Unit 1

Proof

Proof

Proof

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Unit 2

Algebra and functions

Algebra and functions

Indices and surds

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Quadratic functions

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Simultaneous equations and inequalities

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Polynomials, algebraic fractions and partial fractions

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Graphs of functions, modulus and proportion

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Composite and inverse functions

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Transformations of graphs

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Unit 3

Coordinate geometry in the (x, y) plane

Coordinate geometry in the (x, y) plane

Straight lines

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Circles

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Parametric equations

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Unit 4

Sequences and series

Sequences and series

The binomial expansion

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Sequences, recurrence relations and sigma notation

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Arithmetic sequences and series

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Geometric sequences and series

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Unit 5

Trigonometry

Trigonometry

Sine and cosine rules, radians, arcs and sectors

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Trigonometric graphs, exact values and small angles

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Reciprocal and inverse trigonometric functions and identities

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Addition and double angle formulae and R cos(θ ± α)

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Solving trigonometric equations

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Unit 6

Exponentials and logarithms

Exponentials and logarithms

Exponential functions and exponential models

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Logarithms and logarithmic graphs

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Unit 7

Differentiation

Differentiation

First principles and standard derivatives

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Tangents, normals and stationary points

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The chain, product and quotient rules

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Implicit and parametric differentiation

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Connected rates of change and forming differential equations

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Unit 8

Integration

Integration

Integrating standard functions

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Definite integrals and areas

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Integration by substitution

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Integration by parts

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Integration using partial fractions

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Differential equations

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Unit 9

Numerical methods

Numerical methods

Locating roots, iteration and the Newton-Raphson method

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The trapezium rule

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Unit 10

Vectors

Vectors

Vectors

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