BGCSE Mathematics Past Papers: Topics, Format, and Grades A-G
BGCSE Mathematics is taken at the end of Grade 12 and, unlike BJC Mathematics, it has three separate papers. Whether you sit all three or just two depends on the grades you are aiming for. Understanding the structure of the exam before you start preparing makes a real difference in how you use your time.
The format of BGCSE Mathematics
BGCSE Mathematics uses a tiered system with two schemes:
| Paper | Code | Duration | Marks | Format | Calculator |
|---|---|---|---|---|---|
| Paper 1 | 3815/1 | 1 hr 30 min | 100 | Structured short-answer, all compulsory | Yes (not graphing) |
| Paper 2 | 3815/2 | 2 hrs | 100 | Structured and multi-step, all compulsory, with graph paper | Yes (not graphing) |
| Paper 3 | 3815/3 | ~2 hrs | ~100 | Extended structured questions, higher-level content | Yes (not graphing) |
Materials permitted for all papers: non-graphing calculator (required), geometrical instruments (ruler, protractor, compasses), tracing paper. Graph paper is provided for Paper 2. A formula sheet is included at the front of every paper.
How grading works: Core and Extended
Papers 1 and 2 are sat by all students and determine grades C through G. To be eligible for grades A or B, a student must also sit Paper 3 (the Extended paper) and achieve at least grade C on Papers 1 and 2 first.
| Grade target | Papers required |
|---|---|
| Grades C, D, E, F, G | Papers 1 and 2 only |
| Grades A or B | Papers 1, 2, and 3 (must achieve at least grade C on 1 and 2 first) |
This matters for how you approach preparation. If your goal is a C or above for university entry requirements, Papers 1 and 2 cover everything you need. If you are aiming for A or B, you also need to be comfortable with the Paper 3 content: calculus, matrices, further trigonometry, and extended algebraic reasoning.
What is on each paper
Paper 1: Structured short-answer (1 hr 30 min, 100 marks)
Paper 1 has 15-20 structured short-answer questions, each with sub-parts (a, b, c). These are not multiple choice. Questions are compulsory and cover the entire syllabus. Topics that appear consistently on Paper 1 include:
- Number sequences: find the next terms, identify the pattern
- Unit price and proportional reasoning
- Standard form, rounding, and significant figures
- Unit conversions (grams to kilograms, metres to centimetres)
- Time calculations: duration, 24-hour clock
- Venn diagrams: complete a diagram, list members of a set, find n(Q)
- Budgeting and money problems
- 3D shape identification
- Probability: single events and complementary events
- Best-buy and unit rate comparisons
- Ratio problems in simplest form
Paper 2: Structured multi-step (2 hrs, 100 marks, with graph paper)
Paper 2 has approximately 11 structured questions, all compulsory, with multi-step problems. Working must be shown. Topics include:
- Percentage decrease and increase
- Algebraic inequalities with number line representation
- Fractions of a whole, finding totals from given fractions
- Mean and weighted mean problems
- Interior and exterior angles of polygons
- Vectors: column vectors, addition, scalar multiplication
- Speed, distance, and time
- Factorisation and simplification of algebraic expressions
- Powers and indices
- Unit conversions including area in square metres
- Circle theorems: tangent properties, angles in a circle
- Perimeter and area of shaded regions involving circles
Paper 3: Extended (for grades A-B only)
Paper 3 covers content beyond the core syllabus. Topics include:
- Trigonometric equations (solving for an unknown angle)
- Compound interest calculations
- Exponential equations
- Inverse proportion
- Graphing inequalities and identifying feasible regions
- Volume problems using algebra
- Circle theorem proofs with tangents
- Matrix equations, inverse matrices, singular matrices
- Algebraic fractions: simplify and combine
- Bearings and cosine rule in navigation problems
- Differentiation of polynomials and stationary points
- Basic integration
The formula sheet
A formula sheet is provided in every paper. The core sheet (Papers 1 and 2) includes area formulas, circle formulas (circumference, area), volume of a cuboid and cylinder, and standard form notation. The Paper 3 sheet adds the sine rule, cosine rule, area of a triangle using sine, the quadratic formula, matrix determinant and inverse, sphere and cone formulas, and the differentiation rule for polynomials.
Knowing what is on the formula sheet and practising how to apply each formula under time pressure is different from knowing the formulas by heart. Both matter.
Topics by strand (Grades 10-12)
Number and Operations
- Finding the nth term given a formula
- Upper and lower bounds; percentage error
- Standard form: operations, reading, and writing
Algebra
- Quadratic expressions: factorisation, completing the square, quadratic formula
- Functions: domain, range, mapping notation, composite and inverse functions
- Variation: direct, inverse, and joint
- Matrix algebra: 2x2 operations, determinant, inverse
- Linear programming: graphing constraints, identifying feasible region
- Arithmetic and geometric sequences
Geometry
- Circle theorems: angles in a circle, tangent properties, cyclic quadrilaterals
- Trigonometry: sin/cos/tan ratios, sine rule, cosine rule, area of a triangle using sine
- 3D trigonometry
- Vectors: column vector notation, addition, subtraction, scalar multiplication
- Bearings: three-figure bearings in navigation problems
Measurement
- Volume and surface area of cones, spheres, and pyramids
- Compound shapes combining multiple solids
Statistics and Probability
- Standard deviation
- Cumulative frequency curves (ogives) and box-and-whisker plots
- Conditional probability
Calculus (Paper 3 only, Grades 11-12)
- Differentiation from first principles
- Differentiation of polynomials: gradient at a point, stationary points
- Basic integration
Practise BGCSE Mathematics by topic
Waypoint has BGCSE Mathematics questions across all strands above, with worked explanations. Whether you are targeting C or aiming for A-B on Paper 3, start with your weakest area.
Start FreeHow to use BGCSE Mathematics past papers effectively
Work each paper under realistic exam conditions rather than with it open for reference:
- Paper 1: sit for exactly 1 hour 30 minutes with your non-graphing calculator and the formula sheet. Attempt every question.
- Paper 2: sit for exactly 2 hours. Show working on every question. Multi-step questions award marks for method shown, not just for the correct final answer.
- Paper 3 (if attempting): expect questions requiring several steps of reasoning. A partially correct solution with working shown can still earn marks.
- After marking: separate wrong answers into content gaps (need to study the topic) and application errors (need to practise the question type). These have different fixes.
Frequently asked
What is the format of BGCSE Mathematics?
Three papers. Paper 1: structured short-answer, 1 hour 30 minutes, 100 marks. Paper 2: structured multi-step, 2 hours, 100 marks, with graph paper. Paper 3: Extended only, required for grades A or B. Non-graphing calculator required for all papers. A formula sheet is provided for all three.
Is a calculator allowed on BGCSE Mathematics?
Yes, and it is required. Non-graphing calculators only. Graphing calculators are not permitted. Geometrical instruments and tracing paper are also allowed.
What are grades A and B on BGCSE Mathematics?
To be eligible for grade A or B, a student must sit Paper 3 (the Extended paper) and achieve at least grade C on Papers 1 and 2 first. A weak performance on Paper 3 cannot reduce the grade earned on Papers 1 and 2.
What topics do Paper 1 and Paper 2 cover?
Both papers cover the full core syllabus: number (standard form, bounds, sequences), algebra (quadratics, functions, matrices), geometry (circle theorems, trigonometry, vectors, bearings), measurement (volume and surface area of all standard solids), and statistics (standard deviation, cumulative frequency, conditional probability). Paper 2 tends to have longer multi-step questions than Paper 1.