Mathematics
IGCSE · 33 topics available
Chapter 1 · Number
Types of Number and Sets
Learn to classify numbers as primes, integers, rationals and irrationals, find HCF and LCM, and use set notation like union and intersection.
OpenFractions, Decimals and Percentages
Convert between fractions, decimals and percentages, and add, subtract, multiply, divide and compare them with confidence.
OpenRatio and Proportion
Simplify ratios, share amounts in a given ratio, and solve direct and inverse proportion problems including map scales.
OpenIndices and Standard Form
Apply the laws of indices, work with zero and negative powers, and write large and small numbers in standard form.
OpenRounding, Estimation and Limits of Accuracy
Round to decimal places and significant figures, estimate calculations, and find the upper and lower bounds of measurements.
OpenPercentage Change and Reverse Percentage
Increase and decrease quantities by percentages, find percentage change, and use reverse percentages to find original values.
OpenHCF, LCM and Primes
Prime factorisation used to find the highest common factor and lowest common multiple, and to solve grouping and coincidence problems.
OpenChapter 2 · Algebra and Graphs
Algebraic Manipulation
Expanding brackets, factorising, index laws and simplifying expressions and fractions — the core toolkit of IGCSE algebra.
OpenSolving Linear Equations and Inequalities
Balance both sides to solve linear equations, and apply the sign-reversal rule for inequalities involving negative numbers.
OpenSolving Quadratic Equations
Solve ax² + bx + c = 0 by factorising or the quadratic formula, and use the discriminant to count real roots.
OpenSimultaneous Equations
Solve two equations in two unknowns by elimination or substitution — the pair of values that satisfies both.
OpenSequences
Term-to-term and nth-term rules for linear, geometric and special sequences such as squares and Fibonacci.
OpenFunctions
How to evaluate f(x), find inverse and composite functions, and state domain and range.
OpenGraphs of Functions
Recognising and using graphs: intercepts, gradient, parabolas, turning points and intersections.
OpenChapter 3 · Coordinate Geometry
Chapter 4 · Geometry
Angles and Polygons
Use interior and exterior angle rules for triangles, quadrilaterals and regular polygons.
OpenCircle Theorems
Apply key circle theorems: centre and circumference angles, semicircles, cyclic quadrilaterals and tangents.
OpenSimilar and Congruent Shapes
Congruent shapes match exactly; similar shapes share the same angles with sides in a fixed ratio (scale factor).
OpenConstructions and Bearings
Bearings are three-figure directions measured clockwise from North; ruler-and-compass constructions build bisectors and loci accurately.
OpenChapter 5 · Mensuration
Perimeter and Area
Perimeter is the distance around a shape; area is the space inside, found with standard formulas for common 2-D shapes.
OpenSurface Area and Volume
Volume measures space inside a solid (cubic units); surface area is the total area of its faces and curved surfaces (square units).
OpenArc Length and Sector Area
An arc and a sector are fractions theta/360 of a circle, giving arc length = (theta/360)*2*pi*r and sector area = (theta/360)*pi*r*r.
OpenChapter 6 · Trigonometry
Pythagoras and Right-Angled Trigonometry
Pythagoras (c^2 = a^2 + b^2) finds sides of right triangles; SOH CAH TOA links sides and angles.
OpenSine and Cosine Rules
Solve non-right-angled triangles with the sine and cosine rules, and find area using ½ ab sin C.
OpenTrigonometric Graphs
Recognise and sketch y = sin x, y = cos x and y = tan x, including period, amplitude and key values.
OpenChapter 7 · Transformations and Vectors
Chapter 8 · Probability
Chapter 9 · Statistics
Averages and Range
Find and compare the mean, median and mode, and measure spread with the range, for lists, frequency tables and grouped data.
OpenStatistical Diagrams
Read and draw bar charts, pictograms, pie charts and stem-and-leaf diagrams, and choose the right diagram to display data.
OpenCumulative Frequency and Histograms
Build cumulative frequency curves to estimate the median and quartiles, and draw histograms using frequency density for unequal class widths.
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