9231 · Cambridge International A Level
Mathematics - Further (9231) Exam Tips
In Further Pure Mathematics (Papers 1 and 2), mathematical induction is a foundational pillar where students routinely surrender easy marks. Examiner reports show that the difference between an outstanding score and a mediocre one often lies in the formality of the proof. Top sco…
Papers
4
Total marks
250
Time limit
7h
Grade scale
Additional note
Calculator policy
A silent scientific calculator is required where the syllabus permits one. It must NOT be graphical, programmable, or capable of symbolic algebra (CAS), and it must contain no stored programs or notes.
4
Papers
6
Strategies
7
Mistakes
- In Further Pure Mathematics (Papers 1 and 2), mathematical induction is a foundational pillar where students routinely surrender easy marks. Examiner reports show that the difference between an outstanding score and a mediocre one often lies in the formality of the proof. Top scorers never treat the base case as a trivial formality. When proving a statement like (65)n≥1+15n (\frac{6}{5})^n \ge 1 + \frac{1}{5}n (56)n≥1+51n, you must explicitly evaluate and state the Left-Hand Side (LHS) and Right-Hand Side (RHS) for n=1 n = 1 n=1 (e.g., LHS=65 = \frac{6}{5} LHS=56 and RHS=1+15=65 = 1 + \frac{1}{5} = \frac{6}{5} RHS=1+51=56), concluding clearly that LHS≥RHS \ge LHS≥RHS. Then, state your inductive hypothesis clearly: 'Assume the statement is true for some positive integer n=k n = k n=k'. Do not omit the word assume or reference an undefined variable.
Tips are paraphrased for study purposes from exam structure data and marking patterns. Always verify against your official syllabus and mark scheme.