POST UTME OSUSTECH 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Determine the volume of the frustum of a cone with a height of 6 units, a lower base radius of 4 units, and an upper base radius of 2 units.
A. 24π
B. 48π
C. 96π
D. 192π
Question 2
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. x = -2
B. x = -1
C. x = 0
D. x = 1
Question 3
A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a range of scores. The first bar represents scores from 0-20, the second bar represents scores from 21-40, the third bar represents scores from 41-60, the fourth bar represents scores from 61-80, and the fifth bar represents scores from 81-100. The heights of the bars are 2, 10, 15, 18, and 5, respectively. Find the mean score of the class.
A. 50
B. 60
C. 70
D. 80
Question 4
Find the value of \( \sin 2\theta \) given that \( \sin \theta = \frac{3}{5} \) and \( \cos \theta = \frac{4}{5} \).
A. \frac{24}{25}
B. \frac{16}{25}
C. \frac{20}{25}
D. \frac{12}{25}
Question 5
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 90?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 6
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 12143
B. 12145
C. 12147
D. 12149
Question 7
A binary operation ( ast ) is defined as \( a ast b = ab + 2 \). Find the value of ( 3 ast 4 ).
A. 14
B. 16
C. 18
D. 20
Question 8
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 9
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times \frac{4^2}{2} - 2 \times 4 \)
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. 1/2
B. 1/3
C. 2/3
D. 3/4
Question 11
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 12
Determine the value of x in the equation \( \frac{x}{2} + \frac{3}{4} = \frac{5}{8} \).
A. 1
B. 2
C. 3
D. 4
Question 13
In the circuit below, what is the equivalent resis\tance between points A and B?
A. 2Ω
B. 4Ω
C. 6Ω
D. 8Ω
Question 14
Find the derivative of the function \( y = \sin \( 2x \ \) ) u\sing the chain rule.
A. \( \frac{d}{dx} \( \sin (2x \ \) ) = 2 \cos (2x) )
B. \( \frac{d}{dx} \( \sin (2x \ \) ) = \cos (2x) )
C. \( \frac{d}{dx} \( \sin (2x \ \) ) = 2 \sin (2x) )
D. \( \frac{d}{dx} \( \sin (2x \ \) ) = \sin (2x) )
Question 15
A right circular cone has a height of 10 cm and a base radius of 4 cm. Find the volume of the cone.
A. \frac{160 \pi}{3}
B. \frac{160 \pi}{2}
C. \frac{160 \pi}{1}
D. \frac{160 \pi}{4}

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