1Topic 1
Number & Algebra
Partial fractions, sequences, induction, binomial theorem, complex numbers, systems
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Topic 1
Number & Algebra
Partial fractions, sequences, induction, binomial theorem, complex numbers, systems
Sequences and Series
Notation, sigma notation, arithmetic and geometric sequences, series, infinite sums, compound interest, depreciation, and applications.
Exponentials and Logarithms
Logarithm basics, log laws, exponential equations, and related applications.
Proof, Logic, Induction and Contradiction
Deduction, counterexamples, mathematical induction, contradiction, and clear reasoning strategies.
Binomial Expansion and Coefficients
Binomial coefficients, Pascal’s triangle, expansion methods, and extended binomial expressions.
Complex Numbers — Foundation and Advanced Applications
Operations, Argand diagrams, modulus and argument, polar and Euler forms, complex roots, De Moivre’s theorem, and roots of complex numbers.
Permutations and Combinations
Permutations, combinations, arrangements, selections, and related problem-solving strategies.
System of Linear Equations
Simultaneous equations, row reduction, matrix methods, and the number of solutions to a system.
2Topic 2
Functions
Polynomials, rational functions, transformations, inequalities, modulus
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Topic 2
Functions
Polynomials, rational functions, transformations, inequalities, modulus
Straight-Line Functions and Coordinate Graphs
Straight-line equations, gradients, intercepts, coordinate graphs, parallel lines, and perpendicular lines.
Linear Graphs, Function Notation and Core Skills
Function notation, composite and inverse functions, odd, even, periodic and self-inverse functions, graph features, and intersections.
Quadratic Functions, Models and Graphs
Quadratic functions, factorising, completing the square, solving equations, quadratic inequalities, and discriminants.
Exponential and Logarithmic Functions
Equation solving, graphical methods, modelling, and interpretation of function behaviour.
Rational Functions and Reciprocal Graphs
Reciprocal graphs, rational expressions, asymptotes, transformations, and rational functions involving quadratics.
Polynomial Functions
Polynomial division, factor and remainder theorems, roots and graphs, and sum and product of roots.
Transformations of Graphs
Translations, reflections, stretches, composite transformations, and their effects on function graphs.
Algebraic and Graphical Inequalities
Graphical solutions, polynomial inequalities, sign diagrams, critical values, and solution intervals.
Absolute Value Functions and Advanced Transformations
Modulus functions, modulus equations and inequalities, reciprocal transformations, square transformations, and graph behaviour.
3Topic 3
Geometry & Trigonometry
Trig identities, inverse trig, vectors, lines and planes in 3D
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Topic 3
Geometry & Trigonometry
Trig identities, inverse trig, vectors, lines and planes in 3D
Geometry of Circles, Sectors and Arcs
Coordinate geometry, angle measure, arc length, sector area, and geometric problem-solving.
Geometry of 3D Shapes
3D coordinates, distances, volume, surface area, and geometric problem-solving with solids.
Trigonometry — Exact Values and Identities
The unit circle, exact trigonometric values, angle relationships, and key trig ratios.
Non-Right Triangle Trigonometry
Pythagoras, right-angled triangles, sine rule, cosine rule, triangle area, bearings, constructions, and elevation and depression angles.
Trigonometric Graphs and Modelling
Graph shapes, transformations, graphical equation solving, modelling, and interpretation of trigonometric functions.
Inverse and Reciprocal Trigonometric Functions
Reciprocal trigonometric functions, inverse trigonometric functions, graphs, domains, ranges, and related equations.
Advanced Trigonometric Equations and Proof
Identities, compound and double angle formulae, trigonometric ratios, and linear and quadratic trigonometric equations.
Basic Operations and Vector Properties
Vector notation, magnitude, unit vectors, parallel vectors, vector operations, scalar product, vector product, angles, perpendicularity, area applications, and geometric proof.
Vector Equation of Lines
Vector, parametric, and Cartesian equations of lines, line relationships, kinematics applications, angles between lines, and shortest-distance problems.
Vector Planes and Properties
Vector and Cartesian equations of planes, normal vectors, intersections, angles, and geometric applications.
4Topic 4
Statistics & Probability
Stats, regression, discrete & continuous random variables, distributions
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Topic 4
Statistics & Probability
Stats, regression, discrete & continuous random variables, distributions
Exploring and Summarising Data
Sampling, data collection, averages, spread, frequency tables, transformed data, outliers, box plots, cumulative frequency, histograms and data interpretation.
Correlation and Regression
Scatter plots, correlation strength, Pearson’s correlation coefficient and linear regression.
Probability
Probability rules, event types, independence, mutual exclusivity, conditional probability, Bayes’ theorem, Venn diagrams and tree diagrams.
Discrete Probability Distributions
Discrete distributions, expected value, variance and transformations.
Binomial Distributions
Binomial conditions and binomial probability calculations.
Normal Distributions and z-Score
Normal probabilities, z-scores, standardisation and unknown parameters.
Probability Density Functions
Density functions, probabilities, median, mode, mean and variance.
5Topic 5
Calculus
Differentiation, integration, optimisation, ODEs, Maclaurin series, l’Hôpital
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Topic 5
Calculus
Differentiation, integration, optimisation, ODEs, Maclaurin series, l’Hôpital
Differentiation
Basic differentiation, powers of x, gradients, tangents, normals, increasing and decreasing functions.
Differentiation Rules, Graphs and Applications
Trig, exponential and logarithmic derivatives, chain rule, product rule, quotient rule and higher derivatives.
Integration
Basic integration, powers of x, constants of integration and GDC-based area calculations.
Integration Methods, Areas and Applications
Trig, exponential and reciprocal integrals, reverse chain rule, substitution and definite integrals.
Optimisation
Using differentiation to model and solve maximum and minimum problems.
Kinematics
Displacement, velocity, acceleration and calculus-based motion.
Advanced Differentiation Techniques and Applications
First principles, inverse functions, implicit differentiation and related rates.
Further Integration and Applications
Substitution, parts, partial fractions, y-axis areas and volumes of revolution.
Differential Equations
Euler’s method, separation of variables, homogeneous equations, integrating factors and modelling.
Maclaurin Series
Standard series, composite series, product series and series from differential equations.
Limits, L’Hôpital’s Rule and Series
L’Hôpital’s rule and Maclaurin-based limits.
Need theory or method first?
Read the Revision Notes or try the Skills before tackling exam questions.