AS & A Level Mathematics 9709 · Topic 6

Probability & Statistics 2 (for Paper 6): past paper questions

213 real questionsasked in 9 of the last 10 exam series2020–2025usually: Find, Use, State, Explain, Calculate

Real questions on probability & statistics 2 (for paper 6)

The newest 20 of 213 written questions. Open one to see it on the real paper.

9709/61 · October/November 2025 · Q1a[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/61 · October/November 2025 · Q1b[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/61 · October/November 2025 · Q3a[3]
3-mark “Use” question — its maths and diagrams are best seen on the paper.
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9709/61 · October/November 2025 · Q3b[3]
3-mark “Use” question — its maths and diagrams are best seen on the paper.
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9709/61 · October/November 2025 · Q5c[1]
1-mark “Explain” question — its maths and diagrams are best seen on the paper.
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9709/62 · October/November 2025 · Q1a[1]
1-mark “State” question — its maths and diagrams are best seen on the paper.
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9709/62 · October/November 2025 · Q1b[3]
3-mark “Calculate” question — its maths and diagrams are best seen on the paper.
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9709/62 · October/November 2025 · Q1c[4]
4-mark “Use” question — its maths and diagrams are best seen on the paper.
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9709/63 · October/November 2025 · Q1a[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/63 · October/November 2025 · Q1b[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/63 · October/November 2025 · Q3a[3]
3-mark “Use” question — its maths and diagrams are best seen on the paper.
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9709/63 · October/November 2025 · Q3b[3]
3-mark “Use” question — its maths and diagrams are best seen on the paper.
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9709/53 · May/June 2025 · Q6a[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/53 · May/June 2025 · Q6b[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/53 · May/June 2025 · Q6c[5]
5-mark question — its maths and diagrams are best seen on the paper.
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9709/61 · May/June 2025 · Q1[3]
3-mark “Use” question — its maths and diagrams are best seen on the paper.
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9709/61 · May/June 2025 · Q5a(i)[2]
2-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/61 · May/June 2025 · Q5a(ii)[6]
6-mark “Use” question — its maths and diagrams are best seen on the paper.
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9709/61 · May/June 2025 · Q5b[3]
3-mark question — its maths and diagrams are best seen on the paper.
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9709/62 · May/June 2025 · Q3a[1]
1-mark “Write” question — its maths and diagrams are best seen on the paper.
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What examiners said

The hypothesis test was reasonably well attempted, with the null and alternative hypotheses generally correctly stated. The most common error noted was the omission of √𝟔𝟎 in the denominator when standardising, and premature approximation of 14.44 to 14.4 caused a loss of accuracy for some candidates. After standardising to find z, a clear comparison was required and a common error for those who c...
— Examiner report, February/March 2025, 9709/62 Q2(b) (Cambridge)

This part was not well answered and showed a basic lack of understanding of the Central Limit Theorem by a large number of candidates. There were some candidates who realised that the underlying distribution was not given, but failed to qualify that this was the ‘population’ distribution; the distribution being referred to must be clear, so merely saying ‘the distribution is unknown’ is not precis...
— Examiner report, February/March 2025, 9709/62 Q2(c) (Cambridge)

This question was well attempted with most candidates correctly calculating 1- P(0, 1, 2). The most common errors were to calculate P(0, 1, 2) rather than 1– P(0, 1, 2) or to calculate 1– P(0, 1, 2, 3). It was important that the full Poisson expression was shown in order to fully justify the answer; candidates are advised to show all necessary working.
— Examiner report, February/March 2025, 9709/62 Q3(a) (Cambridge)

Practise this topic

Answer these questions online and get each one marked against the official mark scheme, with what you missed and how to fix it.

Practise probability & statistics 2 (for paper 6)

In the syllabus

6.1 The Poisson distribution

use formulae to calculate probabilities for the
use the fact that if X + Po ^mh then the mean Proofs are not required.
understand the relevance of the Poisson
use the Poisson distribution as an The conditions that n is large and p is small should
be known; n > 50 and np < 5, approximately.
use the normal distribution, with continuity The condition that m is large should be known;
m 2 15 , approximately.

6.2 Linear combinations of random variables

use, when solving problems, the results that Proofs of these results are not required.
E(aX + b) = aE(X) + b and
E(aX + bY) = aE(X) + bE(Y)
Var(aX + bY) = a2 Var(X) + b2 Var(Y) for
if X has a normal distribution then so does
if X and Y have independent normal
if X and Y have independent Poisson

6.3 Continuous random variables

understand the concept of a continuous For density functions defined over a single interval
only; the domain may be infinite,
e.g. for x H 1. x4
use a probability density function to solve Including location of the median or other percentiles
of a distribution by direct consideration of an area
using the density function.
Explicit knowledge of the cumulative distribution function is not included.

6.4 Sampling and estimation

understand the distinction between a sample
explain in simple terms why a given sampling Including an elementary understanding of the use
of random numbers in producing random samples
Knowledge of particular sampling methods, such as quota or stratified sampling, is not required.
recognise that a sample mean can be regarded
use the fact that _X i has a normal distribution
use the Central Limit Theorem where Only an informal understanding of the Central Limit
Theorem (CLT) is required; for large sample sizes, the distribution of a sample mean is approximately normal.
calculate unbiased estimates of the population Only a simple understanding of the term ‘unbiased’
is required, e.g. that although individual estimates
will vary the process gives an accurate result ‘on average’.
determine and interpret a confidence interval

6.5 Hypothesis tests

understand the nature of a hypothesis test, the Outcomes of hypothesis tests are expected to
be interpreted in terms of the contexts in which
questions are set.
formulate hypotheses and carry out a
direct evaluation of probabilities
a normal approximation to the binomial or
formulate hypotheses and carry out a
understand the terms Type I error and Type II
calculate the probabilities of making Type I and
Cambridge International AS & A Level Mathematics 9709 syllabus for 2026 and 2027.

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