A LevelMathsCambridge (CIE)Pure 3Revision Notes

Cambridge (CIE) A Level Maths: Pure 3
Revision Notes

Exam code: 9709

Concise resources for the Cambridge (CIE) A Level Maths: Pure 3 course.

Algebra & Functions

Sketching Graphs of Modulus Functions

Solving Equations with Modulus Functions

Polynomial Division

Factor & Remainder Theorem

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

Logarithms & Exponentials

Exponential Functions

Logarithmic Functions

Derivatives of Exponential Functions

Laws of Logarithms

Exponential Equations

Exponential Growth & Decay

Using Exponentials & Logarithms in Modelling

Logarithmic Graphs

Trigonometry

Definitions of Reciprocal Trigonometric Functions

Graphs of Reciprocal Trigonometric Functions

Identities with Reciprocal Trigonometric Functions

Compound Angle Formulae

Double Angle Formulae

Strategy for Further Trigonometric Equations

Trigonometric Proof

Differentiation

Differentiating Other Functions

Implicit Differentiation

Basics of Parametric Equations

Eliminating the Parameter of Parametric Equations

Sketching Graphs of Parametric Equations

Parametric Differentiation

Integration

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

Numerical Methods

Failure of the Change of Sign Method

x = g(x) Iteration

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

Complex Numbers

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

Exam boards

Study tools

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