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A-Level Mathematics Past Papers & Drilling (Paper 6): Poisson, Hypothesis Tests
TUTORZONE ORIGINAL DRILLING MOCK · CAMBRIDGE A-LEVEL MATHEMATICS (9709) PAPER 6
Written to the Cambridge 9709 syllabus (2026-2027): Paper 6 Probability & Statistics 2, 50 marks, 1 h 15 min, 20% of A Level (6-8 structured questions, A Level only). This is a Paper 6 drilling mock: 8 questions for 50 marks with answers and techniques.
What is in A-Level Mathematics (9709) Paper 6?
Direct answer: Paper 6 Probability & Statistics 2, 50 marks, 1 h 15 min, 20% of A Level (6-8 structured questions).
Assessment at a glance (2027)
| Component | Content | Weighting | Duration |
|---|---|---|---|
| Paper 6 (Probability & Statistics 2) | 6-8 structured questions, 50 marks | 20% A-Level | 1 h 15 min |
| Paper 5 (Probability & Statistics 1) | 6-8 structured questions, 50 marks | 20% A-Level | 1 h 15 min |
A-Level Statistics 2 drilling technique: 8 questions in 1 h 15 min. Poisson P(X=r)=e^-lambda lambda^r/r!; Var(aX±bY) adds for independent variables; state H0, H1 and the critical value.
How this paper was built
This is a TutorZone original drilling mock: the questions follow the Cambridge 9709 structure (Paper 6, 50 marks, 20%) and the answers are our own, not Cambridge past papers or marking references.
Every answer was recomputed programmatically.
Pacing
| Section | Marks | Suggested time | What to do first |
|---|---|---|---|
| Paper 6 (Probability & Statistics 2) | 20% A-Level | about 9 min per question | Poisson, estimation, hypothesis tests |
| Paper 5 (Probability & Statistics 1) | 20% A-Level | about 9 min per question | permutations, probability, variables |
What is the Poisson formula?
Direct answer: P(X = r) = e^-lambda x lambda^r / r!.
Paper 6: statistics drilling (8 questions, 50 marks)
Poisson formula, add variances, state H0/H1.
Question 1 (6 marks)
X ~ Poisson(2). Find P(X = 2) (three significant figures).
Question 2 (7 marks)
E(X) = 2 and E(Y) = 1. Find E(3X + 4Y).
Question 3 (6 marks)
X ~ Poisson(3). Find P(X = 0) (three significant figures).
Question 4 (7 marks)
X and Y are independent with Var(X) = 4 and Var(Y) = 9. Find Var(2X – 3Y).
Question 5 (6 marks)
A continuous variable X is uniform on [0, 2]. Find P(X > 1).
Question 6 (6 marks)
For a one-tailed test at the 5% significance level, what is the critical z value?
Question 7 (6 marks)
Sample mean 50, population SD 10, sample size 25. Find the standard error of the mean.
Question 8 (6 marks)
A population has mean 100 and SD 15. A sample value is 130. Find its z-score.
How is Var(2X – 3Y) computed?
Direct answer: for independent X and Y variances add (not subtract): Var(2X-3Y) = 2^2 Var(X) + 3^2 Var(Y).
Paper 6 answers
Question 1
P(X=2) = e^-2 x 2^2 / 2! = 0.271 (6).
Question 2
E(3X+4Y) = 3×2 + 4×1 = 10 (7).
Question 3
P(X=0) = e^-3 = 0.0498 (6).
Question 4
Var(2X-3Y) = 2^2 x 4 + 3^2 x 9 = 16 + 81 = 97 (7).
Question 5
P(X>1) = (2-1) / (2-0) = 1/2 (6).
Question 6
The one-tailed 5% critical value is 1.645 (6).
Question 7
Standard error = sigma / sqrt n = 10 / 5 = 2 (6).
Question 8
z = (130 – 100) / 15 = 2 (6).
Which topics does this paper drill?
Direct answer: Poisson distribution, linear combinations, continuous variables, sampling and estimation, hypothesis tests.
Where these marks are usually lost
| Mistake | What it looks like | What it costs | Instead |
|---|---|---|---|
| Poisson formula | Missing e^-lambda | P(X=r)=e^-lambda lambda^r/r! | 0.271 |
| Variances subtracted | Var(2X-3Y) subtracted | Add variances when independent | 16+81 = 97 |
| SE missing sqrt n | Just sigma | SE = sigma / sqrt n | 10/5 = 2 |
How to use this paper
First drill: the full 1 h 15 min on all 8 questions with no references.
Mark it: check the Poisson formula and hypothesis tests.
Second drill: redo three to seven days later, aiming to finish inside 1 hour.
What should I do after drilling this paper?
Direct answer: log questions with wrong Poisson or variance work; redo in three to seven days; and drill Paper 5 Statistics 1.
FAQ
Is this a Cambridge past paper?
No. The questions and answers are TutorZone originals, not Cambridge past papers or marking references.
What does A-Level Mathematics Paper 6 test?
Probability & Statistics 2: Poisson, linear combinations, continuous variables, estimation, hypothesis tests, 50 marks, 20% of A Level.
What is the Poisson formula?
P(X = r) = e^-lambda x lambda^r / r!.
Official references
| Resource | What to check |
|---|---|
| Cambridge A-Level Mathematics 9709 syllabus (2026-2027) | Confirm the Paper 1-6 marks and times |
| https://www.tutorzone.com.hk/en-alevel-mathematics-9709-paper-5-mock-2027/ | A-Level Mathematics Paper 5 Statistics 1 drilling mock |
Related: practice area · A-Level Mathematics Paper 5 Statistics 1 drilling mock
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