Cambridge International A-Level Mathematics 9709: Frequent mistakes

Cambridge Principal Examiner Reports for Mathematics 9709 emphasise showing working and correct technique. The rubric states “no marks will be given for unsupported answers from a calculator.”

Calculator usage and working

Unsupported answers

Candidates frequently fail to show sufficient working. Using calculators to solve equations and only writing the answer is insufficient.

Fix: Show every step. For quadratics: show factorisation, quadratic formula with substituted values, or completing the square.

Quadratic equations

Must show method—factorisation, formula, or completing the square. Answer alone scores zero if wrong.

Fix: x = (−b ± √(b² − 4ac)) / 2a with a, b, c substituted. Or factorise. Or complete the square.

Algebraic and trigonometric techniques

Basic manipulation

Many struggle with algebraic manipulation and trigonometric functions. Converting tan(x) to sin(x)/cos(x); applying identities correctly.

Fix: tan x = sin x / cos x. sin²x + cos²x = 1. Learn identities. Practise.

Incorrect identities

Some use incorrect identities entirely. Wrong substitution leads to wrong answer.

Fix: Check identity. sin(A+B) = sin A cos B + cos A sin B. Not sin A + sin B.

Binomial expansion

Sign errors

Sign errors frequently in second and third terms. Attempting to multiply brackets instead of using expansion formula.

Fix: (a + b)ⁿ: use formula. Check signs. (a − b)ⁿ: b is negative.

Omitted terms

Omitting the constant term; struggling to identify which terms are needed for a specific power of x.

Fix: Write general term. Set power of x equal to required power. Solve for r.

Differentiation and rates of change

Chain rule

Many fail to recognise when differentiation and chain rule are required for rates of change. Attempting solutions without calculus.

Fix: “Rate of change” often means d/dt or d/dx. Use chain rule: dy/dt = dy/dx × dx/dt.

Discriminant

Misunderstanding

Candidates state discriminant equals zero rather than understanding that positive discriminant indicates intersection for all values of the parameter.

Fix: b² − 4ac > 0 → two distinct roots. = 0 → repeated. < 0 → no real roots. Interpret in context.

Presentation

Poor presentation

Poor presentation causes marks to be lost. Multiple attempts—clearly indicate which solution should be marked.

Fix: Write clearly. If reattempting, cross out old work. Write “marked” or use a star.

Pencil and ink

Writing in pencil superimposed with ink creates unclear images when scripts are scanned.

Fix: Use pen. Erase pencil fully if changing.

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Based on Cambridge International A-level Mathematics 9709 Principal Examiner Reports (2015–2023).

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