GCSE Maths, one topic at a time

Master GCSE Maths fractions with adaptive practice questions, step-by-step worked examples, and instant AI feedback. Covering AQA, Edexcel, OCR and Eduqas.

• Simplifying fractions
• Adding and subtracting fractions
• Multiplying and dividing fractions

Practise GCSE Maths percentages including percentage change, reverse percentages and compound interest. Full AQA, Edexcel, OCR and Eduqas coverage.

• Finding percentages of amounts
• Percentage increase and decrease
• Reverse percentages

Practise GCSE Higher Maths surds — simplifying, rationalising the denominator and expanding surds. Targeted AQA, Edexcel, OCR and Eduqas questions.

• Simplifying surds
• Adding and subtracting surds
• Multiplying and dividing surds

Master GCSE Maths standard form (scientific notation) with practice questions on converting, multiplying and dividing. AQA, Edexcel, OCR and Eduqas.

• Writing numbers in standard form
• Converting from standard form
• Multiplying in standard form

Practise GCSE Maths indices including the laws of indices, negative powers, fractional powers and zero index. AQA, Edexcel, OCR and Eduqas.

• Laws of indices
• Negative indices
• Fractional indices

Calculate upper and lower bounds and error intervals. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Find upper and lower bounds
• Write error intervals
• Calculate with bounds

Perform the four operations with decimals accurately. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Add and subtract decimals
• Multiply decimals
• Divide by a decimal

Identify factors, multiples, and prime numbers. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Find all factors of a number
• List multiples of a number
• Identify prime numbers

Find the highest common factor and lowest common multiple using prime factor trees. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Find the HCF of two or more numbers
• Find the LCM of two or more numbers
• Use prime factor decomposition

Add, subtract, multiply and divide with negative numbers. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Add and subtract negative numbers
• Multiply and divide negative numbers
• Order negative numbers

Apply the correct order of operations in calculations. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Apply BIDMAS to calculations
• Insert brackets to make statements true
• Evaluate expressions with mixed operations

Compare and order integers, decimals, and negative numbers using place value. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Identify the value of any digit in a number
• Compare and order whole numbers and decimals
• Use < > and = signs correctly

Express numbers as products of their prime factors. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Draw factor trees
• Write numbers as products of prime factors
• Use index notation for repeated primes

Count the total number of possible combinations by multiplying choices. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Apply the product rule to two or more stages
• Count arrangements where items cannot be repeated
• Count the possibilities for codes and menus

Convert recurring decimals to fractions using algebraic proof. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Identify recurring decimals
• Convert recurring decimals to fractions
• Use algebraic proof for the conversion

Find the original amount when you are given the value after a percentage change. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Recognise a reverse percentage question from its wording
• Write down the multiplier that was applied
• Divide by the multiplier to recover the original amount

Round to decimal places, significant figures, and use estimation. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Round to a given number of decimal places
• Round to significant figures
• Use estimation to check calculations

Work with the 24-hour clock, durations and timetables. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Convert between 12-hour and 24-hour time
• Find the duration between two times
• Convert between hours, minutes and decimal hours

Use a scientific calculator accurately, including fractions, powers and memory. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Use brackets to control the order of a calculation
• Use the fraction, power and root keys
• Keep full accuracy between steps and round only at the end

Solve GCSE Maths linear equations with step-by-step practice, including equations with brackets, fractions and unknowns on both sides. AQA, Edexcel, OCR and Eduqas.

• Solving one-step equations
• Equations with brackets
• Equations with unknowns on both sides

Master GCSE Maths quadratics — factorising, completing the square, the quadratic formula and sketching parabolas. AQA, Edexcel, OCR and Eduqas.

• Factorising quadratics
• Completing the square
• Quadratic formula

Practise GCSE Maths simultaneous equations using elimination and substitution methods, including non-linear pairs. AQA, Edexcel, OCR and Eduqas.

• Elimination method
• Substitution method
• Graphical method

Practise GCSE Maths sequences including arithmetic and quadratic sequences, nth term formulae and geometric sequences. AQA, Edexcel, OCR and Eduqas.

• Arithmetic sequences
• Finding the nth term of arithmetic sequences
• Geometric sequences

Master GCSE Maths straight-line graphs — gradient, y-intercept, y = mx + c, perpendicular and parallel lines. AQA, Edexcel, OCR and Eduqas.

• Gradient of a straight line
• y = mx + c
• Finding the equation of a line

Simplify, add, subtract, multiply and divide algebraic fractions. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Simplify algebraic fractions by factorising
• Multiply and divide algebraic fractions
• Add and subtract algebraic fractions

Simplify algebraic expressions by collecting like terms. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Use algebraic notation correctly
• Collect like terms
• Simplify expressions with multiple variables

Rewrite a quadratic in completed-square form and use it to solve and sketch. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Complete the square for a quadratic with a leading coefficient of 1
• Solve a quadratic by completing the square
• Read the turning point off the completed-square form

Expand single and double brackets in algebraic expressions. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Expand single brackets
• Expand double brackets using FOIL
• Expand and simplify expressions

Factorise expressions by taking out common factors. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Find the HCF of terms
• Factorise into single brackets
• Factorise expressions with multiple variables

Use function machines to work forwards and backwards through a rule. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Find the output of a function machine from a given input
• Find the input from a given output by working backwards
• Write the rule of a function machine as an expression

Use function notation, find composite functions, and calculate inverse functions. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Evaluate functions for given inputs
• Find composite functions fg(x) and gf(x)
• Find the inverse of a function f⁻¹(x)

Apply translations and reflections to given graph functions. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Translate graphs using f(x) + a and f(x + a)
• Reflect graphs using -f(x) and f(-x)
• Describe transformations fully

Solve and represent inequalities on a number line. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Solve linear inequalities
• Represent on a number line
• Solve double inequalities

Use iteration to find approximate solutions to equations. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Use an iterative formula to generate a sequence of values
• Find a solution to an equation using iteration to a specified accuracy
• Rearrange an equation into an iterative form

Recognise and sketch cubic, reciprocal and exponential graphs from their equations. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Identify a graph as linear, quadratic, cubic, reciprocal or exponential from its equation
• Sketch the general shape of a cubic and a reciprocal graph
• Explain what an asymptote is and why a reciprocal graph has two

Plot and read parabolas: roots, the turning point, the line of symmetry, and solving equations from a graph. Adaptive practice for AQA, Edexcel, OCR and Eduqas.

• Plot a quadratic graph from a table of values
• Read the roots of a quadratic from its graph
• Find the turning point and the line of symmetry

Solve a linear and a quadratic equation together by substitution. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Rearrange the linear equation and substitute it into the quadratic
• Solve the resulting quadratic
• Pair each x value with its matching y value

Change the subject of a formula using inverse operations. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Rearrange simple formulae
• Rearrange with powers and roots
• Rearrange formulae where the subject appears twice

Find and use the nth term of linear and quadratic sequences. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Find the nth term of a linear sequence
• Generate terms from an nth term formula
• Determine if a value is in a sequence

Replace letters with numbers and evaluate the expression correctly. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Substitute positive and negative numbers into expressions
• Apply BIDMAS correctly after substituting
• Substitute into formulas with more than one letter

Recognise and sketch the sine, cosine, tangent and exponential curves. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Sketch the sine and cosine curves between 0 and 360 degrees
• Recognise the tangent curve and its asymptotes
• Sketch an exponential curve and state its intercept

Practise GCSE Maths ratio and proportion with problems on sharing quantities, simplifying ratios and direct/inverse proportion. AQA, Edexcel, OCR and Eduqas.

• Simplifying ratios
• Sharing in a given ratio
• Direct proportion

Master GCSE Maths compound measures including speed, density and pressure. Practice forming and rearranging formulae from real-world contexts.

• Speed, distance, time
• Density, mass, volume
• Pressure, force, area

Compare prices fairly by working out the cost of one unit, or how much you get for £1. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Work out unit price by dividing cost by quantity
• Work out quantity per pound by dividing quantity by cost
• Compare two or more options and state which is better value

Set up and solve equations for direct and inverse proportion. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Write equations for direct proportion (y ∝ x)
• Write equations for inverse proportion (y ∝ 1/x)
• Find the constant of proportionality k

Convert between currencies by multiplying or dividing by the exchange rate, and compare prices across countries. Adaptive practice for AQA, Edexcel, OCR and Eduqas.

• Convert an amount from one currency to another using a given rate
• Convert back again by reversing the operation
• Decide whether to multiply or divide from the way the rate is written

Calculate compound interest, depreciation, and repeated percentage change. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Find multipliers for percentage increases and decreases
• Calculate compound interest
• Calculate depreciation and exponential decay

Use a single multiplier to increase or decrease by a percentage, and to reverse the process. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Write the multiplier for any percentage increase or decrease
• Apply a multiplier to increase or decrease an amount
• Calculate a percentage change from an original and a new value

Calculate acceleration and distance from velocity-time graphs. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Calculate acceleration from the gradient of a velocity-time graph
• Calculate distance from the area under a velocity-time graph
• Interpret different sections of kinematic graphs

Practise GCSE Maths angles — angles in triangles, polygons, parallel lines and circle theorems. Full AQA, Edexcel, OCR and Eduqas coverage.

• Angles on a straight line and around a point
• Angles in triangles and quadrilaterals
• Interior and exterior angles of polygons

Practise GCSE Maths area and volume questions — 2D shapes, prisms, cylinders, cones, pyramids and spheres. AQA, Edexcel, OCR and Eduqas.

• Area of 2D shapes (triangle, trapezium, parallelogram, circle)
• Volume of prisms and cylinders
• Volume of pyramids, cones and spheres

Master GCSE Maths Pythagoras theorem and trigonometry (SOH-CAH-TOA) with practice questions for both Foundation and Higher tiers. AQA, Edexcel, OCR and Eduqas.

• Pythagoras theorem: a² + b² = c²
• SOH-CAH-TOA for right-angled triangles
• Finding missing sides and angles

Use Pythagoras and SOHCAHTOA inside 3D solids by finding a right-angled triangle to work in. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Find the length of a diagonal across the base of a cuboid
• Find the space diagonal of a cuboid using Pythagoras twice
• Identify the right-angled triangle needed for a 3D problem

Apply circle theorems to find missing angles and prove geometric statements. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Identify and apply the 7 key circle theorems
• Provide rigorous geometric reasons for angle calculations
• Spot isosceles triangles formed by radii

Congruent shapes are identical; similar shapes are the same shape at a different size, linked by a scale factor. Adaptive practice for AQA, Edexcel, OCR and Eduqas.

• Decide whether two shapes are congruent, similar, or neither
• Name the condition (SSS, SAS, ASA, RHS) that proves two triangles congruent
• Find the scale factor between two similar shapes

Use compasses and a straight edge to build accurate constructions, and to draw the set of points satisfying a rule. Adaptive practice for AQA, Edexcel, OCR and Eduqas.

• Construct the perpendicular bisector of a line segment
• Construct the bisector of an angle
• Draw the locus of points a fixed distance from a point or a line

Recall and use the exact values of sin, cos and tan for key angles. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Recall the exact values of sin, cos and tan at 0, 30, 45, 60 and 90 degrees
• Derive them from the two standard triangles
• Use exact values in non-calculator trigonometry

Use map scales to convert between drawing and real distances, and measure bearings as three figures clockwise from north. Adaptive practice for AQA, Edexcel, OCR and Eduqas.

• Convert between map distance and real distance using a scale
• Measure and draw a bearing correctly
• Write bearings as three figures

Calculate the area and circumference of circles and semicircles. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Calculate circumference given radius or diameter
• Calculate area given radius or diameter
• Solve reverse problems to find radius/diameter

Draw and interpret the front elevation, side elevation and plan of a solid. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Draw the plan of a solid made from cubes
• Draw the front and side elevations
• Work out which stack determines each column of an elevation

Calculate interior and exterior angles of regular and irregular polygons. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Calculate the sum of interior angles
• Calculate individual interior and exterior angles of regular polygons
• Find the number of sides given an angle

Identify 2D and 3D shapes and describe their properties. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Identify and describe properties of triangles and quadrilaterals
• Identify lines of symmetry and order of rotational symmetry
• Name 3D solid shapes

Calculate arc lengths and areas of sectors of circles. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Calculate arc length
• Calculate sector area
• Calculate perimeter of a sector

Apply the sine rule and cosine rule in non-right-angled triangles. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Label non-right-angled triangles correctly
• Choose between sine and cosine rules
• Apply the sine rule to find sides and angles

Calculate the total surface area of prisms, cylinders and other 3D shapes. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Calculate surface area of cubes and cuboids
• Calculate surface area of triangular prisms
• Calculate surface area of cylinders

Reflect, rotate, translate and enlarge shapes, and describe a transformation fully. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Translate a shape using a column vector
• Reflect a shape in a given mirror line
• Rotate a shape about a given centre

Convert standard metric units, areas, volumes, and use map scales. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Convert standard metric units of length, mass and capacity
• Convert metric units of area and volume
• Interpret map scales as ratios

Add, subtract and scale column vectors, and use vector paths to describe journeys around a diagram. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Add and subtract column vectors
• Multiply a vector by a scalar
• Find a vector path between two points on a diagram

Practise GCSE Maths probability — listing outcomes, the probability scale, mutually exclusive and independent events. AQA, Edexcel, OCR and Eduqas.

• Probability scale (0 to 1)
• P(event) = favourable outcomes / total outcomes
• Mutually exclusive events: P(A or B) = P(A) + P(B)

Practise GCSE Maths tree diagrams for combined events, with and without replacement, and conditional probability. AQA, Edexcel, OCR and Eduqas.

• Drawing tree diagrams
• Multiplying along branches
• Adding outcomes between branches

Solve probability problems involving dependent events and without replacement. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Understand dependent and independent events
• Calculate probabilities without replacement
• Use conditional probability notation P(A|B)

Complete a frequency tree and use it to find probabilities. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Complete a frequency tree from given information
• Use the branch-total rule to find missing frequencies
• Find a probability from a completed frequency tree

Calculate relative frequency and use it to estimate probability. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Calculate relative frequency from experimental data
• Estimate future outcomes using relative frequency
• Understand that more trials increase reliability

Use sample space diagrams to list outcomes and calculate probabilities. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• List all possible outcomes systematically
• Draw sample space diagrams for two events
• Use sample spaces to calculate probabilities

Use Venn diagrams to represent sets and calculate probabilities. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Sort data into Venn diagrams
• Understand set notation (∩, ∪, ')
• Calculate probabilities from Venn diagrams

Practise GCSE Maths averages — mean, median, mode and range from raw data, frequency tables and grouped data. AQA, Edexcel, OCR and Eduqas.

• Mean, median, mode
• Range and interquartile range
• Mean from frequency tables

Practise GCSE Maths scatter graphs — plotting, correlation, lines of best fit and interpolation/extrapolation. AQA, Edexcel, OCR and Eduqas.

• Plotting scatter graphs
• Types of correlation (positive, negative, none)
• Lines of best fit

Draw and interpret basic statistical diagrams. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Draw and interpret bar charts
• Draw and interpret pictograms
• Calculate angles for pie charts

Estimate the size of a population from a marked sample. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Write down the capture-recapture proportion
• Estimate a population size from the two samples
• State the assumptions the method relies on

Compare two or more datasets using statistical measures. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Compare averages to describe general trends
• Compare spread (range/IQR) to describe consistency
• Write clear comparative statements in context

Draw and interpret cumulative frequency curves and box plots. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Calculate cumulative frequency
• Plot a cumulative frequency curve
• Find median and quartiles from a curve

Calculate estimated mean, median and mode from grouped tables. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Find modal class
• Find median class
• Estimate mean from grouped data

Draw and interpret histograms using frequency density for grouped data. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Calculate frequency density from a grouped frequency table
• Draw histograms with unequal class widths
• Read frequency from a histogram using area

Read, complete and use a two-way table to answer questions. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

• Read values from a completed two-way table
• Fill in missing values using row and column totals
• Calculate probabilities from a two-way table