STP Mathematics for CSEC

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Description

Contents

Reviews

Language

English

ISBN

9781382009720

CONTENTS

INTRODUCTION

PREFACE

To the teacher

To the student

Acknowledgements

1 NUMBER THEORY AND COMPUTATION

Whole numbers

Number bases and place value

Negative numbers

Order of operations

Properties of operations

Fractions

Powers and roots

Irrational numbers

Indices

Decimals

Approximations

Scientific notation

Converting fractions to decimals

Converting decimals to fractions

Percentages

Ratio

Division in a given ratio

2 SETS

Describing a set

Definitions and notation

Union and intersection

Venn diagrams

Harder problems

3 ALGEBRA 1

Algebra

Definitions and conventions

Simplifying expressions

Factorising

Simplifying fractions

Substituting values into algebraic expressions

Linear equations in one unknown

Forming expressions and equations

Simultaneous linear equations in two unknowns

Linear inequalities

4 MEASUREMENT

Measurements

Units of measurement

Units of length

Units of mass

Units of time

Converting between units of measure

Temperature

Currencies

Speed

Imperial units

Units of length

Units of mass

Conversions between metric and imperial units

Polygons

Circles

Perimeter

Units of area

Areas of polygons and circles

Areas of irregularly shaped plane figures

Volume

Capacity

Prisms

Sources of error

5 CONSUMER ARITHMETIC

Percentage increase and decrease

Compound percentage change

Reverse percentage problems

Profit and loss

Sales tax

Invoices and shopping bills

Utility bills and property tax

Hire purchase and mortgages

Salaries, wages and commission

Income tax

Investments and insurance

REVIEW TEST 1 Chapters 1–5

Multiple choice questions

General proficiency questions

6 RELATIONS, FUNCTIONS AND GRAPHS

Relations

Diagrams representing relations

Types of relation

Functions

Linear functions

Straight line graphs

The standard equation of a straight line

Parallel lines and perpendicular lines

The intercept form of the equation of a straight line

7 GEOMETRY AND TRIGONOMETRY

Symmetry

Transformations

Describing a transformation

Parallel lines

Triangles

Quadrilaterals

Polygons

Necessary and sufficient conditions to prove that a quadrilateral is a parallelogram

Similar shapes

Congruent triangles

Pythagoras’ theorem

Bearings

Angles of elevation and depression

Trigonometry

Coordinate geometry

8 STATISTICS

Categorical and numerical data

Measures of central tendency

Frequency tables

Bar charts

Line graphs

Probability

Independent events

Mutually exclusive events

Contingency tables

9 ALGEBRA 2

Binary operations

The product of two brackets

Factorising by grouping

Factorising quadratic expressions

Simplification of algebraic expressions

Quadratic equations

Solution by factorisation

Solution by completing the square

Solution by the formula

Changing the subject of a formula

10 CIRCLE THEOREMS

Definitions

Angles in circles

Cyclic quadrilaterals

Tangents to circles

Alternate segment theorem

REVIEW TEST 2 Chapters 6–10

Multiple choice questions

General proficiency questions

11 MATRICES

Definitions

Matrix multiplication

Determinants

The inverse of a matrix

Applications of matrices

Simultaneous equations

Numerical applications

12 SEQUENCES

Sequences

13 QUADRATIC FUNCTIONS

The graph of a quadratic function

Estimation of the gradient at a point

Graphical solution of quadratic equations

Graphical solution of quadratic inequalities

Finding the maximum or minimum value of a quadratic function algebraically

Sketching the graphs of quadratic functions

Simultaneous equations – one linear and the other quadratic

14 MORE FUNCTIONS

Cubic functions

The shape of a cubic curve

Reciprocal functions

Reciprocal curves

Recognising curves

Trigonometric functions

The graph of f(x) = sin x°

The graph of f(x) = cos x°

The sine and cosine functions

The tangent function

Growth curves

Decay curves

Exponential growth and decay

Vertical line test for a function

Inverse functions

The graph of a function and its inverse

Compound functions

Function of a function

15 TRAVEL GRAPHS

Straight line distance–time graphs

Rates of change

Tangents to curves

Travel graphs

Curved distance–time graphs

Velocity

Finding velocity from a distance–time graph

Velocity at an instant

Acceleration

Velocity–time graphs

Finding the distance from a velocity–time graph

REVIEW TEST 3 Chapters 11–15

Multiple choice questions

General proficiency questions

16 INEQUALITIES

Linear inequalities

Inequalities involving two variables

Shading the required region

Coordinates of points in a region

Greatest and least values

Linear programming

17 VARIATION

Formulae

Relationships

Direct variation

Dependent and independent variables

Inverse variation

Equations for inverse variation

18 VECTORS IN GEOMETRY

Definition of a vector

Representation of a vector

The magnitude of a vector

Equal vectors

Negative vectors

Multiplication of a vector by a scalar

Equivalent displacements

Addition of vectors

Subtraction of vectors

Position vectors

Vectors and geometry

Using vectors to model practical situations

Further problems

19 TRANSFORMATIONS AND MATRICES

The position vector of a point

The image of a position vector

Transformation matrix

Finding the image

Identifying a transformation

Reflections

Rotations

Enlargements

Transformations that cannot be described simply

Mixed transformations

The identity transformation

Transformations and images

Inverse transformations

Inverse matrix transformations

Inverse matrices and inverse transformations

An invariant point

Transformations not using matrices

20 COMPOUND TRANSFORMATIONS

Compound transformations

Equivalent single transformations

The identity transformation

Common transformation matrices

Area scale factor

Unit vectors and the unit square

Finding a transformation matrix

Compound transformations

Defining transformations as matrix equations

Compound transformations and matrices

REVIEW TEST 4 Chapters 16–20

Multiple choice questions

General proficiency questions

21 SINE AND COSINE FORMULAE

Sines of obtuse angles

Cosines of obtuse angles

Trigonometric ratios as fractions

Trigonometric ratios of 30°, 45° and 60°

Triangle notation

The sine rule

Using the sine rule to find an angle

The cosine rule

Mixed questions

The area of a triangle

Sine formula for area of a triangle

Heron’s formula

The area of a segment of a circle

Applications

22 CONSTRUCTIONS AND TRANSFORMATIONS

Constructions using ruler and compasses

Accuracy

Scales

Transformations

Finding the mirror line

Finding the centre of rotation

Circles and tangents

Parallel lines

23 GROUPED DATA

Collecting information

Frequency tables

Class intervals

Measures of central tendency of a grouped frequency distribution

The modal group

The group containing the median

The mean

Histograms

Frequency polygons

Using the area under a histogram

24 MEASURES OF SPREAD

Range

Cumulative frequency tables

Cumulative frequency curves

Drawing a cumulative frequency curve

Quartiles

Statistical investigations

Deciding which statistical measure to use

25 AREAS AND VOLUMES

Pyramids

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

Volume of a sphere

Surface area of a sphere

REVIEW TEST 5 Chapters 21–25

Multiple choice questions

General proficiency questions

MULTIPLE CHOICE TESTS

Multiple choice test 1

Multiple choice test 2

Multiple choice test 3

Model exams

MODEL EXAM 1

Paper 2

MODEL EXAM 2

Paper 2

MODEL EXAM 3

Paper 2

SAMPLE PAPER WITH SOLUTIONS

Section I

Section II

CSEC MATHEMATICS SBA

What is the SBA?

What is the process for completing the SBA?

How is the SBA marked?

What makes a suitable project?

What are some examples of projects?

How should the SBA be written?

ANSWERS

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 60

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 16

Chapter 17

Chapter 18

Chapter 19

Chapter 21

Chapter 23

Chapter 24

Chapter 25

INDEX

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