Student resources
Topic summaries
275 HTML overviews with worked examples — filter by pack, then open a card for the Learning Sheet. Worksheets browse
Showing 275 of 275 summaries
Foundation
3D Shapes
3D shape work names solids, counts faces/edges/vertices, and uses nets. Euler’s relation … is a useful check for convex polyhedra.
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IGCSE
Accuracy
Bounds and appropriate accuracy: a measurement rounded to a given unit lies within half a unit either way.
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Topic Review
Algebra 1
Algebra 1 revision consolidates collecting like terms, expanding brackets and solving linear equations.
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Topic Review
Algebra 2
Algebra 2 revision develops simultaneous equations, inequalities and early quadratics.
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Topic Review
Algebra 3
Algebra 3 revision covers harder quadratics, algebraic fractions and changing the subject.
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Topic Review
Algebra 4
Algebra 4 revision targets functions, composites/inverses and mixed algebraic exam questions.
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IGCSE
Algebraic Fractions
Algebraic fractions simplify by factorising, then cancelling common factors — never cancel terms across a sum until factorised.
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A Level lesson
Algebraic Fractions
Algebraic fractions simplify by factorising and cancelling common factors, then combine over a common denominator.
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Topic Review
Algebraic Fractions Topic Review
Self-review on simplifying, multiplying/dividing, and adding algebraic fractions — prep for equations and partial fractions.
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A Level lesson
Algorithms
Decision-maths algorithms are precise recipes. Show each step in order — examiners mark the process as well as the final output.
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A Level lesson
Algorithms on Graphs
Graph algorithms — shortest paths and minimum connectors — need careful labelling of vertices and growing sets.
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Topic Review
Algorithms on Graphs Topic Review
Self-review on graph algorithms: Kruskal, Prim, Dijkstra, and network terminology for D1.
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Topic Review
Algorithms Topic Review
Self-review on algorithmic thinking for Decision maths: sorting, packing, and analysing efficiency with bubble/quick ideas and bin packing.
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Foundation
Angles
Angle facts underpin almost every shape question: vertically opposite angles, angles on a straight line, and angles around a point. The handout drills recogniti…
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IGCSE
Angles
Angle facts underpin almost every shape question: vertically opposite angles, angles on a straight line, and angles around a point. The handout drills recogniti…
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PPT lesson
Angles
Angles PPT lesson — Foundation (CIE Core). These slides walk a lower-secondary class through the key ideas with diagrams and worked examples on screen. This pag…
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Topic Review
Approximations with the Normal Distribution Topic Review
Self-review on Normal approximations to binomial/Poisson with continuity corrections.
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Foundation
Area
Area questions mix rectangles, triangles, parallelograms, trapeziums and compound shapes. Keep units consistent and show how you split a compound region.
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IGCSE
Area
Area questions mix rectangles, triangles, parallelograms, trapeziums and compound shapes. Keep units consistent and show how you split a compound region.
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PPT lesson
Area
Area PPT lesson — Foundation (CIE Core). These slides walk a lower-secondary class through the key ideas with diagrams and worked examples on screen. This page …
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IGCSE
Area and Volume
Mixed area and volume problems combine 2D nets with 3D measures — keep formulas listed and units cubed or squared as required.
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A Level lesson
Assignment
The assignment problem allocates tasks at minimum total cost, typically via Hungarian reduction on a cost matrix.
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Topic Review
Assignment Problems Topic Review
Self-review on the Hungarian algorithm for assignment (cost) matrices in D2.
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Foundation
Averages
Mean, median, mode and range summarise a data set in different ways. Know which average is appropriate and how outliers shift the mean.
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IGCSE
Averages
Mean, median, mode and range summarise a data set in different ways. Know which average is appropriate and how outliers shift the mean.
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PPT lesson
Averages
Averages PPT lesson — Foundation (CIE Core). These slides walk a lower-secondary class through the key ideas with diagrams and worked examples on screen. This p…
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Foundation
Basic Algebra
Basic algebra is about collecting like terms, expanding brackets carefully, and simplifying expressions before solving.
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IGCSE
Basic Algebra
Basic algebra is about collecting like terms, expanding brackets carefully, and simplifying expressions before solving.
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PPT lesson
Basic Algebra
Basic Algebra PPT lesson — Foundation (CIE Core). These slides walk a lower-secondary class through the key ideas with diagrams and worked examples on screen. T…
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Foundation
Basic Numeracy
Numeracy fluency — place value, the four operations, and order of operations — unlocks every later topic. The handout rebuilds that foundation with short, focus…
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IGCSE
Basic Numeracy
Numeracy fluency — place value, the four operations, and order of operations — unlocks every later topic. The handout rebuilds that foundation with short, focus…
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A Level lesson
Binomial Theorem
Binomial expansions at P4 often need the general term or a small-… approximation. Keep validity conditions explicit.
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Topic Review
Binomial Theorem (P2) Topic Review
Self-review binomial expansions for P2.
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Topic Review
Binomial Theorem (P4) Topic Review
Self-review binomial expansions for P4.
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Topic Review
Centre of Mass Topic Review
Self-review on centres of mass of particles, laminas, and composite bodies; toppling vs sliding cues.
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A Level lesson
Centres of Mass
Centre of mass is the balance point. Use symmetry for uniform shapes and mass-weighted averages for composites.
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Foundation
Circle Properties
Circle properties at foundation level focus on radius, diameter, chord language and basic angle facts before full theorem proofs.
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IGCSE
Circle Theorems
Circle theorems give angle relationships: angle at the centre, angles in the same segment, cyclic quadrilaterals, tangent–radius.
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Foundation
Circles
Circle measures use …: circumference … or …, area …. Leave answers in terms of … when asked.
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IGCSE
Circles
Circle measures use …: circumference … or …, area …. Leave answers in terms of … when asked.
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A Level lesson
Collisions
Direct collisions combine conservation of momentum with Newton’s experimental law involving the restitution coefficient ….
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Topic Review
Collisions Topic Review
Self-review on direct impacts, Newton’s experimental law, and kinetic energy loss.
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A Level lesson
Complex Numbers
Complex numbers extend the reals with …. Move fluently between Cartesian and modulus–argument form.
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Topic Review
Complex Numbers Topic Review
Self-review on complex arithmetic, Argand diagrams, moduli/arguments, and solving simple equations in ….
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A Level lesson
Connected Particles
Connected particles share string tension and related accelerations. Draw a separate force diagram for each particle before applying ….
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Foundation
Constructions
Constructions use ruler and compasses only: perpendicular bisectors, angle bisectors, and equilateral triangles.
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IGCSE
Constructions
Constructions use ruler and compasses only: perpendicular bisectors, angle bisectors, and equilateral triangles.
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Topic Review
Continuous Random Variables Topic Review
Self-review on continuous RVs: PDFs, CDFs, expectation, and variance.
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A Level lesson
Coordinate Geometry
Coordinate geometry links algebra to the Cartesian plane: distances, midpoints, gradients and line equations. Use the worksheet for practice and the answers PDF…
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Topic Review
Coordinate Geometry Topic Review
Self-review on straight lines: gradients, equations, midpoints, distances, and parallel/perpendicular conditions.
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A Level lesson
Coordinate Systems
Further coordinate work describes curves with parametric or alternative coordinate descriptions beyond basic Cartesian graphs.
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Topic Review
Coordinate Systems Topic Review
Self-review on further coordinate geometry: parabolas, ellipses/hyperbolas as taught in FP1, and parametric forms.
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A Level lesson
Correlation
Correlation measures the strength of linear association. Always interpret alongside the scatter diagram.
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Topic Review
Correlation and Regression Topic Review
Self-review on scatter diagrams, PMCC, and least-squares regression lines.
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A Level lesson
Critical Path Analysis
Critical path analysis schedules activities with precedence constraints. Early/late times reveal float and the critical path.
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Topic Review
Critical Path Analysis Topic Review
Self-review on activity networks, earliest/latest times, float, and the critical path.
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IGCSE
Cumulative Frequency
Cumulative frequency graphs estimate medians and quartiles and lead to box plots and interquartile range.
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Foundation
Decimals
Decimals connect place value to fractions and percentages. Accuracy of rounding and careful column arithmetic matter in exams.
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IGCSE
Decimals
Decimals connect place value to fractions and percentages. Accuracy of rounding and careful column arithmetic matter in exams.
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IGCSE
Differentiation
Differentiation finds gradients of curves. For polynomials, differentiate term by term: ….
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A Level lesson
Differentiation
Differentiation finds instantaneous rates of change. Differentiate polynomials term by term, then use the gradient function for tangents, normals and stationary…
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A Level lesson
Differentiation
Differentiation finds instantaneous rates of change. Differentiate polynomials term by term, then use the gradient function for tangents, normals and stationary…
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A Level lesson
Differentiation
Differentiation finds instantaneous rates of change. Differentiate polynomials term by term, then use the gradient function for tangents, normals and stationary…
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Topic Review
Differentiation (P1) Topic Review
Self-review differentiation test for AS Pure (P1): techniques and applications expected on this paper band.
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Topic Review
Differentiation (P2) Topic Review
Self-review differentiation test for Pure intermediate (P2): techniques and applications expected on this paper band.
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Topic Review
Differentiation (P3) Topic Review
Self-review differentiation test for Pure advanced (P3): techniques and applications expected on this paper band.
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Topic Review
Differentiation (P4) Topic Review
Self-review differentiation test for Pure advanced (P4): techniques and applications expected on this paper band.
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A Level lesson
Differentiation 2
Advanced differentiation uses product, quotient and chain rules, including trig, exponential and log forms.
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A Level lesson
Discrete Random Variables
A discrete random variable assigns probabilities to distinct outcomes. Use the distribution to find mean and variance.
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Topic Review
Discrete Random Variables Topic Review
Self-review on discrete RVs: probability mass functions, expectation, and variance.
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A Level lesson
Dynamic Programming
Dynamic programming builds an optimum from overlapping subproblems using stage–state tables.
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Topic Review
Dynamic Programming Topic Review
Self-review on stagecoach-style DP: stages, states, and optimal substructure backwards/forwards.
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Foundation
Equations
Solving linear equations means undoing operations to isolate the unknown, keeping both sides balanced.
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IGCSE
Equations
Solving linear equations means undoing operations to isolate the unknown, keeping both sides balanced.
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PPT lesson
Equations
Equations PPT lesson — Foundation (CIE Core). These slides walk a lower-secondary class through the key ideas with diagrams and worked examples on screen. This …
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A Level lesson
Expanding and Factorising
Expanding removes brackets; factorising rebuilds them. These reverse skills drive equations and algebraic fractions.
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Topic Review
Expanding, Factorising and Quadratics Topic Review
Self-review on expanding brackets, factorising, and solving quadratics by factors, completing the square, and the formula.
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A Level lesson
Exponential and Logarithmic Functions
Natural exponential and logarithm as functions: derivatives, integrals, and growth/decay models.
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Topic Review
Exponential and Logarithmic Functions Topic Review
Self-review linking …, …, logs, and their graphs/equations at Pure 3 depth.
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A Level lesson
Exponentials and Logarithms
Exponentials and logarithms are inverse functions. Log laws turn products into sums and unlock exponential equations.
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Topic Review
Exponentials and Logarithms Topic Review
Self-review on exponential and log laws, solving exponential equations, and log graphs — core AS Pure skill.
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A Level lesson
Factor and Remainder Theorems
The factor and remainder theorems connect polynomial values to factors. Division then finishes a full factorisation.
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Topic Review
Factor and Remainder Theorems Topic Review
This Topic Review is a self-review test that complements the Factor and Remainder Theorems lesson worksheet. Work without notes first, then check the answers PD…
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IGCSE
Factors and Primes
Prime factorisation, HCF and LCM unlock fraction work, surds and index laws later.
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Foundation
Factors, Primes, Powers and Roots
Powers and roots sit alongside primes and factors: square numbers, cubes, and estimating roots without a calculator.
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Topic Review
First Order Differential Equations Topic Review
Self-review on first-order DEs: separable variables, integrating factor, and particular solutions.
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A Level lesson
First-order Differential Equations
First-order differential equations are often solved by separating variables, then applying a condition to find the constant.
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A Level lesson
Flows in Networks
Network flows move material from source to sink under capacity constraints. Max-flow equals min-cut capacity.
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Topic Review
Flows in Networks Topic Review
Self-review on maximum flow, cuts, and Ford–Fulkerson / labelling methods.
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A Level lesson
Forces
Force modelling resolves vectors into components. Balance forces for equilibrium or use … when there is acceleration.
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Foundation
Formulas
Formula work means substituting carefully and rearranging (changing the subject) with inverse operations.
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IGCSE
Formulas
Formula work means substituting carefully and rearranging (changing the subject) with inverse operations.
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Foundation
Fractions
Fraction arithmetic — equivalence, addition with common denominators, multiplication and division — appears across algebra and probability.
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IGCSE
Fractions
Fraction arithmetic — equivalence, addition with common denominators, multiplication and division — appears across algebra and probability.
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IGCSE
Functional Mathematics
Functional mathematics applies number skills to real contexts: money, timetables, best buys and interpreting charts.
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IGCSE
Functions
Function notation … means ‘apply the rule’. Composite functions apply rules in order; inverses undo.
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A Level lesson
Functions
Function language — domain, range, composite and inverse — structures later calculus and transformations.
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Topic Review
Functions Topic Review
Self-review on domain/range, composite and inverse functions, and function graphs.
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A Level lesson
Further Complex Numbers
Further complex numbers: de Moivre’s theorem, roots of complex numbers, and Argand loci.
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Topic Review
Further Complex Numbers Topic Review
Self-review on de Moivre, …th roots, and advanced Argand loci.
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A Level lesson
Game Theory
Two-player zero-sum games use payoff matrices, pure and mixed strategies, and expected-value calculations.
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Topic Review
Game Theory Topic Review
Self-review on zero-sum games, play-safe strategies, and mixed-strategy equilibria for … games.
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A Level lesson
Geometric Series
Geometric series scale by a constant ratio each term. Sum formulae and the condition … for an infinite sum are standard.
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Topic Review
Geometric Series Topic Review
Self-review test on geometric sequences and series: nth term, finite sums, and infinite sums when ….
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Foundation
Graphical Representation of Data
Choosing and reading charts — bar charts, pie charts, line graphs — is about clear scales and what each representation emphasises.
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A Level lesson
Graphical Representation of Data
Statistical diagrams communicate distribution shape and spread — histograms, box plots and cumulative frequency curves.
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PPT lesson
Graphical Representation of Data
Graphical Representation of Data PPT lesson — Foundation (CIE Core). These slides walk a lower-secondary class through the key ideas with diagrams and worked ex…
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Topic Review
Graphical Representation of Data Topic Review
Self-review on charts for S1: histograms, stem-and-leaf, box plots, and cumulative frequency.
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Foundation
Graphs
Graphs turn equations into pictures. Know intercepts, gradient, and how to plot from a table of values.
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IGCSE
Graphs
Graphs turn equations into pictures. Know intercepts, gradient, and how to plot from a table of values.
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PPT lesson
Graphs
Graphs PPT lesson — Foundation (CIE Core). These slides walk a lower-secondary class through the key ideas with diagrams and worked examples on screen. This pag…
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A Level lesson
Graphs and Transformations
Graphs of standard functions and transformations — translations, stretches and reflections — are examined heavily at AS.
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Topic Review
Graphs and Transformations Topic Review
Self-review on sketching standard graphs and applying transformations — AS Pure foundation.
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Topic Review
Handling Data 2
Handling Data 2 revision strengthens averages and reading statistical charts.
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Topic Review
Handling Data 3
Handling Data 3 revision includes cumulative frequency, quartiles and comparing distributions.
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Topic Review
Handling Data 4
Handling Data 4 revision mixes histograms, probability language and exam-style data problems.
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IGCSE
Histograms
Histograms use frequency density when class widths vary: area of each bar represents frequency.
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IGCSE
Indices
Index laws compress repeated multiplication: …, …, …, ….
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A Level lesson
Indices
Index laws rewrite products and quotients of powers. Fractional and negative indices connect roots and reciprocals.
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Topic Review
Indices and Surds Topic Review
Self-review on index laws, negative/fractional indices, and simplifying surds including rationalising denominators.
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Foundation
Inequalities
Inequalities use …. Solving mirrors equations, except multiplying/dividing by a negative reverses the sign.
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IGCSE
Inequalities
Inequalities use …. Solving mirrors equations, except multiplying/dividing by a negative reverses the sign.
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A Level lesson
Inequalities
Further inequalities often involve rational expressions. Critical values and sign charts organise the solution set.
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Topic Review
Inequalities Topic Review
Self-review on polynomial and rational inequalities, including critical values and sign charts.
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A Level lesson
Integration
Integration reverses differentiation. Raise powers and divide for polynomials; evaluate definite integrals between limits.
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Topic Review
Integration (P1) Topic Review
Self-review integration test for AS Pure (P1): antiderivatives, definite integrals, and area.
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Topic Review
Integration (P2) Topic Review
Self-review integration test for Pure intermediate (P2): antiderivatives, definite integrals, and area.
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A Level lesson
Integration 1
Integration techniques begin with standard forms and reverse chain-rule recognition.
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Topic Review
Integration 1 Topic Review
Self-review on core integration skills before advanced techniques: powers, standard forms, and definite area problems.
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A Level lesson
Integration 2
Further integration uses substitution and integration by parts.
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Topic Review
Integration 2 Topic Review
Self-review on further integration: by parts, trig identities, partial fractions, and harder definite evaluations.
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A Level lesson
Kinematics
Kinematics describes motion with SUVAT (constant acceleration) or calculus when acceleration varies.
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A Level lesson
Kinematics
Kinematics describes motion with SUVAT (constant acceleration) or calculus when acceleration varies.
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Topic Review
Kinematics (M1) Topic Review
M1 self-review on particle kinematics in a straight line and simple 2D motion with constant acceleration.
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Topic Review
Kinematics (M2) Topic Review
M2 self-review extending kinematics with projectiles links and calculus-based variable acceleration.
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A Level lesson
Linear Programming
Linear programming optimises a linear objective under linear inequalities. Graph the feasible region and test vertices.
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A Level lesson
Linear Programming
Linear programming optimises a linear objective under linear inequalities. Graph the feasible region and test vertices.
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Topic Review
Linear Programming (D1) Topic Review
Self-review linear programming for D1: formulation and graphical solution.
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Topic Review
Linear Programming (D2) Topic Review
Self-review linear programming for D2: formulation and graphical solution.
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A Level lesson
Maclaurin and Taylor Series
Maclaurin series expand functions about 0 using successive derivatives and factorial denominators.
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Topic Review
Maclaurin and Taylor Series Topic Review
Self-review on Maclaurin/Taylor expansions, validity, and approximating functions.
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A Level lesson
Matchings
Bipartite matching pairs two sets such as people and tasks. Alternating paths improve incomplete matchings.
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Topic Review
Matchings Topic Review
Self-review on bipartite matchings, alternating paths, and the maximum matching algorithm.
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Topic Review
Mathematical Models in Mechanics Topic Review
Self-review on modelling assumptions: particles, light rods, smooth surfaces, and g as constant.
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Topic Review
Mathematical Models in Statistics Topic Review
Self-review on statistical modelling assumptions and choosing distributions.
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A Level lesson
Matrix Algebra
Matrices encode linear transformations and simultaneous equations. Master multiplication order, determinants and … inverses.
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Topic Review
Matrix Algebra Topic Review
Self-review on … matrices: arithmetic, determinants, inverses, and linear transformations.
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A Level lesson
Measures of Dispersion
Dispersion measures spread: range, IQR, variance and standard deviation. Know which react strongly to outliers.
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Topic Review
Measures of Dispersion Topic Review
Self-review on range, IQR, variance, and standard deviation (including coding).
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A Level lesson
Measures of Location
Measures of location summarise a typical value: mean, median and mode each behave differently under skew.
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Topic Review
Measures of Location Topic Review
Self-review on mean, median, mode, and coded means for raw and frequency data.
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A Level lesson
Moments
Moments measure turning effect: force times perpendicular distance from the pivot. Rigid-body equilibrium needs force and moment balance.
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Topic Review
Moments Topic Review
Self-review on moments, tipping/turning, and equilibrium of rigid bodies in a plane.
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A Level lesson
Momentum and Impulse
Momentum … changes when an impulse acts. Impulse equals change in momentum; momentum is conserved when external impulse is zero.
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Topic Review
Momentum and Impulse Topic Review
Self-review on impulse–momentum and conservation of momentum in one dimension.
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A Level lesson
Newton's Laws of Motion
Newton’s laws connect force and motion. Clear free-body diagrams and consistent SI units make … reliable.
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Topic Review
Newton's Laws of Motion and Connected Particles Topic Review
Self-review on Newton’s laws, pulleys, and connected particles with a common magnitude of acceleration.
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Topic Review
Number 1
Number 1 revision rebuilds place value, order of operations and core arithmetic fluency.
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Topic Review
Number 2
Number 2 revision focuses on fractions, decimals and percentages.
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Topic Review
Number 3
Number 3 revision covers ratio, proportion and standard form.
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Topic Review
Number 4
Number 4 revision mixes bounds, error intervals and multi-topic number problems.
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A Level lesson
Numerical Methods
Numerical methods approximate roots: change of sign, decimal search/bisection, and iterative formulae.
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Topic Review
Numerical Methods Topic Review
Self-review on locating roots numerically: change of sign, iteration, and Newton–Raphson where taught.
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Topic Review
Numerical Solution of Equations Topic Review
Self-review on numerical root-finding in Further Pure: iteration, Newton–Raphson, and error/interval arguments.
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A Level lesson
Parametric Functions
Parametric equations define … and … via a parameter. Differentiate with ….
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Topic Review
Parametric Functions Topic Review
Self-review on parametric curves: converting forms, …, and tangent problems.
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A Level lesson
Partial Fractions
Partial fractions decompose rational functions into simpler pieces for integration or series work.
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Topic Review
Partial Fractions Topic Review
Self-review on decomposing rational functions and linking to integration or binomial expansions.
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Foundation
Percentages
Percentages are hundredths. Multipliers turn increase/decrease and reverse-percentage problems into one-line calculations.
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IGCSE
Percentages
Percentages are hundredths. Multipliers turn increase/decrease and reverse-percentage problems into one-line calculations.
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A Level lesson
Polar Coordinates
Polar coordinates … describe curves such as cardioids and roses. Convert to Cartesian when recognition helps.
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Topic Review
Polar Coordinates Topic Review
Self-review on polar curves: converting forms, sketching, and area ….
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Foundation
Polygons
Polygon angle sums and regular-polygon exterior angles are standard: exterior angles of any convex polygon sum to ….
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IGCSE
Polygons
Polygon angle sums and regular-polygon exterior angles are standard: exterior angles of any convex polygon sum to ….
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PPT lesson
Polygons
Polygons PPT lesson — Foundation (CIE Core). These slides walk a lower-secondary class through the key ideas with diagrams and worked examples on screen. This p…
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Foundation
Probability
Probability measures likelihood from 0 to 1. Listing outcomes carefully and using fractions in lowest terms keeps marks safe.
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IGCSE
Probability
Probability measures likelihood from 0 to 1. Listing outcomes carefully and using fractions in lowest terms keeps marks safe.
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A Level lesson
Probability
A-level probability develops trees, Venn methods, conditional probability and independence.
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Topic Review
Probability Topic Review
Self-review on basic probability, Venn/tree diagrams, mutually exclusive and independent events.
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A Level lesson
Projectiles
Projectile motion splits into horizontal constant-velocity and vertical constant-acceleration components.
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Topic Review
Projectiles Topic Review
Self-review on projectile motion under constant gravity with no air resistance.
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IGCSE
Proof
Mathematical proof needs clear statements, defined starting points, and reasons — algebra identities and geometric angle chains are typical IGCSE proofs.
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A Level lesson
Proof by Induction
Induction proves a statement for all integers …: base case, inductive assumption, inductive step, conclusion.
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Topic Review
Proof by Induction Topic Review
Self-review on mathematical induction for sums, divisibility, and inequalities.
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IGCSE
Proportion
Proportion problems scale quantities. Direct and inverse proportion equations let you find the constant … from one pair of values.
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Foundation
Pythagoras
Pythagoras’ theorem links the three sides of a right-angled triangle: … with … the hypotenuse.
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IGCSE
Pythagoras
Pythagoras’ theorem links the three sides of a right-angled triangle: … with … the hypotenuse.
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PPT lesson
Pythagoras
Pythagoras PPT lesson — Foundation (CIE Core). These slides walk a lower-secondary class through the key ideas with diagrams and worked examples on screen. This…
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IGCSE
Quadratic Equations
Quadratics solve by factorising, completing the square, or the quadratic formula. Sketching links roots to intercepts.
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A Level lesson
Quadratics
Quadratics appear as equations, inequalities and graphs. Factorising, completing the square and the formula are the three standard routes.
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Foundation
Ratio and Proportion
Ratios compare quantities; proportion scales them. Sharing in a ratio and unitary method are core exam skills.
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IGCSE
Ratio and Proportion
Ratios compare quantities; proportion scales them. Sharing in a ratio and unitary method are core exam skills.
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PPT lesson
Ratio and Proportion
Ratio and Proportion PPT lesson — Foundation (CIE Core). These slides walk a lower-secondary class through the key ideas with diagrams and worked examples on sc…
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IGCSE
Rearranging Formulas
Changing the subject is inverse-operation discipline — especially with fractions, roots and formulas with the new subject on both sides.
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IGCSE
Recurring Decimals and Surds
Recurring decimals convert to fractions via powers of 10; surds simplify by extracting square factors.
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A Level lesson
Regression
Least-squares regression fits … for prediction near the observed data range.
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Foundation
Rounding
Rounding and estimation control accuracy. Significant figures and decimal places are not the same — read the question.
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IGCSE
Rounding
Rounding and estimation control accuracy. Significant figures and decimal places are not the same — read the question.
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A Level lesson
Route Inspection
Route inspection (Chinese Postman) finds a shortest closed walk covering every edge by pairing odd-degree vertices optimally.
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Topic Review
Route Inspection Topic Review
Self-review on the Chinese Postman problem: odd vertices, pairings, and shortest closed tours.
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Topic Review
Sampling and Hypothesis Tests Topic Review
Self-review on sampling ideas and hypothesis tests for means/proportions as taught in S2.
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Topic Review
Second Order Differential Equations Topic Review
Self-review on linear second-order DEs with constant coefficients: auxiliary equation and particular integrals.
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A Level lesson
Second-order Differential Equations
Second-order linear DEs with constant coefficients: auxiliary equation, complementary function, and particular integral.
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Foundation
Sequences
Sequences follow rules: term-to-term or position-to-term (…th term). Linear sequences have a constant difference.
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Topic Review
Sequences and Arithmetic Series Topic Review
Self-review on arithmetic sequences: nth term, sum formulae, and worded progression problems.
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A Level lesson
Sequences and Series
Arithmetic and geometric sequences have closed …th-term formulae and sum formulae. Identify the type from the common difference or ratio.
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A Level lesson
Series
Further series techniques go beyond AS arithmetic/geometric sums — induction, standard sums and telescoping.
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A Level lesson
Series
Further series techniques go beyond AS arithmetic/geometric sums — induction, standard sums and telescoping.
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Topic Review
Series (FP1) Topic Review
FP1 self-review on series: standard summation formulae, method of differences, and inductive proofs of sums.
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Topic Review
Series (FP2) Topic Review
FP2 self-review emphasising Maclaurin/Taylor-style series and convergence alongside summation techniques.
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Foundation
Sets
Set notation — …, …, …, …, … — describes collections of objects. Venn diagrams make intersections visible.
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IGCSE
Sets
Set notation — …, …, …, …, … — describes collections of objects. Venn diagrams make intersections visible.
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Topic Review
Shape 1
Shape 1 revision covers angle facts and basic polygon properties.
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Topic Review
Shape 2
Shape 2 revision develops area and perimeter of standard and compound shapes.
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Topic Review
Shape 3
Shape 3 revision includes circles, arcs and sectors.
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Topic Review
Shape 4
Shape 4 revision strengthens Pythagoras and right-angled trigonometry.
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Topic Review
Shape 5
Shape 5 revision covers transformations and similarity.
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Topic Review
Shape 6
Shape 6 revision covers volume and surface area of prisms and cylinders.
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Topic Review
Shape 7
Shape 7 revision mixes constructions, loci and introductory vectors — diagram quality matters.
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Topic Review
Shape 8
Shape 8 revision consolidates harder geometry: circle theorems, non-right trig and mixed problems.
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Foundation
Similar Shapes
Similar shapes have the same angles and proportional sides. This Foundation summary explains length scale factors and how to find missing sides; use the workshe…
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PPT lesson
Similar Shapes
Similar Shapes PPT lesson — Foundation (CIE Core). These slides walk a lower-secondary class through the key ideas with diagrams and worked examples on screen. …
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IGCSE
Similar Shapes 2
Similarity scales lengths by …, areas by …, volumes by …. Matching angles and proportional sides define similarity.
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Foundation
Simultaneous Equations
Two equations, two unknowns: elimination or substitution. Check by substituting back into both originals.
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IGCSE
Simultaneous Equations
Two equations, two unknowns: elimination or substitution. Check by substituting back into both originals.
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A Level lesson
Simultaneous Equations
Simultaneous equations model two constraints. Elimination and substitution are the algebraic workhorses; graphs show the intersection.
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PPT lesson
Simultaneous Equations
Simultaneous Equations PPT lesson — Foundation (CIE Core). These slides walk a lower-secondary class through the key ideas with diagrams and worked examples on …
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IGCSE
Simultaneous Equations 2
Harder simultaneous systems may need scaling both equations or handling fractional coefficients before eliminating.
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Topic Review
Simultaneous Equations Topic Review
Self-review on solving linear and linear–quadratic simultaneous systems.
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IGCSE
Sine and Cosine Rules
For non-right triangles: sine rule …, cosine rule ….
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Foundation
Speed and Travel Graphs
Distance–time and speed–time graphs tell stories of journeys: gradient and area under the graph carry the meaning.
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IGCSE
Speed and Travel Graphs
Distance–time and speed–time graphs tell stories of journeys: gradient and area under the graph carry the meaning.
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PPT lesson
Speed and Travel Graphs
Speed and Travel Graphs PPT lesson — Foundation (CIE Core). These slides walk a lower-secondary class through the key ideas with diagrams and worked examples on…
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IGCSE
Standard Form
Standard form … with … handles very large or small numbers cleanly.
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A Level lesson
Statics
Rigid-body statics needs both force equilibrium and moment equilibrium about a sensible point.
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A Level lesson
Statics of a Particle
Statics of a particle: forces in equilibrium so the vector sum is zero. Resolve into two perpendicular directions.
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Topic Review
Statics of a Particle Topic Review
Self-review on particle equilibrium under concurrent forces, including friction.
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Topic Review
Statics Topic Review
Self-review on rigid-body statics: forces, moments, and reactions for ladders and frameworks as taught in M2.
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IGCSE
Straight Line Graphs
Straight-line graphs encode gradient and intercept. Parallel lines share …; perpendicular lines have ….
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A Level lesson
Surds
Surds are exact irrational roots. Simplify by extracting square factors and rationalise denominators when required.
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Foundation
Symmetry and Transformations
Line and rotational symmetry describe balance in shapes; linking them to reflections and rotations deepens transformation fluency.
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Topic Review
The Binomial Distribution Topic Review
Self-review on …: probabilities, mean/variance, and cumulative tables.
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A Level lesson
The Binomial Theorem
The binomial theorem expands … for positive integer …, and extends to fractional/negative … with a validity range.
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A Level lesson
The Circle
Circle equations: centre–radius form and the expanded form. Completing the square recovers centre and radius.
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Topic Review
The Circle Topic Review
Self-review on the circle equation, centre–radius form, intersections with lines, and tangent conditions.
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Foundation
The Metric System
The metric system links length, mass and capacity by powers of ten. This Foundation summary reviews the common conversions you need in worded measures questions…
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A Level lesson
The Normal Distribution
The normal distribution is continuous and symmetric. Standardise to … for tables or calculator work.
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Topic Review
The Normal Distribution Topic Review
Self-review on the Normal model: standardisation and table/calculator probabilities.
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Topic Review
The Poisson Distribution Topic Review
Self-review on …: probabilities, mean=variance, and approximating binomials.
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IGCSE
Transformations
The four plane transformations are translation, reflection, rotation and enlargement. Describe each with the full set of required details.
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IGCSE
Transformations of Graphs
Graph transformations move …: translations, stretches and reflections using function notation.
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A Level lesson
Transformations of Graphs
Function transformations combine translations and stretches. Apply them consistently and track key points.
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Topic Review
Transformations of Graphs Topic Review
Self-review on translations, stretches, and reflections of ….
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A Level lesson
Transportation
Transportation problems ship supply to demand at minimum cost. Construct a basic feasible solution, then improve it.
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Topic Review
Transportation Problems Topic Review
Self-review on balanced transportation problems: northwest corner / Vogel starts and improvement via shadow costs.
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A Level lesson
Travelling Salesman Problem
The travelling salesman problem seeks a shortest Hamiltonian tour. Upper and lower bounds frame the optimum on small networks.
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Topic Review
Travelling Salesman Problem Topic Review
Self-review on TSP: classical vs practical, nearest neighbour, and lower bounds from MST ideas.
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IGCSE
Tree Diagrams
Tree diagrams organise multi-stage probability. Multiply along branches; add across mutually exclusive complete paths.
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IGCSE
Trigonometric Functions
Beyond right triangles: …, …, … as functions of any angle, with graphs and exact values for key angles.
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Foundation
Trigonometry
Right-angled trigonometry uses …, …, … with opposite, adjacent and hypotenuse. Label the triangle before choosing a ratio.
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IGCSE
Trigonometry
Right-angled trigonometry uses …, …, … with opposite, adjacent and hypotenuse. Label the triangle before choosing a ratio.
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A Level lesson
Trigonometry
A-level trigonometry covers identities, equations and graphs beyond right-angled triangle ratios.
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A Level lesson
Trigonometry
A-level trigonometry covers identities, equations and graphs beyond right-angled triangle ratios.
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Topic Review
Trigonometry (P2) Topic Review
Self-review trigonometry for P2: identities and equations at this Pure depth.
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Topic Review
Trigonometry (P3) Topic Review
Self-review trigonometry for P3: identities and equations at this Pure depth.
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IGCSE
Trigonometry in Three Dimensions
3D trigonometry combines Pythagoras in space with right-angled trig in carefully chosen planes.
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IGCSE
Vectors
Vectors describe movement with both size and direction. This Vectors summary pairs the IGCSE Vectors worksheet with its answers PDF: practise from the sheet (di…
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A Level lesson
Vectors
A-level vectors extend column vectors into magnitude, unit vectors, scalar product and geometry.
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PPT lesson
Vectors — Collinear points
IGCSE Additional Mathematics (CIE 0606) PPT lesson on proving points are collinear with vectors. This summary outlines the method, notation, and a typical exam-…
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Topic Review
Vectors and Forces Topic Review
Self-review on forces as vectors: resultants, components, and equilibrium in a plane.
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PPT lesson
Vectors in a triangle
IGCSE Additional Mathematics (CIE 0606) PPT lesson on vectors in a triangle and finding an intersection point P. Use this page to revise the vector geometry set…
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Topic Review
Vectors Topic Review
Self-review on 3D vectors: magnitude, scalar product, equations of lines, and intersections.
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IGCSE
Volume
Volume measures space in 3D: prisms (including cylinders) use area of cross-section × length.
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Topic Review
Work and Energy Topic Review
Self-review on work, kinetic/potential energy, and the work–energy principle.
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A Level lesson
Work, Energy and Power
Work–energy methods relate force and motion without always finding acceleration. Power is the rate of doing work.
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