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| Functions | |
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| Introducing functions | |
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| The domain and range of a relation on a Cartesian plane | |
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| Function notation | |
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| Composite functions | |
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| Inverse functions | |
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| Transforming functions | |
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| Quadratic functions and equations | |
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| Solving quadratic equations | |
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| The quadratic formula | |
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| Roots of quadratic equations | |
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| Graphs of quadratic functions | |
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| Applications of quadratics | |
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| Probability | |
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| Definitions | |
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| Venn diagrams | |
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| Sample space diagrams and the product rule | |
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| Conditional probability | |
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| Probability tree diagrams | |
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| Exponential and logarithmic functions | |
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| Exponents | |
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| Solving exponential equations | |
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| Exponential functions | |
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| Properties of logarithms | |
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| Logarithmic functions | |
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| Laws of logarithms | |
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| Exponential and logarithmic equations | |
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| Applications of exponential and logarithmic functions | |
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| Rational functions | |
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| Reciprocals | |
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| The reciprocal function | |
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| Rational functions | |
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| Patterns, sequences and series | |
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| Patterns and sequences | |
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| Arithmetic sequences | |
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| Geometric sequences | |
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| Sigma (∑) notation and series | |
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| Arithmetic series | |
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| Geometric series | |
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| Convergent series and sums to infinity | |
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| Applications of geometric and arithmetic patterns | |
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| Pascal's triangle and the binomial expansion | |
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| Limits and derivatives | |
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| Limits and convergence | |
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| The tangent line and derivative of x<sup>n</sup> | |
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| More rules for derivatives | |
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| The chain rule and higher order derivatives | |
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| Rates of change and motion in a line | |
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| The derivative and graphing | |
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| More on extrema and optimization problems | |
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| Descriptive statistics | |
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| Univariate analysis | |
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| Presenting data | |
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| Measures of central tendency | |
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| Measures of dispersion | |
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| Cumulative frequency | |
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| Variance and standard deviation | |
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| Integration | |
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| Antiderivatives and the indefinite integral | |
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| More on indefinite integrals | |
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| Area and definite integrals | |
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| Fundamental Theorem of Calculus | |
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| Area between two curves | |
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| Volume of revolution | |
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| Definite integrals with linear motion and other problems | |
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| Bivariate analysis | |
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| Scatter diagrams | |
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| The line of best fit | |
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| Least squares regression | |
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| Measuring correlation | |
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| Trigonometry | |
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| Right-angled triangle trigonometry | |
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| Applications of right-angled triangle trigonometry | |
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| Using the coordinate axes in trigonometry | |
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| The sine rule | |
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| The cosine rule | |
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| Area of a triangle | |
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| Radians, arcs and sectors | |
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| Vectors | |
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| Vectors: basic concepts | |
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| Addition and subtraction of vectors | |
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| Scalar product | |
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| Vector equation of a line | |
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| Application of vectors | |
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| Circular functions | |
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| Using the unit circle | |
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| Solving equations using the unit circle | |
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| Trigonometric identities | |
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| Graphing circular functions | |
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| Translations and stretches of trigonometric functions | |
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| Combined transformations with sine and cosine functions | |
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| Modeling with sine and cosine functions | |
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| Calculus with trigonometric functions | |
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| Derivatives of trigonometric functions | |
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| More practice withderivatives | |
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| Integral of sine and cosine | |
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| Revisiting linear motion | |
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| Probability distributions | |
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| Random variables | |
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| The binomial distribution | |
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| The normal distribution | |
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| The Exploration | |
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| About the exploration | |
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| Internal assessment criteria | |
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| How the exploration is marked | |
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| Academic Honesty | |
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| Recordkeeping | |
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| Choosing a topic | |
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| Getting started | |
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| Using a graphic display calculator | |
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| Functions | |
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| Differential calculus | |
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| Integral calculus | |
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| Vectors | |
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| Statistics and probability | |
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| Prior learning | |
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| Number | |
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| Algebra | |
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| Geometry | |
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| Statistics | |
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| Practice papers | |
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| Practice paper 1 | |
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| Practice paper 2 | |
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| Answers | |
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| Index | |