AQA AS LEVEL MATHEMATICS
2025 PAPER 1
Pure Mathematics and
Statistics - Examination
Practice Questions
1. Solve the equation 3x + 7 = 22 for x.
A) x = 3
B) x = 5
C) x = 7
D) x = 9
Answer: B) x = 5
Rationale: Subtract 7 from both sides: 3x = 15. Divide both sides by 3: x = 5.
Verification: 3(5) + 7 = 15 + 7 = 22, confirming the solution is correct.
2. What is the gradient of the line passing through points (2, 3) and (5, 9)?
A) 1
B) 2
C) 3
D) 4
Answer: B) 2
Rationale: Gradient = (y₂ - y₁)/(x₂ - x₁) = (9 - 3)/(5 - 2) = 6/3 = 2. The gradient
represents the rate of change of y with respect to x along the line.
,3. Expand (x + 3)(x - 2).
A) x² + x - 6
B) x² - x - 6
C) x² + 5x - 6
D) x² - 5x - 6
Answer: A) x² + x - 6
Rationale: Using the FOIL method: x·x + x·(-2) + 3·x + 3·(-2) = x² - 2x + 3x - 6 = x² + x
- 6. The x terms combine to give +x.
4. Factorise completely: x² - 9.
A) (x - 3)(x - 3)
B) (x + 3)(x - 3)
C) (x + 9)(x - 1)
D) (x - 9)(x + 1)
Answer: B) (x + 3)(x - 3)
Rationale: This is a difference of squares: a² - b² = (a + b)(a - b). Here, x² - 9 = x² - 3²
= (x + 3)(x - 3).
5. What is the value of 2³ × 2⁴?
A) 2⁷
B) 2¹²
C) 4⁷
D) 8⁷
Answer: A) 2⁷
Rationale: When multiplying powers with the same base, add the exponents: 2³ ×
2⁴ = 2^(3+4) = 2⁷. This equals 128.
6. Solve the inequality: 2x + 5 > 13.
A) x > 4
, B) x > 9
C) x < 4
D) x < 9
Answer: A) x > 4
Rationale: Subtract 5 from both sides: 2x > 8. Divide both sides by 2: x > 4. The
inequality sign remains the same because we divided by a positive number.
7. What is the equation of a line with gradient 3 passing through (1, 2)?
A) y = 3x + 2
B) y = 3x - 1
C) y = 2x + 3
D) y = x + 2
Answer: B) y = 3x - 1
Rationale: Using y - y₁ = m(x - x₁): y - 2 = 3(x - 1) → y - 2 = 3x - 3 → y = 3x - 1.
Substitute (1, 2) to verify: 2 = 3(1) - 1 = 2.
8. Simplify: (x⁴)/(x²).
A) x²
B) x⁶
C) x⁻²
D) x⁸
Answer: A) x²
Rationale: When dividing powers with the same base, subtract the exponents:
x⁴/x² = x^(4-2) = x². This follows from the laws of indices.
9. What is the y-intercept of the line y = 4x - 7?
A) -7
B) 4
C) 7
D) -4
2025 PAPER 1
Pure Mathematics and
Statistics - Examination
Practice Questions
1. Solve the equation 3x + 7 = 22 for x.
A) x = 3
B) x = 5
C) x = 7
D) x = 9
Answer: B) x = 5
Rationale: Subtract 7 from both sides: 3x = 15. Divide both sides by 3: x = 5.
Verification: 3(5) + 7 = 15 + 7 = 22, confirming the solution is correct.
2. What is the gradient of the line passing through points (2, 3) and (5, 9)?
A) 1
B) 2
C) 3
D) 4
Answer: B) 2
Rationale: Gradient = (y₂ - y₁)/(x₂ - x₁) = (9 - 3)/(5 - 2) = 6/3 = 2. The gradient
represents the rate of change of y with respect to x along the line.
,3. Expand (x + 3)(x - 2).
A) x² + x - 6
B) x² - x - 6
C) x² + 5x - 6
D) x² - 5x - 6
Answer: A) x² + x - 6
Rationale: Using the FOIL method: x·x + x·(-2) + 3·x + 3·(-2) = x² - 2x + 3x - 6 = x² + x
- 6. The x terms combine to give +x.
4. Factorise completely: x² - 9.
A) (x - 3)(x - 3)
B) (x + 3)(x - 3)
C) (x + 9)(x - 1)
D) (x - 9)(x + 1)
Answer: B) (x + 3)(x - 3)
Rationale: This is a difference of squares: a² - b² = (a + b)(a - b). Here, x² - 9 = x² - 3²
= (x + 3)(x - 3).
5. What is the value of 2³ × 2⁴?
A) 2⁷
B) 2¹²
C) 4⁷
D) 8⁷
Answer: A) 2⁷
Rationale: When multiplying powers with the same base, add the exponents: 2³ ×
2⁴ = 2^(3+4) = 2⁷. This equals 128.
6. Solve the inequality: 2x + 5 > 13.
A) x > 4
, B) x > 9
C) x < 4
D) x < 9
Answer: A) x > 4
Rationale: Subtract 5 from both sides: 2x > 8. Divide both sides by 2: x > 4. The
inequality sign remains the same because we divided by a positive number.
7. What is the equation of a line with gradient 3 passing through (1, 2)?
A) y = 3x + 2
B) y = 3x - 1
C) y = 2x + 3
D) y = x + 2
Answer: B) y = 3x - 1
Rationale: Using y - y₁ = m(x - x₁): y - 2 = 3(x - 1) → y - 2 = 3x - 3 → y = 3x - 1.
Substitute (1, 2) to verify: 2 = 3(1) - 1 = 2.
8. Simplify: (x⁴)/(x²).
A) x²
B) x⁶
C) x⁻²
D) x⁸
Answer: A) x²
Rationale: When dividing powers with the same base, subtract the exponents:
x⁴/x² = x^(4-2) = x². This follows from the laws of indices.
9. What is the y-intercept of the line y = 4x - 7?
A) -7
B) 4
C) 7
D) -4
