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Book details

Copyright year: 2012 Publisher: Oxford University Press Publication date: 7/12/2012 Binding: Mixed Media Pages: 800 Size: 8.00" wide x 10.00" long x 1.25" tall Weight: 3.740

AuthorTable of Contents

Functions

Introducing functions

The domain and range of a relation on a Cartesian plane

Function notation

Composite functions

Inverse functions

Transforming functions

Quadratic functions and equations

Solving quadratic equations

The quadratic formula

Roots of quadratic equations

Graphs of quadratic functions

Applications of quadratics

Probability

Definitions

Venn diagrams

Sample space diagrams and the product rule

Conditional probability

Probability tree diagrams

Exponential and logarithmic functions

Exponents

Solving exponential equations

Exponential functions

Properties of logarithms

Logarithmic functions

Laws of logarithms

Exponential and logarithmic equations

Applications of exponential and logarithmic functions

Rational functions

Reciprocals

The reciprocal function

Rational functions

Patterns, sequences and series

Patterns and sequences

Arithmetic sequences

Geometric sequences

Sigma (∑) notation and series

Arithmetic series

Geometric series

Convergent series and sums to infinity

Applications of geometric and arithmetic patterns

Pascal's triangle and the binomial expansion

Limits and derivatives

Limits and convergence

The tangent line and derivative of x<sup>n</sup>

More rules for derivatives

The chain rule and higher order derivatives

Rates of change and motion in a line

The derivative and graphing

More on extrema and optimization problems

Descriptive statistics

Univariate analysis

Presenting data

Measures of central tendency

Measures of dispersion

Cumulative frequency

Variance and standard deviation

Integration

Antiderivatives and the indefinite integral

More on indefinite integrals

Area and definite integrals

Fundamental Theorem of Calculus

Area between two curves

Volume of revolution

Definite integrals with linear motion and other problems

Bivariate analysis

Scatter diagrams

The line of best fit

Least squares regression

Measuring correlation

Trigonometry

Right-angled triangle trigonometry

Applications of right-angled triangle trigonometry

Using the coordinate axes in trigonometry

The sine rule

The cosine rule

Area of a triangle

Radians, arcs and sectors

Vectors

Vectors: basic concepts

Addition and subtraction of vectors

Scalar product

Vector equation of a line

Application of vectors

Circular functions

Using the unit circle

Solving equations using the unit circle

Trigonometric identities

Graphing circular functions

Translations and stretches of trigonometric functions

Combined transformations with sine and cosine functions

Modeling with sine and cosine functions

Calculus with trigonometric functions

Derivatives of trigonometric functions

More practice withderivatives

Integral of sine and cosine

Revisiting linear motion

Probability distributions

Random variables

The binomial distribution

The normal distribution

The Exploration

About the exploration

Internal assessment criteria

How the exploration is marked

Academic Honesty

Recordkeeping

Choosing a topic

Getting started

Using a graphic display calculator

Functions

Differential calculus

Integral calculus

Vectors

Statistics and probability

Prior learning

Number

Algebra

Geometry

Statistics

Practice papers

Practice paper 1

Practice paper 2

Answers

Index

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