OCR MEI A Level Mathematics B (H640/03) — Pure Mathematics and Comprehension
June 2026 Practice Test Bank — 500 Exam-Style Questions with Verified Answers & Detailed
Rationales
Table of Contents
1. Exam Overview ................................................. 1
2. Domain I: Proof (8%) ......................................... 2
3. Domain II: Algebra (12%) ..................................... 22
4. Domain III: Functions (10%) .................................. 52
5. Domain IV: Graphs (8%) ....................................... 78
6. Domain V: Coordinate Geometry (8%) ........................... 98
7. Domain VI: Sequences and Series (10%) ........................ 118
8. Domain VII: Trigonometry (12%) ............................... 142
9. Domain VIII: Exponentials and Logarithms (10%) ............... 172
10. Domain IX: Calculus (14%) ................................... 196
11. Domain X: Numerical Methods (4%) ............................ 238
12. Domain XI: Vectors (4%) ..................................... 252
13. Comprehension Practice (Section B) .......................... 262
14. Answer Key Summary .......................................... 272
15. Formulae and References .................................... 276
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Exam Overview
About OCR MEI A Level Mathematics B — Paper 3 (H640/03)
,Paper 3 (H640/03) is the Pure Mathematics and Comprehension paper of the OCR MEI A
Level Mathematics B qualification. It assesses content from Area 1: Pure Mathematics only;
Mechanics (Area 2) and Statistics (Area 3) are assumed knowledge but are not directly
examined on this paper . The paper is divided into two sections:
- Section A — 60 marks of synoptic pure mathematics questions.
- Section B — 15 marks on a previously unseen comprehension passage based on the pure
mathematics content of the specification .
The overarching themes of mathematical argument, language and proof, mathematical
problem solving, and mathematical modelling are applied across all questions .
Exam Format
| Parameter | Specification |
|---|---|
| Paper Code | H640/03 |
| Total Marks | 75 |
| Time Allowed | 2 hours |
| Weighting | 27.3% of A Level |
| Section A | 60 marks (pure core content) |
| Section B | 15 marks (comprehension passage) |
| Calculator | Scientific or graphical calculator permitted |
| Exam Series | May/June (one series per year) |
Prerequisites
- Learners must complete all three components (01, 02, and 03) to be awarded the A Level in
Mathematics B (MEI) .
,- Grade scale: A, A, B, C, D, E (U for unclassified) .
Domain Weightings (Based on Paper 3 Pure Content)
| Domain | Topic | Approx. Weighting |
|---|---|---|
| I | Proof | 8% |
| II | Algebra | 12% |
| III | Functions | 10% |
| IV | Graphs | 8% |
| V | Coordinate Geometry | 8% |
| VI | Sequences and Series | 10% |
| VII | Trigonometry | 12% |
| VIII | Exponentials and Logarithms | 10% |
| IX | Calculus | 14% |
| X | Numerical Methods | 4% |
| XI | Vectors | 4% |
How to Use This Practice Bank
This bank contains 500 exam-style questions organised by domain. Each question includes:
- Question (multiple-choice or short-answer format)
- Correct Answer
- Detailed Rationale explaining the solution and marking principles
For best results, attempt each question under timed conditions, then review the rationale
for every question, including those answered correctly.
, ---
Domain I: Proof (8%)
Questions 1–40
1. Which of the following is a statement?
A) Is x > 3?
B) x > 3
C) x + 3 = 7
D) All of the above
Correct Answer: B
Rationale: A statement is a sentence that is either true or false. Option B is a statement
(though its truth depends on x). Option A is a question, and Option C is an equation that
becomes a statement only when a value of x is specified.
---
2. What is the negation of the statement "All prime numbers are odd"?
A) No prime numbers are odd
B) All prime numbers are even
C) There exists a prime number that is not odd
D) Some prime numbers are odd
Correct Answer: C
June 2026 Practice Test Bank — 500 Exam-Style Questions with Verified Answers & Detailed
Rationales
Table of Contents
1. Exam Overview ................................................. 1
2. Domain I: Proof (8%) ......................................... 2
3. Domain II: Algebra (12%) ..................................... 22
4. Domain III: Functions (10%) .................................. 52
5. Domain IV: Graphs (8%) ....................................... 78
6. Domain V: Coordinate Geometry (8%) ........................... 98
7. Domain VI: Sequences and Series (10%) ........................ 118
8. Domain VII: Trigonometry (12%) ............................... 142
9. Domain VIII: Exponentials and Logarithms (10%) ............... 172
10. Domain IX: Calculus (14%) ................................... 196
11. Domain X: Numerical Methods (4%) ............................ 238
12. Domain XI: Vectors (4%) ..................................... 252
13. Comprehension Practice (Section B) .......................... 262
14. Answer Key Summary .......................................... 272
15. Formulae and References .................................... 276
---
Exam Overview
About OCR MEI A Level Mathematics B — Paper 3 (H640/03)
,Paper 3 (H640/03) is the Pure Mathematics and Comprehension paper of the OCR MEI A
Level Mathematics B qualification. It assesses content from Area 1: Pure Mathematics only;
Mechanics (Area 2) and Statistics (Area 3) are assumed knowledge but are not directly
examined on this paper . The paper is divided into two sections:
- Section A — 60 marks of synoptic pure mathematics questions.
- Section B — 15 marks on a previously unseen comprehension passage based on the pure
mathematics content of the specification .
The overarching themes of mathematical argument, language and proof, mathematical
problem solving, and mathematical modelling are applied across all questions .
Exam Format
| Parameter | Specification |
|---|---|
| Paper Code | H640/03 |
| Total Marks | 75 |
| Time Allowed | 2 hours |
| Weighting | 27.3% of A Level |
| Section A | 60 marks (pure core content) |
| Section B | 15 marks (comprehension passage) |
| Calculator | Scientific or graphical calculator permitted |
| Exam Series | May/June (one series per year) |
Prerequisites
- Learners must complete all three components (01, 02, and 03) to be awarded the A Level in
Mathematics B (MEI) .
,- Grade scale: A, A, B, C, D, E (U for unclassified) .
Domain Weightings (Based on Paper 3 Pure Content)
| Domain | Topic | Approx. Weighting |
|---|---|---|
| I | Proof | 8% |
| II | Algebra | 12% |
| III | Functions | 10% |
| IV | Graphs | 8% |
| V | Coordinate Geometry | 8% |
| VI | Sequences and Series | 10% |
| VII | Trigonometry | 12% |
| VIII | Exponentials and Logarithms | 10% |
| IX | Calculus | 14% |
| X | Numerical Methods | 4% |
| XI | Vectors | 4% |
How to Use This Practice Bank
This bank contains 500 exam-style questions organised by domain. Each question includes:
- Question (multiple-choice or short-answer format)
- Correct Answer
- Detailed Rationale explaining the solution and marking principles
For best results, attempt each question under timed conditions, then review the rationale
for every question, including those answered correctly.
, ---
Domain I: Proof (8%)
Questions 1–40
1. Which of the following is a statement?
A) Is x > 3?
B) x > 3
C) x + 3 = 7
D) All of the above
Correct Answer: B
Rationale: A statement is a sentence that is either true or false. Option B is a statement
(though its truth depends on x). Option A is a question, and Option C is an equation that
becomes a statement only when a value of x is specified.
---
2. What is the negation of the statement "All prime numbers are odd"?
A) No prime numbers are odd
B) All prime numbers are even
C) There exists a prime number that is not odd
D) Some prime numbers are odd
Correct Answer: C
