Cambridge (CIE) A Level Maths: Pure 3
Exam Questions

Sketching Graphs of Modulus Functions, Solving Equations with Modulus Functions

Polynomial Division, Factor & Remainder Theorem, Factorisation, Rational Expressions, Improper Algebraic Fractions

Partial Fractions with Linear Denominators, Partial Fractions with Squared Linear Denominators, Partial Fractions with Quadratic Denominators

Further Modelling with Functions

General Binomial Expansion, Subtleties of the General Binomial Expansion, Multiple General Binomial Expansions, Approximating Values using the Binomial Expansion

Exponential Functions, Logarithmic Functions, "e", Derivatives of Exponential Functions

Laws of Logarithms, Exponential Equations

Exponential Growth & Decay, Using Exponentials & Logarithms in Modelling, Logarithmic Graphs

Definitions of Reciprocal Trigonometric Functions, Graphs of Reciprocal Trigonometric Functions, Identities with Reciprocal Trigonometric Functions

Compound Angle Formulae, Double Angle Formulae, Harmonic Form

Strategy for Further Trigonometric Equations

Trigonometric Proof

Differentiating Other Functions, Product Rule, Quotient Rule

Implicit Differentiation

Basics of Parametric Equations, Eliminating the Parameter of Parametric Equations, Sketching Graphs of Parametric Equations, Parametric Differentiation

Integrating Other Functions, Integrating with Trigonometric Identities, Integrating f'(x)/f(x), Integration by Substitution, Harder Substitution, Integration by Parts, Integration using Partial Fractions, Integration Decision Making

General Solutions, Particular Solutions, Separation of Variables, Modelling with Differential Equations, Solving & Interpreting Differential Equations

Change of Sign, Failure of the Change of Sign Method, x = g(x) Iteration

Basic Vectors, Magnitude & Direction, Vector Addition, Position Vectors, Problem Solving using Vectors

Vectors in 3 Dimensions, Problem Solving using 3D Vectors

Equation of a Line in Vector Form, Parallel, Intersecting & Skew Lines, The Scalar (Dot) Product, Uses of the Scalar Product

Operations with Complex Numbers, Complex Conjugation & Division, Square Roots of a Complex Number, Complex Roots of Polynomials

Argand Diagrams, Geometry of Complex Addition, Subtraction & Conjugation, Modulus & Argument, Loci in Argand Diagrams, Inequalities & Regions in Argand Diagrams

Exponential Form of Complex Numbers, Geometry of Complex Multiplication & Division, Square Roots of a Complex Number using Exponential Form