Elementary Mathematics II — 2026-test Past Questions

University of Ilorin MTH102: 67 questions.

Topics: Functions of a real variable, graphs, limits, and continuity

1. Find the image of x = −2 in the mapping defined by y = 7 − 3x
   1. 13
   2. 7
   3. 19
   4. 14
2. Find the image of x = 3 in the mapping defined by y = 3x − 4
   1. 4
   2. 5
   3. 8
   4. 6
3. Find the image of x = 3 in the mapping defined by y = 5x − 4
   1. 4
   2. 11
   3. 6
   4. 8
4. Find the image of x = 0 in y = x² − x + 5
   1. 9
   2. 5
   3. 11
   4. 2
5. Find the domain of y = x + 2 when the range is y = {−1, 0, 1, 2}
   1. {−3, −2, −1, 0}
   2. {5, −4, −3, −1}
   3. {−6, 3, −2, −8}
   4. {−2, −1, −7, 0}
6. Find the domain of y = −7x + 7 when the range is y = {7, 0, −7, −14}
   1. {0, 1, 2, 3}
   2. {3, 2, 5, 7}
   3. {1, 3, 5, 2}
   4. {4, 5, 6, 7}
7. Find the domain of y = x − 1 when the range is y = {0, 2, 3, 4}
   1. {1, 3, 4, 5}
   2. {2, 3, 4, 5}
   3. {0, 1, 2, 3}
   4. {−1, 0, 1, 2}
8. Find the domain of y = x − 3 when the range is y = {−1, 0, 1, 2}
   1. {2, 3, 4, 5}
   2. {−4, −3, −2, −1}
   3. {1, 2, 3, 4}
   4. {0, 1, 2, 3}
9. Find the domain of the mapping y = 16 − 2x when the range is y = {10, 6, 4, 0}
   1. {3, 5, 6, 8}
   2. {0, 2, 3, 5}
   3. {1, 2, 3, 4}
   4. {2, 4, 6, 8}
10. Find the codomain (set of images) of the mapping y = −2x + 8 for the domain {−2, −4, 0, 6}
    1. {12, 16, 8, −4}
    2. {−3, −4, 6, 7}
    3. {0, 3, 5, 8}
    4. {6, 8, −4, 4}
11. Find the range of the mapping defined by y = x + 1 when x = {−4, 5, 6, 7}
    1. {−3, 6, 7, 8}
    2. {5, 6, 7, 8}
    3. {1, 8, 8, 9}
    4. {4, 16, 10, 7}
12. Find the range of the mapping defined by y = 4 + x when x = {−1, 0, 1, 2}
    1. {4, 7, 9, 1}
    2. {3, 4, 9, 0}
    3. {3, 4, 5, 6}
    4. {5, 1, 7, 3}
13. Find the range of the mapping y = 5 + x when the domain = {0, 3, 5, 6} and the codomain = {5, 8, 10, 11, 13, 15}
    1. {12, 13, 6, 3}
    2. {1, 7, 4, 13}
    3. {5, 8, 10, 11}
    4. {1, 5, 4, 15}
14. Suppose {−1, 0, 1, 2} and {−1, W, 17, 26} are the domain and codomain of the mapping y = 9x + 8. Find W.
    1. 12
    2. 28
    3. 4
    4. 8
15. Find the value of K if f(x) = 5x − 1, domain = {1, 2, 3, 4} and codomain = {4, 9, K, 19}
    1. 4
    2. 17
    3. 18
    4. 14
16. Given y = −7x + 7 and the codomain {7, 0, −7, −14}, find the domain.
    1. {0, 1, 2, 3}
    2. {−1, 0, 1, 2}
    3. {1, 2, 3, 4}
    4. {0, −1, −2, −3}
17. Find the set of codomain for the domain {0, 1, 2, 3} of the mapping y = 5 − 2x
    1. {5, 3, 1, −1}
    2. {5, 2, 3, 1}
    3. {2, 3, 4, 5}
    4. {−1, 1, 3, 5}
18. Find the range of the mapping defined by y = 2x + 1 when the domain = {0, 3, 5, 6}
    1. {1, 7, 11, 13}
    2. {1, 8, 8, 9}
    3. {2, 6, 10, 13}
    4. {3, 7, 9, 13}
19. A function is considered even when:
    1. f(x) = −f(x)
    2. f(x) = −f(−x)
    3. f(x) = f(x)
    4. f(x) = f(−x)
20. Which of the following represents a linear function?
    1. f(x) = √x
    2. f(x) = 2x − 3
    3. f(x) = x² + 1
    4. f(x) = 1/x
21. Let f: R → R be defined by f(x) = 5x² + 3. Find f(−2).
    1. 14
    2. −23
    3. 23
    4. −17
22. Given f(x) = 2x² + 1 (x > 0), find f⁻¹(9), that is, the value of x such that f(x) = 9.
    1. 4
    2. 2
    3. 3
    4. 9
23. If f(x) = −x² − 4, find f(2a).
    1. 4a² − 4
    2. −2a² − 4
    3. −4a² − 4
    4. −4
24. If f(x) = 2 (a constant function), find f(x + 2).
    1. 2
    2. 4
    3. 8
    4. 0
25. If f(x) = 3x² + 2x + 1, find f(2).
    1. 8
    2. 17
    3. 16
    4. 11
26. Let f: [−3, 8] → R and f(x) = x³ − 2x − 1. Find f(−2).
    1. 5
    2. −2
    3. −5
    4. 3
27. Let f: [−4, 8] → R be defined by f(x) = (x − 1)². Find f(−1).
    1. 2
    2. 4
    3. 0
    4. −2
28. Given f: [−4, 8] → R such that f(x) = (x − 1)². Find f(3).
    1. 1
    2. 2
    3. 4
    4. −2
29. If f: {−4, 8} → R is defined by f(x) = (x − 1)², find the set of images (range) of f.
    1. {25, 49}
    2. {10, 1}
    3. {16, 49}
    4. {8, −4}
30. Given f: [−4, 8] → R such that f(x) = (x − 1)². What is the domain of f?
    1. [−4, 8]
    2. R
    3. −4
    4. 8
31. If f: R → R, f(x) = x² − 1, find f(p − 2).
    1. p² − 4p + 3
    2. p² + 4p + 3
    3. p² + 2p + 3
    4. p² − 2p + 3
32. If f(x) = 2x² − 1, find f(p − 3).
    1. 2p² − 12p + 17
    2. 2p² + 12p − 17
    3. 2p² − 12p − 17
    4. 2p² + 12p + 17
33. If f(x) = 2x + 4 and g(x) = 3x + 1, find x where f(x) = −g(x).
    1. 1
    2. −1
    3. −2
    4. 2
34. If lim(x→4) f(x) = 64 and lim(x→4) g(x) = 20, find lim(x→4) f(x)·g(x).
    1. 640
    2. 320
    3. 1280
    4. 1380
35. If f(x) = kx + 3, g(x) = 2x − 4 and g(f(2)) = 34, find k.
    1. 7
    2. 8
    3. 9
    4. 10
36. If g(x) = 3x + 2 and f(x) = x² − 1, find g(f(x)).
    1. 3x² + 1
    2. 3x² − 1
    3. 3x² + 2x − 1
    4. 3x² + 3x − 2
37. If f(x) = x²/(x + 1) and g(x) = (x² + 1)/(3x), find (f/g)(x).
    1. 3x³ / [(x + 1)(x² + 1)]
    2. x³ / [3(x + 1)(x² + 1)]
    3. 3x / [(x + 1)(x² + 1)]
    4. (x + 1)(x² + 1) / (3x³)
38. If f(x) = (x² + 2x + 2)² and g(x) = 2x² + 6x + 7, find (f − g)(x).
    1. x⁴ + 4x³ + 6x² + 2x − 3
    2. x⁴ + 4x³ + 10x² + 14x + 11
    3. x⁴ + 4x³ + 6x² + 2x + 3
    4. x⁴ + 4x³ + 8x² + 2x − 3
39. Given that f(x) = x² + 2x + 1, find f(x + 2) − f(x).
    1. 4x + 8
    2. 4x + 4
    3. 2x + 8
    4. 4x + 6
40. Given f(x) = 4x − 9, compute [f(x + h) − f(x)] / h.
    1. 8h
    2. 4
    3. 4h
    4. 2
41. If f(x) = 2x − 3 and g(x) = 5x + 7, find f(3) + g(2).
    1. 20
    2. 21
    3. 17
    4. 14
42. If f(x) = 3x² + 4x³ − 5x + 2 and g(x) = −x³ − x³ + 5, find f(x) − g(x).
    1. 6x³ + 3x² − 5x − 3
    2. 2x³ + 3x² − 5x − 3
    3. 6x³ + 3x² − 5x + 7
    4. 4x³ + 3x² − 5x − 3
43. If f(x) = 3x + 2 and g(x) = x² − 1, find (fg)(x).
    1. 3x³ + 2x² − 3x − 2
    2. 3x² + 2x − 1
    3. 3x³ + 3x² − 3x − 2
    4. 3x² + 3x − 2
44. Find the inverse of f(x) = 3x + 7.
    1. (x − 7)/2
    2. (x + 7)/2
    3. (x + 7)/3
    4. (x − 7)/3
45. Find the inverse function of f(x) = x³.
    1. √x
    2. ³√x
    3. 3√x
    4. x^(1/2)
46. Find f⁻¹(9) if f(x) = 2x² + 1 (x ≥ 0).
    1. 1
    2. 3
    3. 2
    4. 4
47. If f(x) = x³ and x ≥ 0, find f⁻¹(27).
    1. 9
    2. 3
    3. 2
    4. 5
48. Find the zeros of f(x) = x³ + 4x² + 4x.
    1. {0, −2}
    2. {2, −2}
    3. {0, 2}
    4. {−2}
49. If f(x) = 3x − 8 for x > 5; x² − 3 for −3 ≤ x ≤ 5; 2x + 5 for x < −3. Find f(1).
    1. −3
    2. −2
    3. 3
    4. −5
50. If f(x) = 3x − 8 for x > 5; x² − 3 for −3 ≤ x ≤ 5; 2x + 5 for x < −3. Find f(−10).
    1. −15
    2. −25
    3. −10
    4. −5
51. If f(x) = 3x − 8 for x > 5; x² − 3 for −3 ≤ x ≤ 5; 2x + 5 for x < −3. Find f(6).
    1. 33
    2. 10
    3. 17
    4. 18
52. Evaluate: lim(x→0) (x² + 8x)/(2x)
    1. 8
    2. 12
    3. 16
    4. 4
53. Evaluate: lim(x→5) (x² − 4)/(x + 2)
    1. 3
    2. 5
    3. 4
    4. 2
54. Evaluate: lim(x→4) (x² − 16)/(x − 4)
    1. 8
    2. 6
    3. 2
    4. 4
55. Evaluate: lim(x→0) (sin x)/x
    1. 1
    2. 0
    3. 3
    4. −1
56. Evaluate: lim(x→0) (cos x + sin x)/(3 cos x)
    1. 3
    2. −1
    3. 1
    4. 1/3
57. Find: lim(x→∞) (x² + 2x − 3)/(3x² + 6)
    1. 1/4
    2. 1/2
    3. 1/3
    4. 1
58. Find: lim(x→∞) (3x⁴ − 2x² + 1)/(6x⁴ + x³ − 3x)
    1. 1
    2. 1/2
    3. 1/3
    4. 1/4
59. Find: lim(x→1) (x² − 1)/(x² − 3x + 2)
    1. −2
    2. 2
    3. 1
    4. −1
60. Evaluate: lim(x→2) (3x² + 7x − 6)
    1. 20
    2. 30
    3. 40
    4. 10
61. If lim(x→3) f(x) = 81, find lim(x→3) ⁴√f(x).
    1. 3
    2. 2
    3. 4
    4. 1
62. If f(x) = 3x + 2 for x < 3 and f(x) = 5x − 4 for x ≥ 3, find lim(x→3⁺) f(x).
    1. 12
    2. 9
    3. 11
    4. 10
63. If f(x) = 3x + 2 for x < 3 and f(x) = 5x − 4 for x ≥ 3, find lim(x→3⁻) f(x).
    1. 11
    2. 12
    3. 9
    4. 10
64. If f(x) = 5x − 4 for x ≥ 3 and f(x) = 3x + 2 for x < 3, does lim(x→3) f(x) exist?
    1. Yes, it equals 11
    2. Yes, it equals 12
    3. The limit does not exist
    4. Yes, it equals 9
65. Find δ if f(x) = 5x + 10, ε = 0.1 and a = 3.
    1. 0.01
    2. 0.1
    3. 0.2
    4. 0.02
66. Find δ if f(x) = (x² − 1)/(x − 1), ε = 0.01 and a = 3.
    1. 0.01
    2. 0.1
    3. 0.02
    4. 0.2
67. Find δ if f(x) = 5x − 10, ε = 0.1 and a = 3.
    1. 0.01
    2. 0.02
    3. 0.1
    4. 0.2

Register free to unlock all 67 questions with answers and explanations