New General Mathematics - Pearson
New General
Mathematics
FOR SENIOR SECONDARY SCHOOLS TEACHER'S GUIDE
New General Mathematics
for Secondary Senior Schools 1
H. Otto
Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world
? Pearson PLC All rights reserved. No part of this publication may be reproduced, stored in a 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 2015 ISBN 9781292119748 Cover design by Mark Standley Typesetting by Author: Helena Otto
Acknowledgements The Publisher would like to thank the following for the use of copyrighted images in this publication: Cover image: Science Photo Library Ltd;
It is illegal to photocopy any page of this book without the written permission of the copyright holder. Every effort has been made to trace the copyright holders. In the event of unintentional omissions or errors, any information that would enable the publisher to make the proper arrangements will be appreciated.
Contents
Review of Junior Secondary School course
iv
Chapter 1: Numerical processes 1: Indices and logarithms
1
Chapter 2: Geometry 1: Formal geometry: Triangles and polygons
5
Chapter 3: Numerical processes 2: Fractions, decimals, percentages and number bases
13
Chapter 4: Algebraic processes 1: Simplification and substitution
15
Chapter 5: Sets 1
18
Chapter 6: Algebraic processes 2: Equations and formulae
21
Chapter 7: Algebraic processes 3: Linear and quadratic graphs
25
Chapter 8: Sets 2: Practical applications
28
Chapter 9: Logical reasoning: Simple and compound statements
29
Chapter 10: Algebraic processes 4: Quadratic equations
30
Chapter 11: Trigonometry 1: Solving right-angled triangles
34
Chapter 12: Mensuration 1: Plane shapes
37
Chapter 13: Numerical processes 3: Ratio, rate and proportion
39
Chapter 14: Statistics: Data presentation
41
Chapter 15: Mensuration 2: Solid shapes
43
Chapter 16: Geometry 2: Constructions and loci
45
Chapter 17: Trigonometry 2: Angles between 0? and 360?
47
Chapter 18: Algebraic processes 5: Variation
50
Chapter 19: Numerical processes 4: Tax and monetary exchange
51
Chapter 20: Numerical processes 5: Modular arithmetic
52
Review of Junior Secondary School course
1. Learning objectives
1. Number and numeration 2. Algebraic processes 4. Geometry and mensuration 5. Statistics and probability
2. Teaching and learning materials
Teachers should have the Mathematics textbook of the Junior Secondary School Course and Book 1 of the Senior Secondary School Course.
Students should have: 1. Book 1 2. An Exercise book 3. Graph paper 4. A scientific calculator, if possible.
3. Glossary of terms
Algebraic expression A mathematical phrase that
can contains ordinary numbers, variables (such
as x or y) and operators (such as add, subtract,
multiply, and divide). For example, 3x2y ? 3y2 + 4.
Algebraic sentence is another word for an
algebraic equation where two algebraic
expressions are equal to each other.
Angle A measure of rotation or turning and we use
a protractor to measure the size of an angle.
Angle of depression The angle through which the
eyes must look downward from the horizontal to
see a point below.
Angle of elevation The angle through which the
eyes must look upward from the horizontal to see
a point above.
Bimodal means that the data has two modes.
Cartesian plane A coordinate system that
specifies each point in a plane uniquely by a
pair of numerical coordinates, which are the
perpendicular distances of the point from
two fixed perpendicular directed lines or axes,
measured in the same unit of length. The word
Cartesian comes from the inventor of this plane
namely Ren? Descartes, a French mathematician.
Coefficient a numerical or constant or quantity 0
placed before and multiplying the variable in an
algebraic expression (for example, 4 in 4xy).
Common fraction (also called a vulgar fraction
or simple fraction)
Any
number
written
as
_ a
b
where a and b are both whole numbers and
where a < b.
Coordinates of point A, for example, (1, 2)
gives its position on a Cartesian plane. The
first coordinate (x-coordinate) always gives
the distance along the x-axis and the second
coordinate (y-coordinate) gives the distance
along the y-axis.
Data Distinct pieces of information that can exist
in a variety of forms, such as numbers. Strictly
speaking, data is the plural of datum, a single
piece of information. In practice, however,
people use data as both the singular and plural
form of the word.
Decimal place values A positional system of
notation in which the position of a number
with respect to the decimal point determines its
value. In the decimal (base 10) system, the value
of each digit is based on the number 10. Each
position in a decimal number has a value that is
a power of 10.
Denominator The part of the fraction that is
iws rtihtteendebneolomwintahteorlinofe.thTehfera4citnio_n34 ,.
for example, It also tells
you what kind of fraction it is. In this case, the
kind of fraction is quarters.
Directed numbers Positive and negative numbers
are called directed numbers and are shown on
a number line. These numbers have a certain
direction with respect to zero.
? If a number is positive, it is on the right-hand
side of 0 on the number line.
? If a number is negative, it is on the left-hand
side of the 0 on the number line.
Direct proportion The relationship between
quantities of which the ratio remains constant.
If a and b are directly proportional,
then Direct
v_baa=riaatcioonnstTanwtovqaluuaen(tfiotiresexaaamnpdleb,
k). vary
directly if, when a changes, then b changes in the
same ratio. That means that:
? If a doubles in value, b will also double in
value.
? If a increases by a factor of 3, then b will also
increase by a factor of 3.
Edge A line segment that joins two vertices of a
solid.
iv Review of Junior Secondary School course
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