4024 O Level Mathematics: past papers
112 papers from 2012 to 2025, with 166 questions sorted by syllabus topic.
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.