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A-Level Mathematics Past Papers & Drilling (Paper 2): Logarithms, Calculus, Series
TUTORZONE ORIGINAL DRILLING MOCK · CAMBRIDGE A-LEVEL MATHEMATICS (9709) PAPER 2
Written to the Cambridge 9709 syllabus (2026-2027): Paper 2 Pure Mathematics 2, 50 marks, 1 h 15 min, 20% of A Level (6-8 structured questions); plus Paper 1 Pure 1 (75, 30%), Paper 3 Pure 3 (75, 30%), Paper 4 Mechanics and Paper 5/6 Statistics. This is a Paper 2 drilling mock: 6 questions for 50 marks with answers and techniques.
What is in A-Level Mathematics (9709) Paper 2?
Direct answer: Paper 2 Pure Mathematics 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 2 (Pure Mathematics 2) | 6-8 structured questions, 50 marks | 20% A-Level | 1 h 15 min |
| Paper 3 (Pure Mathematics 3) | 6-8 structured questions, 75 marks | 30% A-Level | 1 h 50 min |
A-Level Maths Paper 2 drilling technique: about 10 min per question. Formulas: log_2 8 = 3; d/dx(x^n) = nx^(n-1); integral of x^n = x^(n+1)/(n+1); AP sum S_n = n/2[2a+(n-1)d]; sin^2+cos^2 = 1.
How this paper was built
This is a TutorZone original drilling mock: the questions follow the Cambridge 9709 structure (Paper 2, 50 marks, 20%) and the answers are our own, not Cambridge past papers or marking references.
Every numeric answer was recomputed programmatically.
Pacing
| Section | Marks | Suggested time | What to do first |
|---|---|---|---|
| Paper 2 (Pure Mathematics 2) | 20% A-Level | about 10 min per question | logs, calculus, series |
| Paper 3 (Pure Mathematics 3) | 30% A-Level | about 14 min per question | vectors, complex numbers, advanced calculus |
What is log base 2 of 8?
Direct answer: 3, because 2^3 = 8.
Paper 2: pure maths drilling (6 questions, 50 marks)
Convert between logs and exponentials; know the calculus formulas.
Question 1 (8 marks)
Find the value of log base 2 of 8.
Question 2 (8 marks)
Find the value of e^0.
Question 3 (8 marks)
Find the gradient of y = x^3 at x = 2.
Question 4 (9 marks)
Evaluate the integral of x from 1 to 3.
Question 5 (9 marks)
An arithmetic series has first term 2 and common difference 2. Find the sum of the first 10 terms.
Question 6 (8 marks)
Simplify sin^2 theta + cos^2 theta.
What is the integral of x from 1 to 3?
Direct answer: integral of x = x^2/2; with limits, 4.5 – 0.5 = 4.
Paper 2 answers
Question 1
2^3 = 8, so log base 2 of 8 = 3 (8).
Question 2
Any non-zero number to the power 0 equals 1, so e^0 = 1 (8).
Question 3
dy/dx = 3x^2; at x = 2: 3 x 4 = 12 (8).
Question 4
integral of x = x^2/2; [x^2/2] from 1 to 3 = 4.5 – 0.5 = 4 (9).
Question 5
S_n = n/2[2a + (n-1)d] = 10/2 x [4 + 18] = 5 x 22 = 110 (9).
Question 6
By the Pythagorean identity, sin^2 theta + cos^2 theta = 1 (8).
Which topics does this paper drill?
Direct answer: logarithms, exponentials, differentiation, definite integration, arithmetic series and trigonometric identities.
Where these marks are usually lost
| Mistake | What it looks like | What it costs | Instead |
|---|---|---|---|
| Log/exponential mixed | log_2 8 = 2^3 | log_2 8 = 3 | 3 |
| Definite integral | Ignore the limits | Substitute the limits | 4 |
| AP formula wrong | n[2a+(n-1)d] | Divide by 2 | 110 |
How to use this paper
First drill: the full 1 h 15 min on all 6 questions with no references.
Mark it: check the formulas and substitutions.
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 answers with wrong formulas or substitutions; redo in three to seven days; and drill Paper 3 Pure Mathematics 3.
FAQ
Is this a Cambridge past paper?
No. The questions and answers are TutorZone originals, not Cambridge past papers or marking references.
What is in A-Level Mathematics 9709 Paper 2?
Pure 2: logarithms, exponentials, trigonometry, calculus, series; 50 marks, 1 h 15 min, 20% of A Level.
What is log base 2 of 8?
3, because 2^3 = 8.
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-3-mock-2027/ | A-Level Mathematics Paper 3 drilling mock |
Related: practice area · A-Level Mathematics Paper 3 drilling mock · A-Level Further Maths 9231 Paper 1 drilling mock · A-Level Further Maths 9231 Paper 2 drilling mock
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