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O Level & A Level Mathematics (Cambridge)

A Level Maths (Pure 1) — Trigonometry, Series and Calculus, Set 2

Take the A Level Maths (Pure 1) — Trigonometry, Series and Calculus, Set 2: 20 multiple-choice questions (30 minutes) with instant scoring and a full…

What this test covers

Sample questions with answers

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

  1. Q1. Simplify sin θ / tan θ.

    • A. 1/cos θ
    • B. tan θ
    • C. sin θ
    • D. cos θ ✓

    Answer: D. cos θ

    Explanation: sin θ ÷ (sin θ / cos θ) = cos θ.

  2. Q2. Solve tan x = 1 for 0° ≤ x ≤ 360°.

    • A. 45° and 135°
    • B. 135° and 315°
    • C. 45° and 315°
    • D. 45° and 225° ✓

    Answer: D. 45° and 225°

    Explanation: tan has period 180°, so 45° and 45° + 180°.

  3. Q3. Solve 2 sin x = −1 for 0° ≤ x ≤ 360°.

    • A. 210° and 330° ✓
    • B. 150° and 210°
    • C. 240° and 300°
    • D. 30° and 150°

    Answer: A. 210° and 330°

    Explanation: sin x = −½ is negative in the third and fourth quadrants: 180° + 30° and 360° − 30°.

  4. Q4. What is the exact value of cos 30°?

    • A. √3/2 ✓
    • B. 1/2
    • C. 1/√2
    • D. √3

    Answer: A. √3/2

    Explanation: From the 30°-60°-90° triangle, cos 30° = √3/2.

  5. Q5. What is the amplitude of y = 3 sin x?

    • A. 3 ✓
    • B. 1
    • C. 6
    • D. 1/3

    Answer: A. 3

    Explanation: The graph rises to 3 and falls to −3.

The other 15 questions

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  1. Q6. Solve sin² x = 1/4 for 0° ≤ x ≤ 180°.

    • A. 30°, 150° and 210°
    • B. 30° and 150°
    • C. 30° only
    • D. 60° and 120°

  2. Q7. Find the coefficient of x² in the expansion of (1 − 3x)⁴.

    • A. −54
    • B. 6
    • C. 18
    • D. 54

  3. Q8. What are the first three terms of (1 + x)⁶ in ascending powers of x?

    • A. 1 + 6x + 15x²
    • B. 1 + 6x + 12x²
    • C. 1 + 6x + 36x²
    • D. 1 + 6x + 30x²

  4. Q9. An arithmetic progression has first term 7 and 7th term 25. What is the common difference?

    • A. 3
    • B. 2.6
    • C. 18
    • D. 4

  5. Q10. Find the sum 5 + 9 + 13 + … + 81.

    • A. 880
    • B. 1720
    • C. 840
    • D. 860

  6. Q11. Find the 6th term of the geometric progression 2, 6, 18, …

    • A. 162
    • B. 486
    • C. 1458
    • D. 243

  7. Q12. Find the sum of the first 5 terms of the geometric progression with a = 3 and r = 2.

    • A. 96
    • B. 93
    • C. 45
    • D. 48

  8. Q13. Differentiate y = 3x⁴ − 5x² + 7.

    • A. 12x³ − 10x + 7
    • B. 3x³ − 5x
    • C. 12x³ − 10x
    • D. 12x⁴ − 10x²

  9. Q14. Differentiate y = √x.

    • A. −1/(2√x)
    • B. √x/2
    • C. 1/(2√x)
    • D. 2√x

  10. Q15. Find the equation of the tangent to y = x² at the point (3, 9).

    • A. y = 9x − 18
    • B. y = 6x + 9
    • C. y = 6x − 9
    • D. y = 3x

  11. Q16. What is the gradient of the normal to y = x² at (3, 9)?

    • A. −6
    • B. 1/6
    • C. −1/6
    • D. 6

  12. Q17. Find the maximum point of y = x³ − 3x.

    • A. (0, 0)
    • B. (−1, −2)
    • C. (1, −2)
    • D. (−1, 2)

  13. Q18. Why is y = x³ + 2x an increasing function for all x?

    • A. Its second derivative is always positive
    • B. dy/dx = 3x² + 2 is always positive
    • C. It has a stationary point at x = 0
    • D. Its graph passes through the origin

  14. Q19. Find ∫ (4x³ − 3) dx.

    • A. 12x² + c
    • B. 4x⁴ − 3x + c
    • C. x⁴ − 3x + c
    • D. x⁴ − 3 + c

  15. Q20. Evaluate ∫₀² (3x² + 1) dx.

    • A. 13
    • B. 10
    • C. 12
    • D. 8