Mathematics exam 4 | Academic Curator

46. Which one of the following is the range of the function $f (x) = \frac{2 x - 1}{x + 3}$ ?

A. ℝ \ {−3}
B. ℝ \ {2}
C. ℝ \ {−1/3}
D. ℝ \ {−1/2}

47. Let z = −a + 2i and w = 5 − bi be two complex numbers, where a and b are real numbers. If z = w, then which one of the following pairs of numbers are equal to a and b respectively?

A. 5 and −2
B. −5 and −2
C. 5 and 2
D. −5 and 2

48. The following table presents the number of traffic accidents in a certain city per year for five consecutive years from 2019 to 2023.

Year	2019	2020	2021	2022	2023
Number of Accidents	3500	2750	2850	3500	3750

What is the average number of accidents per year for the given five years?

A. 3250
B. 3270
C. 3200
D. 3210

49. Which one of the following is the solution set of the equation ${(\sqrt{16})}^{2 x + 1} = {(\sqrt[3]{4096})}^{3 x - 5}$ ?

A. {9/4}
B. {9/2}
C. {11/2}
D. {11/4}

50. Which one of the following is a primary data?

A. The data obtained from a chart prepared by Ministry of Health regarding the spread of HIV/AIDS.
B. The data obtained by reading a journal regarding the opinion of the society about holidays.
C. The data obtained by measuring the weights of students in a certain school.
D. The data obtained from a document prepared by the MOE regarding the achievements of students in National Examination.

51. Which one of the following ordered pairs of numbers gives the coordinates of the point that divides a line segment with end points A(1, 1) and B(−6, 8) in the ratio of 3:4?

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

52. Which one of the following pairs of functions is an inverse of each other in their respective domains?

A. f(x) = √(x + 3) and g(x) = x² − 9
B. f(x) = x⁵ and g(x) = 1/x⁵
C. f(x) = x³ − 1 and g(x) = ∛(x + 1)
D. f(x) = (x + 1)/(x − 1) and g(x) = (x − 1)/(x + 1)

53. Which one of the following numbers is the determinant of the matrix $M = (\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 10 \end{matrix})$ ?

A. −3
B. 6
C. −6
D. 3

54. Which one of the following is a simple random sampling?

A. First the population is divided into homogenous groups and a sample is selected from each homogenous group.
B. First divide a city into ten groups and choose the secondary school principals from the randomly selected 3 groups.
C. Selecting five students from grade 12 students of the same school randomly.
D. Selecting a group randomly from groups formed by dividing the population into groups.

55. Let A and B be two sets that contain 15 and 17 elements respectively. If A ∩ B contains 10 elements, what is the number of elements in A ∪ B?

22
12
42
32

56. Which one of the following is the position vector of the vector with initial point A(1, −1) and terminal point B(2, −3)?

A. 3i + 4j
B. i − 4j
C. 3i − 4j
D. i − 2j

57. Let θ be an angle in standard position and P(−3, 4) be a point on the terminal side of θ. Which one of the following is true about the corresponding trigonometric functions?

A. cos θ = −3/5
B. sin θ = −4/5
C. sin θ = 3/5
D. cos θ = 4/5

58. Which one of the following conic section is defined by "the set of points in a plane such that the sum of the distances from two given points is constant"?

A. Ellipse
B. Hyperbola
C. Parabola
D. Circle

59. If the fifth and the tenth terms of a geometric sequence are 640 and 20 respectively, then which of the following numbers are the first term and the common ratio of the given geometric sequence respectively?

A. 1024 and 2
B. 1024 and 1/2
C. 10240 and 2
D. 10240 and 1/2

60. Given that a graph of system of linear inequalities as shown below.

Which one of the following system of linear inequalities is represented by the shaded region in the graph?

A.

{\begin{cases} 2 x + y \leq 4 \\ 3 x - y \leq 6 \end{cases}

B.

{\begin{cases} 2 x + y \geq 4 \\ 3 x - y \leq 6 \end{cases}

C.

{\begin{cases} 2 x + y \geq 4 \\ 3 x - y \geq 6 \end{cases}

D.

{\begin{cases} 2 x + y \leq 4 \\ 3 x - y \geq 6 \end{cases}

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