4024 O Level Mathematics: past papers
112 papers from 2012 to 2025, with 166 questions sorted by syllabus topic.
Number Paper 1 · 35 questions
Types of number, factors and multiples7
A multiple of 7 that rounds to 30.
Arithmetic with negative numbers, powers and roots.
Write a number as a product of primes.
Temperature change with negative numbers.
Rational and irrational numbers.
Prime factorisation and lowest common multiple.
Prime numbers and multiples.
Fractions and decimals7
Two short calculations without a calculator.
Calculate with fractions, giving a mixed number.
Calculations with fractions.
Order fractions, decimals and percentages.
Adding fractions and mixed numbers.
Order numbers given as fractions, decimals and percentages.
Calculating with fractions and mixed numbers.
Ratio, proportion and rates3
Simplify a ratio and share a total in a ratio.
Speed, distance and time.
Time and average speed.
Indices and standard form8
Negative and fractional indices.
Arithmetic with negative numbers, powers and roots.
Evaluate powers, including roots and negative indices.
Indices and powers.
Standard form.
Laws of indices and expanding brackets.
Standard form.
Fractional and negative indices.
Surds2
Expand brackets with surds and rationalise a denominator.
Simplify surds and rationalise a denominator.
Percentages, interest, growth and decay4
Order fractions, decimals, roots and percentages.
Sales value from an hourly wage plus a percentage bonus.
Percentage decrease and reverse percentage.
Percentage decrease.
Estimation and limits of accuracy5
A multiple of 7 that rounds to 30.
Estimate an area by rounding to 1 significant figure.
Rounding to decimal places.
Estimate by rounding to 1 significant figure.
Bounds and error intervals.
Algebra Paper 1 · 18 questions
Expanding and factorising2
Factorising.
Laws of indices and expanding brackets.
Algebraic fractions and formulae4
Form and solve a quadratic from a rate of work problem.
Simplify algebraic fractions.
Substitute into and rearrange a formula.
Solve an equation with algebraic fractions.
Linear and simultaneous equations4
Solve a linear equation.
Solve an equation with a bracket and a fraction.
Form and solve simultaneous equations from a problem about masses.
Form and solve a linear equation.
Quadratic equations2
Form and solve a quadratic from a rate of work problem.
Complete the square, find the turning point and sketch a quadratic.
Inequalities and regions2
Linear inequalities and the area of a region.
Linear inequalities and a region on a graph.
Sequences2
Write an inequality from a number line and solve one.
Patterns and the nth term of a linear sequence.
Functions3
Inverse and composite functions with unknown constants.
Functions, inverse and composite functions.
Function notation, inverse and composite functions.
Coordinate geometry Paper 1 · 6 questions
Gradients and straight lines3
Coordinates, a gradient and the missing vertex of a parallelogram.
Rearrange a linear equation and find a perpendicular line.
Midpoint, gradient and a perpendicular line.
Parallel and perpendicular lines2
Rearrange a linear equation and find a perpendicular line.
Midpoint, gradient and a perpendicular line.
Travel graphs and curves1
Acceleration and distance from a speed–time graph.
Gradients of curves and graphical solutions2
Complete a table, plot a graph and read roots from it.
Gradient of a curve by a tangent, and solving an equation graphically.
Geometry Paper 1 · 12 questions
Angles and polygons3
An angle in a parallelogram using isosceles triangles.
Angle reasoning with isosceles triangles and straight lines.
Interior angles of regular polygons.
Circle theorems2
Circle theorems with a tangent, giving reasons.
Circle theorems with a cyclic quadrilateral.
Similarity and congruence3
Similar triangles: a length and an area scale factor.
Similar shapes and scale factors.
Similar triangles.
Bearings, scale drawings and symmetry4
Distances and bearings from a scale drawing.
Scale drawing, constructions and loci.
Line and rotational symmetry.
Scale drawing, bearings and loci.
Constructions and loci2
Scale drawing, constructions and loci.
Scale drawing, bearings and loci.
Mensuration Paper 1 · 5 questions
Perimeter, area and units2
Converting metric units.
Perimeter of a parallelogram and area of a trapezium.
Circles, arcs and sectors1
Area of a sector from its arc length, in terms of r.
Prisms and cylinders2
Equal volumes of a cylinder and a hemisphere, then a surface area in terms of r.
Draw an accurate net of a cube.
Pyramids, cones and spheres1
Equal volumes of a cylinder and a hemisphere, then a surface area in terms of r.
Trigonometry Paper 1 · 1 question
Pythagoras' theorem1
Pythagoras in a square-based pyramid, giving a surd.
Trigonometry in three dimensions1
Pythagoras in a square-based pyramid, giving a surd.
Transformations and vectors Paper 1 · 8 questions
Reflections, rotations and translations3
Describe a transformation and draw a 90° clockwise rotation.
Describe and carry out reflections and enlargements on a grid.
Translations and describing transformations.
Enlargements and combined transformations1
Describe and carry out reflections and enlargements on a grid.
Column vectors and magnitude2
Column vectors, coordinates and lengths in a trapezium.
Vectors and position vectors.
Vector geometry4
Vectors in a parallelogram with a ratio and a collinear point.
Vectors in terms of a and b using a ratio.
Vectors.
Vectors and position vectors.
Probability Paper 1 · 3 questions
Single events and relative frequency2
Probability of picking a ball from a bag.
Relative frequency and expected frequency.
Combined events and tree diagrams1
Probability from a sample space of spinner sums and products.
Statistics Paper 1 · 8 questions
Charts, tables and scatter diagrams3
Complete a frequency table and draw a bar chart.
Scatter diagram, line of best fit and an estimate.
Pie charts: angles and proportion.
Cumulative frequency2
Median, interquartile range and frequencies from a cumulative frequency graph.
Cumulative frequency and interquartile range.
Histograms2
Histogram and frequency density.
Histogram and frequency density.
Number Paper 2 · 22 questions
Types of number, factors and multiples2
LCM, HCF and cube numbers to find unknowns.
Write a number in figures, spot primes and find a reciprocal.
Sets and Venn diagrams3
Read a Venn diagram and find a probability.
Shade a Venn diagram region and find an overlap from class totals.
Set notation, Venn diagrams and probability.
Fractions and decimals2
Money problems, currency conversion and compound interest.
Exchange rates, simple and compound interest.
Ratio, proportion and rates7
Rice left over after serving 12 people.
Simplify a ratio with a change of units and share an amount in a ratio.
Currency conversion with payouts in fixed amounts, and the change.
Population density using standard form.
Percentages, ratio, proportion, reverse percentages and bounds.
Volume of a cuboid, rates, and surface area of a prism.
Unit costs, reading a graph, unit conversion and ratio.
Indices and standard form3
Standard form, and calculating with it.
Simplify an expression with indices.
Population density using standard form.
Percentages, interest, growth and decay6
Simple interest at two rates.
Exponential decay: find the rate and the year a value is reached.
Simple interest over 5 years and compound interest over 3 years.
Percentages, ratio, proportion, reverse percentages and bounds.
Money problems, currency conversion and compound interest.
Exchange rates, simple and compound interest.
Estimation and limits of accuracy4
Evaluate a calculation and round to 2 decimal places.
Upper and lower bounds of measurements.
Lower bound of an average speed from rounded measurements.
Percentages, ratio, proportion, reverse percentages and bounds.
Algebra Paper 2 · 15 questions
Expanding and factorising4
Factorise an expression.
Expand and simplify brackets.
Combine and rearrange two algebraic expressions.
Factorise an expression.
Algebraic fractions and formulae3
Solve an equation with algebraic fractions.
Combine algebraic fractions into one simplified fraction.
Linear and index equations, inequalities, formulae and algebraic fractions.
Linear and simultaneous equations2
Linear and index equations, inequalities, formulae and algebraic fractions.
Linear and quadratic equations, factorising.
Quadratic equations3
Rectangle problem: form and solve a quadratic, then find a shaded area.
Form and solve a quadratic equation.
Linear and quadratic equations, factorising.
Inequalities and regions1
Linear and index equations, inequalities, formulae and algebraic fractions.
Sequences3
nth terms, and a term of a second sequence.
A bead pattern: complete a table, find nth-term expressions and the largest possible pattern.
Patterns and the nth term of a sequence.
Functions1
Evaluate a function and find the inverse of a linear function.
Coordinate geometry Paper 2 · 5 questions
Gradients and straight lines2
Gradients, parallel lines and the intercept of a perpendicular bisector.
Distance between points, dividing a line and a perpendicular bisector.
Parallel and perpendicular lines2
Gradients, parallel lines and the intercept of a perpendicular bisector.
Distance between points, dividing a line and a perpendicular bisector.
Travel graphs and curves2
Sketch graphs and identify y-intercepts.
Plot a quadratic graph and solve equations graphically.
Gradients of curves and graphical solutions2
Complete a table, plot a curve and solve an equation using a straight line.
Plot a quadratic graph and solve equations graphically.
Geometry Paper 2 · 11 questions
Angles and polygons4
An angle where a pentagon meets a hexagon.
Find two unknown angles from a diagram.
Interior angle of a regular octagon.
Interior angles of polygons and trigonometry.
Circle theorems2
Circle theorems with a cyclic quadrilateral and a tangent.
Circle theorems, arc length and sector area.
Similarity and congruence2
Volume and surface area of a cone on a hemisphere, then a similar solid.
Similar triangles, the cosine rule and the area of a triangle.
Bearings, scale drawings and symmetry2
Real distance from a map scale.
Complete a pattern with rotational symmetry of order 4.
Constructions and loci1
Construct a triangle with compasses and measure an angle.
Mensuration Paper 2 · 7 questions
Perimeter, area and units2
Convert an area from m² to cm².
Unit costs, reading a graph, unit conversion and ratio.
Circles, arcs and sectors3
Percentage of a circle that is shaded.
Circle theorems, arc length and sector area.
Volume and surface area of cones and spheres, sectors and percentage change.
Prisms and cylinders1
Volume of a cuboid, rates, and surface area of a prism.
Pyramids, cones and spheres2
Volume and surface area of a cone on a hemisphere, then a similar solid.
Volume and surface area of cones and spheres, sectors and percentage change.
Trigonometry Paper 2 · 4 questions
Right-angled trigonometry3
Trigonometry and speed for paths across a field.
Cosine rule for a triangle perimeter, rolls of fencing and the shortest distance to a side.
Interior angles of polygons and trigonometry.
Sine rule, cosine rule and area3
Trigonometry and speed for paths across a field.
Cosine rule for a triangle perimeter, rolls of fencing and the shortest distance to a side.
Similar triangles, the cosine rule and the area of a triangle.
Transformations and vectors Paper 2 · 1 question
Reflections, rotations and translations1
Transformations, enlargement and area scale factor.
Enlargements and combined transformations1
Transformations, enlargement and area scale factor.
Probability Paper 2 · 7 questions
Single events and relative frequency2
Estimate faulty items in a batch from a sample.
Relative frequency, and an expected count from a sample size.
Combined events and tree diagrams3
Tree diagram for picking without replacement, and a combined probability.
Probability with and without replacement.
Probability with a sample space diagram for two spins.
Without replacement and Venn diagrams4
Read a Venn diagram and find a probability.
Tree diagram for picking without replacement, and a combined probability.
Probability with and without replacement.
Set notation, Venn diagrams and probability.
Statistics Paper 2 · 5 questions
Averages and range4
Median and range of quiz scores.
Estimate a mean from grouped data and draw a histogram.
Scatter diagram, line of best fit, and averages from a frequency table.
Cumulative frequency, median, percentiles and estimated mean.
Charts, tables and scatter diagrams1
Scatter diagram, line of best fit, and averages from a frequency table.
Cumulative frequency1
Cumulative frequency, median, percentiles and estimated mean.
Histograms2
Estimate a mean from a histogram.
Estimate a mean from grouped data and draw a histogram.