What Cambridge examiners keep telling A Level Math students

Every exam session, Cambridge publishes a report for teachers on each paper. Read one report and it can feel like a list of small complaints. Read many of them in a row and a pattern appears: the same reminders come back session after session, across every paper. This guide collects the ones that apply to the whole of Cambridge A Level Math (9709), whether the paper is Pure Math, Mechanics or Statistics. Most of them are not about knowing more math. They are about how marks are earned and how they are quietly lost.

This guide is based on a reading of the examiner reports for recent sessions. The advice is summarised in our own words.

1. A calculator answer on its own earns very little

The front cover of the question paper says that no marks are given for unsupported answers from a calculator. The reports return to this almost every session, because a minority of students still lose marks to it.

• Quadratic equations: show the factorisation, the quadratic formula with the values substituted into it, or the completed square. Writing down the two roots is not enough, and neither is quoting the formula without substituting.
• Check your factorisation. The brackets must expand to give the coefficients of the original quadratic. Examiners notice factors that do not.
• Trigonometric equations and simultaneous equations: show the steps that lead to the solution.
• Integrals: substitute the limits yourself. Definite integrals evaluated by a calculator function earn no credit for method.
• Equation solvers on "show that" questions: the answer is given, so the marks are for the working. A solver shows none.

Use the calculator to check your work, not to replace it.

2. "Show that" means every step is visible

When the answer is printed in the question, the examiner is not looking for the answer. They are looking for the line of reasoning that gets there. Reports repeatedly mention students who jump from one line to the answer, who skip a simplification, or who quote a result instead of deriving it. Write the line where the printed answer first appears, and make sure each step follows from the one before it. If you are working backwards from the given answer, you are likely to miss a step.

3. "Hence" is an instruction

When a question says "hence", the examiner expects you to use the result you just found. Reports describe many students who restarted from scratch, or ignored their answer to the previous part, and so lost marks, time, or both. If you see "hence", look at the part before it and ask what it was for. The same goes for questions where one part clearly sets up the next: ask yourself why you were asked to do that earlier part.

4. Read the question twice, and read the marks

• Read once to see what is happening and once to pick out what is asked.
• Look at the marks. A one-mark part should not need a page of working. A part worth six marks is rarely a single step.
• Information in the introduction to a question applies to the whole question. Information given inside one part applies to that part only.
• Several reports describe students who answered a different question from the one asked, for example finding an area when the question asked for a volume.
• Re-read the question when you finish. Did you give what it asked for?

5. Give the answer in the form the question asks for

Marks are lost for correct math in the wrong form. The reports mention these again and again:

• Exact answers. If the question asks for an exact value, work with surds, fractions, π or logarithms, and do not switch to decimals.
• An equation of a graph needs "y =" in the final answer, not only the expression.
• A point needs both coordinates.
• A range is a statement about y or f(x), not x, and the inequality signs matter.
• A variable named in the question should be named in the answer. If the question asks for a, write a = and not x =.
• "State" or "write down" signals that little or no working is needed. Do not spend time on it.

6. Accuracy and rounding

Rounding costs marks every session. This is important enough to have its own guide: [Accuracy in A Level Math: significant figures, exact answers and rounding].

7. Find all the solutions

Many reports mention students who found one solution when there were two or more.

• Remember both roots when you take a square root.
• Do not divide by an expression that might be zero. Dividing both sides of an equation by something that contains the unknown can lose a solution. Factorise instead.
• In trigonometry, read the given interval carefully and list every solution inside it, including negative angles.
• When a question has a real-life context, check each solution against it. A negative length or a zero number of terms may need to be rejected, and the question may expect you to say so.

8. Draw the picture

Sketches and diagrams are recommended in reports for every paper.

• In coordinate geometry, a quick sketch often shows which points to use and prevents assumptions such as "this line is perpendicular" or "this triangle is isosceles".
• In mechanics, a force diagram with every force labelled helps you include all the terms in an equilibrium or Newton's law equation.
• On an Argand diagram, use the same scale on both axes.
• Diagrams in the question paper are often not drawn to scale. Do not read lengths or angles from them.

9. Conclusions in context

When a question asks you to conclude, write a sentence about the situation described, not a general statement. In hypothesis testing, the conclusion should be in context and should not sound certain. The same idea applies to other questions: if a quadratic gives two answers, say which one fits the context and why the other does not.

10. Protect yourself from sign and arithmetic slips

Sign errors and algebra slips appear in the reports for every paper. Reports mention more practice with negative numbers, using brackets when substituting, and checking the result by substituting back. Writing one line under the next, in order, makes a missing term easier to spot than a scattered page of working.

11. Presentation counts more than it used to

Papers are now scanned before they are marked.

• Write in black pen. Pencil that has been written over, or erased, can scan badly and the old and new writing can both appear.
• Keep your whole attempt in the space provided, with only diagrams in pencil.
• Offer one solution. If you change your mind, cross out the old attempt and replace it. Overwriting makes both unreadable.
• If you use the additional page, write the question number clearly.
• Arrive with a pencil, black pen, ruler, protractor and compasses.

How to use this list

When you work through a worksheet, mark your own work against these eleven points as well as against the mark scheme. Most students find that a few habits account for most of the marks they lose. Pick the two that apply to you and practise them until they become automatic.

Questions students ask

Can I use my calculator to solve equations in A Level Math?

Only to check. The front of the question paper says no marks are given for unsupported answers from a calculator. For quadratics show the factorisation, the formula with values substituted or the completed square, and substitute definite integral limits yourself. An equation solver on a "show that" question shows no working, so it earns nothing.

What does "show that" mean in an A Level Math exam?

The answer is printed, so the marks are for the line of reasoning. Write the line where the printed answer first appears, and make sure each step follows from the last. Examiners report students who jump to the answer, skip a simplification or quote a result instead of deriving it.

What does "hence" mean?

It is an instruction to use the result you have just found. Students who restart from scratch or ignore the previous part lose marks, time or both.

Why do I lose marks for correct answers in the wrong form?

Because the question asked for a particular form. Exact answers must stay as surds, fractions, π or logarithms. An equation of a graph needs "y =". A point needs both coordinates. A range is a statement about y or f(x), not x.

How do I make sure I find all the solutions?

Remember both roots when taking a square root, factorise instead of dividing by an expression that might be zero, read the given interval in trigonometry and list every solution in it including negative angles, and check each solution against the context.

Does handwriting and layout matter now that papers are scanned?

Yes. Write in black pen, keep your whole attempt in the answer space, offer one solution and cross out rather than overwrite, and label additional pages with the question number. Overwriting makes both attempts unreadable.