O Level & A Level Mathematics (Cambridge)

A Level Maths (Pure 1) — Quadratics, Functions and Coordinate Geometry, Set 2

Take the A Level Maths (Pure 1) — Quadratics, Functions and Coordinate Geometry, Set 2: 20 multiple-choice questions (30 minutes) with instant scoring and…

What this test covers

20 A Level Pure Mathematics

Sample questions with answers

The first 5 questions of this test, with the correct answer and explanation.

Q1. Express x² + 10x + 30 in the form (x + a)² + b, and state its minimum value.
- A. (x + 10)² − 70, minimum −70
- B. (x + 5)² + 30, minimum 30
- C. (x + 5)² − 5, minimum −5
- D. (x + 5)² + 5, minimum 5 ✓
Answer: D. (x + 5)² + 5, minimum 5
Explanation: (x + 5)² = x² + 10x + 25, so add 5.
Q2. For which values of k does x² − 4x + k = 0 have two distinct real roots?
- A. k = 4
- B. k < 4 ✓
- C. k < −4
- D. k > 4
Answer: B. k < 4
Explanation: 16 − 4k > 0, so k < 4.
Q3. For which value of c is the line y = 2x + c a tangent to y = x² + 3?
- A. −2
- B. 2 ✓
- C. 4
- D. 3
Answer: B. 2
Explanation: x² − 2x + 3 − c = 0 must have equal roots: 4 − 4(3 − c) = 0, so c = 2.
Q4. Solve x² − 5x + 4 ≥ 0.
- A. 1 ≤ x ≤ 4
- B. x ≤ 1 or x ≥ 4 ✓
- C. x ≥ 4
- D. x ≤ −4 or x ≥ −1
Answer: B. x ≤ 1 or x ≥ 4
Explanation: (x − 1)(x − 4) ≥ 0 outside the roots.
Q5. f(x) = 2x + 1 and g(x) = x − 3. Find fg(x).
- A. 2x − 2
- B. 2x + 4
- C. 2x − 5 ✓
- D. 2x − 6
Answer: C. 2x − 5
Explanation: f(x − 3) = 2(x − 3) + 1 = 2x − 5.

The other 15 questions

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Q6. Find f⁻¹(x) for f(x) = 5 − 2x.
- A. 1/(5 − 2x)
- B. (x − 5)/2
- C. (5 − x)/2
- D. 5 + 2x
Q7. f(x) = x² + 2 for x ≥ 0. Find f⁻¹(x) and its domain.
- A. √(x − 2), for x ≥ 2
- B. √(x + 2), for x ≥ −2
- C. √x − 2, for x ≥ 0
- D. (x − 2)², for x ≥ 2
Q8. Describe the transformation that maps y = f(x) onto y = f(−x).
- A. Reflection in the y-axis
- B. Rotation of 180° about the origin
- C. Translation 1 unit left
- D. Reflection in the x-axis
Q9. Describe the transformation that maps y = f(x) onto y = f(x/2).
- A. Stretch parallel to the y-axis, scale factor ½
- B. Stretch parallel to the y-axis, scale factor 2
- C. Stretch parallel to the x-axis, scale factor 2
- D. Stretch parallel to the x-axis, scale factor ½
Q10. Find the equation of the line through (2, 3) that is perpendicular to 3x + 4y = 8.
- A. 4x − 3y − 1 = 0
- B. 4x + 3y − 17 = 0
- C. 3x + 4y − 18 = 0
- D. 4x − 3y + 1 = 0
Q11. Which equation describes the circle with centre (−2, 1) and radius 4?
- A. x² + y² + 2x − y − 16 = 0
- B. x² + y² + 4x − 2y + 11 = 0
- C. x² + y² − 4x + 2y − 11 = 0
- D. x² + y² + 4x − 2y − 11 = 0
Q12. Does the point (1, 3) lie inside, on or outside the circle (x − 2)² + (y − 1)² = 9?
- A. Outside, because 1 + 3 > 2 + 1
- B. Inside, because its distance² from the centre is 5 < 9
- C. Outside, because 5 > 3
- D. On the circle
Q13. Find the x-coordinates where the line y = 2x − 1 meets the circle x² + y² = 10.
- A. 1 and −9/5
- B. −1 and 3
- C. −1 and 9/5
- D. 0 and 4/5
Q14. Find the arc length when r = 10 cm and θ = 0.8 radians.
- A. 12.5 cm
- B. 80 cm
- C. 40 cm
- D. 8 cm
Q15. Find the perimeter of a sector with radius 5 cm and angle 1.2 radians.
- A. 6 cm
- B. 16 cm
- C. 15 cm
- D. 11 cm
Q16. Convert 2.5 radians to degrees, to 1 decimal place.
- A. 45.0°
- B. 2.5°
- C. 143.2°
- D. 157.1°
Q17. Find the area of the segment cut off by a chord in a circle of radius 6 cm, where the angle at the centre is π/3. Give the answer to 3 significant figures.
- A. 3.26 cm²
- B. 15.6 cm²
- C. 18.8 cm²
- D. 6.28 cm²
Q18. What is the discriminant of 3x² − 2x + 5?
- A. −56
- B. −64
- C. 56
- D. 64
Q19. Find the vertex of y = −2x² + 8x − 3.
- A. (2, 5)
- B. (4, −3)
- C. (−2, −27)
- D. (2, −3)
Q20. f(x) = x² and g(x) = 2x − 1. Solve fg(x) = 9.
- A. x = 2 only
- B. x = 5 only
- C. x = 3 or x = −3
- D. x = 2 or x = −1