STP Caribbean Mathematics Book 3

US$ 28.49

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Description

Contents

Reviews

Language

English

ISBN

9780198426608

Contents

Introduction

1 Making sure of arithmetic

Prime numbers

Factors

Prime factors

Multiples

Sieve of Eratosthenes

Squares

Multiplying a string of numbers

Names for numbers

Addition and subtraction of fractions

Multiplication of fractions

Reciprocals

Division by a fraction

Decimal fractions

Interchanging decimals and fractions

Recurring decimals

Addition and subtraction of decimals

Multiplication of decimals

Division by decimals

Relative sizes

Indices

Laws of indices

Zero and negative indices

Standard form (scientific notation)

Approximations (decimal places and significant figures)

Base 2 and base 3 numbers

Mixed exercises

2 Areas

Areas of familiar shapes

Areas of compound shapes

Area of a trapezium

Shapes that have equal areas

3 Arc length and area of the sector of a circle

The length of an arc

The area of a sector of a circle

4 Prisms and pyramids

Making solids from nets

Prisms

Surface area of a prism

Pyramids

Net for a pyramid

Volume of a pyramid

Surface area of a pyramid

Volume of a cylinder

Curved surface area of a cylinder

Volume of a cone

Surface area of a cone

Mixed exercise

5 Enlargements

Enlargements

Centre of enlargement

Scale factors

Finding an image under enlargement

Fractional scale factors

6 Scale drawing

Scale drawing

Accurate drawing with scaled down measurements

Scale drawings without measurements

Map ratio (or representative fraction)

Angles of elevation

Angles of depression

Enlargement and the effect on areas and volumes

Volumes and scale factor

Mixed exercises

7 Congruent triangles

The basic facts

Congruent shapes

Transformations and congruent figures

Congruent triangles

Three pairs of sides

Two angles and a side

Two sides and an angle

Problems

Using congruent triangles

Properties of parallelograms

Using properties of special quadrilaterals

Review test 1: Chapters 1–7

8 Similarity

Similar figures

Similar triangles

Corresponding vertices

Using the scale factor to find a missing length

Corresponding sides

One pair of equal angles and two pairs of sides

Summary: similar triangles

Mixed exercise

9 Pythagoras’ theorem

Squares and square roots

Pythagoras’ theorem

Finding the hypotenuse

The 3, 4, 5 triangle

Finding one of the shorter sides

Mixed examples

Pythagoras’ theorem using areas

Finding lengths in an isosceles triangle

Finding the distance of a chord from the centre of a circle

Problems using Pythagoras’ theorem

The converse of Pythagoras’ theorem

Mixed exercises

10 Trigonometry

Tangent of an angle

Using a calculator

Finding an angle

Finding a side

Using the hypotenuse

The sine of an angle

The cosine of an angle

Summary

Sines, cosines and tangents

Finding the hypotenuse

Angles of elevation and depression

Mixed exercise

11 Polygons

Polygons

The exterior angle of a regular polygon

The sum of the interior angles of a polygon

Formula for the sum of the interior angles

Mixed problems

Pattern-making with regular polygons

12 Constructions

Basic constructions

To construct a line parallel to a given line through a given point

The rhombus

Properties of the diagonals of a rhombus

Circle constructions

To construct the circumcircle to a given triangle

Constructing regular polygons

Mixed exercises

13 Consumer arithmetic

Percentage change

Earnings

Taxes

Property tax

Saving and borrowing

Telephone bills

Electricity bills

Mixed exercise

14 Simultaneous equations

Equations with two unknown quantities

Elimination method

Harder elimination

Mixed questions

Special cases

Substitution method

Problems

Graphical solutions of simultaneous equations

Mixed exercise

Review test 2: Chapters 8–14

15 Sets

Reminders

Notation

Problems

Number of members

Further problems

Mixed exercise

16 Straight-line graphs

Straight lines

Lines parallel to the axes

Slant lines

Points on a line

Comparing slopes

Gradients

Calculating the gradient of a line

The intercept on the y-axis

Parallel lines

Different forms of the equation of a straight line

Getting information from the equation of a line

The equation of a line through two given points

Problems

Mixed exercises

17 Linear equations and inequalities

Linear equations

Multiplication and division of fractions

Fractional equations

Problems

Substituting numerical values into formulae involving fractions

Solving inequalities

Using two-dimensional space

18 Algebraic products

Brackets

The product of two brackets

Finding the pattern

Important products

The difference between two squares

Harder expansions

Summary

Mixed exercises

19 Algebraic factors

Finding factors

Common factors

Factorising by grouping

Factorising quadratic expressions

Calculations using factorising

Mixed questions

Mixed exercises

20 Algebraic fractions

Simplifying fractions

Factors

Further simplifying

Multiplying and dividing fractions

Lowest common multiple

Addition and subtraction of fractions

Mixed questions

Solving equations with fractions

Mixed exercises

21 Quadratic equations

Multiplication by zero

Quadratic equations

Solution by factorisation

Summary

Problems

Mixed exercises

22 Probability

Outcomes of experiments

Probability

Experiments where an event can happen more than once

Certainty and impossibility

Probability that an event does not happen

The number of times an event is likely to happen

Using probability to help decision making

Mixed exercise

Review test 3: Chapters 15–22

Review test 4: Chapters 1–22

Glossary

Answers

Index

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