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Algebra

Grade 1–3
Algebra: Sequences
Term-to-term rules
Grade 4–6
Algebra: Algebraic notation
Algebra: Brackets
Algebra: Functions
Algebra: Graphs and coordinates
Algebra: Inequalities
Algebra: Iteration
Algebra: Motion-time graphs
Algebra: Non-linear graphs
Algebra: Real-life graphs
Algebra: Rearranging formulae
Algebra: Sequences
Algebra: Simplifying expressions
Algebra: Simultaneous equations
Algebra: Solving equations
Algebra: Solving quadratic equations
Algebra: Substituting into expressions and formulae
Calculating acceleration from velocity-time graphs
Calculating distances from velocity-time graphs
Calculating midpoints
Calculating speed from distance-time graphs
Changing the subject when the subject appears more than once
Changing the subjects of formulae with one step
Changing the subjects of formulae with two or more steps
Constructing and solving equations
Constructing and solving inequalities
Constructing and solving linear and quadratic simultaneous equations
Constructing and solving linear simultaneous equations
Constructing and solving quadratic equations
Equations of circles
Equations of parallel and perpendicular lines
Equations of parallel lines
Equations of tangents
Estimating areas under non-linear graphs
Estimating gradients of non-linear graphs using tangents
Expanding double brackets
Expanding single brackets
Expanding triple brackets
Factorising into one bracket
Factorising quadratic expressions of the form $ax^2+bx+c$
Factorising quadratic expressions of the form $x^2+bx+c$
Factorising the difference of two squares
Factorising to solve quadratic equations of the form $ax^2+bx+c=0$
Factorising to solve quadratic equations of the form $x^2+bx+c=0$
Finding equations of straight line graphs
Finding the equation of a straight line from its gradient and a point
Finding the equation of a straight line from two points on the line
Graphs of cubic functions
Graphs of exponential functions
Graphs of linear inequalities
Graphs of reciprocal functions
Interpreting distance-time graphs
Interpreting equations of straight line graphs
Interpreting graphs of quadratic functions
Interpreting quadratic real-life graphs
Plotting distance-time graphs
Plotting distance-time graphs using speeds
Plotting graphs of quadratic functions
Plotting linear real-life graphs
Plotting straight line graphs
Plotting velocity-time graphs
Position-to-term rules for arithmetic sequences
Position-to-term rules for geometric sequences
Position-to-term rules for quadratic sequences
Position-to-term rules for sequences of patterns
Reading and drawing inequalities on number lines
Reading and plotting coordinates
Reflecting graphs
Simplifying expressions by collecting like terms
Simplifying expressions using index laws
Sketch graphs of water flows
Sketching quadratic graphs
Solving double inequalities
Solving equations with one step
Solving equations with the unknown in the denominator
Solving equations with the unknown on both sides
Solving equations with two or more steps
Solving inequalities with the unknown on both sides
Solving quadratic equations graphically
Solving shape problems involving coordinates
Solving simultaneous equations graphically
Solving simultaneous equations involving quadratics
Solving simultaneous equations involving quadratics graphically
Solving simultaneous equations using elimination
Solving simultaneous equations using substitution
Solving single inequalities
Special sequences
Substituting into algebraic formulae
Substituting into expressions
Substituting into functions
Substituting into iterative formulae
Substituting into position-to-term rules
Substituting into real-life formulae
Using algebraic notation
Using and finding equations of linear real-life graphs
Using recurrence relations
Grade 7–9
Adding and subtracting algebraic fractions
Algebra: Algebraic fractions
Algebra: Algebraic proofs
Algebra: Brackets
Algebra: Functions
Algebra: Inequalities
Algebra: Iteration
Algebra: Non-linear graphs
Algebra: Solving quadratic equations
Completing the square
Dividing algebraic fractions
Finding approximate solutions to equations using iteration
Finding composite functions
Finding inverse functions
Finding the turning point of a quadratic graph by completing the square
Multiplying algebraic fractions
Simplifying algebraic fractions by cancelling common factors
Simplifying algebraic fractions by factorising into one bracket
Simplifying algebraic fractions by factorising into two brackets
Solving quadratic equations by completing the square
Solving quadratic equations using the quadratic formula
Solving quadratic inequalities
Substituting into composite functions
Transforming graphs
Translating graphs
Writing algebraic proofs

Geometry

Grade 4–6
Alternate segment theorem
Angles in polygons
Angles in quadrilaterals
Angles in segments and cyclic quadrilaterals
Angles in triangles
Angles of elevation and depression
Angles on a line and about a point
Angles on parallel lines
Angles subtended at the centre or circumference of a circle
Applying Pythagoras' theorem in 2D
Calculating bearings
Calculating with trigonometry and bearings
Combining angle facts
Combining transformations
Congruent triangles
Constructing bisectors of angles
Constructing loci
Constructing perpendicular bisectors and lines
Constructing triangles
Drawing and interpreting scale diagrams
Enlargement by a positive or negative scale factor
Enlargement by a positive scale factor
Finding the arc length of sectors
Finding the area of circles
Finding the area of compound shapes
Finding the area of compound shapes containing triangles
Finding the area of parallelograms
Finding the area of sectors
Finding the area of trapeziums
Finding the area of triangles
Finding the circumference of circles
Finding the perimeter and area of similar shapes
Finding the perimeter of compound shapes
Finding the surface area and volume of similar shapes
Finding the surface area of composite shapes
Finding the surface area of cones
Finding the surface area of cubes and cuboids
Finding the surface area of cylinders
Finding the surface area of frustums
Finding the surface area of prisms
Finding the surface area of pyramids
Finding the surface area of spheres
Finding the volume of composite shapes
Finding the volume of cones
Finding the volume of cubes and cuboids
Finding the volume of cylinders
Finding the volume of frustums
Finding the volume of prisms
Finding the volume of pyramids
Finding the volume of spheres
Finding unknown angles in right-angled triangles
Finding unknown sides in right-angled triangles
Finding unknown sides in similar shapes
Geometric proofs with angle facts
Geometric proofs with congruence and similarity
Geometry: Angles
Geometry: Area and perimeter
Geometry: Bearings
Geometry: Circle theorems
Geometry: Circles
Geometry: Constructions and loci
Geometry: Geometric proofs
Geometry: Line and shape properties
Geometry: Nets, plans and elevations
Geometry: Pythagoras' theorem
Geometry: Scale diagrams
Geometry: Similarity and congruence
Geometry: Surface area
Geometry: Transformations
Geometry: Trigonometry
Geometry: Volume
Identifying parts of circles
Line and shape properties
Measuring and drawing bearings
Mixed problems: Constructing bisectors and perpendicular lines
Mixed problems: Finding the area and perimeter of simple shapes
Mixed problems: Finding the surface area of cones and spheres
Mixed problems: Finding the surface area of cuboids, prisms and pyramids
Mixed problems: Finding the volume of cones and spheres
Mixed problems: Understanding similarity and congruence
Nets of 3D shapes
Plans and elevations
Problem solving: Area and perimeter of rectangles and compound shapes (Foundation)
Problem solving: Area and perimeter of rectangles and compound shapes (Higher)
Problem solving: Area of triangles, parallelograms and trapeziums (Foundation)
Problem solving: Area of triangles, parallelograms and trapeziums (Higher)
Properties of 3D shapes
Reflection
Rotation
Symmetry
The area rule
Translation
Trigonometry in 3D shapes
Understanding congruence
Understanding similarity
Understanding sin, cos and tan
Understanding, measuring and drawing angles
Using a pair of compasses
Using Pythagoras' theorem in 2D
Using Pythagoras' theorem in 3D
Using quadrilateral properties to find angles
Using the exact values of trigonometric ratios
Using the exact values of trigonometric ratios (Higher)
Vertically opposite angles
Grade 7–9
Adding and subtracting column vectors
Circle theorems for chords and tangents
Geometric proofs with vectors
Geometry: Circle theorems
Geometry: Geometric proofs
Geometry: Trigonometry
Geometry: Vectors
Identifying parallel vectors
Mixed problems: Circle theorems
Multiplying column vectors by a scalar
Properties of trigonometric graphs
Proving the circle theorems
Solving geometric problems using vectors
The cosine rule
The sine rule
Understanding column vectors
Using trigonometric graphs

Number

Grade 1–3
Constructing fractions
Dividing fractions
Number: Fractions and mixed numbers
Number: Fractions, decimals and percentages
Ordering fractions
Ordering fractions and mixed numbers
Ordering fractions, decimals and percentages
Grade 4–6
Adding and subtracting decimals
Adding and subtracting fractions
Adding and subtracting integers
Adding and subtracting mixed numbers
Adding and subtracting numbers in standard form
Adding and subtracting surds
Adding and subtracting with negative numbers
Calculating with roots and powers
Compound interest calculations
Converting between fractions, decimals and percentages
Converting between mixed numbers and improper fractions
Converting fractions to recurring decimals
Dividing with mixed numbers
Estimating calculations
Estimating roots and powers
Expanding brackets with surds
Finding bounds for calculations
Finding equivalent fractions
Finding error intervals
Finding error intervals for truncated numbers
Finding factors and using divisibility tests
Finding fractions of amounts with a calculator
Finding fractions of amounts without a calculator
Finding fractions of shapes
Finding original values in percentage calculations
Finding percentages of amounts with a calculator
Finding percentages of amounts without a calculator
Finding prime numbers
Finding the HCF and LCM using prime factor decomposition
Finding the highest common factor (HCF)
Finding the lowest common multiple (LCM)
Finding the percentage an amount has been changed by
Growth and decay
Index rules with negative indices
Index rules with positive indices
Indices of the form $\frac{1}{a}$
Indices of the form $\frac{a}{b}$
Multiplying and dividing numbers in standard form
Multiplying and dividing surds
Multiplying and dividing with negative numbers
Multiplying and dividing with place value
Multiplying fractions
Multiplying with mixed numbers
Number: Factors, multiples and primes
Number: Fractions and mixed numbers
Number: Fractions and percentages of amounts
Number: Fractions, decimals and percentages
Number: Index rules
Number: Negative numbers
Number: Number skills
Number: Operations
Number: Percentage change
Number: Place value
Number: Roots and powers
Number: Rounding
Number: Standard form
Number: Surds
Number: The order of operations
Ordering negative numbers
Percentage change with a calculator
Percentage change without a calculator
Prime factor decomposition
Problem solving: Finding the HCF and LCM
Problem solving: Fractions and mixed numbers
Rationalising denominators containing a single term
Rationalising denominators containing two terms
Rounding decimals
Rounding decimals using significant figures
Rounding integers
Rounding integers using significant figures
Simple interest calculations
Simplifying fractions
Simplifying surds
Standard form with a calculator
Truncating decimals
Understanding and ordering decimals
Understanding and ordering integers
Using a calculator
Using a written method to divide integers
Using a written method to divide with decimals
Using a written method to multiply decimals
Using a written method to multiply integers
Using number lines
Using standard form with negative indices
Using standard form with positive indices
Using the correct order of operations
Writing numbers as percentages of other numbers
Sparx GCSE topic list (reference)
Edexcel GCSE Maths past papers (Higher)
Bonus practice banks (topic questions)
Grade 7–9
Converting recurring decimals to fractions
Number: Fractions, decimals and percentages

Probability

Grade 4–6
Calculating experimental probabilities
Conditional probabilities from tree diagrams
Conditional probabilities from Venn diagrams
Expected results from repeated experiments
Frequency trees
Probabilities of mutually exclusive events
Probability: Conditional probability
Probability: Counting outcomes
Probability: Experimental probability
Probability: Theoretical probability
Sample space diagrams
Tree diagrams for dependent events
Tree diagrams for independent events
Using probability phrases
Using set notation
Using the product rule for counting
Venn diagrams
Venn diagrams with set notation
Writing probabilities as fractions
Writing probabilities as fractions, decimals and percentages
Grade 7–9
Conditional probabilities from tables
Probability: Conditional probability
Using the conditional probability formula

Ratio, Proportion and Rates of Change

Grade 1–3
Ratio, Proportion and Rates of Change: Ratio
Writing and simplifying ratios
Grade 4–6
Calculating with ratios and algebra
Changing ratios
Combining ratios
Constructing direct proportion equations
Constructing inverse proportion equations
Converting between ratios, fractions and percentages
Converting units of area
Converting units of length, mass and capacity
Converting units of volume
Currency conversion
Estimating and measuring
Graphs of direct and inverse proportion
Interpreting direct proportion equations
Interpreting inverse proportion equations
Mixed problems: Calculating density and pressure
Problem solving: Converting units of length, area and volume
Problem solving: Sharing amounts in a given ratio (Higher)
Ratio, Proportion and Rates of Change: Compound measures
Ratio, Proportion and Rates of Change: Measures
Ratio, Proportion and Rates of Change: Proportion
Ratio, Proportion and Rates of Change: Ratio
Ratio, Proportion and Rates of Change: Time
Reading, converting and calculating with time
Sharing amounts in a given ratio
Solving direct proportion word problems
Solving inverse proportion word problems
Using appropriate units
Using equivalent ratios to find unknown amounts
Grade 7–9
Calculating with density
Calculating with pressure
Calculating with rates
Calculating with speed
Ratio, Proportion and Rates of Change: Compound measures

Statistics

Grade 1–3
Drawing and interpreting frequency polygons
Drawing bar charts
Drawing pie charts
Drawing stem-and-leaf diagrams
Interpreting pie charts
Interpreting stem-and-leaf diagrams
Statistics: Bar charts
Statistics: Frequency polygons
Statistics: Pie charts
Statistics: Stem-and-leaf diagrams
Grade 4–6
Calculating averages from histograms
Calculating the mean
Capture-recapture
Choosing suitable averages and solving problems
Collecting and recording data using tables
Comparing populations using box plots and cumulative frequency graphs
Comparing populations using diagrams
Designing and using questionnaires
Drawing and interpreting tally charts
Drawing box plots
Drawing cumulative frequency graphs
Drawing line graphs
Finding averages from diagrams
Finding averages from frequency tables
Finding averages from grouped data
Finding the mode
Interpreting bar charts
Interpreting box plots
Interpreting cumulative frequency graphs
Interpreting frequency tables and two-way tables
Interpreting frequency tables with grouped data
Plotting scatter graphs
Presenting data and making conclusions
Sampling and bias
Statistics: Averages and range
Statistics: Bar charts
Statistics: Box plots
Statistics: Collecting and presenting data
Statistics: Cumulative frequency graphs
Statistics: Frequency tables
Statistics: Histograms
Statistics: Line graphs
Statistics: Scatter graphs
Statistics: Tally charts and pictograms
Types of data
Using lines of best fit
Grade 7–9
Calculating the median
Calculating the range
Drawing and interpreting pictograms
Drawing histograms with equal class widths
Drawing histograms with unequal class widths
Interpreting histograms
Interpreting line graphs
Interpreting scatter graphs
Statistics: Averages and range
Statistics: Histograms
Statistics: Line graphs
Statistics: Scatter graphs
Statistics: Tally charts and pictograms