Essential Mathematics. Book 1

193 Pages·2016·52.82 MB·English

by  Rayner D.

Essential Mathematics
Book I
David Rayner
Oxford
Essential Mathematics
Book I
David Rayner
Oxford University Press
Oxford University Press, Walton Street, Oxford OX2 6DP
Oxford New York
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Oxford is a trade mark of Oxford University Press
© David Rayner
All rights reserved. This publication may not be reproduced, stored
or transmitted, in any forms or by any means, except in accordance
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or except for fair dealing for the purposes of research or private
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outside those terms should be addressed to the Permissions
Department, Oxford University Press.
First published 1995 by Elmwood Press
Reprinted 1996 by Oxford University Press
ISBN 0 19 914661 6
Artwork by Angela Lumley
Emma Djonokusumo
Rachel Flowerday
Lisa Lawton
Lisa Lee
Bidisha Bandyopadahay
Fiona Lait
Paulina Spencer
Eleanor Galvin
Typeset and illustrated by Tech-Set, Gateshead, Tyne and Wear.
Printed in Great Britain by
Butler & Tanner Ltd, Frome and London
PREFACE
This is the first of a three book series written for pupils in the age
range 11-14 years. Many classrooms will contain children with a
range of abilities in mathematics. This book is written to cater for
this situation and also has an ample supply of questions and
activities to stretch the most able.
The author believes that children learn mathematics most effectively
by doing mathematics. Interest and enthusiasm for the subject is
engendered by working at questions which stretch the pupil
forward in his or her knowledge and understanding. The author,
who is a teacher, emphasises a thorough grounding in the
fundamentals of number and algebra when working in the lower
secondary classroom.
It is hoped that the material in the books will stimulate young minds
and encourage logical thinking. Some exercises provide the neces-sary
practice in the basic mathematical skills required for later study.
There is no set path through the book and it is anticipated that
most teachers will prefer to take sections in the order of their own
choice.
Many activities, investigations, games and puzzles are included to
provide a healthy variety of learning experiences. The author is
aware of the difficulties of teaching on 'Friday afternoons' or on
the last few days of term, when both pupils and teachers are tired,
and suitable activities are included.
The author is indebted to the many students and colleagues who
have assisted him in this work. He is particularly grateful to Julie
Anderson, David Moncur and Philip Cutts for their contributions
to the text. The author would also like to thank Michelle Hawke
for her work and sense of humour in editing and checking answers
and Micheline Rayner whose encouragement to write instead of
playing golf has been invaluable.
David Rayner

CONTENTS
Page
Part 1
1.1 Accurate drawing 1
1.2 Three dimensional objects : nets 9
1.3 Coordinates 12
1.4 Prime numbers, factors, multiples 26
1.5 Puzzles and games 1 31
Crossnumbers 1, Gel).eral Knowledge, Lines,
Curves from straight lines.
Part 2
2.1 Calculating angles 35
2.2 Decimals 45
2.3 Mixed problems 52
2.4 Area 60
2.5 Sequences 68
2.6 Puzzles and games 2 75
Puzzles, Happy numbers.
Part 3
3.1 Using algebra 78
3.2 Solving equations 85
3.3 Percentages 93
3.4 Symmetry 102
3.5 Puzzles and games 3 108
Clocks, Puzzles.
Part 4
4.1 Approximating 110
4.2 Using a calculator 112
4.3 Travel graphs 114
4.4 Problem solving I 120
4.5 Puzzles and games 4 124
Triangles and quadrilaterals,
Crossnumbers 2, Biggest number.
Part 5
5.1 Metric and Imperial units 128
5.2 Fractions 135
5.3 Charts and graphs 141
5.4 Puzzles and games 5 154
Printing a book, Diagonals,
Find the hidden treasure.
Part 6
6.1 Probability 156
6.2 Problem solving 2 168
6.3 Mental arithmetic 170
6.4 Puzzles and games 6 175
Puzzles, Boxes, Break the codes,
Part 7
7.1 Multiple choice papers 177
7.2 Mixed exercises 182
Part 1
1.1 Accurate drawing
When an architect designs a
house he has to draw accurate
plans for a builder to follow.
In this section you will use a
protractor and a pair of
compasses to construct
accurate diagrams involving
triangles and quadrilaterals.
You will also construct nets
from which three dimensional
shapes can be made.
Measuring angles
When angles are measured accurately they
are usually measured in degrees.
We write degrees as a number followed
by the degree symbol
o.
A full tum = 360°
A half tum = 180°
A quarter tum = 90°.
An angle of 90° is called a right angle.
Exercise 1
In the drawings below some of the angles are correct and some are
obviously wrong. State which are correct and which are wrong.
You are not expected to measure the angles.
p;- 4., 5.\ 6. \
3.~
I
I~~~
2 Part 1
; r -
7. 8. 9. 10. 11. 12.
~~2701 ~
13. 14. 15. 16. 17. 18.
~ ~160°
/
~ ~
Labelling angles
The angle shown is ABC (or CBA). This angle is POR (or ROP).
A
p
The 'B' must be in the middle. The '0' must be in the middle.
Exercise 2
Write down the size of the angles stated.
1. D 2. z 3. B
\
~
A c
B
X
(a) ABD (b) DBC (a) WXZ (b) ZXY (a) B~C
(b) ACB
(c) CBA
Accurate drawing 3
K 6. D
c
F
L A
(a) DEF (a) KLM (a) DCB
(b) DFE (b) KML (b) ABD
(c) FDE (c) NM:K (c) COB
Using a protractor
The protractor is one of the most commonly misused of
mathematical instruments.
It is important to read the answer from the correct scale.
Remember: When measuring an acute angle the answer must be less
than 90°.
When measuring an obtuse angle the answer must be
more than 90°.
Exercise 3
Copy and complete the table.
Q
p \
HI ~" "' <§l
~
G'---......_
-B
--A
(a) AQD = 20° AON= AOL = 60° AOK=
(b) ZOF = ZOP = ZOR = ZOT =
(c) ZQI = ZOG = AOC= AOV =
(d) AOQ = AQP = AOF = AOB =
(e) ZOH = ZOB = zoe= ZOD =
(f) AOG = AOH= AOI AOM=
(g) AOR = ZOE = 155° ZOJ = ZOK =