AQA A LEVEL MATHS PAPER 1 2025 WORKED SOLUTIONS
200 Multiple‑Choice Practice Questions – AQA A‑Level Mathematics
(7357/1) Paper 1 – Worked Solutions
1. Solve the inequality 3x – 2 > 10
A) x > 4
B) x > 12
C) x < 4
D) x > 6
Correct Answer: A
Add 2 to both sides: 3x > 12 → x > 4
2. Find the gradient of the line passing through (2,3) and (5,9)
A) 1
B) 2
C) 3
D) 4
Correct Answer: B
Gradient m = (9 – 3)/(5 – 2) = 6/3 = 2
3. Differentiate y = 5x⁴ with respect to x
A) 20x⁵
B) 20x³
C) 5x³
D) 4x³
,Correct Answer: B
d/dx (5x⁴) = 5 × 4x³ = 20x³
4. Which of the following is an odd function?
A) f(x) = x³ + 2
B) f(x) = x³ + x
C) f(x) = x²
D) f(x) = |x|
Correct Answer: B
f(–x) = –x³ – x = –(x³ + x) = –f(x)
5. A circle has centre (3,–2) and radius 4. Its equation is:
A) (x – 3)² + (y – 2)² = 16
B) (x + 3)² + (y – 2)² = 4
C) (x – 3)² + (y + 2)² = 16
D) (x – 3)² + (y + 2)² = 4
Correct Answer: C
General form: (x – h)² + (y – k)² = r² = (x – 3)² + (y + 2)² = 16
6. Evaluate ∫ 6x² dx
A) 2x³ + c
B) 12x + c
C) 6x³ + c
D) 2x³ + c
Correct Answer: A
∫ 6x² dx = 6 × x³/3 + c = 2x³ + c
,7. Find the coefficient of x⁴ in the binomial expansion of (1 + x)⁶
A) 6
B) 15
C) 20
D) 1
Correct Answer: B
Coefficient = C(6,4) = 15
8. Evaluate log₃ 81
A) 2
B) 3
C) 4
D) 5
Correct Answer: C
3⁴ = 81 → log₃ 81 = 4
9. The curve y = e²x + 4x. Find dy/dx
A) 2e²x + 4
B) e²x + 4
C) e²x + 4x
D) 2e²x + 4x
Correct Answer: A
d/dx(e²x) = 2e²x, d/dx(4x) = 4 → dy/dx = 2e²x + 4
10. Find the tangent to y = 4√x at x = 4
, A) y = x + 4
B) y = x – 4
C) y = x – 8
D) y = x + 8
Correct Answer: A
At x = 4, y = 4√4 = 8. dy/dx = 4 × (1/2)x⁻¹/² = 2/√x → at x = 4, m = 1. Equation: y – 8 = 1(x – 4) → y = x + 4
11. A sequence is defined by u_{n+1} = 2u_n – 3 with u₁ = 2. Find u₃
A) –5
B) 1
C) 5
D) –1
Correct Answer: D
u₂ = 2×2 – 3 = 1, u₃ = 2×1 – 3 = –1
12. Write as a single logarithm: log₂ x + log₂ x²
A) log₂ x³
B) log₂ x²
C) 3log₂ x
D) 2log₂ x
Correct Answer: A
log₂ x + log₂ x² = log₂(x × x²) = log₂ x³
13. The smallest value of x² – 4x + 7 is:
A) 3
B) 4
200 Multiple‑Choice Practice Questions – AQA A‑Level Mathematics
(7357/1) Paper 1 – Worked Solutions
1. Solve the inequality 3x – 2 > 10
A) x > 4
B) x > 12
C) x < 4
D) x > 6
Correct Answer: A
Add 2 to both sides: 3x > 12 → x > 4
2. Find the gradient of the line passing through (2,3) and (5,9)
A) 1
B) 2
C) 3
D) 4
Correct Answer: B
Gradient m = (9 – 3)/(5 – 2) = 6/3 = 2
3. Differentiate y = 5x⁴ with respect to x
A) 20x⁵
B) 20x³
C) 5x³
D) 4x³
,Correct Answer: B
d/dx (5x⁴) = 5 × 4x³ = 20x³
4. Which of the following is an odd function?
A) f(x) = x³ + 2
B) f(x) = x³ + x
C) f(x) = x²
D) f(x) = |x|
Correct Answer: B
f(–x) = –x³ – x = –(x³ + x) = –f(x)
5. A circle has centre (3,–2) and radius 4. Its equation is:
A) (x – 3)² + (y – 2)² = 16
B) (x + 3)² + (y – 2)² = 4
C) (x – 3)² + (y + 2)² = 16
D) (x – 3)² + (y + 2)² = 4
Correct Answer: C
General form: (x – h)² + (y – k)² = r² = (x – 3)² + (y + 2)² = 16
6. Evaluate ∫ 6x² dx
A) 2x³ + c
B) 12x + c
C) 6x³ + c
D) 2x³ + c
Correct Answer: A
∫ 6x² dx = 6 × x³/3 + c = 2x³ + c
,7. Find the coefficient of x⁴ in the binomial expansion of (1 + x)⁶
A) 6
B) 15
C) 20
D) 1
Correct Answer: B
Coefficient = C(6,4) = 15
8. Evaluate log₃ 81
A) 2
B) 3
C) 4
D) 5
Correct Answer: C
3⁴ = 81 → log₃ 81 = 4
9. The curve y = e²x + 4x. Find dy/dx
A) 2e²x + 4
B) e²x + 4
C) e²x + 4x
D) 2e²x + 4x
Correct Answer: A
d/dx(e²x) = 2e²x, d/dx(4x) = 4 → dy/dx = 2e²x + 4
10. Find the tangent to y = 4√x at x = 4
, A) y = x + 4
B) y = x – 4
C) y = x – 8
D) y = x + 8
Correct Answer: A
At x = 4, y = 4√4 = 8. dy/dx = 4 × (1/2)x⁻¹/² = 2/√x → at x = 4, m = 1. Equation: y – 8 = 1(x – 4) → y = x + 4
11. A sequence is defined by u_{n+1} = 2u_n – 3 with u₁ = 2. Find u₃
A) –5
B) 1
C) 5
D) –1
Correct Answer: D
u₂ = 2×2 – 3 = 1, u₃ = 2×1 – 3 = –1
12. Write as a single logarithm: log₂ x + log₂ x²
A) log₂ x³
B) log₂ x²
C) 3log₂ x
D) 2log₂ x
Correct Answer: A
log₂ x + log₂ x² = log₂(x × x²) = log₂ x³
13. The smallest value of x² – 4x + 7 is:
A) 3
B) 4
