Probability generating functions: past paper questions
Real questions on probability generating functions
The newest 20 of 163 written questions. Open one to see it on the real paper.
- 9231/41 · October/November 2025 · Q7a[2]
2-mark “Write” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/41 · October/November 2025 · Q7b[3]
3-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/41 · October/November 2025 · Q7c[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/42 · October/November 2025 · Q6a[5]
5-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/42 · October/November 2025 · Q6b[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/43 · October/November 2025 · Q7a[2]
2-mark “Write” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/43 · October/November 2025 · Q7b[3]
3-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/43 · October/November 2025 · Q7c[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/41 · May/June 2025 · Q2a[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/41 · May/June 2025 · Q2b[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/41 · May/June 2025 · Q6b[3]
3-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/41 · May/June 2025 · Q6c[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/43 · May/June 2025 · Q6a[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/43 · May/June 2025 · Q6b[1]
1-mark “Explain” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/43 · May/June 2025 · Q6c[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/43 · May/June 2025 · Q6d[2]
2-mark “Use” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · October/November 2024 · Q8a[5]
5-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/21 · October/November 2024 · Q8b[4]
4-mark “Show” question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/31 · October/November 2024 · Q4a[4]
4-mark question — its maths and diagrams are best seen on the paper.
See it on the paper → - 9231/31 · October/November 2024 · Q4b[3]
3-mark question — its maths and diagrams are best seen on the paper.
See it on the paper →
What examiners said
Most candidates stated the formula for the sum of the geometric progression accurately. Some wrote the exponent as n − 1 , which hindered their progress in part (b). A few incorrectly stated that the sum was equal to zero.
— Examiner report, October/November 2023, 9231/21 Q8(a) (Cambridge)
This was a ‘show that’ question so candidates were required to include sufficient detail in their response so that the derivation of the probability generating function was clear. The best responses first derived P (X = r) before writing the function in extensive form. They then clearly indicated that this was an infinite geometric progression, either by explicitly stating the first term and commo...
— Examiner report, October/November 2023, 9231/41 Q5(a) (Cambridge)
Most candidates knew what was required for this part and attempted to find the first and second derivatives of the probability function given in the stem of the question. The majority of candidates used the quotient rule to find the first derivative but often left the numerator unsimplified which sometimes led to errors in finding the second derivative. A number of candidates used the quotient rul...
— Examiner report, October/November 2023, 9231/41 Q5(b) (Cambridge)
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