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Circular and simultaneous inequalities

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Counting techniques in probability

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Definite integrals and substitution

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Differentiation of inverse trigonometric functions

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Direction fields

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Division of polynomials and the remainder theorem

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Double angle formulae

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Expansion of (1 + x)^n, Pascal’s triangle

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Exponential growth and decay

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Fundamental counting principle

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Graphing polynomials by adding ordinates

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Graphing polynomials by multiplying ordinates

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Half-angle formulae

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Indefinite integrals and substitution

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Inequalities involving absolute value and square roots

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Integrals involving trigonometric substitution

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Integrals of the type ∫f(x)(f(x))^n dx

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Integration involving inverse trigonometric functions

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Integration of sin^2x and cos^2x

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Introduction to differential equations

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Introduction to vectors

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Inverse functions

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Inverse trigonometric functions

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Mathematical induction involving series

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Mean and variance of the binomial distribution

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Modelling with first-order differential equations

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More Pascal’s triangle expansions

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Multiple roots of a polynomial equation

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Overview of trigonometric equations

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Parametric form of a function or relation

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Pascal’s triangle relations and the binomial theorem

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Permutations

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Pigeonhole principle

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Polynomial functions

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Polynomials

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Problems involving displacement and velocity

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Problems involving forces

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Projectile motion

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Projections of vectors

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Proving divisibility by induction

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Quadratic inequalities

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Rates of change with respect to time

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Rational function inequalities

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Reciprocal functions

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Related rates of change

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Relationship between roots and coefficients

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Scalar product of vectors

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Simple trigonometric equations

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Solving differential equations of the form dy/dx = f(x)

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Solving differential equations of the form dy/dx = g(y)

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Solving differential equations using separation of variables

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Solving equations using angle formulae

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Solving quadratic trigonometric equations

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Solving trigonometric equations using the auxiliary angle method

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Square root functions

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Sum and difference of two angles

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The factor theorem

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Trigonometric equations involving angle formulae

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Trigonometric products as sums or differences

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Using identities to simplify expressions and prove results

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Vectors in component form

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Vectors in geometric proofs

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Vectors in two dimensions

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When induction doesn’t work

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