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Number & Proportion
8 topicsFractions and Decimals
Connect fractions, decimals and exact arithmetic instead of treating them as separate procedures.
Integers
Build reliable signed-number arithmetic and use integers to model changes above and below a reference point.
Percentage
Move fluently between percentage change, reverse percentages and repeated multipliers.
Prime Numbers, HCF, and LCM
Use prime structure to analyse factors, multiples, divisibility and repeating cycles.
Ratio and Rate
Use ratios as multiplicative relationships and rates as comparisons between unlike quantities.
Rounding and Estimation
Use place value, significant figures and bounds to judge sensible numerical accuracy.
Speed
Connect distance, time and speed while handling units and multi-stage journeys correctly.
Standard Form
Use scientific notation to compare scales and calculate with very large or small quantities.
Algebra
16 topicsAlgebra Foundations
Build the symbolic habits that support equations, functions and calculus.
Algebraic Expressions
Translate between words and symbols, substitute values and simplify expressions with confidence.
Linear Equations
Solve one-variable equations by preserving equality and interpreting solutions in context.
Algebraic Fractions
Simplify and combine rational expressions while tracking excluded values.
Expansion of Algebraic Expressions
Expand products systematically and recognise important algebraic identities.
Factorisation
Reverse expansion by identifying common factors, difference of squares and quadratic structure.
Linear Inequalities
Solve and represent inequalities while understanding why multiplying by a negative reverses order.
Quadratic Equations
Solve quadratics using factorisation, completing the square and the quadratic formula.
Quadratic Expressions
Analyse quadratics through expansion, factorisation, completing the square and coefficient relationships.
Simultaneous Equations (Linear)
Interpret simultaneous equations as intersecting constraints and solve them efficiently.
Indices
Use exponent laws across integer, zero, negative and fractional powers.
Surds
Keep irrational quantities exact through simplification, operations and rationalisation.
Equations and Inequalities (Advanced)
Solve equations and inequalities involving absolute values, rational expressions and polynomial structure.
Inequalities (Advanced)
Analyse polynomial, rational and absolute inequalities with critical points and sign structure.
Quadratic Equations (Advanced)
Use discriminants, parameter conditions and root relations to analyse whole families of quadratics.
Simultaneous Equations (Advanced)
Solve systems where linear and non-linear constraints intersect.
Functions & Graphs
7 topicsLinear Graphs
Read and construct straight-line graphs using gradient, intercept and coordinate relationships.
Number Patterns and Sequences
Describe patterns with term-to-term rules and nth-term formulas.
Linear and Quadratic Graphs
Compare line and parabola behaviour using equations, intersections and models.
Quadratic Graphs
Read roots, vertex and symmetry from quadratic forms and connect algebra to the shape of a parabola.
Functions
Treat functions as mappings with domains, compositions and inverses rather than just formulas.
Graph Transformations
Predict how algebraic changes move, stretch and reflect graphs.
Functions and Graphs (Advanced)
Analyse domains, ranges, asymptotes, inverses and composite behaviour across common function families.
Geometry & Mensuration
13 topicsAngles (Basic)
Use angle facts as logical constraints rather than isolated rules.
Perimeter and Area
Calculate and reason about lengths and areas of composite plane figures.
Triangles and Polygons
Use angle sums and polygon structure to reason about shapes.
Volume (Basic)
Use volume as three-dimensional measure and connect dimensions with capacity.
Angle Properties (Advanced)
Chain multiple angle facts in parallel-line and polygon arguments.
Pythagoras’ Theorem
Use right-triangle structure for lengths, coordinates and converse reasoning.
Circle Properties
Connect radius, chord, tangent, arc and sector relationships in circles.
Congruence and Similarity
Distinguish exact congruence from scaled similarity and use scale factors across length, area and volume.
Coordinate Geometry
Use coordinates to encode gradient, distance, midpoint and straight-line relationships.
Surface Area and Volume
Calculate surface areas and volumes of common solids and compare how they scale.
Circle Theorems (Advanced)
Use circle theorems in multi-step proofs and angle calculations.
Coordinate Geometry (Advanced)
Use analytic geometry for line relationships, loci and coordinate proofs.
Mensuration (Advanced)
Solve compound area and volume problems involving sectors, cones, frustums and scale.
Trigonometry
4 topicsSolving Triangles
Solve triangles from mixed side-angle information, beginning with right triangles and extending to sine/cosine rules.
Trigonometry
Build exact-value, equation and graph fluency across sine, cosine and tangent.
Trigonometry (sin, cos, tan)
Choose the correct right-triangle ratio and solve for unknown sides or angles.
Trigonometry (Identities and Applications)
Manipulate identities, solve equations and model non-right triangles and periodic phenomena.
Statistics & Probability
7 topicsBar Graphs and Charts
Read categorical displays critically and convert between frequencies and proportions.
Basic Probability
Build probability from equally likely outcomes, complements and simple combined events.
Mean, Median, and Mode
Choose and calculate measures of centre while recognising the effect of outliers.
Data Interpretation
Extract claims from tables and graphs while distinguishing absolute and relative comparisons.
Probability: Conditional & Expected Value
Use event notation, conditional reasoning and expectation to analyse uncertainty.
Probability: Counting & Bayes
Handle conditional probability, counting, repeated trials and dependent events in multi-stage problems.
Statistics (Data Analysis)
Analyse distributions using centre, spread, grouped data and statistical interpretation.
Vectors, Matrices & Sets
3 topicsMatrices
Use matrices for structured arithmetic, transformations and small linear systems.
Set Notation
Use set notation, Venn relationships and counting principles precisely.
Vectors (2D)
Use vector components, magnitude and linear combinations to represent geometry and displacement.
Calculus
4 topicsDifferentiation
Understand derivative as local rate of change and apply core differentiation rules accurately.
Integration
Use antiderivatives, definite integrals and the Fundamental Theorem to measure accumulation.
Applications of Derivatives
Use derivatives to optimise, approximate and analyse motion and graph behaviour.
Applications of Integration
Use integration for area, volume, average value and accumulated change.
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