POST UTME OSUSTECH 2023 Mathematics | Objective

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Question 1
In a right pyramid with a square base of side length 6 cm, the height is 8 cm. Find the volume of the pyramid.
A. 288 cm^3
B. 384 cm^3
C. 512 cm^3
D. 768 cm^3
Question 2
Find the sum of the first 5 terms of the geometric progression: \{2, 6, 18, 54, 162\}
A. 242
B. 242.5
C. 243
D. 243.5
Question 3
Solve the equation $x^3 - 2x^2 - 5x + 6 = 0$.
A. x = -1, x = 2, x = 3
B. x = -2, x = 1, x = 3
C. x = -1, x = 2, x = -3
D. x = 1, x = 2, x = -3
Question 4
In the diagram below, a circle is inscribed in a square. If the radius of the circle is 4 cm, what is the area of the shaded region?
A. 16π
B. 64
C. 32
D. 128
Question 5
Find the mean and s\tandard deviation of the data set: \{2, 4, 6, 8, 10\}
A. \text{Mean: } 6, \text{S\tandard Deviation: } 2
B. \text{Mean: } 4, \text{S\tandard Deviation: } 2
C. \text{Mean: } 6, \text{S\tandard Deviation: } 4
D. \text{Mean: } 4, \text{S\tandard Deviation: } 4
Question 6
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.
A. 4
B. 6
C. 8
D. 10
Question 7
In a histogram, the class width is 5 and the number of classes is 6. If the total frequency is 30, what is the class frequency?
A. 5
B. 10
C. 15
D. 20
Question 8
Find the equation of the circle with center at (2, 3) and radius 4.
A. \text{Equation: } \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \text{Equation: } \( x + 2 \)^2 + \( y - 3 \)^2 = 16
C. \text{Equation: } \( x - 2 \)^2 + \( y + 3 \)^2 = 16
D. \text{Equation: } \( x + 2 \)^2 + \( y + 3 \)^2 = 16
Question 9
Solve the inequality $\frac{2x + 3}{x - 1} > 0$.
A. \( -\infty, -3 \) \cup \( 1, \infty \)
B. \( -\infty, -3 \) \cup (1, 2) \cup \( 2, \infty \)
C. \( -\infty, -3 \) \cup \( 1, \infty \)
D. \( -\infty, -3 \) \cup (1, 2]
Question 10
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. \frac{1}{2}
B. \frac{3}{5}
C. \frac{3}{8}
D. \frac{5}{8}
Question 11
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 12
A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Find the volume of the prism.
A. 400
B. 500
C. 600
D. 800
Question 13
A die is rolled twice. What is the probability that the sum of the two numbers is 7?
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{1}{2}
D. \frac{2}{3}
Question 14
Determine the mean of the following dataset: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?
A. 12
B. 14
C. 16
D. 18
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70

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