Examiner's Perspective: Decision Mathematics D1 (WDM11/01) Jan 2024

The January 2024 Decision Mathematics D1 paper presented a balanced mixture of traditional algorithmic questions and rigorous conceptual challenges. With a total of 75 marks, the paper tested core execution skills, graphical interpretation, and algebraic formulation. The overall difficulty was moderate, though several boundary-case questions in the later sections pushed high-achieving students to their limits.

Where the Marks Are Won and Lost

As is typical in D1, accuracy and formatting are paramount. Many candidates lost easy marks on Dijkstra's algorithm (Question 3) simply by listing the working values out of order at node D. The examiner's report noted that values must be shown in a strictly decreasing sequence (e.g., \( 39, 37, 35 \)) to receive credit. Similarly, in Quick Sort (Question 6), failing to explicitly circle or underline pivots in each pass resulted in the loss of the final accuracy mark, even if the final sorted list was correct.

The most significant mark differentiator was Question 1(e) (determining the minimum number of workers using a cascade chart) and Question 7 (formulating and solving a three-variable linear programming problem). In Question 1(e), candidates failed to secure both marks because they omitted the specific time interval, such as \( 12 < t < 13 \), or failed to list the exact overlapping activities (F, H, I, and L) active during that period.

Key Pitfalls to Avoid

  • Incomplete Float Calculations: When asked for the total float of an activity (e.g., activity D in Question 1b), you must show the full calculation: \( 12 - 4 - 5 = 3 \). Simply writing "3" is insufficient.
  • Vague Explanations in Bin Packing: In Question 6, justifying the lower and upper bounds of the bin size \( n \) requires explicit numerical evidence, such as referencing the sum of the elements in Bin 3 equaling 72.
  • LP Formulation Signs: In formulation questions, ensure that all inequality signs are correct and that integer coefficients are used. Writing decimal fractions in constraints is heavily penalised.

Preparation Strategy & Predictions

To secure a top grade in upcoming sessions, focus on the following high-yield strategies:

First, practice drawing precedence networks with multiple dummies. The examiner's report indicated that many students struggled to draw the minimum number of dummies (exactly 4) in Question 4, often introducing redundant dependencies. Second, master the Travelling Salesperson lower bound method using vertex deletion, as it is highly likely to appear in a more complex format next season.