The papers and your combination

📋The six components

Each paper is a separate component with its own code. Papers 1 and 3 are the long ones; the other four are shorter.

• Paper 1 — Pure Mathematics 1 (P1). 1 hour 50 minutes, 75 marks. Sat by every 9709 candidate at both levels.
• Paper 2 — Pure Mathematics 2 (P2). 1 hour 15 minutes, 50 marks. AS Level only.
• Paper 3 — Pure Mathematics 3 (P3). 1 hour 50 minutes, 75 marks. A Level only. Largely contains P2, plus vectors, differential equations, complex numbers, partial fractions and several further integration techniques.
• Paper 4 — Mechanics (M). 1 hour 15 minutes, 50 marks.
• Paper 5 — Probability & Statistics 1 (S1). 1 hour 15 minutes, 50 marks.
• Paper 6 — Probability & Statistics 2 (S2). 1 hour 15 minutes, 50 marks.

Papers 1 and 3 carry 9 to 12 structured questions each; the four shorter papers carry 6 to 8. Every question is compulsory on every paper — there is no choice anywhere in 9709.

🧭The valid combinations

AS Level Mathematics — two papers. Paper 1 is worth 60% and the second paper 40%.

• Papers 1 and 2 — pure mathematics only.
• Papers 1 and 4 — pure and Mechanics.
• Papers 1 and 5 — pure and Probability & Statistics 1.

A Level Mathematics — four papers. Papers 1 and 3 are worth 30% each, and each applied paper 20%.

• Papers 1, 3, 4 and 5 — the “Mechanics and Statistics” route.
• Papers 1, 3, 5 and 6 — the “Statistics” route.

You do not have to sit all four A Level papers at once. Cambridge allows a staged route — two papers in the first year for the AS Level, then two more in a later series, carrying the AS result forward — as well as a linear route where all four are taken in the same series. The staged route spreads the load and gives you a qualification in hand after year one; the linear route leaves everything to one series. Which one you are on is your school's decision, so ask.

Two consequences are worth pulling out. Paper 5 appears in both A Level routes, so essentially every A Level candidate sits Probability & Statistics 1 — it is the second most universal component after Paper 1. And Paper 2 is not part of any A Level combination: if you are taking the full A Level, your second pure paper is Paper 3, and P2 past papers are useful practice for the shared topics but do not cover everything you need.

🔢The list of formulae (MF19)

You are given a clean copy of the list of formulae in every paper. It carries a great deal — the binomial expansion, the trigonometric identities, the standard derivatives and integrals, the vector results, the summary of the discrete distributions, and the statistical formulae. So do not spend revision time memorising what is printed for you.

Spend it instead on two things. First, knowing which formula applies and why: the list tells you nothing about when a question wants the cosine rule rather than the sine rule. Second, the things the list does not give you — the exact trigonometric values, the shapes of the standard graphs, the laws of logarithms as manipulation habits, and the derivative and integral of the very simplest functions.

Work with the list open from the start of the course. Finding a result in it under time pressure should be automatic, not a search.

🔢Calculators

You need a scientific calculator. Computers, graphic calculators, and calculators capable of symbolic algebra, differentiation or integration are all forbidden — the ban is wider than most students assume, and it rules out the machine many arrive with. That has a consequence people underestimate: you cannot check a stationary point by looking at a graph, and you cannot solve an equation by finding an intersection on a screen. Sketching by hand from the algebra is a genuinely examinable skill in this syllabus, not a fallback.

Bring a ruler. A protractor and compasses are not required.

Note too that no marks are given for an unsupported answer taken from a calculator. Solving a quadratic on the machine and writing down the roots scores nothing where the working was the point — use the calculator to check what you have already done by hand.

Check the current syllabus for the exact calculator specification, and make sure the machine you practise on is the one you take into the hall.

✍️Accuracy, working and the mark scheme

Unless a question says otherwise, give non-exact numerical answers to three significant figures, and angles in degrees to one decimal place. Keep full accuracy through the middle of a question and round only at the end — rounding at each step is how a correct method produces an answer the mark scheme rejects.

Marks are split into method marks and accuracy marks, and method marks survive an arithmetic slip. This is the single strongest argument for writing your working down: a wrong final answer with visible correct method routinely scores most of the marks, while a wrong final answer with no working scores none.

📝Command words are instructions

Cambridge publishes the command words it uses, with a fixed meaning for each. These are the eleven that appear in 9709:

• Calculate — work out from given facts, figures or information.
• Describe — state the points of a topic; give characteristics and main features.
• Determine — establish with certainty.
• Evaluate — judge or calculate the quality, importance, amount or value of something.
• Explain — set out purposes or reasons; make the relationships between things clear; say why and/or how, and support with relevant evidence.
• Identify — name, select or recognise.
• Justify — support a case with evidence or argument.
• Show (that) — provide structured evidence that leads to a given result.
• Sketch — make a simple freehand drawing showing the key features, taking care over proportions.
• State — express in clear terms.
• Verify — confirm a given statement or result is true.

Two more words are not on that list but govern how a question must be answered. Hence means you must use your work from the previous part; a fresh method scores nothing. Hence or otherwise means you may use the previous part (usually the easier route) or start again. And where a question asks for an exact answer, leave surds, \( \pi \), logarithms and fractions as they are — converting \( \dfrac{\pi}{6} \) to 0.524 throws the mark away.

Note the difference between Show (that) and Verify: showing requires a structured argument that arrives at the printed result, while verifying accepts confirming that a given value works. A “show that” answered by substituting the answer back in has verified, not shown, and scores accordingly.

“Show that” deserves special attention because it appears constantly in 9709 and is generous when handled properly: the answer being given means you can still do the next part even if you cannot do this one. Never abandon a question because you got stuck on a “show that”.