate of 8% each year. At the beginning of

the year 2000 there were 40 000 occupants. How many occupants are there likely to be by

the end of 2010?

9. When a ball is dropped, the height of each bounce is 20% less than the height of the

previous bounce.

a) If the first bounce was at a height of 300cm, how high did the ball bounce on the

second bounce?

b) Find the height of the fifth bounce. (Be careful)

S J Cooper

Number (13) Standard Form

1. Express each of the following numbers in standard form

a) 42 000

b) 17 000 000 000

c) 9130 000 000 000 000

d) 8 000 000 000

e) 6721 000 000 000

f) 0.0002

g) 0.000 00045

h) 0.000 000 000185

i) 0.000 000 0037

j) 0.000 000 000 000 000 000 26

k) 292 000 000

l) 147 000 000 000 000 0

m) 0.000346

n) 0.00008

o) 0.075

p) 75000 000

q) 3190

r) 0.0125

s) 1809 000 000 000 000 000 000

t) 0.00405

2. Express each of the following numbers in standard form correct to 2 significant figures

a) 357004

b) 14870000

c) 94572564012

d) 0.00000007895

e) 0.000472575

f) 0.00000002136

g) 3428420510

h) 4545833710000

i) 0.00000000000001944

j) 0.00001945147

3. The solar system was formed over 454 000 000 years ago. Express this number in standard form.

4. The ice age pattern began over 40 million years ago. Express this number in standard from. {be

careful}

5. The mass of the earth is given as 6 000 000 000 000 000 000 000 000 kg. Express this quantity in

standard from.

6. Write each of the following as a single value

a) 7103.6

b) 5108.1

c) 91042.5

d) 7103.6

e) 3101.8

f) 31074.3

g) 4107

h) 10107

i) 61072.1

j) 210701.4

S J Cooper

Number (14) Standard Form

1. Arrange these numbers in order of size with the smallest first.

a) 0.0004 , 5103 , 0.000 021, 3107.2 , 4103.4

b) 7103 , 960000, 876 000 000, 6106.7 , 91092.1

2. Work out each of the following, leaving your answer in standard form

a) 200000 x 8000000

b) 4000 x 300000

c) 0.0004 x 0.0007

d) 0.006 x 500000

e) 0.00007 x 0.0000007

f) 840000 4000

g) 12000000 3000000

h) 0.00028 0.00004

i) 0.00000012 0.03

j) 80000 0.0002

3. Work out each of the following

a) 37 108104

b) 33 105103

c) 35 104107

d) 82 106109

e) 95 102103

f) 84 102102.1

g) 108 103103.2