NSM 8 Chapter 1

Review of lastyears work

1

1

I hope you remember

last years work!

Id better work

through this

chapter, just to

make sure.

Chapter Contents

1:01

Beginnings in number

NS41

1:02

Number: Its order and structure

NS41

1:03

Fractions

NS43

1:04

Decimals

NS43

1:05

Percentages

NS43

1:06

Angles

SGS42

1:07

Plane shapes

SGS43

1:08

Solid shapes

SGS41

1:09

Measurement

MS41,

MS42,

MS43

1:10

Directed numbers

NS42

1:11

The number plane

PAS45

1:12

Algebra

PAS414

Working Mathematically

Learning Outcomes

As this is a review chapter many outcomes are addressed. These include:NS41, NS42, NS43, PAS41, PAS42, PAS43, PAS44, PAS45, MS41, MS42, MS43, SGS41, SGS42, SGS43

Working Mathematically Stage 4

1 Questioning, 2 Applying Strategies, 3 Communicating, 4 Reasoning, 5 Reflecting

Note: A complete review of Year 7 content is found in Appendix A located on

the Interactive Student CD.

Click here

Appendix A

2 NEW SIGNPOST MATHEMATICS 8

This is a summary of the work covered in New Signpost Mathematics 7. For an explanation of the work, refer to the cross-reference on the right-hand side of the page which will direct you to the

Appendixes on the Interactive Student CD.

1:01 | Beginnings in Number Outcome NS41

Write these Roman numerals as basic numerals in our number system.

a LX b XL c XXXIV d CXVIIIe MDCCLXXXVIII f MCMLXXXVIII g VCCCXXI h MDCXV

Write these numerals as Roman numerals.

a 630 b 847 c 1308 d 3240e 390 f 199 g 10 000 h 1773

Write the basic numeral for:

a six million, ninety thousandb one hundred and forty thousand, six hundredc (8 10 000) + (4 1000) + (7 100) + (0 10) + (5 1)d (7 104) + (4 103) + (3 102) + (9 10) + (8 1)

Write each of these in expanded form and write the basic numeral.

a 52 b 104 c 23 d 25

Write 6 6 6 6 as a power of 6.

Write the basic numeral for:

a 8 104 b 6 103 c 9 105 d 2 102

Use leading digit estimation to find an estimate for:

a 618 + 337 + 159 b 38 346 16 097 c 3250 114d 1987 4 e 386 195 f 84 963 38

1:02 | Number: Its Order and Outcome NS41Structure

Simplify:

a 6 2 + 4 5 b 12 6 2 c 4 + 20 (4 + 1)d (6 + 7 + 2) 4 e 50 (25 5) f 50 (25 [3 + 19])

Simplify:

a 347 1 b 84 0 c 36 + 0d 3842 + 0 e 1 30 406 f 864 17 0

Write true or false for:

a 879 + 463 = 463 + 879 b 76 9 = 9 76c 4 + 169 + 96 = (4 + 96) + 169 d 4 83 25 = (4 25) 83e 8 (17 + 3) = 8 17 + 8 3 f 4 (100 3) = 4 100 4 3g 7 99 = 7 100 7 1 h 17 102 = 17 100 + 17 2

Exercise 1:01

Basic means simple.

A:01A

A:01A

A:01B

A:01D

A:01D

A:01E

A:01F

CD Appendix

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2

3

4

5

6

7

Exercise 1:02

A:02A

A:02B

A:02B

CD Appendix

1

2

3

CHAPTER 1 REVIEW OF LAST YEARS WORK 3

List the set of numbers graphed on each of the number lines below.

a

b

c

d

e

f

Use the number lines in Question 4 to decide true or false for:

a 3 < 5 b 1 < 0 c 7 > 4 d 0 > 1e 75 < 9 f 0 > 07 g < h 1 >

Which of the numbers in the set {0, 3, 4, 6, 11, 16, 19, 20} are:

a cardinal numbers? b counting numbers? c even numbers?d odd numbers? e square numbers? f triangular numbers?

List all factors of:

a 12 b 102 c 64 d 140

List the first four multiples of:

a 7 b 5 c 12 d 13

Find the highest common factor (HCF) of:

a 10 and 15 b 102 and 153 c 64 and 144 d 294 and 210

Find the lowest common multiple (LCM) of:

a 6 and 8 b 15 and 9 c 25 and 20 d 36 and 24

a List all of the prime numbers that are less than 30.b List all of the composite numbers that are between 30 and 40.

a Use a factor tree to write 252 as a product of prime factors.b Write 400 as a product of prime factors.c Write 1080 as a product of prime factors.d Find the HCF of 400 and 1080.e Find the LCM of 400 and 1080.

Find the smallest number that is greater than 2000 and:

a is divisible by 2 b is divisible by 3 c is divisible by 4d is divisible by 5 e is divisible by 6 f is divisible by 8g is divisible by 9 h is divisible by 10 i is divisible by 11j is divisible by 25 k is divisible by 100 l is divisible by 12

Complete the following:

a If 152 = 225, then b If 83 = 512, then

c If 132 = 169, then d If 43 = 64, then

A:02C

A:02C

A:02D

A:02E

A:02E

A:02E

A:02E

A:02F

A:02G

A:02H

A:02I

4

6 754320 11

6 754320 11

22 232120191816 1715

95 1098587565 76

07 080605040301 020

0 1412

34

14

12

341 1 1 1 2

5

1

4---

1

2---

1

4---

3

4---

6

7

8

9

10

11

12

13

14

225 . . .= 5123 . . .=

169 . . .= 643 . . .=


1:03 | Fractions Outcome NS43

Change each fraction to a whole or mixed numeral.

a b c d

Change each mixed numeral to an improper fraction.

a 3 b 5 c 1 d 3

Simplify each fraction.

a b c d

Complete the following equivalent fractions.

a = b = c = d =

a + b c + d

a + b c + d

a Which fraction is the smaller: or ?

b Which fraction is the larger: or ?

c Arrange in order, from smallest to largest: { , , }.

d Arrange in order, from largest to smallest: { , , , }.

a 3 + 1 b 10 3 c 5 2 d 10 1

a b c d

a 4 b 1 3 c 3 1 d 2 1

a b c 4 d 1 3

a Find of 2 km. b What fraction of 2 m is 40 cm?

1:04 | Decimals Outcome NS43

a Write (1 10) + (7 1) + (5 ) + (3 ) + (7 ) as a decimal. A:04A

b Write (6 100) + (8 10) + (4 1) + (0 ) + (2 ) as a decimal.

Exercise 1:03

A:03B

A:03C

A:03D

A:03E

A:03F

A:03G

A:03H

A:03I

A:03J

A:03K

A:03L

A:03M

CD Appendix

1

10

2------

9

4---

87

10------

11

8------

2

1

2---

3

10------

3

4---

1

7---

3

8

10------

20

50------

15

100---------

18

24------

4

2

5---

10------

3

4---

100---------

4

1---

10------

1

3---

120---------

53

10------

4

10------

19

100---------

6

100---------

3

8---

7

8---

5

12------

1

12------

63

5---

3

10------

9

10------

3

4---

3

4---

2

5---

31

100---------

1

5---

73

4---

6

10------

2

5---

1

3---

8

10------

17

20------

3

4---

1

2---

3

5---

1

4---

2

3---

82

5---

3

4---

7

8---

1

2---

3

5---

1

5---

1

2---

92

5---

3

4---

3

10------

7

10------

3

5---

2

3---

9

10------

15

16------

103

5---

7

8---

3

4---

1

3---

1

2---

4

5---

119

10------

1

2---

3

8---

3

5---

3

5---

1

2---

3

4---

123

5---

Exercise 1:04

A:04A

CD Appendix

11

10------

1

100---------

1

1000------------

1

10------

1

100---------


Change each decimal to a fraction or mixed numeral in simplest form.

a 07 b 213 c 0009 d 53e 085 f 0025 g 18 h 904

Change each fraction or mixed numeral to a decimal.

a b c 1 d 2

e f g h

Write in ascending order (smallest to largest):

a {03, 033, 0303} b {2, 05, 31} c {0505, 0055, 55}

Do not use a calculator to do these.

a 37 + 152 b 6385 25 c 8 + 1625 d 8 1625

a 0006 05 b 382 011 c (005)2 d 13 191

a 06 100 b 0075 10 c 816 100 d 0045 10

a 489 3 b 15 5 c 8304 8 d 0123 4e 38 02 f 08136 004 g 875 005 h 3612 12

a $362 + $3.42 b $100 $41.63 c $8.37 8 d $90 8

a Round off 96 700 000 to the nearest million.b Round off 0085 to the nearest hundredth.c Round off 86149 correct to one decimal place.d Write , rounded off to two decimal places.

1:05 | Percentages Outcome NS43

Write each percentage as a fraction or mixed numeral in simplest form.

a 9% b 64% c 125% d 14 %

Write each fraction or mixed numeral as a percentage.

a b 1 c d 4

Write each percentage as a decimal.

a 47% b 4% c 325% d 300%e 50% f 104% g 127% h 03%

Change each decimal to a percentage.

a 087 b 13 c 5 d 0825

a 8% of 560 L b 70% of 680 g c 5% of $800 d 10% of 179 me Joan scored 24 marks out of 32. What is this as a percentage?f 250 g of sugar is mixed with 750 g of salt. What percentage of the mixture

is sugar.

A:04B

A:04C

A:04B

A:04D

A:04E

A:04F

A:04G

A:04I

A:04J

2

3

9

10------

13

100---------

1

2---

99

100---------

3

5---

33

200---------

5

8---

3

11------

4

5

6

7

8

9

When you round off, you are making an approximation.

10

0.6.

Exercise 1:05

A:05A

A:05B

A:05C

A:05D

A:05F

CD Appendix

1

1

2---

2

3

4---

3

8---

37

300---------

3

5---

3

4

5


1:06 | Angles Outcome SGS42

Name each angle marked with a dot, using the letters on the figures.

a b c d

Use a protractor to measure ABC.a b

Classify each angle using one of these terms: acute, right, obtuse, straight, reflex,

revolution.

a b c d

e f g h

Draw a pair of:

a adjacent complementary angles b vertically opposite anglesc alternate angles d adjacent supplementary angles.

Find the value of the pronumeral in each.

a b c d

e f g h

Exercise 1:06

A:06A

A:06B

A:06C

A:06D

A:06D

A

BC TE

B

S D

NM

P Q

D

C

B

A

BC

A C

B

A

58a 47 b

48 c

72 105

d

73

e 120f

68g 122h

CD Appendix

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2

3

4

5


1:07 | Plane Shapes Outcome SGS43

a What is the name of the shape on the right.b How many vertices has this shape?c How many sides has this shape?d How many angles has this shape?e How many diagonals has this shape?

Choose two of these names for each triangle and find the vale of the pronumeral:

equilateral, isosceles, scalene, acute-angled, right-angled, obtuse-angled

a b c d

e f g h

Calculate the value of the pronumeral in each quadrilateral.

a b c d

a Give the special name of each figure in Question 3.b Which of the shapes in Question 3 have:

i opposite sides equal? ii all sides equal? iii two pairs of parallel sides?iv only one pair of parallel sides? v diagonals meeting at right angles?

Use a ruler, a pair of compasses and a protractor to construct each of these figures.

a b c

Exercise 1:07

A:07A

A:07D

A:07G

A:07F

A:07B

A:07E

a60

60 b

7070

c

40110

d

55

e

45

f

100

g

75

40

h

65

a b c

60 60

120

d 80

100120

5 cm 4 cm

6 cm

4 cm

5 cm60

32

cm

5 cm60 80

38 cm

CD Appendix

1

2

3

4

5


1:08 | Solid Shapes Outcome SGS41

a Give the name of each solid above.b Which of these solids have curved surfaces?c For solid B, find:

i the number of faces (F) ii the number of vertices (V)iii the number of edges (E) iv number of edges + 2 (ie E + 2)v number of faces + number of vertices (ie F + V)

Name the solid corresponding to each net.

a b c

a Draw the front view of this prism.b Draw the side view of this prism.c Draw the top view of this prism.

Exercise 1:08

A:08A

A:08E

A:08B

A:08C

A:08D

A B C D E

Front

CD Appendix

1

2

3


1:09 | Measurement Outcome MS41, MS42, MS43

Write down each measurement in centimetres, giving answers correct to 1 decimal

place.

a b c d e

Complete each of these.

a 3000 mm = . . . . . . . cm b 2500 mL = . . . . . . . L c 630 mg = . . . . . . . gd 7 km = . . . . . . . m e 78 kg = . . . . . . . g f 25 m = . . . . . . . cm

An interval is 84 cm long. It must be divided into 12 equal parts. How many

millimetres would be in each part?

Find the perimeter of each of these figures.

a b c

Write the time on each clock in both conventional and digital time.

a b c d

Write each of these as a 24-hour time.

a 20 minutes past 5 (before noon) b 30 minutes past 5 (after noon)c 12 noon d 57 minutes past 11 (after noon)

a Rajiv ran at a speed of 5 m/s for 20 s. How far did he run?b Taya walked at a constant speed for 50 s. During this time she travelled 150 m.

What was her speed?

c A train travelling with a speed of 30 km/h travelled a distance of 120 km.How long did it take?

Find the area of each figure below.

a b c

Exercise 1:09

A:09B

A:09E

A:09C

A:09C

A:09D

A:09E

A:09F

A:09G

0 mm 10 20 30 40 50 60 70 80 90 100 110 120

9 m

8 m

10 m

5 m

82 m 38 cm

62 cm

12

39

6

12

39

12

39

12

3

6

45 cm

3 cm

30 cm

1 m

50 cm

30 cm

7 mm

CD Appendix

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2

3

4

5

6

7

8


d e f

Find the volume of each prism.

a b c d

Select the most likely answer.

a A teaspoon of water would contain: A 5 L B 5 mL C 5 kLb A milk carton would contain: A 1 mL B 1 kL C 1 Lc 1 mL is the same volume as: A 1 m3 B 1 cm3 C 1 mm3

d A small packet of peas has a mass of: A 5 kg B 50 g C 5 ge A bag of potatoes has a mass of: A 20 kg B 20 g C 20 mg

The gross mass, net mass and containers mass of a product are required.

Find the missing mass.

a Gross mass = 500 g, net mass = 400 g, containers mass = g.b Net mass = 800 g, containers mass = 170 g, gross mass = g.

A:09I

A:09H

A:09J

6 m

8 m7 cm

5 cm

12 cm

5 cm

9

3 cm

3 cm3 cm

3 cm

2 cm

7 cm2 cm

3 cm

5 cm

20 m

9 m 11 m

10

11

List the 3D shapes that you can find in this picture.


1:10 | Directed Numbers Outcome NS42

Which members of the following set are integers: {3, , 15, 4, 0, 10}? A:10A

Give the basic numeral for each of the following. A:10B

a 7 + 11 b 3 + 15 c 9 + 2 d 25 + 5e 2 13 f 7 10 g 7 5 h 10 3i 6 (10) j 14 (1) k 3 + (+7) l 15 + (+1)m 10 (3 9) n 15 (2 5) o 3 + (7 + 11) p 11 + (5 + 18)

Simplify:

a 4 3 b 8 2 c 02 3 d 01 15e 4 14 f 5 8 g 7 (11) h 6 (12)i 35 (5) j (40) (10) k 60 6 l 14 7

m n o p

Write down the basic numeral for:

a 3 + 6 2 b 4 8 2 c 6 4 4 d 30 + 2 10e 8 + 6 3 f 10 + 5 2 g (2 20) 3 h (8 38) 3i 8 $1.15 18 $1.15 j 35 + 2 15 4 20

1:11 | The Number Plane Outcome PAS45

Find the coordinates of each of the points A to J. A:11B

On a number plane like the one in Question 1, plot the following points.Join them in the order in which they are given, to draw a picture.(2, 0) (3, 0) (3, 1) (1, 1) (1, 15) (2, 15) (2, 1) (2, 1) (2, 15)(1, 15) (1, 1) (3, 1) (3, 0) (2, 0) (1, 1) (1, 1) (2, 0) (2, 0)

Exercise 1:10

A:10A

A:10B

A:10D

A:10

A:10C

CD Appendix

11

2---

2

3

21

3---------

24

4---------

48

6---------

18

2-----------

4

Exercise 1:11

A:11B

A:11C

y

x

3

2

1

0

1

2

3

123 1 2 3

G D

B

A

C

E

FJ

H

I

(0, 0) isthe

origin

The negatives are on the left on the x-axis. The negatives are at the bottom on the y-axis.

CD Appendix

1

2


1:12 | Algebra Outcome PAS414

If s represents the number of squares formed and m is the number of matchesused, find a rule to describe each pattern and use it to complete the table given.

a

m = . . . . . . . . . .

b

m = . . . . . . . . . .

Rewrite each of these without the use of or signs.

a 5 h + 2 b a + 3 y c 6 (a + 7) d 5 a 7

Rewrite each of these, showing all multiplication and division signs.

a 3a + 8 b 5p 6q c 4(x + 2) d

Given that x = 3, find the value of:

a 6x b 2(x + 5) c 5x2 d 10 3x

If a = 2 and b = 5, find the value of:

a 3a + 7b b c 4a(b a) d a2 + b2

If m = 2t + 1, find the value of m when t = 100.

Discover the rule connecting x and y in each table.

Simplify:

a 1m b 1 a c 4 y d y + y + y + ye f 5 f a b g 5 k h 5 a bi 8x 0 j 4y 0 k 6m + 0 l 3a 1

s 1 2 3 4 10 20 30 100

m

s 1 2 3 4 10 20 30 100

m

a x 1 2 3 4 5 b x 1 2 3 4 5

y 7 10 13 16 19 y 11 15 19 23 27

Exercise 1:12

A:12A

A:12B

A:12B

A:12C

A:12E

A:12C

A:12C

A:12D

, ...,,

, ..., ,

CD Appendix

1

2

3a 7+

3------------

4

5

10a

b---------

6

7

8


m 7a + 5a n 10a + a o 7b b p 114a 64aq m 3m r 4b 6b s 4x2 + 3x2 t 6ab 5ab

Simplify:

a 3 5a b 6 10b c 7m 3p d 8x 4ye a 4b f 6m 5 g 3k 5 h 6y 3i 12t 3 j 30t 3 k 6m 2a l 10a 5bm 15r 10 n 8m 6 o 3ab 7a p 5ab 4b

Simplify:

a 5m + 7m 10m b 8x 6x x c 5x + 2y + 7yd 12a + 3b 2a e 7p + 2q + 3p + q f 3r + 2A + 3A + 5rg 6a + 7b 2a + 5b h 4m + 3 2m + 1 i 8m + 2a 2m 8aj 7a2 4a + 2a2 k 2x2 + 3x + 2x l 2x2 + 3x + 2x + 3

Expand, by removing grouping symbols:

a 3(a + 9) b 5(x + 2) c 10(m 4)d 9(2a 3) e 6(4t + 3) f 5(2 + 4x)g m(m + 7) h a(a 3) i a(6 + a)

Solve these equations.

a x + 5 = 9 b x + 4 = 28 c 12 a = 5 d 6 a = 1e 6m = 42 f 5m = 100 g m + 7 = 2 h m 1 = 5

The sum of two consecutive numbers is 91. What are the numbers?

1:12 Fraction, decimal and percentage equivalents

Challenge worksheet 1:12 The bridges of Knigsberg

A:12H

A:12E

A:12E

A:12F

A:12I

A:11AA:11B

9

10

11

12

13

14

, ...,,

0 1 2 3 4 5

1

3

5

7

9m

t

This pattern of triangles formed from matches

gives the following table.

Plot these ordered pairs on a number plane like

the one to the right.

Number of triangles (t) 1 2 3 4

Number of matches (m) 3 5 7 9


Chapter 1 | Working Mathematically1 Use ID Card 7 on page xx to identify:

a 5 b 7 c 8 d 17e 18 f 19 g 20 h 21i 22 j 23

2 Use a calculator to find:a three consecutive numbers that have a

sum of 822.

b three consecutive numbers that have a sum of 1998.

c three consecutive numbers that have a sum of 24 852.

d three consecutive numbers that have a product of 336.

e three consecutive numbers that have a product of 2184.

f three consecutive numbers that have a product of 15 600.

3 Which counting number, when squared, is closest to:

a 210? b 3187? c 26?

4 After the twin towers of the World Trade Centre fell in New York on 11 September

2001, it took 3.1 million hours of labour to

remove 1 590 227 tons of debris. If this was

completed on 10 May 2002, find:

a the number of days that passed until all debris was removed.

b the average mass of debris that was removed in each hour of labour.

c the number of tonnes of debris removed if 1 ton = 907 kilograms. (Remember:

1 tonne = 1000 kg.)

5 This graph appeared in the Sunday Telegraph where a survey carried out by the Commonwealth Bank of Australia

suggested that Australians are not saving

enough of their income.

a If the wage represented here is $960 per week, how much is allocated to:

i savings? ii mortgage/rent?iii credit card? iv motoring?

b What do you think was the most popular reason for saving?

c The three top reasons for saving were given in the article. Try to guess these

three reasons in just five guesses.

1 Roman numerals

2 Multiplication tables A

3 Multiplication tables B

4 Order of operations

5 Operations with decimals

6 Equivalent fractions

tnemngissa

1A

Consecutive numbers followone after the other.

Mortgage/rent176%

Savings127%

Entertainment103%

Credit card82%

Motoring64%

Other184%

Household264%

CB ContentsFeatures of New Signpost MathematicsTreatment of OutcomesMetric EquivalentsThe Language of MathematicsArithmetic and Algebra CardsChapter 1 Review of Last Year's Work1:01 Beginnings in Number1:02 Number: Its Order and Structure1:03 Fractions1:04 Decimals1:05 Percentages1:06 Angles1:07 Plane Shapes1:08 Solid Shapes1:09 Measurement1:10 Directed Numbers1:11 The Number Plane1:12 AlgebraWorking Mathematically

Chapter 2 Working MathematicallyChapter 3 Investigating Pythagoras' TheoremChapter 4 PercentagesChapter 5 Patterns and AlgebraChapter 6 ProbabilityChapter 7 Reasoning in GeometryChapter 8 Graphs and TablesChapter 9 Area and VolumeChapter 10 Equations, Formulae and InequationsChapter 11 Ratio, Rates and Scale DrawingChapter 12 The Number PlaneChapter 13 Geometric Constructions and Congruent FiguresChapter 14 StatisticsChapter 15 Circles and CylindersChapter 16 SimilarityChapter 17 Using Calculators and SpreadsheetsAnswersAnswers to ID CardsIndexAcknowledgementsAppendixesAppendix AnswersFoundation WorksheetsChallenge WorksheetsWorksheet Answers

NSM 8 Chapter 1

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Transcript of NSM 8 Chapter 1