Maths in Action Fm2 SB.indd  Pearson
Pearson Education Botswana (Pty) Ltd
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First published in 2010
ISBN 9789991274522 Student’s Pack (includes a Student’s Book and
Key Concept Chart)
ISBN 9789991292663 Student’s Book
Cover Design by Firebrand
Typesetting by A1 Graphics
Artwork by A1 Graphics, Robert Hichens, Bennie Kruger
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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
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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
Endofyear 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 crosssection
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 crosssections.
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
examstyle questions for
more practice.
v