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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 | |