CIE A Level Maths: Pure 3
Exam Questions

Modulus Functions - Sketching Graphs, Modulus Functions - Solving Equations

Polynomial Division, Factor & Remainder Theorem, Factorisation, Rational Expressions, Top Heavy Rational Expressions

Linear Denominators, Squared Linear Denominators, Quadratic Denominators

Further Modelling with Functions

General Binomial Expansion, General Binomial Expansion - Subtleties, General Binomial Expansion - Multiple, Approximating values

Laws of Logarithms, Exponential Equations

Exponential Growth & Decay, Using Exps & Logs in Modelling, Using Log Graphs in Modelling

Reciprocal Trig Functions - Definitions, Reciprocal Trig Functions - Graphs, Trigonometry - Further Identities

Compound Angle Formulae, Double Angle Formulae, R addition formulae Rcos Rsin etc

Strategy for Further Trigonometric Equations

Trigonometric Proof

Differentiating Other Functions (Trig, ln & e etc), Product Rule, Quotient Rule

Implicit Differentiation

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

Integrating Other Functions (Trig, ln & e etc), Integrating with Trigonometric Identities, f'(x)/f(x), Substitution (Reverse Chain Rule), 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, Change of Sign Failure, 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

Intro to Complex Numbers, Complex Conjugation & Division, Square Roots of a Complex Number, Complex Roots of Polynomials

Argand Diagrams - Basics, 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 - Advanced