CIE · IGCSE · Mathematics
CIE IGCSE Mathematics Syllabus
The complete CIE IGCSE Mathematics specification mapped to 403 topics. Click any topic for free revision notes and practice questions.
Algebra
Algebraic fractions
0 Qs
Algebraic fractions — simplification, addition, subtraction, multiplication and division
20 Qs⚡ Practice
Composite and inverse functions
0 Qs
Direct and inverse proportion (algebraic and graphical)
0 Qs
Exponential and logarithmic functions
0 Qs
Factorisation — common factors, difference of two squares, trinomials
0 Qs
Factorisation and expansion of brackets
20 Qs⚡ Practice
Functions — notation, composite functions and inverse functions
0 Qs
Functions, domain and range
0 Qs
Indices and index laws in algebraic contexts
0 Qs
Indices and rules of indices
20 Qs⚡ Practice
Inequalities and regions on a graph
0 Qs
Inequalities and regions on a number line and coordinate plane
20 Qs⚡ Practice
Introduction to algebra — substitution and formulating expressions
0 Qs
Introduction to algebra and algebraic notation
0 Qs
Linear equations and inequalities
0 Qs
Linear equations and linear inequalities
0 Qs
Linear programming
0 Qs
Quadratic equations — factorisation, completing the square, quadratic formula
0 Qs
Quadratic expressions and equations
0 Qs
Rearranging and transforming formulae
0 Qs
Sequences — nth term, arithmetic and geometric sequences, patterns
0 Qs
Sequences and nth term rules
0 Qs
Simplification and manipulation of expressions
0 Qs
Simplification of algebraic expressions — collecting like terms, expanding brackets
0 Qs
Simultaneous linear equations
0 Qs
Substitution and evaluation of expressions and formulae
0 Qs
The quadratic formula and completing the square
0 Qs
Algebra and graphs
Algebraic fractions
0 Qs
Area under a curve
0 Qs
Distance–time and speed–time graphs
0 Qs
Function notation, composite and inverse functions
0 Qs
Gradient of a curve and rates of change
0 Qs
Graphs of other functions (cubic, reciprocal, exponential)
0 Qs
Graphs of quadratic functions and their properties
0 Qs
Inequalities and regions on a graph
0 Qs
Introduction to algebra, algebraic notation and substitution
0 Qs
Linear equations and linear inequalities
0 Qs
Linear graphs — gradient, intercept, equation of a straight line
0 Qs
Proportion: direct and inverse proportion
0 Qs
Quadratic expressions, equations and factorisation
0 Qs
Sequences (nth term of arithmetic and geometric sequences)
0 Qs
Simplification, expansion of brackets and factorisation
0 Qs
Sketching and interpreting graphs
0 Qs
The quadratic formula and completing the square
20 Qs⚡ Practice
Transformations of graphs and functions
0 Qs
Algebra and Graphs
Algebraic fractions — simplification and the four operations
0 Qs
Area under a graph
0 Qs
Coordinates and straight-line graphs — gradient, intercept and equation y = mx + c
0 Qs
Direct and inverse proportion — algebraic and graphical
Drawing and interpreting graphs of linear, quadratic, cubic, reciprocal and exponential functions
0 Qs
Expanding brackets and factorising algebraic expressions
0 Qs
Function notation, composite functions and inverse functions
0 Qs
Gradient of a curve and rate of change (tangents)
Graph transformations — translations, reflections and stretches
0 Qs
Graphs of inequalities — regions in the Cartesian plane
0 Qs
Interpreting and using distance–time and speed–time graphs
0 Qs
Length and midpoint of a line segment
Linear inequalities and number lines
0 Qs
Parallel and perpendicular lines
0 Qs
Quadratic expressions — factorising, completing the square
0 Qs
Rearranging and changing the subject of a formula
0 Qs
Recognising and sketching graphs of functions (linear, quadratic, cubic, reciprocal, exponential, trigonometric)
0 Qs
Sequences — nth term rules, arithmetic and geometric sequences
0 Qs
Setting up and solving linear equations
0 Qs
Simplifying expressions — collecting like terms and laws of indices
0 Qs
Simultaneous equations — one linear and one non-linear
0 Qs
Simultaneous linear equations
Solving quadratic equations (factorising, quadratic formula, completing the square)
Writing and evaluating algebraic expressions
0 Qs
Algebraic fractions
simplification, addition, subtraction, multiplication and division
0 Qs
Algebraic manipulation
simplification, expansion of brackets, factorisation
0 Qs
Angle properties
angles on a line, at a point, in triangles and polygons, vertically opposite angles
0 Qs
Angles in parallel lines
alternate, corresponding and co-interior angles
0 Qs
Averages and measures of spread
mean, median, mode, range, interquartile range for listed and grouped data
0 Qs
Combined events
sample space diagrams, Venn diagrams, addition rule for mutually exclusive events
0 Qs
Coordinate geometry
Coordinates and midpoints in two dimensions
0 Qs
Coordinates in two dimensions
0 Qs
Equation of a straight line
0 Qs
Equation of a straight line through two points or given gradient and point
0 Qs
Gradient and equation of a straight line
0 Qs
Gradient of a line segment
0 Qs
Gradient of a straight line and parallel/perpendicular lines
0 Qs
Length and midpoint of a line segment
0 Qs
Midpoint of a line segment, length of a line segment
0 Qs
Parallel and perpendicular lines
0 Qs
Coordinate Geometry
Equation of a circle centred at the origin
Coordinates in two dimensions and straight-line graphs
gradient, y-intercept, equation y = mx + c
0 Qs
Cumulative frequency
tables, curves, median, quartiles and interquartile range
Distance–time graphs and speed–time graphs
interpretation and calculation
Fractions, decimals and percentages
conversions and equivalences
0 Qs
Geometry
Angle properties — angles on a line, at a point, vertically opposite angles
0 Qs
Angle properties — angles on a straight line, at a point, vertically opposite, in triangles and polygons
0 Qs
Angle properties of lines, triangles and polygons
0 Qs
Angle properties of triangles and polygons
0 Qs
Angle properties of triangles and quadrilaterals
20 Qs⚡ Practice
Angles — types, properties and calculations
0 Qs
Angles and properties of polygons (interior and exterior angles)
40 Qs⚡ Practice
Angles in parallel lines — alternate, corresponding and co-interior angles
0 Qs
Angles in parallel lines (alternate, corresponding, co-interior)
0 Qs
Bearings
0 Qs
Circle theorems and angle properties of circles
Circle theorems and properties of circles
0 Qs
Congruence and similarity
0 Qs
Congruence and similarity — conditions and applications
Congruence and similarity — shapes, areas and volumes
0 Qs
Construction — triangles, quadrilaterals, perpendicular and angle bisectors
0 Qs
Constructions and loci
20 Qs⚡ Practice
Geometric constructions using ruler and compass
0 Qs
Interior and exterior angles of regular and irregular polygons
0 Qs
Loci
0 Qs
Loci and constructions
0 Qs
Nets, plans and elevations of 3D shapes
20 Qs⚡ Practice
Nets, plans and elevations of 3D solids
Properties and classification of triangles, quadrilaterals and polygons
0 Qs
Properties and constructions of 2D shapes (triangles, quadrilaterals, polygons)
0 Qs
Properties of circles — angles, chords, tangents, cyclic quadrilaterals and circle theorems
0 Qs
Properties of circles and angle theorems
0 Qs
Properties of quadrilaterals and other polygons
0 Qs
Scale drawings and bearings
Symmetry — line and rotational symmetry
0 Qs
Symmetry — line and rotational symmetry of 2D shapes
0 Qs
Symmetry (line and rotational)
0 Qs
Graphs
Area under a curve (estimation using trapezium rule or counting squares)
20 Qs⚡ Practice
Area under a curve and kinematics graphs
0 Qs
Coordinates in two dimensions
0 Qs
Distance–time and speed–time graphs
0 Qs
Drawing and interpreting other graphs — cubic, reciprocal, exponential
0 Qs
Drawing and interpreting quadratic graphs
0 Qs
Drawing, reading and interpreting straight-line graphs; gradient and y-intercept
20 Qs⚡ Practice
Equation of a straight line (y = mx + c) and parallel/perpendicular lines
20 Qs⚡ Practice
Gradients of curves and tangents
0 Qs
Plotting and interpreting cubic, reciprocal and exponential graphs
0 Qs
Plotting and interpreting quadratic graphs
40 Qs⚡ Practice
Plotting and interpreting straight-line graphs
0 Qs
Recognising and sketching graph types from their equations
0 Qs
Sketching and recognising graphs of functions
0 Qs
Solving equations graphically
0 Qs
Tangents and estimation of gradient of a curve
0 Qs
Transformations of graphs
0 Qs
Graphs of other functions
cubic, reciprocal, exponential and trigonometric
0 Qs
Graphs of quadratic functions
plotting, interpreting and identifying key features
0 Qs
Independent and dependent events
multiplication rule
0 Qs
Linear inequalities
solving and representing on a number line or graph
Linear programming
graphical representation of linear inequalities in two variables
0 Qs
Matrices
Determinant and inverse of a 2×2 matrix
0 Qs
Determinant, inverse matrix and solving simultaneous equations using matrices
0 Qs
Matrix multiplication
0 Qs
Matrix notation, order, addition, subtraction and multiplication
0 Qs
Matrix notation, order, addition, subtraction and scalar multiplication
0 Qs
Matrix operations (addition, subtraction, multiplication)
0 Qs
notation, addition, subtraction, multiplication, determinant, inverse of a 2×2 matrix
0 Qs
Transformation matrices
0 Qs
Transformations represented by matrices and combined transformations
0 Qs
Transformations using matrices
0 Qs
Mensuration
Arc length and sector area
0 Qs
Area and circumference of circles, arcs and sectors
0 Qs
Areas and volumes of similar shapes
0 Qs
Circumference and area of circles and sectors
0 Qs
Compound shapes — areas and volumes
0 Qs
Perimeter and area of 2D shapes — rectangles, triangles, parallelograms, trapeziums, circles
0 Qs
Perimeter and area of plane figures (triangles, quadrilaterals, circles, compound shapes)
0 Qs
Perimeter and area of plane shapes
0 Qs
Similar shapes — areas and volumes of similar figures
0 Qs
Surface area and volume of compound solids
0 Qs
Surface area and volume of prisms, cylinders and composite solids
0 Qs
Surface area and volume of prisms, cylinders, pyramids, cones and spheres
0 Qs
Surface area and volume of prisms, pyramids, cylinders, cones and spheres
0 Qs
Surface area and volume of pyramids, cones and spheres
20 Qs⚡ Practice
Volume and surface area of compound 3D shapes
Money
profit, loss, discount, tax, currency conversions
0 Qs
Number
Bounds and limits of accuracy
0 Qs
Direct and inverse proportion
0 Qs
Directed numbers
0 Qs
Estimation and rounding
0 Qs
Estimation and rounding (decimal places and significant figures)
0 Qs
Estimation, rounding and significant figures
0 Qs
Estimation, rounding, significant figures and decimal places
0 Qs
Exponential growth and decay
0 Qs
Four operations and order of operations
0 Qs
Fractions, decimals and percentages
0 Qs
Fractions, decimals and percentages — conversions and equivalence
0 Qs
Fractions, decimals and percentages — conversions and equivalences
0 Qs
Indices and index notation (positive, negative, zero and fractional)
0 Qs
Indices and powers (positive, negative, zero and fractional)
0 Qs
Limits of accuracy and bounds
0 Qs
Ordering and comparing numbers
0 Qs
Percentage calculations including reverse percentages and percentage change
0 Qs
Percentages — percentage change, reverse percentage, profit and loss
20 Qs⚡ Practice
Percentages and percentage change
0 Qs
Percentages including percentage change, reverse percentage and compound interest
0 Qs
Personal and household finance
0 Qs
Personal and household finance (bills, wages, currency exchange)
0 Qs
Personal and household finance (profit, loss, discount, tax, simple and compound interest)
0 Qs
Powers, roots and indices
0 Qs
Prime factors, highest common factor (HCF) and lowest common multiple (LCM)
0 Qs
Prime factors, LCM and HCF
0 Qs
Rates — speed, distance, time; unit conversions
0 Qs
Rates, including speed, density and pressure
0 Qs
Rates, including speed, distance and time
0 Qs
Ratio and proportion
0 Qs
Ratio, proportion and rates
0 Qs
Set notation and Venn diagrams
0 Qs
Sets and Venn diagrams
0 Qs
Simple and compound interest
0 Qs
Speed, distance and time
0 Qs
Squares, square roots, cubes and cube roots
0 Qs
Standard form (scientific notation)
0 Qs
Surds — simplification and rationalisation of the denominator
0 Qs
Surds and irrational numbers
0 Qs
The four operations (addition, subtraction, multiplication, division)
0 Qs
The four operations applied to integers, fractions and decimals
0 Qs
Time, currency and money calculations
0 Qs
Time, money and financial mathematics
20 Qs⚡ Practice
Types of number, factors, multiples and primes
0 Qs
Types of number, integer definitions and properties
0 Qs
Types of number, integer properties and set notation
0 Qs
Number sequences
term-to-term rules, nth term of arithmetic sequences
0 Qs
Percentage calculations
percentage of a quantity, percentage increase and decrease, reverse percentages
0 Qs
Perimeter and area of 2D shapes
triangle, quadrilateral, circle, sector, compound shapes
Probability
Basic probability — probability scale, equally likely outcomes, relative frequency
20 Qs⚡ Practice
Basic probability — single events, sample space, equally likely outcomes
Basic probability and probability scale
20 Qs⚡ Practice
Basic probability, sample space and probability scale
0 Qs
Combined events, sample space diagrams and two-way tables
0 Qs
Conditional probability
20 Qs⚡ Practice
Mutually exclusive and independent events
0 Qs
Probability from Venn diagrams, tables and sample space diagrams
20 Qs⚡ Practice
Relative frequency and experimental probability
20 Qs⚡ Practice
single event probability, expected frequency, relative frequency
Tree diagrams — with and without replacement
0 Qs
Tree diagrams and combined events
0 Qs
Tree diagrams and conditional probability
0 Qs
Venn diagrams and set notation in probability
0 Qs
Proportionality
direct and inverse proportion, algebraic and graphical representations
0 Qs
Rounding
decimal places, significant figures and estimation
0 Qs
Scatter diagrams and correlation
plotting, interpreting, drawing and using lines of best fit
0 Qs
Sets
notation, Venn diagrams, union, intersection, complement, subsets
Similarity and congruence
conditions, identifying and applying
0 Qs
Statistical diagrams
bar charts, pie charts, pictograms, stem-and-leaf diagrams, frequency diagrams, histograms with equal class widths
Statistics
Averages (mean, median, mode) and range
0 Qs
Averages and range — mean, median, mode and range from raw data, tables and diagrams
0 Qs
Bar charts, pie charts, pictograms and stem-and-leaf diagrams
0 Qs
Box-and-whisker plots
0 Qs
Collection, classification and representation of data
0 Qs
Collection, classification and tabulation of data
0 Qs
Correlation and lines of best fit
0 Qs
Correlation and lines of best fit on scatter diagrams
20 Qs⚡ Practice
Cumulative frequency — tables, curves and estimation of median, quartiles and interquartile range
0 Qs
Cumulative frequency tables and diagrams — median, quartiles and interquartile range
0 Qs
Cumulative frequency tables and graphs, median and interquartile range
0 Qs
Cumulative frequency tables, curves and box-and-whisker plots
0 Qs
Data collection — types of data, sampling methods
0 Qs
Data collection, classification and tabulation
0 Qs
Estimated mean from grouped frequency tables
0 Qs
Frequency tables and grouped frequency distributions
0 Qs
Frequency tables and grouped frequency tables
0 Qs
Frequency tables, grouped data and estimated mean
0 Qs
Frequency tables, grouped frequency tables and frequency polygons
0 Qs
Histograms with frequency density
20 Qs⚡ Practice
Histograms with frequency density and frequency polygons
20 Qs⚡ Practice
Histograms with unequal class widths and frequency density
Interpreting and comparing statistical measures and distributions
0 Qs
Mean, median, mode and range
0 Qs
Mean, median, mode and range from listed data and frequency tables
0 Qs
Reading and interpreting statistical diagrams (bar charts, pictograms, pie charts, stem-and-leaf, scatter diagrams)
0 Qs
Scatter diagrams and lines of best fit
0 Qs
Scatter diagrams, correlation and lines of best fit
0 Qs
Statistical diagrams — bar charts, pie charts, pictograms, frequency diagrams
0 Qs
Statistical diagrams — bar charts, pie charts, pictograms, stem-and-leaf, scatter diagrams
0 Qs
Stem-and-leaf diagrams and back-to-back stem-and-leaf diagrams
0 Qs
Surface area and volume of 3D shapes
prisms, cylinders, pyramids, cones, spheres and compound solids
0 Qs
Symmetry
line symmetry and rotational symmetry in 2D shapes
0 Qs
Transformations
Combined and inverse transformations
40 Qs⚡ Practice
Enlargement with negative and fractional scale factors
0 Qs
Reflection, rotation, translation and enlargement
0 Qs
reflection, rotation, translation, enlargement (including fractional and negative scale factors)
0 Qs
Reflections, rotations, translations and enlargements
0 Qs
Trigonometry
Applications of trigonometry in three dimensions
0 Qs
Area of a triangle using ½ab sin C
0 Qs
Exact trigonometric values
0 Qs
Exact trigonometric values (30°, 45°, 60°)
0 Qs
Exact values of trigonometric ratios for 0°, 30°, 45°, 60°, 90°
0 Qs
Graphs of sine, cosine and tangent functions
0 Qs
Graphs of trigonometric functions and their transformations
0 Qs
Pythagoras' theorem in 2D and 3D
0 Qs
Pythagoras' theorem in two and three dimensions
0 Qs
Sine rule and cosine rule
0 Qs
Sine rule and cosine rule for non-right-angled triangles
0 Qs
Solution of trigonometric equations in a given interval
20 Qs⚡ Practice
Trigonometric graphs and exact values
0 Qs
Trigonometric graphs and functions for angles beyond 90°
0 Qs
Trigonometric ratios (sin, cos, tan) in right-angled triangles
0 Qs
Trigonometric ratios (sine, cosine, tangent) in right-angled triangles
0 Qs
Trigonometric ratios in right-angled triangles (sin, cos, tan)
0 Qs
Trigonometry in 3D — angles and lengths in solids
Trigonometry in 3D problems
0 Qs
Trigonometry in three dimensions
40 Qs⚡ Practice
Types of number
natural numbers, integers, prime numbers, square numbers, cube numbers, rational and irrational numbers, real numbers
0 Qs
Vector geometry
expressing paths and proving geometric results using vectors
0 Qs
Vectors
Addition, subtraction and scalar multiplication of vectors
Column vectors and magnitude of a vector
0 Qs
Column vectors and position vectors
0 Qs
notation, addition, subtraction, scalar multiplication, magnitude
0 Qs
Position vectors and geometric proofs using vectors
Vector geometry and geometric proofs using vectors
0 Qs
Vector geometry and proof using vectors
0 Qs
Vector notation and representation
20 Qs⚡ Practice
Vector notation, addition, subtraction and scalar multiplication
0 Qs
Vector notation, magnitude and direction
All topics
Absolute value (modulus)
0 Qs
Algebra & Sequences
Algebra and Graphs
0 Qs
Algebraic fractions
0 Qs
Algebraic manipulation and expansion of brackets
0 Qs
Angles, parallel lines and polygon angle properties
0 Qs
Arc length and sector area
0 Qs
Area and perimeter of 2D shapes
0 Qs
Area of a triangle using ½ab sin C
0 Qs
Area under a curve (estimation using trapezium rule)
0 Qs
Bearings
0 Qs
Bearings and 3D trigonometry
0 Qs
Bounds and limits of accuracy
0 Qs
Box-and-whisker plots
0 Qs
Circle theorems
0 Qs
Circle theorems and properties of circles
0 Qs
Co-ordinate Geometry
0 Qs
Combined and inverse transformations
Combined events, tree diagrams and conditional probability
0 Qs
Compound interest and growth/decay
0 Qs
Constructions and loci using ruler and compasses
0 Qs
Coordinate geometry — equation of a straight line
0 Qs
Coordinate Geometry & Graphs
Cumulative frequency and quartiles
0 Qs
Direct and inverse proportion
Estimation, rounding, significant figures and bounds
0 Qs
Exact trigonometric values for 0°, 30°, 45°, 60°, 90°
0 Qs
Factorisation — common factor, grouping, quadratics
0 Qs
Factorisation including difference of two squares and trinomials
0 Qs
Four operations with integers, fractions and decimals
Frequency tables, grouped data and histograms
0 Qs
Function notation, domain and range, composite functions and inverse functions
0 Qs
Functions, composite and inverse functions
0 Qs
Geometrical constructions and loci
0 Qs
Geometry
Gradient of a curve and rate of change using a tangent
0 Qs
Graphs of linear functions and their properties
0 Qs
Graphs of linear, quadratic, cubic, reciprocal and exponential functions
0 Qs
HCF, LCM and prime factorisation
0 Qs
Histograms with unequal class widths and frequency density
0 Qs
Interior and exterior angles of polygons
0 Qs
Length and midpoint of a line segment
0 Qs
Linear equations and linear inequalities
0 Qs
Matrices and Transformations
41 Qs⚡ Practice
Mensuration
Multiples, factors, highest common factor (HCF) and lowest common multiple (LCM)
0 Qs
nth term of quadratic and other sequences
0 Qs
Number
Number sets — natural, integer, rational, irrational, real
0 Qs
Order of operations (BIDMAS/BODMAS)
0 Qs
Parallel and perpendicular lines
0 Qs
Percentages, percentage change and reverse percentages
0 Qs
Powers, roots and indices
0 Qs
Powers, roots and indices including rules of indices
0 Qs
Prime factorisation
0 Qs
Probability
Probability of single events and Venn diagrams
0 Qs
Properties of triangles and special quadrilaterals
0 Qs
Pythagoras theorem
0 Qs
Pythagoras' theorem in 2D and 3D
0 Qs
Quadratic equations and the quadratic formula
Rates including speed, distance, time and other compound measures
0 Qs
Ratio and proportion
0 Qs
Ratio, proportion and rates of change
Rearranging formulae (changing the subject)
0 Qs
Scale drawings and maps
0 Qs
Scatter diagrams and correlation
0 Qs
Sequences — linear, quadratic and the nth term
0 Qs
Setting up and solving linear equations
0 Qs
Setting up and solving simultaneous linear equations
0 Qs
Similar shapes and congruent triangles
0 Qs
Simple interest and compound interest
0 Qs
Simultaneous equations — linear and one quadratic
0 Qs
Sine and cosine rules
0 Qs
Sine rule and cosine rule for non-right-angled triangles
0 Qs
Solving quadratic equations by completing the square
0 Qs
Solving quadratic equations by factorisation
0 Qs
Solving quadratic equations using the quadratic formula
0 Qs
Standard form (scientific notation)
0 Qs
Statistical measures — mean, median, mode, range, IQR
0 Qs
Statistics
Substitution into formulae and expressions
0 Qs
Transformations — translation, reflection, rotation, enlargement
0 Qs
Transformations and Vectors
Transformations using matrices
0 Qs
Tree diagrams and conditional probability
0 Qs
Trigonometric ratios (sine, cosine, tangent) in right-angled triangles
0 Qs
Trigonometric ratios in right-angled triangles
0 Qs
Trigonometry
0 Qs
Trigonometry in 3D problems
0 Qs
Units of measurement and conversion between units including area and volume units
0 Qs
Vectors — notation, magnitude and operations
Volume and surface area of 3D shapes
0 Qs
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