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O Level & A Level Mathematics (Cambridge)

O Level Mathematics — Algebra and Graphs, Set 2

Take the O Level Mathematics — Algebra and Graphs, Set 2: 20 multiple-choice questions (30 minutes) with instant scoring and a full answer review. Covers…

What this test covers

Sample questions with answers

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

  1. Q1. Simplify 5a − 3b + 2a + 7b.

    • A. 11ab
    • B. 7a − 10b
    • C. 3a + 4b
    • D. 7a + 4b ✓

    Answer: D. 7a + 4b

    Explanation: Collect like terms: 5a + 2a = 7a and −3b + 7b = 4b.

  2. Q2. Factorise x² − 16.

    • A. (x − 4)²
    • B. x(x − 16)
    • C. (x − 4)(x + 4) ✓
    • D. (x − 8)(x + 2)

    Answer: C. (x − 4)(x + 4)

    Explanation: Difference of two squares.

  3. Q3. Factorise x² − 5x − 14.

    • A. (x − 7)(x + 2) ✓
    • B. (x + 7)(x − 2)
    • C. (x − 7)(x − 2)
    • D. (x − 14)(x + 1)

    Answer: A. (x − 7)(x + 2)

    Explanation: Two numbers that multiply to −14 and add to −5: −7 and 2.

  4. Q4. Solve 4(x − 3) = 2(x + 5).

    • A. x = −1
    • B. x = 1
    • C. x = 22
    • D. x = 11 ✓

    Answer: D. x = 11

    Explanation: 4x − 12 = 2x + 10, so 2x = 22 and x = 11.

  5. Q5. Solve x² − 2x − 8 = 0.

    • A. x = 2 or x = 4
    • B. x = 4 or x = −2 ✓
    • C. x = 8 or x = −1
    • D. x = −4 or x = 2

    Answer: B. x = 4 or x = −2

    Explanation: (x − 4)(x + 2) = 0.

The other 15 questions

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  1. Q6. Make t the subject of v = u + at.

    • A. t = (v − u)/a
    • B. t = (v + u)/a
    • C. t = v − u − a
    • D. t = a/(v − u)

  2. Q7. Solve 2x + y = 7 and 3x − y = 8.

    • A. x = 1, y = 5
    • B. x = 3, y = 1
    • C. x = 3, y = −1
    • D. x = 2, y = 3

  3. Q8. What is the gradient of the line 2y = 6x − 4?

    • A. 3
    • B. −2
    • C. 6
    • D. 2

  4. Q9. Find the equation of the line parallel to y = −2x + 1 that passes through (0, 5).

    • A. y = −2x + 1
    • B. y = 0.5x + 5
    • C. y = −2x + 5
    • D. y = 2x + 5

  5. Q10. Find the midpoint of the line joining (2, −3) and (8, 5).

    • A. (5, 1)
    • B. (5, −1)
    • C. (10, 2)
    • D. (3, 4)

  6. Q11. Find the length of the line joining (1, 1) and (4, 5).

    • A. 5
    • B. 7
    • C. √7
    • D. 25

  7. Q12. Find the nth term of 2, 6, 10, 14, …

    • A. 4n + 2
    • B. n + 4
    • C. 4n − 2
    • D. 2n + 4

  8. Q13. Which term of the sequence 2, 6, 10, 14, … is equal to 98?

    • A. 24th
    • B. 49th
    • C. 26th
    • D. 25th

  9. Q14. Find the nth term of the sequence 1, 4, 9, 16, …

    • A. n + 3
    • B. 2n − 1
    • C. n²
    • D. 3n − 2

  10. Q15. y varies as the square root of x, and y = 6 when x = 9. Find y when x = 25.

    • A. 50
    • B. 10
    • C. 30
    • D. 15

  11. Q16. How many integers satisfy −3 < 2x + 1 ≤ 9?

    • A. 4
    • B. 5
    • C. 7
    • D. 6

  12. Q17. Expand (2x + 3)(x − 4).

    • A. 2x² + 5x − 12
    • B. 2x² − 5x − 12
    • C. 2x² − 11x − 12
    • D. 2x² − 12

  13. Q18. Simplify (x² + 3x)/(x² − 9).

    • A. 3x/(x − 3)
    • B. x/(x − 3)
    • C. x/(x + 3)
    • D. (x + 3)/(x − 3)

  14. Q19. f(x) = 3x − 4. Solve f(x) = 11.

    • A. x = 7/3
    • B. x = 15
    • C. x = 29
    • D. x = 5

  15. Q20. By completing the square, find the minimum value of x² − 8x + 10.

    • A. −4
    • B. 10
    • C. −6
    • D. 4