Maths in Action Fm2 SB.indd - Pearson

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Maths in Action Fm2 SB.indd - Pearson

Pearson Education Botswana (Pty) Ltd

(Longman and Heinemann)

PO Box 1083, Gaborone, Botswana

Plot 14386, New Lobatse Road, Gaborone, West Industrial Site

Botswana

Longman is an imprint of Pearson Education Botswana (Pty) Ltd

© Pearson Education Botswana (Pty) Ltd

All rights reserved. No part of this publication may be reproduced, stored

in retrieval system or transmitted in any form or by any means, electronic,

mechanical, photocopying, recording, or otherwise, without the prior

permission of the publishers.

First published in 2010

ISBN 978-99912-745-2-2 Student’s Pack (includes a Student’s Book and

Key Concept Chart)

ISBN 978-99912-926-6-3 Student’s Book

Cover Design by Firebrand

Typesetting by A1 Graphics

Artwork by A1 Graphics, Robert Hichens, Bennie Kruger

Printed by

It is illegal to photocopy any page of this book without the written permission

of the copyright holder.

Acknowledgements

The authors and publisher would like to thank the following for use of

copyright material:

Deborah Heimann, Director: Editorial Policy and Content, The

Communication Initiative (p. 9, 10), Bank Gaborone Limited

(p. 132), Ashley Bell, Director/General Manager: BSI, Lowtax Network

(p. 135, 141), Commissioner General, Botswana Unified Revenue Service

(p. 137), Government Statistician, Central Statistics Office of Botswana

(p. 154, 160, 200), www.worldatlas.com (p. 168).

The authors and publisher would like to thank the following for use of

photographs:

Gracious Studios (p. 10), iStcok Photo (p. 12, 13 (top, second from top,

bottom), 60 (right), 102), Big Stock Photo (p. 13 (second from bottom), 16,

117, 152, 178, 199), Roger de la Harpe/CORBIS/Great Stock (p. 40), CORBIS/

Great Stock (p. 60 (left)), Hannah Mason/CORBIS (p. 82), Media Club South

Africa (p. 86), Karin Duthie/Africa Media Online (p. 110), Travail Personnel

(p. 113), Per-Anders Pettersson/Getty Images/Gallo Images (p. 126), Getty

Images/Gallo Images (p. 181).

Every effort has been made to trace the copyright holders. In the event of

unintentional omissions or errors, any information which would enable the

publisher to make the proper arrangements will be appreciated.


Contents

How to use this book . .........................................v

TOPIC 1 Work with numbers ...............................2

Summary ..................................................15

Revision ..................................................15

TOPIC 2 Squares, square roots, cubes and cube roots ........16

Summary ..................................................23

Revision ..................................................23

TOPIC 3 Indices ...........................................24

Summary ..................................................33

Revision ..................................................33

TOPIC 4 Matrices .........................................34

Summary ..................................................39

Revision ..................................................39

TOPIC 5 Angle properties ..................................40

Summary ..................................................49

Revision ..................................................49

TOPIC 6 Geometrical constructions ........................50

Summary ..................................................59

Revision ..................................................59

TOPIC 7 Polygons .........................................60

Summary ..................................................69

Revision ..................................................69

Assessment 1: Topics 1 to 7 ...................................70

TOPIC 8 Coordinate geometry .............................72

Summary ..................................................81

Revision ..................................................81

TOPIC 9 Transformations ..................................82

Summary ..................................................93

Revision ..................................................93

TOPIC 10 Perimeter and area ...............................94

Summary .................................................101

Revision .................................................101

TOPIC 11 Total surface area ................................102

Summary .................................................109

Revision .................................................109

TOPIC 12 Volume .........................................110

Summary .................................................117

Revision .................................................117


TOPIC 13 Algebraic variables ...............................118

Summary .................................................125

Revision .................................................125

TOPIC 14 Money ..........................................126

Summary .................................................139

Revision .................................................139

Assessment 2: Topics 8 to 14 .................................140

TOPIC 15 Data processing and presentation ................142

Summary .................................................153

Revision .................................................153

TOPIC 16 Central tendency ................................154

Summary .................................................161

Revision .................................................161

TOPIC 17 Scatter graphs ...................................162

Summary .................................................167

Revision .................................................167

TOPIC 18 Probability ......................................168

Summary .................................................175

Revision .................................................175

TOPIC 19 Time, distance and speed ........................176

Summary .................................................183

Revision .................................................183

TOPIC 20 Formulae ........................................184

Summary .................................................191

Revision .................................................191

TOPIC 21 Equations .......................................192

Summary .................................................199

Revision .................................................199

TOPIC 22 Graphs ..........................................200

Summary .................................................211

Revision .................................................211

TOPIC 23 Problem solving and research ....................212

Summary .................................................221

Revision .................................................221

Assessment 3: Topics 15 to 23 ................................222

End-of-year Practice Examination ...........................224

Syllabus objectives ..........................................240

Useful formulae .............................................246

Comprehension skills .......................................248

Glossary .....................................................250


3x

PAIR

2 m

How to use this book

Mathematics in Action Form 2 is divided into 23 topics following the

Mathematics syllabus.

TOPIC 6

Geometrical constructions

By the end of this topic, you should be able to:

ü Construct triangles from given information

ü Identify congruent triangles and their corresponding measurements

ü Identify similar triangles and their properties

ü Construct quadrilaterals from given information

ü Identify congruent quadrilaterals and their corresponding

measurements.

Oral activity Discuss the construction of an

Egyptian pyramid

1 Give another word for “construction”.

2 In this topic, you will construct triangles and quadrilaterals.

a) Describe the similarities between your constructions

and the construction in the picture.

b) Describe the differences between your constructions

and the construction in the picture.

3 a) Find an example of a triangle in this picture.

b) Find an example of a quadrilateral in this picture.

4 Explain where you would expect to find Egypt on a map

of Africa.

Topic opener pages list the specific objectives

that will be covered in the topic. Use this list

to help you check that you are covering all

the work in the syllabus.

Oral activities provide questions to introduce

the new topic. Work through these activities

in class to get an understanding of what the

topic is about.

50

The ancient Egyptians constructed pyramids in which they buried their kings and queens.

Specific objectives are listed at the bottom of

each page.

Mathematics in Action Form 2 has the following features.

Activity 1 Fi

1 Find an appr

expression a

2 Discuss how

answers.

3 U l l

Activities help you explore,

experiment, research and discover.

Key concept

Approximate answers

of computations.

Key concept boxes state

important points that you

need to take note of.

Exercise 1 P

1 Find the nu

a) 12.45

2 Round each

a) 4 315

d) 0 00876

Extension C

a

Construct a

1

2 Construct a

the circle to

of the regul

Experiments, case studies and projects

provide practical learning opportunities.

These icons identify individual, pair and

group work.

SINGLE Individual

PAIR Pairs

GROUP Groups

Exercises reinforce the work you

have learnt.

Extension work provides advanced

work for you when you need it.

You can use the glossary for

revision. You can find all the

glossary words in colour on

the page given in brackets.

Summary

ü The volume of a 3D object is the amount

of space that the object occupies.

ü We measure volume in cubic units,

such as:

ü Cubic metres, or m3

Cubic centimetres, or cm3

ü Cubic millimetres, or mm 3 .

ü A prism with a composite cross-section

is a prism of which the base consists of

a combination of two or more different

basic 2D shapes.

ü The formula for the volume of a prism is

V = A base ⊥h.

ü The formula for the volume of a prism

also applies to cylinders.

ü If you have Microsoft Excel®, you can

use spreadsheets to calculate the volume

of prisms, cylinders and prisms with

composite cross-sections.

Revision

1 a) Give the mathematical name for the

base of this prism.

75 mm

6 cm

18 cm

42 mm

b) Calculate the volume of this prism.

2 a) Give the mathematical name for the

base of this prism.

b)

x x

x x

x

Calculate the volume of this prism

in terms of x.

x

3

ASSESSMENT 1

TOPIC 12 Volume

c) Calculate the value of x if the volume

of the prism is 1 000 m 3 .

Felicity dug a flower bed in the shape of

the letter “F”. She dug out soil to a depth

of 0.5 m. Calculate the volume of soil that

Felicity dug out of the flower bed.

Assessment 1: Topics 1 to 7

1 Calculate 3.47(78.4 6.7 2 ). Write the

answer correct to two decimal places. (2)

2 Find the number of significant figures

in 603.210. (1)

3 Find the missing numbers in each

number sequence.

a) 1; 4; 7; 10; …; … (1)

b) 16; 8; 4; 2; …; … (1)

c) 0.1; 0.01; 0.001; 0.0001; …; … (1)

4 Round each decimal to two decimal

places.

a) 236.872 (1)

b) 31.5768 (1)

c) 400.22592 (1)

5 Find the number of significant figures in

each decimal.

a) 17.60 (1)

b) 1.953 (1)

c) 0.0045 (1)

6 Round each decimal to four significant

figures.

a) 465.88 (1)

b) 0.045182 (1)

7 Calculate the value of each computation.

Give the answers correct to two decimal

places.

a) 9 076.35 7 002.876 (2)

b) 35.487 187.94 (2)

c) 509.34 17.02 (2)

8 Write each number correct to two

decimal places.

a) 5.782 (1)

b) √ _______

209.56 (1)

c) 9.123 (1)

d) √ _________

3 2 008.95 (1)

9 Calculate the area of a circle with a radius

of 4.17 cm. Give the answer correct to

two decimal places. (3)

10 Calculate the radius of a sphere with a

volume of 1 600 cm 3 . Give the answer

correct to two decimal places. (3)

11 Write 3 3 3 3 in index notation. (1)

12 Express 108 as the product of its prime

factors. (1)

70

1.5 m

2.5 m

4 The volume of a prism is 625 cm3 and its

height is 25 cm.

a) Calculate the area of the base of the

prism.

b) i) State whether your answer to

Question a) necessarily means that

the base of the prism is a square.

ii) Give a reason for your answer.

5 A cylindrical log

of wood floats

on the water

in a dam. Kitso

estimates that

about 65% of the

log is below the

water’s surface.

The radius of the

log is 22 cm and

the length of the

log is 2.3 m.

a) Calculate the

volume of

wood below the water line.

b) Calculate the volume of wood above

the water line.


Emerging issue

Information in surveys

tells us about national

health problems

such as HIV/AIDS.

This information

encourages and helps

us to support people

in need.

Note

You can write the

trans lation in this

example in a short

way as

(x; y) (x 4; y 2).

117

13 Calculate 34 3 7 . Write the answer in

these formats.

a) Index notation (1)

b) A whole number (1)

14 Write 0.000172 in standard notation. (1)

15 Calculate 7.14 10 7 5.9 10 6 .

Write the answer in these formats.

a) Standard form (1)

b) A decimal (1)

16 Determine all the different factors of

each number.

a) 6 (2)

b) 20 (2)

17 Write each number as the product of

its prime factors.

a) 32 (2)

b) 168 (2)

18 Fill in the missing letters.

a) am a n = a … (1)

b) am a n = a … (1)

c) ( a m ) n = a … (1)

19 a) Find the number of rows in

this matrix. (1)

b) Find the number of columns in

this matrix. (1)

c) Find the number of elements in

this matrix. (1)

| 3 7 5

1 2 8 |

20 Write only the answer. (2)

|

2 7

3 4 | | 5 3

6 4 |

3 2 3 7

21 Write only the answer. (3)

| 4 2

3 5 | | 3

1 3 6

2 0 |

22 Fill in the missing numbers. (4)

| 6 3 7

5 2 4 | | – … … …

… … … | | = 1 1 4

2 1 3 |

8 1 3 … … … 3 1 4

23 Calculate 2A B 3C. (5)

A B C

| 4 7 2

3 6 1 | | 3 3 10

6 5 9 | | 4 3 2

2 0 1 |

2 8 4 2 0 7 7 3 5

Emerging issue boxes are

based on topics of social

interest. They stimulate

debate and advance your

language and

communication skills.

Note boxes give you extra

information that will help

you understand the

concept.

Use the summaries to help

you reflect on the work you

have covered.

Use the revisions to test

your understanding of the

work covered.

Assessments provide

exam-style questions for

more practice.

v

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