OCR MEI A Level Mathematics B Paper 1 (H640/01) — 500 Practice Questions with Verified
Answers & Detailed Rationales
Table of Contents
1. Exam Overview
2. Domain 1: Proof (Questions 1–25)
3. Domain 2: Algebra and Functions (Questions 26–70)
4. Domain 3: Coordinate Geometry (Questions 71–100)
5. Domain 4: Sequences and Series (Questions 101–140)
6. Domain 5: Trigonometry (Questions 141–185)
7. Domain 6: Exponentials and Logarithms (Questions 186–225)
8. Domain 7: Differentiation (Questions 226–285)
9. Domain 8: Integration (Questions 286–340)
10. Domain 9: Numerical Methods (Questions 341–365)
11. Domain 10: Vectors (Questions 366–400)
12. Domain 11: Mechanics – Kinematics (Questions 401–440)
13. Domain 12: Mechanics – Forces and Newton's Laws (Questions 441–480)
14. Domain 13: Mechanics – Moments and Rigid Bodies (Questions 481–500)
15. Answer Key Summary
Exam Overview
The OCR MEI A Level Mathematics B (H640/01) Paper 1 is titled Pure Mathematics and
Mechanics. It is a 2-hour written paper worth 100 marks, representing 36.4% of the total A
Level qualification.
Paper Structure:
,- Section A – Shorter questions with minimal reading and interpretation
- Section B – Longer questions and more problem-solving
Content Coverage: Component 01 assesses content from Pure Mathematics (Area 1) and
Mechanics (Area 2).
Assessment Objectives:
- AO1 (Use and apply standard techniques): 60% (±2%)
- AO2 (Reason, interpret and communicate mathematically): 20% (±2%)
- AO3 (Solve problems within mathematics and other contexts): 20% (±2%)
Core Domains Covered:
| Domain | Topics |
|--------|--------|
| Pure Mathematics | Proof, Algebra, Functions, Graphs, Coordinate Geometry, Sequences
and Series, Trigonometry, Exponentials and Logarithms, Calculus, Numerical Methods,
Vectors |
| Mechanics | Models and Quantities, Kinematics, Projectiles, Forces, Newton's Laws of
Motion, Rigid Bodies |
Key Formulae Provided: Arithmetic series, geometric series, binomial series, differentiation
rules (including quotient and product rules), integration rules, small angle approximations,
and numerical methods.
Calculator: A scientific or graphical calculator is permitted.
DOMAIN 1: PROOF
,Questions 1–25
1. Which of the following is a correct statement of the structure of a proof by contradiction?
A) Assume the statement is true and derive a contradiction
B) Assume the negation of the statement and derive a contradiction
C) Prove the statement directly using known facts
D) Prove the statement for all cases individually
Correct Answer: B) Assume the negation of the statement and derive a contradiction
Rationale: In proof by contradiction, you assume the opposite of what you want to prove. If
this assumption leads to a logical contradiction, the original statement must be true.
---
2. Prove by contradiction that √3 is irrational. Which initial assumption is correct?
A) Assume √3 is rational, so √3 = a/b where a and b are integers with no common factors
B) Assume √3 is irrational
C) Assume √3 is an integer
D) Assume √3 = 0
Correct Answer: A) Assume √3 is rational, so √3 = a/b where a and b are integers with no
common factors
Rationale: To prove √3 is irrational by contradiction, assume it is rational, express it as a
fraction in lowest terms, and show this leads to a contradiction.
, ---
3. Show that (x − 2) is a factor of 3x³ − 8x² + 3x + 2. What is the correct first step?
A) Substitute x = 2 into the polynomial
B) Substitute x = −2 into the polynomial
C) Divide the polynomial by (x + 2)
D) Factorise the polynomial completely
Correct Answer: A) Substitute x = 2 into the polynomial
Rationale: By the Factor Theorem, if (x − 2) is a factor, then f(2) = 0. Substituting x = 2 gives
3(8) − 8(4) + 3(2) + 2 = 24 − 32 + 6 + 2 = 0, confirming (x − 2) is a factor.
---
4. Which of the following is a correct proof that the sum of two odd numbers is even?
A) Let 2m + 1 and 2n + 1 be odd numbers. Sum = 2m + 2n + 2 = 2(m + n + 1), which is even
B) Let m and n be odd numbers. Sum = m + n, which is even
C) Let 2m and 2n be odd numbers. Sum = 2m + 2n, which is even
D) Let m + n be odd. Then m + n is even
Correct Answer: A) Let 2m + 1 and 2n + 1 be odd numbers. Sum = 2m + 2n + 2 = 2(m + n + 1),
which is even
Rationale: Any odd number can be written as 2k + 1. The sum of two odd numbers is 2(m + n
+ 1), which is divisible by 2 and therefore even.
Answers & Detailed Rationales
Table of Contents
1. Exam Overview
2. Domain 1: Proof (Questions 1–25)
3. Domain 2: Algebra and Functions (Questions 26–70)
4. Domain 3: Coordinate Geometry (Questions 71–100)
5. Domain 4: Sequences and Series (Questions 101–140)
6. Domain 5: Trigonometry (Questions 141–185)
7. Domain 6: Exponentials and Logarithms (Questions 186–225)
8. Domain 7: Differentiation (Questions 226–285)
9. Domain 8: Integration (Questions 286–340)
10. Domain 9: Numerical Methods (Questions 341–365)
11. Domain 10: Vectors (Questions 366–400)
12. Domain 11: Mechanics – Kinematics (Questions 401–440)
13. Domain 12: Mechanics – Forces and Newton's Laws (Questions 441–480)
14. Domain 13: Mechanics – Moments and Rigid Bodies (Questions 481–500)
15. Answer Key Summary
Exam Overview
The OCR MEI A Level Mathematics B (H640/01) Paper 1 is titled Pure Mathematics and
Mechanics. It is a 2-hour written paper worth 100 marks, representing 36.4% of the total A
Level qualification.
Paper Structure:
,- Section A – Shorter questions with minimal reading and interpretation
- Section B – Longer questions and more problem-solving
Content Coverage: Component 01 assesses content from Pure Mathematics (Area 1) and
Mechanics (Area 2).
Assessment Objectives:
- AO1 (Use and apply standard techniques): 60% (±2%)
- AO2 (Reason, interpret and communicate mathematically): 20% (±2%)
- AO3 (Solve problems within mathematics and other contexts): 20% (±2%)
Core Domains Covered:
| Domain | Topics |
|--------|--------|
| Pure Mathematics | Proof, Algebra, Functions, Graphs, Coordinate Geometry, Sequences
and Series, Trigonometry, Exponentials and Logarithms, Calculus, Numerical Methods,
Vectors |
| Mechanics | Models and Quantities, Kinematics, Projectiles, Forces, Newton's Laws of
Motion, Rigid Bodies |
Key Formulae Provided: Arithmetic series, geometric series, binomial series, differentiation
rules (including quotient and product rules), integration rules, small angle approximations,
and numerical methods.
Calculator: A scientific or graphical calculator is permitted.
DOMAIN 1: PROOF
,Questions 1–25
1. Which of the following is a correct statement of the structure of a proof by contradiction?
A) Assume the statement is true and derive a contradiction
B) Assume the negation of the statement and derive a contradiction
C) Prove the statement directly using known facts
D) Prove the statement for all cases individually
Correct Answer: B) Assume the negation of the statement and derive a contradiction
Rationale: In proof by contradiction, you assume the opposite of what you want to prove. If
this assumption leads to a logical contradiction, the original statement must be true.
---
2. Prove by contradiction that √3 is irrational. Which initial assumption is correct?
A) Assume √3 is rational, so √3 = a/b where a and b are integers with no common factors
B) Assume √3 is irrational
C) Assume √3 is an integer
D) Assume √3 = 0
Correct Answer: A) Assume √3 is rational, so √3 = a/b where a and b are integers with no
common factors
Rationale: To prove √3 is irrational by contradiction, assume it is rational, express it as a
fraction in lowest terms, and show this leads to a contradiction.
, ---
3. Show that (x − 2) is a factor of 3x³ − 8x² + 3x + 2. What is the correct first step?
A) Substitute x = 2 into the polynomial
B) Substitute x = −2 into the polynomial
C) Divide the polynomial by (x + 2)
D) Factorise the polynomial completely
Correct Answer: A) Substitute x = 2 into the polynomial
Rationale: By the Factor Theorem, if (x − 2) is a factor, then f(2) = 0. Substituting x = 2 gives
3(8) − 8(4) + 3(2) + 2 = 24 − 32 + 6 + 2 = 0, confirming (x − 2) is a factor.
---
4. Which of the following is a correct proof that the sum of two odd numbers is even?
A) Let 2m + 1 and 2n + 1 be odd numbers. Sum = 2m + 2n + 2 = 2(m + n + 1), which is even
B) Let m and n be odd numbers. Sum = m + n, which is even
C) Let 2m and 2n be odd numbers. Sum = 2m + 2n, which is even
D) Let m + n be odd. Then m + n is even
Correct Answer: A) Let 2m + 1 and 2n + 1 be odd numbers. Sum = 2m + 2n + 2 = 2(m + n + 1),
which is even
Rationale: Any odd number can be written as 2k + 1. The sum of two odd numbers is 2(m + n
+ 1), which is divisible by 2 and therefore even.
