Maths · Gbhs Yaounde · April 2021 · Ordinary Level

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Exercices, méthodes & corrigés (50)

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Maths · Gbhs Yaounde · April 2021 · Ordinary Level · Mock Examination

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Exercices, méthodes & corrigés (50)

Méthodes et corrigés

1. (n-th root of a) to the power m is: A: a^(n/m) B: a^(m/n) C: a^n / a^m D: a^m / a^n

10. The sum of the first n terms of an arithmetic progression is Sn = n(2n-7), then the second term of the progression is: A: -11 B: -6 C: -5 D: -1

11. The sum to infinity of the sequence 9,3,1... is: A: 27/2 B: 27/2 C: 27/2 D: 13

12. The value of x for which the geometric mean of 2x and 9 is 6 is: A: 2 B: 3/2 C: 1/3 D: 36

13. nCr = A: n! / ((n-r)! r!) B: n! / (n-r)! C: n! / r! D: (n-r)! / r!

14. The number of terms in the binomial expansion of (2x - 1/x)^10 is: A: 9 B: 10 C: 11 D: 12

15. The number of permutations of the letters of the word "GILLETTE" is: A: 8! / (2!2!) B: 5! / (2!2!2!) C: 5! / (2!2!) D: 8! / (2!2!2!)

16. The coefficient of x² in the binomial expansion of (1 - 2x)⁻¹ is: A: -4 B: -2 C: 2 D: 4

17. cos 2x = A: 2cos²x - 1 B: 2cos²x + 1 C: 1 - 2sin²x D: 2cosxsinx

18. In which quadrant is sinx positive and cosx negative? A: First Quadrant B: Second Quadrant C: Third Quadrant D: Fourth Quadrant

19. Given that tan θ = √3, then the value of θ, for 0° ≤ θ ≤ 90° is: A: 30° B: 45° C: 60° D: 90°

2. log(xy) = A: xlogy B: logx - logy C: logx + logy D: log(x + y)

20. The period of y = sin2x is: A: π B: 2π C: π/2 D: π/4

21. 3π/4 in degrees is: A: 270° B: 330° C: 240° D: 135°

22. Given that triangle ABC is an equilateral triangle with side 4cm, the area of the triangle ABC is: A: 8√3 B: 4√3 C: 2√3 D: 8

23. From the diagram the area, in square units, of the shaded region is: A: 16π B: 8π C: 4π D: 2π

24. The distance between the points A(2, -1) and B(0, -2) is: A: √3 B: √6 C: √10 D: √5

25. The perpendicular distance from the point (1, 2) to the line 4x - 3y + 10 = 0 is: A: 8 B: 8/5 C: 8/√5 D: 12/√5

26. The tangent of the acute angle between the line y + 3x = 2 and the x - axis is: A: -3 B: -2 C: 2 D: 3

27. The equation of the line passing through the point (0, 6) with gradient -2 is: A: y = 2x + 6 B: y = -2x + 6 C: y = -2x - 6 D: y = 2x - 6

28. The values of x for which |x - 2| = 5 are A: -7 and -3 B: -7 and 3 C: 7 and -3 D: 7 and 3

29. The range of values of x for which 4 - 2x > 7 is: A: x < 3/2 B: x > -3/2 C: x < -3/2 D: x > 3/2

3. The conjugate of √5 - 3 is: A: √5+3 B: √5-3 C: -√5-3 D: -√5 + 3

30. The range of values of x for which (2 - x)(x + 1) ≤ 0 is: A: -1 ≤ x ≤ 2 B: -2 ≤ x ≤ -1 C: x ≤ -1 or x ≥ 2 D: x ≤ -2 or x ≥ -1

31. Rose want to a shop and bought x pens at 50 francs each and y rulers at 100 francs each. Given that she spent only 1000francs, the inequality satisfying her expenditure is: A: x + 2y ≥ 20 B: x + 2y < 20 C: x + 2y > 20 D: x + 2y ≤ 20

32. Using the shaded region above, the maximum value of the constraint 3x + 2y is: A: 6 B: 10 C: 12 D: 16

33. Which of the following inequalities represent the shaded region in the figure above? A: y ≥ 0, y ≤ 2x, x + y ≤ 9 B: y ≥ 0, y < 2x, x + y < 9 C: y ≥ 0, y ≤ 2x, x + y < 9 D: y ≥ 0, y < 2x, x + y ≤ 9

34. Given that the functions f and g are defined over the set of real numbers, R by f:x → 2x + 3 and g: x → x - 5, then the composite function gf:x → A: 2x + 2 B: 2x + 7 C: 2x - 2 D: 2x - 7

35. The inverse of the function y = loga x is: A: a^x B: a^y C: logy a D: logx a

36. The transformation, T is defined as T: (x, y) → (x + 2y, 3x + y). The invariant point under T is: A: (2,2) B: (1,1) C: (2,3) D: (0,0)

37. Given the matric equation, M (x/y) = (x/y), then (x/y) = A: M(x/y) B: Mᵀ(x/y) C: M⁻¹(x/y) D: M⁻¹(x/y)

38. The transformation, T, defined by T(x, y) = (-3x + 2y, 5x - y). Which of the following matrices represent the transformation, T? A: ((-3, -2), (5, 1)) B: ((-3, 2), (5, -1)) C: ((2, -3), (-1, 5)) D: ((-2, 3), (1, -5))

39. The binary operation * is defined over the set of integers, Z by x * y = x² - y + 6, then the value of -2 * 1 is: A: -9 B: -1 C: 1 D: 9

4. Given that α and β are the roots of a quadratic equation, then α² + β² is: A: (α + β)² B: (α + β)² – αβ C: (α + β)² – 2αβ D: (α + β)² + 2αβ

40. Given the operation table below. * P Q R S P Q S P R Q S R Q P R P Q R S S R P S Q The inverse of S is: A: P B: Q C: R D: S

41. An operation * is defined on the set, S, where S = {0, 1, 3, 5}. Given that (S,*) forms a group, then the order of the group is: A: 4 B: 5 C: 9 D: 16

42. Given that the set T = {0,1,2,3} as shown on the operation table forms a group under the operation *. * 0 1 2 3 0 3 2 0 1 1 2 3 1 0 2 0 1 2 3 3 1 0 3 2 One subgroup of (T, *) is: A: ({2, 1}, *) B: ({2,3}, *) C: ({0,2}, *) D: ({0,3}, *)

43. The vector equation of a line is given by r = 2i + 3j + t(3i - j). The direction vector of r is: A: 2i + 3j B: 3i - j C: i - 4j D: -i + 4j

44. Given that two vectors 2i - 6j and -2i + tj are parallel, then the value of t is: A: -6 B: -3 C: 3 D: 6

45. Given that p = 6i + 2j and q = 2i - j, then |p - q| = A: √5 B: √17 C: 5 D: 17

46. Given that y = uv, where u and v are real functions in x, then dy/dx = A: v du/dx + u dv/dx B: v du/dx - u dv/dx C: u dv/dx - v du/dx D: u dv/dx + v du/dx

47. d/dx (sinx) = A: cosx B: sinx C: -cosx D: -sinx

48. The value of x for which the function f(x) = 5 - 2x - 2x² has a maximum turning point is: A: 1/2 B: -1/2 C: 1/2 D: -1/2

49. ∫ cos3θdθ = A: -1/3 sin3θ + k B: 1/3 sin3θ + k C: -3sin3θ D: 3sin3θ [Where, k is an arbitrary constant of integration]

5. The minimum value of the function f(x) = (x + 3)² - 7 is: A: -3 B: -7 C: 3 D: 7

50. The area of the shaded region in the diagram above bounded by the curve y = 4 - x² and the positive x-axis is: A: 32/3 B: 16/3 C: 4 D: 0

6. The quadratic equation whose sum of roots is 3 and product of roots -2 is: A: x² - 3x + 2 = 0 B: x² + 3x - 2 = 0 C: x² - 3x - 2 = 0 D: x² + 3x + 2 = 0

7. The remainder when x³ - x² + 7x + 8 is divided by (x + 1) is: A: -1 B: -2 C: 2 D: 1

8. The value of k for which (x + 2) is a factor of x³ - kx² + 3x + 2 is: A: -3 B: 0 C: 3 D: 4

9. The nth term of a sequence is given by Un = (-1)^(2n-1), then 5th term is: A: 1 B: 1/16 C: -1/16 D: -1

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42. Given that the set T = {0,1,2,3} as shown on the operation table forms a group under the operation . 0 1 2 3 0 3 2 0 1 1 2 3 1 0 2 0 1 2 3 3 1 0 3 2 One subgroup of (T, ) is: A: ({2, 1}, ) B: ({2,3}, ) C: ({0,2}, ) D: ({0,3}, *)