Mathematics Exam

31. If a = 2 - 3√5 and b = 3 + 2√5, then which one of the following is true?

A. ab = 36
B. 11a + b = -36 + 13√5
C. a + b = 5
D. a - b = -1 - √5

32. A sector of a circle of diameter 8cm is formed by a central angle of 45°. What is the area of the sector?

A. 8π cm²
B. 2π cm²
C. π cm²
D. (2π + 8) cm²

33. Which one of the following intervals is the solution set of the inequality $|3 - \frac{1}{2}x| < 5$?

A. (−16, 4)
B. (−4, 16)
C. (−2, 8)
D. (−8, 2)

34. The altitude of a frustum of a regular square pyramid is 9 cm. What is the volume of the frustum if the side length of the upper base is 6 cm and the side length of the lower base is 10 cm?

A. 108 cm³
B. 324 cm³
C. 588 cm³
D. 196 cm³

35. Which one of the following numbers is the coefficient of x⁶y⁴ in the expansion of (x + y)¹⁰?

A. 4860
B. 1260
C. 210
D. 240

36. Which one of the following is true about the Range and Interquartile Range of a given data?

A. Both are considering only the middle 50% of the data.
B. Both are measures of variation of the data.
C. Both are affected by extreme values in the data.
D. Both are measures of the variability of each item in the data.

37. Which one of the following is equal to the expression $\frac{{(125)}^{2 / 3} {(81)}^{- 3 / 4}}{{(27)}^{- 2 / 3} {(625)}^{3 / 4}}$ ?

A. 1/15
B. 15
C. 3/5
D. 5/3

38. If the length of the sides of a triangle are 8cm, 6cm and 4cm, then which one of the following is the area of the triangle?

A. 24 cm²
B. 1.5√15 cm²
C. 12 cm²
D. 3√15 cm²

39. The following figure is the graph of a quadratic function f(x) = ax² + bx + c in the set of real numbers.

Which one of the following is the solution set of the inequality f(x) ≤ 0?

A. {x : x ≤ 0 and x ≥ -4}
B. {x : x ≤ -4 or x ≥ 0}
C. {x : x ≤ 2 or x ≥ 6}
D. {x : x ≥ 2 and x ≤ 6}

40. Which one of the following is an onto function from ℝ onto ℝ?

A. f(x) = 2x − 3x²
B. f(x) = 5x³ + 1
C. f(x) = |x − 1|
D. f(x) = √(x² + 1)

41. Let M be a matrix such that M = $(\begin{matrix} 9 & 24 & 6 \\ - 12 & 18 & 15 \\ 0 & 27 & 3 \end{matrix})$ . Which one of the following matrices is equal to ²⁄₃M?

A.

(\begin{matrix} 6 & 16 & 2 \\ - 8 & 12 & 10 \\ 0 & 18 & 2 \end{matrix})

B.

(\begin{matrix} 6 & 16 & 4 \\ - 8 & 12 & 10 \\ 0 & 18 & 2 \end{matrix})

C.

(\begin{matrix} 3 & 8 & 2 \\ - 4 & 6 & 5 \\ 0 & 9 & 1 \end{matrix})

D.

(\begin{matrix} 6 & 8 & 4 \\ - 8 & 6 & 10 \\ 0 & 9 & 2 \end{matrix})

42. Consider that a data set given below: 10, 8, 10, 2, 12, 6, 12, 18, 3, 7, 10, 8, 8. Which one of the following is the coefficient of range of the data?

A. 5/4
B. 20
C. 16
D. 4/5

43. Let r₁ and r₂ be the roots of a quadratic equation ax² + bx + c = 0, such that r₁ + r₂ = −2.5 and r₁r₂ = 1.5, for a, b and c are real numbers and a ≠ 0. Which one of the following can be the values of a, b and c respectively?

A. 1, 6 and 5
B. 2, 3 and 5
C. 1, 5 and 6
D. 2, 5 and 3

44. The following data gives the scores of 10 students in a Mathematics examination: 6, 10, 8, 5, 9, 8, 5, 10, 10, 9. Which one of the following is the standard deviation of the given data?

A. 3.6
B. √3.6
C. 5.8
D. √5.8

45. Which of the following pairs of lines with the given equations are parallel?

A. l₁: x − y + 3 = 0 and l₂: −x + y − 9 = 0
B. l₁: 4x − y = 2 and l₂: −x + 4y − 3 = 0
C. l₁: 2x + 3y = 5 and l₂: 3x + 2y = 4
D. l₁: x − 2y + 1 = 0 and l₂: x + 2y − 1 = 0

Mathematics Exam: Exam fore

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