AQA AS LEVEL MATHS PAPER 1: PURE MATHEMATICS (2026/2027) COMPLETE SOLUTION (PASS GUARANTEE)

AQA AS LEVEL MATHS PAPER 1: PURE MATHEMATICS (2026/2027) COMPLETE

SOLUTION (PASS GUARANTEE)




AQA AS LEVEL MATHEMATICS
Paper 1: Pure Mathematics




Topic: Algebra
1. Solve the equation 2x² − 5x − 3 = 0.
A. x = 3 and x = −½ ✓
B. x = −3 and x = ½
C. x = 3 and x = ½
D. x = −3 and x = −½
Topic: Algebra
2. Expand and simplify (3x − 2)(x + 5).
A. 3x² + 13x − 10 ✓
B. 3x² − 13x − 10
C. 3x² + 13x + 10
D. 3x² − 13x + 10
Topic: Algebra
3. Factorise fully 6x² − 7x − 3.
A. (2x − 3)(3x + 1) ✓
B. (3x + 1)(2x − 3)
C. (6x + 1)(x − 3)
D. (2x + 1)(3x − 3)
Topic: Algebra
4. The discriminant of ax² + bx + c = 0 is b² − 4ac. For what values of k does x² + kx
+ 9 = 0 have no real roots?

, A. −6 < k < 6 ✓
B. k > 6 or k < −6
C. k≥6
D. k ≤ −6
Topic: Algebra
5. Simplify (2x³y²)³.
A. 8x⁹y⁶ ✓
B. 6x⁶y⁵
C. 8x⁶y⁶
D. 2x⁹y⁶
Topic: Algebra
6. Solve 3|2x − 1| = 9.
A. x = 2 or x = −1 ✓
B. x = 1 or x = −2
C. x = 2 or x = 1
D. x = −1 or x = −2
Topic: Algebra
7. Express x² − 6x + 11 in the form (x − a)² + b.
A. (x − 3)² + 2 ✓
B. (x + 3)² + 2
C. (x − 3)² − 2
D. (x − 6)² + 11
Topic: Algebra
8. If f(x) = 2x² − 3x + 1, find f(−2).
A. 15 ✓
B. 3
C. −1
D. 11
Topic: Algebra
9. Solve the simultaneous equations: y = x + 3 and y = x² − 1.
A. x = 2, y = 5 and x = −2, y = 1 ✓
B. x = 2, y = 5 and x = 2, y = 3
C. x = −1, y = 2 and x = 4, y = 15
D. x = 1, y = 4 and x = −3, y = 8
Topic: Algebra

,10. Simplify the expression (x² − 9) / (x − 3).
A. x+3 ✓
B. x−3
C. x² + 3
D. (x + 3)(x − 3)
Topic: Indices and Surds
11. Simplify √75 − √27.
A. 2√3 ✓
B. 3√3
C. √48
D. 4√3
Topic: Indices and Surds
12. Express 8^(2/3) as an integer.
A. 4 ✓
B. 2
C. 16
D. 8
Topic: Indices and Surds
13. Rationalise the denominator of 6 / √3.
A. 2√3 ✓
B. 6√3
C. 3√3
D. √3
Topic: Indices and Surds
14. Simplify (√5 + 2)(√5 − 2).
A. 1 ✓
B. 5
C. 4
D. √5
Topic: Indices and Surds
15. Evaluate 16^(−3/4).
A. 1/8 ✓
B. −8
C. 8
D. 1/16

, Topic: Indices and Surds
16. Simplify 3^4 × 3^(−2).
A. 9 ✓
B. 27
C. 81
D. 3
Topic: Indices and Surds
17. Write √(48x⁴) in its simplest form.
A. 4x²√3 ✓
B. 4x√3
C. 2x²√12
D. 12x²
Topic: Indices and Surds
18. Rationalise the denominator of (3 + √2) / (3 − √2).
A. (11 + 6√2) / 7 ✓
B. (11 − 6√2) / 7
C. (9 + 6√2) / 7
D. (11 + 6√2) / 9
Topic: Indices and Surds
19. Simplify x^(1/2) × x^(3/2).
A. x² ✓
B. x^(3/4)
C. x^(5/2)
D. x
Topic: Indices and Surds
20. Express 2^5 ÷ 2^(−2) in the form 2^n. State n.
A. n=7 ✓
B. n=3
C. n = 10
D. n = −3
Topic: Coordinate Geometry
21. Find the gradient of the line joining (2, 5) and (6, 13).
A. 2 ✓
B. 4
C. ½
D. 3