2019 H2 Maths Paper 2 Q6 — Worked Solution

Part (i)

1 mark

These 22 clubs form a population.

Explanation: Alice’s investigation concerns approaches to training by clubs in Division One specifically, so the group she wants to know about (her population of interest) is exactly those 22 clubs. Since she sends the questionnaire to all 22 of them, she has surveyed the entire population, not a sample of it.

Part (ii)

2 marks

Dilip should take a stratified sample of clubs, with the number of clubs sampled from each of the 4 divisions in proportion to the number of clubs in that division, rather than checking the facilities at all 100 clubs.

Explanation: checking every club’s supporter facilities in detail would take far more time and resources than is needed to draw a reliable conclusion, so a sample is appropriate. Facilities are likely to differ systematically between divisions (e.g. clubs in a higher division may have larger budgets and better facilities), so a simple random sample could by chance under-represent a division; stratifying by division guarantees each division is represented in the sample in fair proportion.

Part (iii)

3 marks

Approach

choosing 5 clubs from each of the 4 divisions are 4 independent choices, so we multiply the number of ways of making each choice.

\text{No. of samples} = \binom{22}{5}\binom{24}{5}\binom{26}{5}\binom{28}{5}

By GC,

= 7\, 236\, 118\, 179\, 312\, 422\, 400

\therefore\ \text{the number of different possible samples is }7\, 236\, 118\, 179\, 312\, 422\, 400\ \left( \approx 7.24 \times 10^{18} \right).

2019 H2 Maths Paper 2, Question 6

Part (i)

Part (ii)

Part (iii)

This is how we mark, and how we teach.