Edexcel · GCSE · Mathematics
Edexcel GCSE Mathematics Syllabus
The complete Edexcel GCSE Mathematics specification mapped to 300 topics. Click any topic for free revision notes and practice questions.
3D shapes
surface area and volume
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Algebraic fractions
simplification and operations
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simplifying, adding, subtracting and solving
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Angle rules
angles on a line, around a point and vertically opposite
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Angles
basic rules, angles on a line and at a point, vertically opposite angles
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measuring, estimating and angle facts
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types, measuring and drawing
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Angles in parallel lines
corresponding, alternate and co-interior
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Angles in polygons
interior and exterior angles
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Angles on parallel lines
alternate, corresponding and co-interior
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Averages and measures of spread
mean, median, mode and range
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Averages and range
mean, median, mode from lists and tables
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Basic probability
outcomes, events and probability scale
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theoretical and experimental
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Collecting and representing data
types of data and sampling
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Collecting data
types of data, sampling methods and bias
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Constructions
bisectors, angles and loci
triangles, perpendicular bisectors and angle bisectors
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Factorising
common factors and into double brackets
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Formulae
substitution, writing and rearranging
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Fractions
operations and calculations
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operations and conversions
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Fractions, decimals and percentages
equivalence and conversion
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Functions
notation, composite and inverse functions
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Graph transformations
translation, reflection and stretches
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Indices
negative and fractional
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Linear equations
forming and solving
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Linear inequalities
solving and representing on a number line
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Listing outcomes
sample space diagrams and systematic listing
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sample spaces, tables and systematic listing
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Percentages
calculating and converting
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calculations, increase and decrease
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Pie charts
drawing and interpreting
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Probability of combined events
AND/OR rules
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Quadratic equations
solving by completing the square
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solving by factorising
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solving using the quadratic formula
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Quadratic graphs
plotting and interpreting
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Sequences
term-to-term and position-to-term rules
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Similarity
lengths, areas and volumes in similar shapes
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lengths, areas and volumes of similar shapes
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Simultaneous equations
linear and linear
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linear and quadratic
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Standard form
conversion and calculations
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Straight-line graphs
plotting and interpreting y = mx + c
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Surds
simplification and rationalisation of the denominator
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Transformations
reflection, rotation, translation and enlargement
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Transformations of graphs
translations, reflections and stretches
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Tree diagrams
independent and conditional probability
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independent and dependent events
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Trigonometric graphs
sine, cosine and tangent
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Types of number
integers, primes, factors and multiples
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integers, primes, factors, multiples
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Vectors
notation, addition, subtraction and scalar multiplication
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notation, arithmetic and geometric problems
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All topics
Algebra
Algebraic fractions
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Algebraic notation, terminology and manipulation
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Algebraic notation, terminology and simplification
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Algebraic notation, terminology and simplifying expressions
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Algebraic notation, vocabulary and manipulation
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Algebraic proof
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Angles in triangles and quadrilaterals
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Angles in triangles, quadrilaterals and polygons
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Angles including parallel lines and polygons
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Applying the four operations to integers, decimals and fractions
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Area and circumference of circles
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Area and circumference of circles and parts of circles
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Area and circumference of circles, arcs, sectors and segments
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Area of a triangle using ½ab sin C
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Area of a triangle using ½ab sinC
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Area of composite shapes
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Area of sectors and length of arcs
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Area under a curve (estimation)
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Area under a curve and gradient of a curve
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Arithmetic sequences and nth term
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Averages and range from lists, tables and grouped frequency tables
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Averages and range including mean, median, mode from lists, tables and grouped data
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Bar charts, pictograms and pie charts
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Bar charts, pictograms and vertical line charts
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Bar charts, pie charts, pictograms and line graphs
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Basic probability and probability scale
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Bearings
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Bearings and scale drawings
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Bounds and error intervals
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Calculations with integers and decimals
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Circle theorems
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Circle theorems and their proofs
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Collecting, representing and interpreting data
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Combined transformations
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Comparing distributions
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Comparing distributions and statistical measures
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Comparing distributions using statistical measures and diagrams
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Completing the square
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Composite and inverse functions
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Compound interest and exponential growth and decay
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Compound interest and reverse percentages
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Conditional probability
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Congruence and geometric proof
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Congruence and similarity including areas and volumes
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Congruence criteria and congruent triangles
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Congruence criteria for triangles (SSS, SAS, ASA, RHS)
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Constructions, loci and scale drawings
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Conversion between units including area and volume units
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Coordinates and midpoints in 2D
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Coordinates in 2D and 3D
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Cubic, reciprocal and exponential graphs
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Cubic, reciprocal and other non-linear graphs
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Cubic, reciprocal, exponential and trigonometric graphs
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Cumulative frequency graphs and box plots
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Decimals and place value
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Density, mass and volume
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Difference of two squares and completing the square
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Difference of two squares and factorising quadratics
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Direct and inverse proportion
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Distance-time and velocity-time graphs
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Dividing a quantity in a given ratio
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Enlargement with negative and fractional scale factors
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Equation of a circle
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Equation of a circle centred at the origin
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Equation of a straight line and parallel/perpendicular lines
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Equation of a straight line between two points
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Error intervals and truncation
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Estimated mean from grouped frequency tables
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Estimation and approximation
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Exact trigonometric values
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Exact trigonometric values (30°, 45°, 60°)
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Expanding brackets and factorising expressions
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Expanding double and triple brackets
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Expanding double brackets and difference of two squares
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Expanding double brackets and factorising quadratics
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Expanding single and double brackets
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Expanding triple brackets
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Expected outcomes and the law of large numbers
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Experimental probability and relative frequency
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Exponential and trigonometric graphs
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Exponential graphs
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Factorising quadratic expressions
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Factorising quadratics including difference of two squares
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Factors, multiples, primes and HCF/LCM
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Factors, multiples, primes, LCM and HCF
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Forming and solving linear equations
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Fractional and negative indices
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Fractions, decimals and percentages
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Frequency polygons
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Frequency polygons and histograms with equal class widths
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Frequency tables and grouped frequency tables
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Frequency tables, grouped frequency tables and tally charts
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Function notation, composite functions and inverse functions
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Functions and composite and inverse functions
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Functions and function notation
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Geometric proof using congruence and similarity
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Geometric sequences and other sequences
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Geometric sequences and other special sequences
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Geometry and Measures
Gradient and equation of a straight line (y = mx + c)
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Gradients and areas under graphs including real-life contexts
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Graphical solution of equations and inequalities
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Graphs of cubic, reciprocal and other functions
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Growth and decay including iterative processes
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HCF, LCM and prime factor decomposition
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Histograms and frequency density
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Histograms with unequal class widths and frequency density
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Inequalities in two variables and regions on graphs
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Inequalities on a number line and regions on a graph
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Interior and exterior angles of polygons
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Interquartile range and comparing distributions
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Iteration and iterative methods
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Iteration to find approximate solutions to equations
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Limits of accuracy and error intervals
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Linear equations and linear inequalities
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Linear graphs, gradients and y-intercepts
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Linear inequalities and number lines
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Linear inequalities and representing on a number line or graph
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Loci and regions
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Maps and scale factors
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Mean from frequency tables and grouped data
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Mutually exclusive and exhaustive events
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Negative and fractional scale factor enlargements
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Negative and fractional scale factors of enlargement
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Nets of 3D shapes
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nth term of arithmetic and quadratic sequences
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nth term of linear sequences
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nth term of quadratic sequences
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Number
Operations with fractions
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Order of operations (BIDMAS/BODMAS)
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Order of operations and integer calculations
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Order of operations and integers
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Parallel and perpendicular lines
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Parallel lines and angle relationships (alternate, corresponding, co-interior)
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Percentage calculations including percentage change, reverse percentages and compound interest
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Percentage change, profit, loss and reverse percentages
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Percentage change, reverse percentages and percentage problems
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Percentages and percentage change
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Perimeter and area of 2D shapes
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Perimeter, area and circles including sectors and arcs
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Plans and elevations
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Plans, elevations and 3D representations
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Plotting and interpreting linear graphs
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Plotting and interpreting quadratic graphs
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Plotting and interpreting real-life graphs and distance–time graphs
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Powers, roots and index laws
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Pressure, force and area
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Prime factor decomposition
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Prime factorisation, HCF and LCM
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Prisms, cylinders, pyramids, cones and spheres
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Probability
Proof and algebraic argument
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Proof and algebraic arguments
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Proof using vectors
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Properties of 2D shapes including polygons and circles
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Properties of quadrilaterals and polygons
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Properties of triangles and quadrilaterals
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Properties of triangles, quadrilaterals and other polygons
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Pythagoras' theorem in 2D and 3D
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Quadratic and higher-degree inequalities
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Quadratic and polynomial inequalities
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Quadratic equations including the quadratic formula
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Quadratic graphs
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Quadratic graphs and other polynomial graphs
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Quadratic sequences and nth term
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Rates of change and estimating areas under curves
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Rates of change including unit pricing and speed, distance, time
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Ratio and proportion
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Ratio Proportion and Rates of Change
Ratio, Proportion and Rates of Change
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Real-life graphs and rates of change
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Real-life graphs and rates of change from graphs
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Rearranging and changing the subject of a formula
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Rearranging formulae
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Rearranging formulae with the subject appearing twice
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Recognising and sketching graphs of functions
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Recurring decimals and conversion to fractions
0 Qs
Relative frequency and expected outcomes
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Relative frequency and experimental probability
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Rounding, estimation and significant figures
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Rounding, estimation and truncation
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Rounding, significant figures and decimal places
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Sample space diagrams and listing outcomes
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Sampling methods and bias
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Sampling methods and questionnaire design
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Scale factors, maps and scale drawings
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Scatter diagrams, correlation and lines of best fit
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Scatter graphs, correlation and lines of best fit
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Sequences including arithmetic and geometric sequences
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Sequences including arithmetic, geometric and nth term
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Set notation and Venn diagrams for probability
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Setting up and solving linear equations
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Similarity and similar shapes including lengths, areas and volumes
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Simplifying expressions and collecting like terms
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Simultaneous equations (linear)
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Simultaneous equations (one linear, one quadratic)
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Sine rule and cosine rule
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Solving equations using graphical methods
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Solving quadratic equations by completing the square
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Solving quadratic equations by factorising
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Solving quadratic equations using the quadratic formula
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Speed, density and pressure (compound measures)
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Speed, distance and time
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Speed, distance and time; density, mass and volume
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Standard form
0 Qs
Statistics
Stem-and-leaf diagrams
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Straight line graphs, gradient and y-intercept
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Substitution and formulae
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Surds and exact calculations
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Surface area of 3D shapes including prisms, cylinders, pyramids, cones and spheres
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Surface area of 3D solids including prisms, pyramids, cones and spheres
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Tables, charts and diagrams including bar charts, pie charts, pictograms and frequency diagrams
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Theoretical probability including sample spaces and Venn diagrams
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Time series and frequency polygons
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Time series and moving averages
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Time series and trend lines
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Time series graphs and frequency polygons
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Transformations of graphs
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Translations, rotations, reflections and enlargements
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Tree diagrams and combined events
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Trigonometric graphs
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Trigonometry in 3D shapes
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Trigonometry in non-right-angled triangles
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Trigonometry in right-angled triangles (sin, cos, tan)
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Trigonometry in right-angled triangles (sine, cosine, tangent)
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Trigonometry in right-angled triangles (SOH CAH TOA)
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Units and unit conversion including compound measures
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Units of measurement and compound measures (density, pressure, speed)
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Units of measurement and unit conversion
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Units, compound measures and converting between units
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Upper and lower bounds
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Using graphs to solve equations
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Vector geometry and proof using vectors
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Vector proof and geometric problems using vectors
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Vector proofs and geometric problems using vectors
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Vectors and vector arithmetic
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Venn diagrams and set notation in probability
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Volume and surface area of composite solids
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Volume and surface area of prisms and cylinders
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Volume and surface area of pyramids, cones and spheres
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Volume of 3D shapes including prisms, cylinders, pyramids, cones and spheres
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Volume of prisms, cylinders, pyramids, cones and spheres
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