Essential Advanced General Mathematics with Student CD-ROM

by Michael Evans , Kay Lipson , Douglas Wallace , Sue Avery

• ISBN13: 9780521612524
• ISBN10: 0521612527
• Edition: 3rd
• Format: Multimedia
• Copyright: 2005-11-23
• Publisher: Cambridge University Press

Summary

Essential Mathematics provides a single unified course of study which addresses all the key skills outcomes.

Table of Contents

Part variation

Sequences and series

Introduction to sequences

Arithmetic sequences

Arithmetic series

Geometric sequences

Geometric series

Infinite geometric series

Algebra II

Polynomial identities

Partial fractions

Simultaneous equations

Revision of chapters 1-5

Summary of chapters 1-5

Short answer questions

Multiple choice questions

Analysis questions

Problem solving and projects

Transformations

Translations

Reflections

Dilations from the axes

Rules for transformations

Composition of transformations

Applying transformations to graphs of functions

Determining transformations

Absolute value function and integer value function

Function notation with transformations

Ratios and similarity

Ratios

An introduction to similarity

Areas, volumes and similarity

Trigonometric functions I

Measuring angles in degrees and radians

Defining trigonometric functions - sine and cosine

Another trigonometric function - tangent

Reviewing trigonometric ratios

Symmetry properties of trigonometric functions

Exact values of trigonometric functions

Graphs of sine and cosine

Transformations applied to graphs of y = sin x and y = cos x

Solution of trigonometric equations

Further sketch graphs

Further symmetry properties

Addition of ordinates

Sketch graphs of the tangent function

Applications

Trigonometric functions II

Trigonometric identities

Addition formulae and double angle formulae

a cos x + b sin x

Trigonometric ratios and applications

Defining sine, cosine and tangent

The sine rule

The cosine rule

The tangent rule

Circle mensuration

Angles of elevation and depression and bearings

Problems in three dimensions

Angles between planes and more difficult 3-D problems

Revision of chapters 7-11

Summary of chapters 7-11

Short answer questions

Multiple choice questions

Analysis questions

Problem solving and projects

Circle theorems

Angle properties of the circle

Tangents

Chords in circles

Vectors

Introduction to vectors

Components of vectors

Vectors in three dimensions

Unit vectors

Applications

Matrices

Introduction to matrices

Addition, subtraction and multiplication by a scalar

Multiplication of matrices

Inverses and determinants for 2x2 matrices

Solution of simultaneous equations using matrices

Transformations

Polar coordinates and complex numbers

Polar coordinates

The set of complex numbers

Multiplication and division of complex numbers

Argand diagrams

Solving equations over the complex field

Polar form of a complex number

Revision of chapters 13-16

Summary of chapters 13-16

Short answer questions

Multiple choice questions

Analysis questions

Problem solving and projects

Kinematics

Position coordinates and displacement

Velocity

Acceleration

Using antiderivatives

Constant acceleration

Velocity-time graphs

Statics of a particle

Triangle of forces

Resolution of forces

Revision of chapters 18 and 19

Summary of chapters 18 and 19

Short answer questions

Multiple choice questions

Analysis questions

Problem solving and projects

Describing the distribution of a single variable

Types of variables

Displaying categorical data - the bar chart

Displaying numerical data - the histogram

Characteristics of distributions of numerical variables

Stem-and-leaf plots

Summarising data

The boxplot

Using boxplots to compare distribut

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