Maths Matters for CSEC® Examinations

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Description

Contents

Reviews

Language

English

ISBN

9780230464957

Cover

Title

Copyright

Contents

Introduction

Scope and sequence

1 Numbers theory

1.1 Classifiying numbers

1.2 Operations, identity and inverse

1.3 Closure

1.4 Distributive law and associative law in number problems

1.5 Other bases (revision)

2 Rounding and errors

2.1 Significant figures, decimal places and standard form

2.2 Errors in measurement

2.3 Rounding effects when substituting in formulae

3 Consumer arithmetic

3.1 Income

3.2 Taxes

3.3 Utilities

3.4 Currency

3.5 Paying by instalments

3.6 Interest

4 Sets and sequences

4.1 Definitions

4.2 Sequences

4.3 Finding the rule of a sequence

5 Algebra: expressions

5.1 Algebraic operations

5.2 Indices

5.3 Binary operations

5.4 Algebraic fractions

6 Algebra: equations

6.1 Linear equations

6.2 Simultaneous equations

6.3 Inequalities

6.4 Changing the subject

7 Coordinate geometry of the straight line

7.1 Straight-line graphs

7.2 Gradients

7.3 Gradients and intercepts of straight lines

7.4 Finding the equation of a straight line

7.5 Parallel and perpendicular lines

7.6 Distance between points

7.7 Midpoints

7.8 Graphical solution of simultaneous equations

7.9 Inequalities in two dimensions

8 Quadratics

8.1 Expanding a bracket (revision)

8.2 Expanding pairs of brackets

8.3 Identities

8.4 Factorising two terms (revision)

8.5 Factorising a quadratic

8.6 The general quadratic ax[sup(2)] + bx + c

8.7 Quadratic equations

8.8 The quadratic formula

8.9 Quadratic equation problems

8.10 The quadratic curve, symmetry, equations and gradient

9 Ratio and proportion

9.1 Ratio

9.2 Rate

9.3 Direct proportion

9.4 Inverse proportion

9.5 Proportion to a power

10 Geometry 1

10.1 Lines, angles, polygons and solids

10.2 Basic drawing and constructions

10.3 Symmetry

11 Geometry problems

11.1 Lines, angles and polygons

11.2 Congruent triangles

11.3 Similar figures

12 Transformations

12.1 Translations using vectors

12.2 Transformations (revision)

12.3 Combining transformations

12.4 Glide reflections

13 Surface area and volume

13.1 Revision of units

13.2 Length and area

13.3 Area of regular shapes (revision)

13.4 Surface area

13.5 Volume

13.6 The cylinder

13.7 Pyramids and cones

13.8 The sphere

13.9 Compound shapes

14 Trigonometry

14.1 Pythagoras' theorem

14.2 The trigonometric ratios

14.3 Bearings

14.4 The sine rule

14.5 Using the sine rule to find angles

14.6 The cosine rule

14.7 Using the cosine rule to find angles

14.8 Solving triangles

15 Circle theorems

15.1 Definitions

15.2 Angle at the centre of a circle

15.3 Angle in a semicircle

15.4 Angles in the same segment

15.5 Cyclic quadrilaterals

15.6 Mixed examples

15.7 Tangents

15.8 Alternate segment theorem

15.9 Midpoint of a chord

16 Functions

16.1 Domain and range

16.2 Composite functions

16.3 Formulae for composite functions

16.4 Inverse functions

17 Statistics

17.1 Data and frequency tables

17.2 Statistical diagrams

17.3 Measures of central tendency

17.4 Range and interquartile range

17.5 Median and quartiles from a frequency table

17.6 Cumulative frequency

17.7 Probability

18 Vectors

18.1 The arithmetic of vectors and geometry

18.2 Position vectors

18.3 Magnitude of a vector, unit vectors

18.4 Midpoints

19 Matrix algebra

19.1 Arrays of numbers

19.2 Adding and subtracting matrices

19.3 Multiplication by a scalar

19.4 Matrix multiplication

19.5 The identity matrix

19.6 Inverse matrices

Optional special objectives

20 Further quadratics

20.1 Completing the square

20.2 Greatest or least value and line of symmetry

20.3 Solving equations by completing the square

20.4 Line of symmetry and turning points by sketching

20.5 Simultaneous equations: one linear, one quadratic

21 Regions and linear programming

21.1 Inequalities revision

21.2 Revision of y = mx + c

21.3 Regions

21.4 Regions with sides not parallel to the axes

21.5 Situations which give rise to inequalities

21.6 Listing the possibilities

21.7 Linear programming

22 Further graphs

22.1 Graphs of powers of x

22.2 Distance–time graphs

22.3 Acceleration

22.4 Velocity–time graphs

23 Measurement, geometry and trigonometry

23.1 Area of a triangle

23.2 Area of a segment

23.3 Lines and planes

23.4 Lengths and angles in three dimensions

23.5 Lengths within solids

23.6 Angle between lines

24 Vectors and matrices

24.1 Equivalent (equal) and null vectors

24.2 Collinear points

24.3 Transformations using matrices

24.4 Enlargements

24.5 The unit square

24.6 Common matrices

24.7 Successive transformations using matrices

24.8 Simultaneous equations

Model examination papers

Glossary

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Answers

Index

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Back Cover

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