Structured Questions

Examiner notes & key calculations

• Base Case Rigour in Induction: In both divisibility and matrix induction proofs, many candidates forgot to state the connection for n=1 n = 1 n=1 or explicitly label the induction hypothesis as an assumption, which cost structural presentation marks.
• Summation Index Shifting: For series differences, a recurring blunder was subtracting the sum to n n n instead of n−1 n-1 n−1 when computing the sum of intermediate terms, leading to massive algebraic errors.
• Neglecting Derivative Scaling: In the parametric differentiation question on Paper 2, candidates frequently overlooked division by dxdt \frac{dx}{dt} dtdx​ when calculating the second derivative d2ydx2 \frac{d^2y}{dx^2} dx2d2y​.
• Small Sample t-Test Failures: In Paper 4, students occasionally selected normal z z z-values instead of appropriate critical t t t-values when population variances were unknown and sample sizes were small, or forgot to pool the variance when equal variances were explicitly given.
• Column Combination in Goodness of Fit: For the χ2 \chi^2 χ2 test, many candidates failed to combine classes where the expected frequency fell below 5, invalidating the degrees of freedom calculations.