BJC Mathematics Past Papers: Topics, Format, and Practice

BJC Mathematics is the exam most students feel most anxious about, and the one where the gap between preparation and performance is most directly closeable. This guide covers what is actually on the papers, the topics that show up every year, how marking works, and what to do with whatever past papers you manage to find.

The format of BJC Mathematics

BJC Mathematics is assessed across two papers. Both papers cover the full syllabus. Calculators are not allowed on either.

Paper 1 is shorter and faster, testing speed and accuracy across all 20 content strands of the syllabus. Paper 2 is more demanding: multi-step structured problems where your working is assessed, not just your final answer. Because Paper 2 carries 60% of the grade, strong performance on it outweighs a weaker Paper 1, and weak performance there cannot be rescued by a good Paper 1 alone.

The no-calculator rule matters more than most students appreciate until they are in the room. Every calculation, every fraction simplification, every percentage must be done on paper. Students who rely on a phone or calculator for basic arithmetic in everyday schoolwork are regularly caught off-guard in a way that students who practise written computation are not.

The 20 strands of the BJC Mathematics syllabus

The BJC Mathematics syllabus is built around 20 numbered strands, all of which are examined across the two papers. The strands span five topic areas:

Number and Operations

• Whole numbers, factors, multiples, HCF, LCM, prime factorisation
• Fractions: adding, subtracting, multiplying, dividing, converting to decimals and percentages, mixed numbers
• Decimals and percentages: four operations, expressing one quantity as a percentage of another
• Directed numbers: the four rules applied to positive and negative integers
• Estimation and approximation: rounding to decimal places and significant figures
• Ratio, direct and indirect proportion, unit pricing, map scales
• Sets: notation, union, intersection, Venn diagrams (up to two sets)

Consumer Mathematics

• Simple interest and compound amounts
• Profit, loss, discount, mark-up
• Hire purchase and instalment payments
• Wages, salaries, taxation
• Foreign currency conversions
• Personal and household budgets

Algebra

• Algebraic notation and use of letters for generalised numbers
• Substitution into formulae and expressions
• Solving linear equations in one unknown (including brackets, variables on both sides)
• Inequalities on a number line
• Coordinate geometry: plotting points, travel graphs, conversion graphs
• Transformations: reflections in horizontal and vertical lines; identifying rotations and translations

Geometry and Measurement

• Perimeter of regular and irregular polygons
• Area: rectangles, triangles, parallelograms, trapeziums, circles, compound shapes
• Volume: cubes and cuboids
• Arc length and sector area
• Angle properties: triangles, quadrilaterals, parallel lines, exterior angles
• Constructions with ruler and compass: 60 degrees, 90 degrees, bisecting angles and lines
• Speed, distance, and time problems
• Both metric and Imperial units are required

Statistics and Probability

• Reading and interpreting tables, bar charts, pictographs, pie charts, travel graphs
• Mean, mode and median of individual and discrete data
• Probability as a fraction, decimal or percentage; independent and dependent events

What to do with a BJC Mathematics past paper

The least useful way to work through a past paper is to sit with it open, use a calculator for the hard parts, and check the answers as you go. That approach removes every condition that makes the exam challenging. The goal is to build the ability to perform under actual exam conditions, and that requires actually recreating those conditions.

1. Sit Paper 1 for exactly 1 hour, no calculator, no notes. Every question you cannot answer in the time available is a data point about your preparation.
2. Sit Paper 2 for exactly 2 hours, no calculator, with working shown on every question. If a question asks you to calculate simple interest, write the formula, write the substitution, write each step. Structured questions award marks for working, not just for correct final answers.
3. Mark the papers strictly. Separate your wrong answers into: questions where you did not know the topic, and questions where you knew the method but made an arithmetic or writing error. These have different fixes.
4. Re-attempt the topic-knowledge gaps later. After studying the topic, close your notes and attempt the same question again without help. If you still cannot do it, you have not learned it yet.

What if you only have one or two papers?

The BJC Mathematics syllabus is stable and has 20 defined strands. All 20 appear on every paper. This means a single past paper, used well, tells you everything you need to know about your preparation across the full syllabus. After marking it, use it a second time by drilling only the questions you got wrong, without notes, until you can answer them correctly. One thoroughly worked paper is more valuable than five papers read without timed practice.

Topic-based practice through any source that covers the BJC syllabus builds the same underlying skill. Past papers are useful because they show you question format and paper pacing. The skill they develop — applying mathematics under time pressure without a calculator — can be built through focused topic drills too.

Frequently asked

What topics appear on BJC Mathematics every year?

All 20 strands of the syllabus appear across the two papers. Consumer mathematics (simple interest, profit and loss, hire purchase), fractions and percentages, algebra (equations, substitution), geometry (perimeter, area, angles), and statistics (averages, graphs, probability) are all tested without exception.

What is the format of BJC Mathematics Paper 1 and Paper 2?

Paper 1 is short-answer questions lasting 1 hour, worth 40% of the grade. Paper 2 is structured questions lasting 2 hours, worth 60%. Calculators are not permitted on either paper.

Is a calculator allowed on BJC Mathematics?

No. The BJC Mathematics syllabus specifies that calculators are not permitted. All arithmetic must be done on paper. This is one of the most important things to prepare for, and students who practise only with a calculator are regularly caught short in the exam.

Does BJC Mathematics include Imperial units?

Yes. Both metric and Imperial units appear on the BJC Mathematics papers. Students need to be able to convert between units and work with compound units (like km/hr) in both systems.