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Number
16 domains · 413 topics
Counting
- Subitising
- Counting within 10
- Counting within 20
- Counting within 100
Skip counting
- Skip counting in 2s
- Skip counting in 5s
- Skip counting in 10s
- Skip counting in 3s
- Skip counting in 4s
- Skip counting in 8s
- Skip counting in 20s
Number lines
- Number lines in steps of 1
- Number lines in steps of 2, 5 and 10
- Number lines in steps of 25, 50 and 100
Types of number
- Identifying integers
- Odd and even numbers
Reading and writing numbers
- Reading numbers to 100
- Writing numbers to 100
- Reading numbers to 1,000,000
- Writing numbers to 1,000,000
- Roman numerals to 100
- Roman numerals to 1000
Understanding place value
- Place value of 2-digit numbers
- Place value of 3-digit numbers
- Place value of 4-digit numbers
- Place value of 5- and 6-digit numbers
- Place value of 7-digit numbers and beyond
- The role of zero in place value
- Partitioning 3-digit numbers
- Partitioning 4-digit numbers
- Partitioning 5-digit numbers
Comparing and ordering
- Comparing 2-digit numbers
- Comparing 3-digit numbers
- Comparing 4-digit numbers
- Comparing 5- and 6-digit numbers
- Comparing 7-digit numbers and beyond
- Ordering 2-digit numbers
- Ordering 3-digit numbers
- Ordering 4-digit numbers
- Ordering 5- and 6-digit numbers
- Ordering 7-digit numbers and beyond
Powers of 10
- Finding 1 more
- Finding 10 more
- Finding 100 more
- Finding 1 less
- Finding 10 less
- Finding 100 less
- Multiplying integers by 10
- Multiplying integers by 100
- Multiplying integers by 1000
- Dividing integers by 10
- Dividing integers by 100
- Dividing integers by 1000
Related calculations
- Related multiplications (scaling one operand)
- Related multiplications (scaling both operands)
- Related multiplications with decimals
- Related divisions
- Related divisions with decimals
Part-whole and number bonds
- Part-whole models (two parts)
- Part-whole models (three parts)
- Bar models (two parts)
- Bar models (three parts)
- Number bonds to 5
- Number bonds to 10
- Number bonds to 20
- Number bonds to 50
- Number bonds to 100
- Number bonds to 1000
Mental addition
- Addition within 10
- Addition within 20 (no crossing 10)
- Addition within 20 (crossing 10)
- Adding a single-digit number (no crossing)
- Adding a single-digit number (crossing 10)
- Adding multiples of 10
- Adding a near-multiple of 10
- Adding two 2-digit numbers (no crossing)
- Adding two 2-digit numbers (crossing 10)
- Adding a multiple of 10 to a 2-digit number
- Adding across 100
- Mental addition with larger numbers
Mental subtraction
- Subtraction within 10
- Subtraction within 20 (no crossing 10)
- Subtraction within 20 (crossing 10)
- Subtracting a single-digit number (no crossing)
- Subtracting a single-digit number (crossing 10)
- Subtracting multiples of 10
- Subtracting a near-multiple of 10
- Subtracting two 2-digit numbers (no crossing)
- Subtracting two 2-digit numbers (crossing 10)
- Subtracting a multiple of 10 from a 2-digit number
- Subtracting across 100
- Mental subtraction with larger numbers
Doubling, halving and more
- Doubling
- Halving
- Trebling
- Quadrupling
- Finding a third
- Finding a quarter
Times tables and division facts
- 1 times table
- 2 times table
- 3 times table
- 4 times table
- 5 times table
- 6 times table
- 7 times table
- 8 times table
- 9 times table
- 10 times table
- 11 times table
- 12 times table
- Multiplying three numbers using times tables facts
Order of operations
- Order of operations (basic)
- Order of operations (brackets)
- Order of operations (powers)
Problem-solving
- Four operations in context
Written addition
- Column addition (2-digit, no carrying)
- Column addition (2-digit, with carrying)
- Column addition (3-digit + 2-digit, no carrying)
- Column addition (3-digit + 2-digit, with carrying)
- Column addition (3-digit, no carrying)
- Column addition (3-digit, with carrying)
- Column addition (4-digit, no carrying)
- Column addition (4-digit, with carrying)
Written subtraction
- Column subtraction (2-digit, no exchanging)
- Column subtraction (2-digit, with exchanging)
- Column subtraction (3-digit − 2-digit, no exchanging)
- Column subtraction (3-digit − 2-digit, with exchanging)
- Column subtraction (3-digit, no exchanging)
- Column subtraction (3-digit, with exchanging)
- Column subtraction (4-digit, no exchanging)
- Column subtraction (4-digit, with exchanging)
Written multiplication
- Short multiplication (2-digit × 1-digit)
- Short multiplication (3-digit × 1-digit)
- Long multiplication (2-digit × 2-digit)
- Long multiplication (3-digit × 2-digit)
Written division
- Short division (2-digit ÷ 1-digit, no remainder)
- Short division (2-digit ÷ 1-digit, with remainder)
- Short division (3-digit ÷ 1-digit, no remainder)
- Short division (3-digit ÷ 1-digit, with remainder)
- Long division (3-digit ÷ 2-digit, no remainder)
- Long division (3-digit ÷ 2-digit, with remainder)
- Long division (4-digit ÷ 2-digit, no remainder)
- Long division (4-digit ÷ 2-digit, with remainder)
- Interpreting remainders
Calculator skills
- Evaluating powers on a calculator
- Evaluating roots on a calculator
- Evaluating powers of negative numbers on a calculator
- Evaluating expressions with powers and roots on a calculator
- Evaluating fraction-bar expressions on a calculator
- Evaluating nested expressions on a calculator (rounding to decimal places)
- Rounding calculator answers to significant figures
- Converting fractions and surds to decimals on a calculator
Factors and multiples
- Factors of a number
- Multiples of a number
- Divisibility rules
Prime numbers
- Identifying prime numbers
- Prime factorisation
- Factors from prime factorisation
HCF and LCM
- HCF by listing
- LCM by listing
- HCF by prime factorisation
- LCM by prime factorisation
- HCF and LCM problems
Systematic listing
- Listing outcomes across two or more sets
- Listing arrangements (order matters)
- Listing selections (order doesn’t matter)
- The product rule for counting
Understanding negatives
- Reading negative integers on a number line
- Negative decimals on a number line
- Comparing negative numbers
- Ordering negative numbers
- Counting through zero
- Negative numbers in context
Operations with negatives
- Adding negative numbers
- Subtracting negative numbers
- Multiplying negative numbers
- Dividing negative numbers
Recognising and counting British money
- Counting coins and notes
- Money notation (pence and pounds)
- Comparing amounts of money
- Coins to make an amount
Operations with British money
- Adding money
- Subtracting money (including change)
- Multiplying money
- Dividing money
- Problem-solving with money
Rounding and truncating
- Rounding to the nearest 10
- Rounding to the nearest 100
- Rounding to the nearest 1000
- Rounding to the nearest whole number
- Identifying decimal places
- Rounding to 1 decimal place
- Rounding to 2 decimal places
- Rounding to 3 or more decimal places
- Identifying significant figures (numbers ≥ 1)
- Identifying significant figures (numbers < 1)
- Rounding to 1 significant figure (large numbers)
- Rounding to 2 or more significant figures (large numbers)
- Rounding to 1 significant figure (small numbers)
- Rounding to 2 or more significant figures (small numbers)
- Truncating decimals
- Truncating to significant figures
Estimation
- Estimating calculations (single operation)
- Estimating calculations (compound expressions)
Bounds and error intervals
- Bounds of a rounded number (integer place values)
- Bounds of a number rounded to decimal places
- Bounds of a number rounded to significant figures
- Bounds of a truncated number (integer place values)
- Bounds of a number truncated to decimal places
- Bounds of a number truncated to significant figures
- Bounds in calculations (addition)
- Bounds in calculations (subtraction)
- Bounds in calculations (multiplication)
- Bounds in calculations (division)
- Bounds in calculations (compound measures)
- Bounds in calculations (multi-step)
- Bounds and a suitable degree of accuracy
Understanding fractions
- Fractions of a shape
- Fractions on a number line
- Equivalent fractions
- Simplifying fractions
- Comparing fractions (same denominator)
- Comparing fractions (same numerator)
- Comparing fractions to a benchmark
- Comparing fractions (different denominators)
- Ordering fractions
- Converting improper fractions to mixed numbers
- Converting mixed numbers to improper fractions
- Reciprocals
Fractions of an amount
- Fractions of an amount (unit fractions)
- Fractions of an amount (non-unit fractions)
- Fractions of an amount (with units)
- Fractional increase
- Fractional decrease
- Finding the whole given a unit fraction
- Finding the whole given a non-unit fraction
Adding and subtracting fractions
- Adding fractions (same denominator)
- Subtracting fractions (same denominator)
- Adding fractions (one denominator is a multiple of the other)
- Subtracting fractions (one denominator is a multiple of the other)
- Adding fractions (different denominators)
- Subtracting fractions (different denominators)
- Adding a whole number and a fraction
- Subtracting a fraction from a whole number
- Adding mixed numbers (same denominator)
- Subtracting mixed numbers (same denominator, no exchange)
- Adding mixed numbers (different denominators)
- Subtracting mixed numbers (different denominators, no exchange)
- Subtracting mixed numbers (same denominator, with exchange)
- Subtracting mixed numbers (different denominators, with exchange)
Multiplying fractions
- Multiplying a fraction by an integer
- Multiplying fractions
- Squaring fractions
- Multiplying with mixed numbers
Dividing fractions
- Dividing a fraction by an integer
- Dividing an integer by a fraction
- Dividing a fraction by a fraction
- Dividing with mixed numbers
Four operations with fractions
- Four operations with fractions
Fractions in context
- Fractions in context (finding and comparing)
- Fractions in context (operations and reverse)
Understanding decimals
- Number lines with decimals
- Decimal place value
- Comparing decimals
- Ordering decimals
- Number bonds with decimals
Operations with decimals
- Adding a decimal to a whole number
- Adding decimals (same decimal places)
- Adding decimals (different decimal places)
- Subtracting a decimal from a whole number
- Subtracting decimals (mixed decimal places)
- Multiplying decimals by 10
- Multiplying decimals by 100
- Multiplying decimals by 1000
- Dividing decimals by 10
- Dividing decimals by 100
- Dividing decimals by 1000
- Multiplying integer × decimal
- Multiplying decimal × decimal
- Dividing integer ÷ integer (decimal answer)
- Dividing integer ÷ decimal
- Dividing decimal ÷ integer
- Dividing decimal ÷ decimal
Four operations with decimals
- Four operations with decimals
Finding percentages
- Percentage of an amount (non-calculator)
- Percentage of an amount (calculator)
- Finding what percentage one number is of another
Percentage change
- Percentage increase (non-calculator)
- Percentage decrease (non-calculator)
- Identifying the multiplier for a percentage change
- Percentage increase (calculator / multipliers)
- Percentage decrease (calculator / multipliers)
- Reverse percentages (given a percentage of a value)
- Reverse percentages (after an increase)
- Reverse percentages (after a decrease)
- Finding a percentage increase
- Finding a percentage decrease
- Simple interest
- Repeated percentage change (compound)
- Percentage error
Converting between forms
- Converting fractions to decimals
- Converting decimals to fractions
- Converting fractions to percentages
- Converting percentages to fractions
- Converting decimals to percentages
- Converting percentages to decimals
Comparing across forms
- Comparing across forms (pairwise)
- Ordering across forms (3 or more)
Recurring decimals
- Fraction to recurring decimal
- Recurring decimal to fraction
Understanding ratio
- Writing ratios from a diagram
- Ratio and bar models
- Writing ratios from context
- Equivalent ratios
- Simplifying ratios (two-part)
- Simplifying ratios (three-part)
- Simplifying ratios with different units
- Ratios in the form 1:n or n:1
Using ratio
- Finding the total number of parts in a ratio
- Sharing in a ratio (total given)
- Finding quantities from a ratio (one part given)
- Finding quantities from a ratio (difference given)
- Ratio to fraction
- Fraction to ratio
- Ratio to percentage
- Percentage to ratio
- Combining two ratios
Direct and inverse proportion
- Direct proportion
- Inverse proportion
- Algebraic direct proportion (y = kx)
- Algebraic direct proportion with powers and roots
- Algebraic inverse proportion (y = k/x)
- Algebraic inverse proportion with powers and roots
- Three-quantity proportion problems
- Combined direct and inverse proportion
Scale, value and recipes
- Using a scale drawing or map (drawing to real)
- Using a scale drawing or map (real to drawing)
- Determining the scale from given measurements
- Best value
- Unit pricing (cost per unit)
- Unitary-method scaling table
- Recipes
Currency and exchange rates
- Using an exchange rate (multiply direction)
- Using an exchange rate (divide direction)
- Finding the exchange rate from two amounts
- Comparing values using two exchange rates
Compound measures
- Finding the speed (given distance and time)
- Finding the distance (given speed and time)
- Finding the time (given speed and distance)
- Speed, distance, time with unit conversions
- Finding the density (given mass and volume)
- Finding the mass (given density and volume)
- Finding the volume (given density and mass)
- Density, mass, volume with mixed units
- Finding the pressure (given force and area)
- Finding the force (given pressure and area)
- Finding the area (given pressure and force)
- Pressure, force, area with mixed units
- Multi-stage journey problems
- Density in shape problems
- Pressure in shape and surface problems
- Rate problems (flow and work)
Powers and roots
- Squaring
- Cubing
- Identifying square numbers
- Identifying cube numbers
- Higher powers (using a calculator)
- Powers of negative numbers
- Square roots
- Cube roots
- Higher roots (using a calculator)
- Estimating roots
Laws of indices
- Multiplying powers (same base)
- Dividing powers (same base)
- Power of a power
- Power of 0
- Negative indices (numeric base)
- Negative indices with fractional base
- Unit fractional indices
- Non-unit fractional indices
- Negative fractional indices
- Expressing a power using a different base
Standard form
- Writing large numbers in standard form
- Writing standard form as ordinary numbers (large)
- Writing small numbers in standard form
- Writing standard form as ordinary numbers (small)
- Normalising incorrect standard form
- Comparing and ordering numbers in standard form
- Adding in standard form
- Subtracting in standard form
- Multiplying in standard form
- Dividing in standard form
- Raising standard form numbers to a power
Surds
- Simplifying basic surds
- Simplifying multiples of surds
- Writing simplified surds as single surds
- Comparing and ordering surds
- Simplifying surds of fractions and mixed numbers
- Adding surds (same root)
- Subtracting surds (same root)
- Adding and subtracting surds with simplification needed
- Multiplying surds
- Multiplying surds with simplification
- Dividing surds
- Dividing surds with simplification
- Raising surds to powers (squaring and higher)
- Expanding a single bracket with surds (no simplification)
- Expanding two brackets with surds (no simplification)
- Squaring a bracket with surds
- Rationalising the denominator (single surd term)
- Rationalising the denominator (single surd, with simplification)
- Rationalising the denominator (conjugate method, two-term)
- Rationalising the denominator (conjugate, with simplification)
Algebra
13 domains · 262 topics
Algebraic notation
- Identifying terms
- Identifying coefficients
- Identifying variables
- Identifying constants
- Writing expressions from words (one operation)
- Writing expressions from words (multiple operations)
- Writing expressions using indices
- Identifying expressions, equations, formulae and identities
Substitution
- Substituting positive integers into expressions (one variable, no powers)
- Substituting positive integers into expressions (one variable, with powers)
- Substituting positive integers into expressions (multiple variables)
- Substituting negative numbers into expressions (no powers)
- Substituting negative numbers into expressions (with powers)
- Substituting decimals into expressions (no powers)
- Substituting decimals into expressions (with powers)
- Substituting fractions into expressions (no powers)
- Substituting fractions into expressions (with powers)
Collecting like terms and simplifying
- Collecting like terms (same variable)
- Collecting like terms (multiple variables)
- Collecting like terms with indices
- Multiplying algebraic terms (no index laws)
- Multiplying algebraic terms using index laws
- Dividing algebraic terms (no index laws)
- Dividing algebraic terms using index laws
- Raising an algebraic term to a power
- Simplifying algebraic expressions using multiple index laws
- Identifying equivalent expressions
Term-to-term rules
- Continuing an arithmetic sequence
- Finding missing terms in an arithmetic sequence
- Generating a sequence from a term-to-term rule
- Pictorial sequences
- Recognising types of sequences
Position-to-term (nth term)
- Using a given linear nth term rule
- Using a given quadratic or other nth term rule
- Finding the nth term of an ascending arithmetic sequence
- Finding the nth term of a descending arithmetic sequence
- Finding the nth term from a pictorial sequence
- Determining if a number is in a sequence
- Finding the nth term of a quadratic sequence (monic)
- Finding the nth term of a quadratic sequence (non-monic)
Special sequences
- Continuing a triangular-number sequence
- Continuing a square or cube number sequence
- Continuing a Fibonacci-type sequence
- Continuing a geometric sequence
- Finding the nth term of a geometric sequence
Expanding brackets
- Expanding single brackets (positive integer coefficient)
- Expanding single brackets (negative integer coefficient)
- Expanding single brackets with algebraic coefficients
- Expanding single brackets (variable common factor)
- Expanding and simplifying multiple single brackets
- Expanding double brackets (all positive)
- Expanding double brackets (negative terms)
- Expanding double brackets (squaring)
- Expanding double brackets (non-monic)
- Expanding double brackets (non-monic with negatives)
- Expanding and simplifying multiple double-bracket expressions
- Expanding triple brackets (monic)
- Expanding triple brackets (non-monic)
- Expanding triple brackets (squared × linear)
- Cubing a bracket
Factorising
- Factorising with a common numeric factor
- Factorising with a common algebraic factor
- Factorising monic quadratics (all positive coefficients)
- Factorising monic quadratics (negative terms)
- Factorising monic perfect square trinomials
- Factorising non-monic quadratics (all positive coefficients)
- Factorising non-monic quadratics (negative terms)
- Factorising non-monic perfect square trinomials
- Difference of two squares (basic)
- Difference of two squares (non-monic / multiple variables)
- Factorising by taking out a common factor first
- Factorising with a negative leading coefficient
- Factorising with a common bracket factor
- Factorising by grouping (four-term expressions)
- Factorising quadratics in two variables
- Factorising using repeated difference of two squares (quartics)
- Factorising a difference of squared binomials
Simplifying algebraic fractions
- Simplifying algebraic fractions (no factorising needed)
- Simplifying algebraic fractions (linear factorising)
- Simplifying algebraic fractions (quadratic factorising)
Multiplying and dividing algebraic fractions
- Multiplying algebraic fractions (no prior factorising)
- Multiplying algebraic fractions (with linear factorising)
- Multiplying algebraic fractions (with quadratic factorising)
- Dividing algebraic fractions (no prior factorising)
- Dividing algebraic fractions (with factorising)
Adding and subtracting algebraic fractions
- Adding and subtracting algebraic fractions (integer denominators)
- Adding algebraic fractions (algebraic single-term denominators)
- Adding algebraic fractions (linear algebraic denominators)
- Adding algebraic fractions (requiring prior factorising)
- Subtracting algebraic fractions (algebraic single-term denominators)
- Subtracting algebraic fractions (linear algebraic denominators)
- Subtracting algebraic fractions (requiring prior factorising)
Four operations with algebraic fractions
- Four operations with algebraic fractions
Function machines
- One-step function machines (finding the output)
- One-step function machines (finding the input)
- Two-step function machines (finding the output)
- Two-step function machines (finding the input)
- Finding the missing operation(s) in function machines
- Writing algebraic expressions from function machines
- Drawing function machines from algebraic expressions
Forming equations
- Forming linear equations (no brackets)
- Forming linear equations (with brackets)
Solving linear equations
- Solving one-step equations (addition and subtraction)
- Solving one-step equations (multiplication and division)
- Solving two-step equations
- Solving two-step equations (negative and fractional solutions)
- Solving equations with a negative coefficient
- Solving equations requiring prior simplification
- Solving equations with brackets (variable on one side)
- Solving equations with unknowns on both sides (no brackets)
- Solving equations with unknowns on both sides (with brackets)
- Solving equations with fractions (multi-term numerator)
- Solving equations with fractions (variable in denominator)
- Solving equations with fractions on both sides
Substituting into formulae
- Substituting into a formula
Writing formulae
- Writing a formula from a given context
Rearranging formulae
- Rearranging with addition and subtraction
- Rearranging with multiplication and division
- Two-step rearranging
- Rearranging with squares and square roots
- Rearranging with brackets
- Rearranging with the subject in a denominator
- Rearranging when the subject appears twice
Functions
- Evaluating a function using f(x) notation
- Finding a composite function
- Finding an inverse function
Completing the square
- Completing the square (monic, b even)
- Completing the square (monic, b odd)
- Completing the square (non-monic, a positive)
- Completing the square (non-monic, a negative)
Solving quadratics
- Rearranging a quadratic into the form ax²+bx+c=0
- Solving x² = a
- Solving two-step equations with x²
- Solving quadratics from factored form
- Solving quadratic equations by factorising (monic)
- Solving quadratic equations by factorising (non-monic)
- Solving quadratics from completed square form
- Solving quadratic equations by completing the square
- Solving quadratic equations using the quadratic formula (calculator)
- Solving quadratic equations using the quadratic formula (exact)
- Using the discriminant to determine the number of solutions
Simultaneous equations
- Solving simultaneous equations graphically
- Solving simultaneous equations by elimination (adding)
- Solving simultaneous equations by elimination (subtracting)
- Solving simultaneous equations by elimination (scaling one equation)
- Solving simultaneous equations by elimination (scaling both equations)
- Solving simultaneous equations by substitution
- Forming and solving simultaneous equations from a context
- Solving simultaneous equations (linear/quadratic)
Iteration
- Showing a solution lies between two values
- Forming an iterative formula
- Using an iterative formula
- Finding a root to a given degree of accuracy by iteration
Reading and plotting
- Reading coordinates (first quadrant)
- Locating a point from its coordinates (first quadrant)
- Reading coordinates (all four quadrants)
- Locating a point from its coordinates (all four quadrants)
Coordinate geometry
- Finding the midpoint of two points
- Finding an endpoint given the midpoint
- Dividing a line segment in a ratio
- Finding a missing vertex from the properties of a shape
Tables and graphs
- Completing a table of values for y = mx + c (given x)
- Completing a table of values for y = mx + c (given y)
- Completing a table of values for ax + by = c
- Deciding whether a point lies on a straight line
- Reading a value from a straight-line graph
- Matching a table of values to its graph
- Identifying the graph of y = mx + c
Gradient and equation
- Finding an integer gradient from a graph
- Finding a fractional gradient from a graph
- Finding an integer gradient from two points
- Finding a fractional gradient from two points
- Finding the gradient from a table of values
- Reading the gradient from y = mx + c
- Reading the y-intercept from y = mx + c
- Finding the x-intercept from y = mx + c
- Equations of horizontal and vertical lines
- Finding the equation of a line from its graph (integer gradient)
- Finding the equation of a line from its graph (fractional gradient)
- Rearranging ax + by = c into the form y = mx + c
- Finding the gradient from ax + by = c
- Finding the y-intercept from ax + by = c
- Finding the equation of a line from its gradient and a point
- Finding the equation of a line through two points
- Finding the area enclosed by a line and the axes
Parallel and perpendicular
- Identifying parallel lines (equations in the form y = mx + c)
- Identifying parallel lines (equations in other forms)
- Finding the equation of a parallel line through a given point (integer gradient)
- Finding the equation of a parallel line through a given point (fractional gradient)
- Identifying perpendicular lines (equations in the form y = mx + c)
- Identifying perpendicular lines (equations in other forms)
- Finding the gradient of a perpendicular line
- Finding the equation of a perpendicular line through a given point (integer gradient)
- Finding the equation of a perpendicular line through a given point (fractional gradient)
- Finding the equation of the perpendicular bisector of a line segment
- Proving perpendicularity in shapes using gradients
- Proving parallelism in shapes using gradients
Quadratic graphs
- Completing a table of values (monic quadratic)
- Completing a table of values (non-monic quadratic)
- Reading the roots from a quadratic graph
- Reading the y-intercept from a quadratic graph
- Reading the turning point from a quadratic graph
- Finding the line of symmetry of a quadratic graph
- Sketching a quadratic from factorised form
- Sketching a quadratic from expanded form
- Writing the equation of a quadratic in factorised form from its graph
- Finding the turning point from completed square form
- Sketching a quadratic from completed square form
- Writing the equation of a quadratic in completed square form from its graph
- Solving a quadratic equation using its graph
Other graph types
- Completing a table of values (cubic)
- Completing a table of values (reciprocal)
- Completing a table of values (exponential)
- Finding the equation y = kaˣ from its graph
- Recognising features of trigonometric graphs
- Using a trigonometric graph to find a second angle
- Sketching the shape of a standard graph
- Matching equations to their graphs
Real-life graphs
- Reading a conversion graph
- Reading values from a distance-time graph
- Finding a duration from a distance-time graph
- Finding speed from a distance-time graph
- Constructing a distance-time graph
- Reading values from a speed-time graph
- Describing motion from a speed-time graph
- Finding acceleration from a speed-time graph
- Finding distance travelled from a speed-time graph
- Interpreting the gradient and y-intercept of a real-life graph
- Recognising graphs of direct and inverse proportion
- Matching graph shapes to real-life situations
Advanced graph skills
- Translating a graph vertically (y = f(x) + a)
- Translating a graph horizontally (y = f(x + a))
- Reflecting a graph in the x-axis (y = −f(x))
- Reflecting a graph in the y-axis (y = f(−x))
- Estimating the gradient of a curve at a point
- Interpreting the gradient of a curve in context
- Estimating the area under a curve
- Interpreting area under a curve in context
- Using the equation of a circle centred at the origin
- Finding the equation of a tangent to a circle centred at the origin
Representing inequalities
- Reading and writing inequality notation
- Listing integers that satisfy an inequality
- Representing a one-ended inequality on a number line
- Representing a two-ended inequality on a number line
- Writing a solution set in set notation
- Writing the inequalities that define a region
Solving inequalities
- Solving one-step linear inequalities
- Solving two-step linear inequalities
- Solving linear inequalities with brackets
- Solving linear inequalities with fractions
- Solving linear inequalities with a negative coefficient
- Solving linear inequalities with unknowns on both sides
- Finding integer solutions to a linear inequality
- Solving two-ended linear inequalities
- Combining two inequalities
- Solving a quadratic inequality using a graph
- Solving a quadratic inequality algebraically
Proof
- Counterexamples
- Representing integers algebraically
- Algebraic proof (odd, even and multiples)
- Algebraic proof (squares and consecutive integers)
- Equating coefficients in identities
Geometry
15 domains · 262 topics
Naming and identifying
- Recognising basic 2D shapes
- Naming polygons
- Sides and vertices of polygons
- Identifying regular and irregular polygons
- Classifying triangles
- Classifying quadrilaterals
- Identifying parallel and perpendicular lines
- Naming the parts of a circle
- Geometric notation for lines and shapes
- Tessellation
Symmetry
- Lines of symmetry
- Rotational symmetry
Naming and properties
- Recognising 3D shapes
- Euler’s formula for polyhedra
- Identifying nets
Plans and elevations
- Sketching the plan and elevations of a 3D shape
- Identifying a 3D shape from its plan and elevations
- Isometric drawing
Classifying and estimating angles
- Classifying angles
- Estimating acute angles
- Estimating obtuse angles
- Estimating reflex angles
Measuring and drawing angles
- Geometric notation for angles
- Comparing and ordering angles
- Measuring non-reflex angles
- Measuring reflex angles
- Drawing non-reflex angles
- Drawing reflex angles
Basic angle facts
- Angles on a straight line
- Angles around a point
- Vertically opposite angles
- Angles in a right angle
Angles in shapes
- Angles in a triangle
- Angles in an isosceles triangle
- Angles in a right-angled triangle
- Exterior angle of a triangle
- Angles in a quadrilateral
- Angles in a parallelogram
- Angles in a trapezium
- Angles in a kite
- Interior angle sum of a polygon
- Missing angles in a polygon
- Exterior angle of a regular polygon
- Interior angle of a regular polygon
- Finding the number of sides from an angle
Angles in parallel lines
- Alternate angles
- Corresponding angles
- Co-interior angles
Measuring
- Choosing an appropriate unit of measure
- Reading scales
- Comparing and ordering measures
Converting units of measure
- Converting metric units of length
- Converting metric units of mass
- Converting metric units of capacity
- Converting between metric and imperial
- Converting between miles and kilometres
- Converting units of area
- Converting metric units of volume
- Converting between volume and capacity
Telling the time
- Telling the time (o’clock)
- Telling the time (half past)
- Telling the time (quarter past)
- Telling the time (quarter to)
- Telling the time (minutes past, 5-minute intervals)
- Telling the time (minutes to, 5-minute intervals)
- Telling the time (minutes past, to the minute)
- Telling the time (minutes to, to the minute)
- Writing the time in 12-hour notation (a.m./p.m.)
- Writing the time in 24-hour notation
- Converting between 12-hour and 24-hour time
Calculating with time
- Knowing time facts
- Finding a duration within the hour
- Finding a duration that bridges the hour
- Finding a duration in hours and minutes
- Finding a start or end time within the hour
- Finding a start or end time that bridges the hour
- Finding a start or end time (hours and minutes)
- Converting between units of time
- Converting to and from mixed units of time
- Converting between decimal and mixed units of time
- Time problems in context
Perimeter
- Perimeter by counting unit lengths
- Perimeter by adding given side lengths
- Perimeter of a square
- Perimeter of a rectangle
- Perimeter of a regular polygon
- Finding a missing side given the perimeter
- Finding a missing length in a compound rectilinear shape
- Perimeter of compound rectilinear shapes
- Perimeter of a rectangle from its area and one side
Area of basic shapes
- Area by counting whole squares
- Area by counting whole and half squares
- Estimating the area of an irregular shape on a grid
- Area of a rectangle
- Finding a missing side given the area of a rectangle
- Area of a right-angled triangle
- Area of a triangle (perpendicular height given)
- Finding a missing length given the area of a triangle
- Area of a parallelogram
- Finding a missing length given the area of a parallelogram
- Area of a trapezium
- Finding a missing length given the area of a trapezium
Area and circumference of a circle
- Converting between radius and diameter
- Circumference of a circle given the radius
- Circumference of a circle given the diameter
- Finding the radius or diameter given the circumference
- Area of a circle given the radius
- Area of a circle given the diameter
- Finding the radius given the area of a circle
- Area and circumference in terms of π
- Area of a semicircle
- Perimeter of a semicircle
- Area of a quarter circle
- Perimeter of a quarter circle
- Arc length of a sector
- Perimeter of a sector
- Area of a sector
- Finding the angle of a sector given its arc length
- Finding the angle of a sector given its area
Area of compound shapes
- Area of compound rectilinear shapes
- Area of a shaded region (rectilinear shapes)
- Area of compound shapes with triangles, parallelograms or trapezia
- Area of compound shapes involving parts of circles
- Area of a shaded region involving circles
Volume
- Volume by counting cubes
- Volume of a cube
- Volume of a cuboid
- Finding a missing side given the volume of a cuboid
- Volume of a prism
- Volume of a cylinder
- Finding a missing length given the volume of a prism or cylinder
- Volume of a pyramid
- Volume of a cone
- Volume of a sphere
- Volume of a composite solid
Surface area
- Surface area from a net
- Surface area of a cube
- Surface area of a cuboid
- Finding a missing side given the surface area of a cuboid
- Surface area of a prism
- Surface area of a cylinder
- Surface area of a pyramid
- Surface area of a cone
- Surface area of a sphere
- Surface area of a composite solid
Reflection
- Reflecting a shape in a line
- Describing a reflection
Rotation
- Rotating a shape about a point
- Describing a rotation
Translation
- Translating a shape (left, right, up and down)
- Describing a translation in words
- Translating a shape by a column vector
- Describing a translation as a column vector
Enlargement
- Enlarging a shape from a centre
- Describing an enlargement (positive integer scale factor)
- Describing an enlargement (fractional scale factor)
- Describing an enlargement (negative scale factor)
Combining transformations
- Finding invariant points
- Describing a combination of transformations as a single transformation
Similarity
- Deciding whether two shapes are similar
- Finding the scale factor between two similar shapes
- Finding missing angles in similar shapes
- Finding a missing length in similar shapes
- Finding a missing length in similar triangles sharing a vertex
- Relating length, area and volume scale factors
- Finding an area using the length-area scale factor
- Finding a length using the area-length scale factor
- Finding a volume using the length-volume scale factor
- Finding a length using the volume-length scale factor
Congruence
- Finding missing angles and lengths in congruent shapes
- Identifying which congruence condition holds (if any)
Constructions
- Constructing the perpendicular bisector of a line segment
- Constructing an angle bisector
- Constructing a perpendicular from a point on a line
- Constructing a perpendicular from a point not on a line
- Constructing a 60° or 90° angle
- Constructing a 30° or 45° angle by bisecting
- Constructing an equilateral triangle
- Constructing a triangle given SSS (strict)
- Constructing a triangle given SAS or ASA (accurate drawing with protractor)
- Constructing a right-angled triangle given hypotenuse and another side
- Constructing regular polygons (square and hexagon)
- Constructing a line parallel to another through a given point
- Dividing a line segment into three or more equal parts
Loci
- Recognising loci from their descriptions
- Locus at a fixed distance from a point
- Locus at a fixed distance from a line or line segment
- Locus equidistant from two points
- Locus equidistant from two intersecting lines
- Shaded region bounded by a single locus
- Shaded region with multiple locus criteria
- Solving locus word problems
Pythagoras
- Finding the hypotenuse
- Finding a shorter side
- Using the converse of Pythagoras’ theorem
- Finding the distance between two points using Pythagoras
- Finding a length in an isosceles triangle
- Finding a length in a square using the diagonal
- Pythagoras with surd-form answers
- Using Pythagoras’ theorem in 3D
Right-angled trigonometry
- Labelling the sides of a right-angled triangle
- Finding the opposite side using sine
- Finding the hypotenuse using sine
- Finding the adjacent side using cosine
- Finding the hypotenuse using cosine
- Finding the opposite side using tangent
- Finding the adjacent side using tangent
- Finding an angle using sine
- Finding an angle using cosine
- Finding an angle using tangent
- Recognising when to use Pythagoras or trigonometry
- Recalling exact trigonometric values
- Using exact trigonometric values in right-angled triangles
- Using angles of elevation and depression
- Using trigonometry in isosceles triangles
- Using trigonometry in 3D
Non-right-angled trigonometry
- Finding a missing side using the sine rule
- Finding an acute angle using the sine rule
- Finding a missing side using the cosine rule
- Finding a missing angle using the cosine rule
- Finding the area of a triangle using ½ab sin C
- Finding an included angle from the area of a triangle
- Finding a missing side from the area of a triangle
Vector basics
- Writing a vector as a column vector
- Calculating the magnitude of a column vector
- Converting from magnitude and direction to components
- Converting from components to magnitude and direction
- Recognising equal vectors
- Finding the negative of a vector
- Recognising parallel vectors
- Recognising the zero vector
Vector arithmetic
- Adding column vectors
- Subtracting column vectors
- Adding and subtracting vectors (drawn form)
- Multiplying a vector by a scalar
Vector geometry
- Finding a vector between two points (single route)
- Finding a vector between two points (multiple routes)
- Finding a vector involving a midpoint
- Finding a vector involving a fraction of a distance
- Finding a vector involving a ratio of a distance
- Finding a vector involving a fraction of a subroute
- Finding an unknown constant for parallel vectors
- Proving two vectors are parallel
- Proving three points are collinear
- Proving points form a parallelogram or rectangle
- Proving points form a trapezium
Circle theorems
- Using angle at the centre = 2 × angle at the circumference
- Using angle in a semicircle = 90°
- Using angles in the same segment
- Using opposite angles in a cyclic quadrilateral = 180°
- Using tangent ⊥ radius
- Using equal tangents from an external point
- Using the alternate segment theorem
- Using the perpendicular from the centre to a chord
- Using the isosceles triangle formed by two radii
Bearings
- Compass directions (four points)
- Compass directions (eight points)
- Converting between bearings and compass directions
- Finding a bearing from a diagram
- Drawing a bearing
- Finding a back bearing
- Finding a bearing using angles in parallel lines
Statistics & Probability
5 domains · 184 topics
Types of data
- Classifying data as qualitative or quantitative
- Classifying data as discrete or continuous
- Classifying data as primary or secondary
Sampling and data collection
- Population, census and sample
- Simple random sampling
- Systematic sampling
- Stratified sampling
- Quota sampling
- Identifying the sampling method used
- Choosing an appropriate sampling method for a context
- Recognising bias in sampling
- Data collection methods
- Designing and critiquing questionnaires
- Designing a data collection sheet or tally chart
Frequency tables
- Reading a tally chart
- Reading an ungrouped frequency table
- Calculating from an ungrouped frequency table (totals and differences)
- Finding a missing frequency in an ungrouped frequency table
- Constructing an ungrouped frequency table from raw data
- Reading a grouped frequency table (class intervals)
- Constructing a grouped frequency table from raw data
- Limitations of grouped data
Two-way tables and frequency trees
- Reading a two-way table
- Finding missing values in a two-way table
- Constructing a two-way table from written information
- Reading a frequency tree
- Constructing a frequency tree from written information
Venn diagrams and set notation
- Set operations on listed elements, 2-set (no set notation)
- Set operations on listed elements, 3-set (no set notation)
- Regions of a 2-set Venn diagram (no set notation)
- Regions of a 3-set Venn diagram (no set notation)
- Reading frequencies from a Venn diagram (no set notation)
- Set operations on listed elements, 2-set (with set notation)
- Set operations on listed elements, 3-set (with set notation)
- Regions of a 2-set Venn diagram (with set notation)
- Regions of a 3-set Venn diagram (with set notation)
- Reading frequencies from a Venn diagram (with set notation)
- Constructing a 2-set Venn diagram from a list of elements
- Constructing a 2-set Venn diagram from given totals (intersection given)
- Constructing a 2-set Venn diagram from given totals (intersection not given)
- Venn diagram special cases (mutually exclusive and subset)
- Constructing a 3-set Venn diagram
Distance charts and timetables
- Reading a distance chart
- Reading a timetable
Pictograms and block diagrams
- Reading a pictogram (1-to-1 key)
- Reading a pictogram (key > 1)
- Calculating from a pictogram (totals and differences)
- Constructing a pictogram
- Reading a block diagram
- Constructing a block diagram
- Reading a line or dot plot
Bar charts and vertical line charts
- Reading a single bar chart
- Calculating from a bar chart (totals and differences)
- Constructing a bar chart
- Reading a vertical line chart
- Constructing a vertical line chart
- Reading a dual bar chart
- Reading a stacked bar chart
- Reading a back-to-back bar chart
Pie charts
- Reading a pie chart using fractions or percentages of a total
- Reading a pie chart using given angles
- Calculating pie chart angles from the angle for one item
- Calculating pie chart angles as a fraction of 360
- Finding a missing frequency in a pie chart
- Interpreting misleading displays
Histograms and frequency polygons
- Reading a histogram (equal class widths)
- Constructing a histogram (equal class widths)
- Reading a histogram (unequal class widths)
- Constructing a histogram (unequal class widths)
- Finding a missing class width in a histogram
- Estimating frequency in a sub-range from a histogram
- Reading a frequency polygon
- Constructing a frequency polygon from grouped data
- Comparing data sets using frequency polygons
- Identifying distribution shape
- Identifying skewness from diagrams
Cumulative frequency and box plots
- Calculating cumulative frequencies from a frequency table
- Estimating the median, quartiles and IQR from a cumulative frequency graph
- Estimating frequencies from a cumulative frequency graph
- Interpreting proportions in a box plot
- Reading a box plot
- Drawing a box plot from summary statistics
- Box plots with outliers
- Comparing two distributions using box plots
- Estimating percentiles, deciles and inter-percentile ranges
- Comparing distributions using cumulative frequency graphs
Line graphs and time series
- Reading a line graph
- Completing a line graph from a table
- Calculating from a line graph (differences and changes)
- Calculating a moving average
- Using moving averages to identify a trend
- Seasonal variation and predictions from a time series
Stem-and-leaf diagrams
- Reading a stem-and-leaf diagram
- Constructing a stem-and-leaf diagram
- Reading a back-to-back stem-and-leaf diagram
- Constructing a back-to-back stem-and-leaf diagram
- Finding averages and the range from a stem-and-leaf diagram
- Finding quartiles and the IQR from a stem-and-leaf diagram
- Comparing data sets using stem-and-leaf diagrams
Averages and range from a list
- Mean from a list of data
- Median from a list of data
- Mode from a list of data
- Range from a list of data
- Selecting an appropriate average for a context
- Finding a missing value given the mean
- Finding a missing value given the median
- Finding a missing value given the mode
- Finding a missing value given the range
- Finding two missing values from two average constraints
- Effect of adding or removing a value on the mean
- Effect of adding or removing a value on the median
- Effect of adding or removing a value on the mode
- Effect of adding or removing a value on the range
- Identifying an outlier and its effect on the mean and the range
- Combined mean of two groups
- Mean and range of a list of algebraic terms
- Comparing two data sets using an average and the range
Averages and range from a frequency table
- Sigma notation for statistical totals and means
- Mean from an ungrouped frequency table
- Median from an ungrouped frequency table
- Mode from an ungrouped frequency table
- Range from an ungrouped frequency table
- Finding a missing frequency given the mean (ungrouped)
- Estimating the mean from a grouped frequency table
- Finding a missing frequency given the estimated mean (grouped)
- Identifying the modal class from a grouped frequency table
- Median class from a grouped frequency table
- Greatest and least possible range (grouped)
- Estimating the median from a grouped frequency table using interpolation
- Comparing two distributions from two frequency tables
Quartiles and interquartile range
- Finding quartiles from a list of data
- Finding the interquartile range from a list of data
- Finding quartiles and the IQR from an ungrouped frequency table
- Identifying the class interval of a quartile from a grouped frequency table
- Quartiles and IQR by interpolation (grouped)
Scatter graphs
- Reading a scatter graph
- Describing correlation from a scatter graph
- Plotting a scatter graph from a table of bivariate data
- Identifying outliers on a scatter graph
- Using a line of best fit to interpolate
- Using a line of best fit to extrapolate
Single-event probability
- Understanding the probability scale from 0 to 1
- Probability of a single event
- Probability of an event NOT happening
- Probability of one event OR another (mutually exclusive events)
- Mutually exclusive events that sum to 1
- Comparing the probability of an event in two situations
- Finding the number of an outcome from its probability
- Finding the total frequency given a probability and a frequency
- Finding the number of an outcome from a table of probabilities
- Using one outcome’s frequency to find another’s
- Common incorrect reasoning in probability
Sample spaces
- Listing the outcomes of combined events systematically
- Listing combined outcomes using a sample space diagram
- Listing combined outcomes using an arithmetic operator
- Finding probability from a given sample space
- Finding probability of a combined outcome without a given sample space
Probability from two-way tables and frequency trees
- Finding probability from a two-way table using the total
- Finding probability from a subgroup of a two-way table
- Finding probability from a frequency tree using the total
- Finding probability from a subgroup of a frequency tree
Experimental probability and expected outcomes
- Relative frequency
- Expected number of outcomes
- Estimating the number of outcomes from experimental results
- Judging bias from two sets of experimental results
- How the number of trials affects reliability
Tree diagrams
- Completing a tree diagram for two independent events
- Finding the probability of a single chain using a tree diagram (independent)
- Finding the probability of a single chain without a tree diagram (independent)
- Finding the probability of multiple chains using a tree diagram (independent)
- Finding the probability of multiple chains without a tree diagram (independent)
- Finding the probability of ‘at least one’
- Completing a tree diagram for two picks without replacement
- Finding the probability of a single chain with dependent events
- Finding the probability of multiple chains with dependent events
- Finding a conditional probability from a tree diagram
- Probability of a given sum or product (with replacement)
- Probability of a given sum or product (without replacement)
- Algebraic probability problems with independent or dependent events
Venn diagrams and set notation in probability
- Finding a probability from a 2-set Venn diagram (single region)
- Finding a probability from a 2-set Venn diagram (multiple regions)
- Finding a probability from a 3-set Venn diagram (single region)
- Finding a probability from a 3-set Venn diagram (multiple regions)
- Finding a conditional probability from a Venn diagram