OCR AS Level Mathematics B (MEI) H630/02 Pure Mathematics & Statistics Final Exam Paper + Official Mark Scheme (May 2025/2026)

OCR AS Level Mathematics B (MEI) H630/02 Pure
Mathematics & Statistics Final Exam Paper +
Official Mark Scheme (2025/2026)



SECTION A: PURE MATHEMATICS




Question 1

Simplify √75 + √48

A) 3√3
B) 5√3
C) 9√3
D) 15√3




Answer: C) 9√3

Rationale: √75 = √(25 × 3) = 5√3 and √48 = √(16 × 3) = 4√3. Sum = 5√3 + 4√3 = 9√3.

Solution: 5√3 + 4√3 = 9√3

,Question 2

Expand and simplify (2 + √3)(3 - √3)

A) 6 + √3
B) 3 + √3
C) 6 - √3
D) 3 - √3




Answer: B) 3 + √3

Rationale: Expand each term: 2×3 = 6, 2×(-√3) = -2√3, √3×3 = 3√3, √3×(-√3) = -3.
Combine: (6-3) + (-2√3+3√3) = 3 + √3.

Solution: (2 + √3)(3 - √3) = 6 - 2√3 + 3√3 - 3 = 3 + √3




Question 3

Rationalise the denominator: 2/(3 - √5)

A) (3 + √5)/2
B) (6 + 2√5)/4
C) 3 + √5
D) (6 + 2√5)/2

,Answer: A) (3 + √5)/2

Rationale: Multiply numerator and denominator by the conjugate (3 + √5).
Denominator becomes 9 - 5 = 4. Numerator becomes 2(3 + √5) = 6 + 2√5. Simplify by
dividing by 2.

Solution: [2(3+√5)]/(9-5) = [6+2√5]/4 = (3+√5)/2




Question 4

Solve the quadratic equation: 2x² - 5x - 3 = 0

A) x = -1/2, x = 3
B) x = 1/2, x = -3
C) x = 3, x = -1/2
D) x = -3, x = 1/2




Answer: A) x = -1/2, x = 3

Rationale: Use the quadratic formula or factorisation. Factorising: (2x + 1)(x - 3) = 0
gives x = -1/2 or x = 3.

Solution: 2x² - 5x - 3 = (2x + 1)(x - 3) = 0 ⇒ x = -1/2, x = 3




Question 5

Find the discriminant of 3x² + 4x - 2 = 0

, A) 16
B) 24
C) 32
D) 40




Answer: D) 40

Rationale: Discriminant Δ = b² - 4ac where a = 3, b = 4, c = -2. Δ = 16 - 4(3)(-2) = 16 +
24 = 40.

Solution: Δ = 4² - 4(3)(-2) = 16 + 24 = 40




Question 6

If the quadratic x² + kx + 9 = 0 has equal roots, find k.

A) ±3
B) ±6
C) ±9
D) ±12




Answer: B) ±6

Rationale: Equal roots means discriminant = 0. k² - 4(1)(9) = 0 ⇒ k² = 36 ⇒ k = ±6.

Solution: Δ = k² - 36 = 0 ⇒ k² = 36 ⇒ k = ±6