POST UTME RSU 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.
A. 64\pi cm^3
B. 128\pi cm^3
C. 256\pi cm^3
D. 512\pi cm^3
Question 2
Solve the equation x^2 + 4x - 5 = 0.
A. \( -5, 1 \)
B. \( -1, 5 \)
C. \( 1, -5 \)
D. \( -1, 5 \)
Question 3
Solve the inequality $\frac{x^2 - 4}{x^2 - 9} > 0$.
A. $\( -\infty, -3 \) \cup \( -3, 2 \) \cup \( 2, \infty \)$
B. $\( -\infty, -3 \) \cup \( 2, \infty \)$
C. $\( -\infty, 2 \) \cup \( 2, \infty \)$
D. $\( -\infty, -3 \) \cup \( 3, \infty \)$
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 3, \infty \)
D. \( -\infty, -3 \) \cup \( 1, \infty \)
Question 5
Solve the system of linear equations u\sing matrices:\n\n\begin{align*}\n2x + 3y &= 7 \\n4x - 2y &= -3\n\end{align*}
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 6
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 6
B. 8
C. 10
D. 12
Question 7
Let ( f(x) = \frac{x^2 - 4}{x + 2} ). Find the derivative of ( f(x) ) u\sing the quotient rule.
A. \frac{2x\( x + 2 \) - \( x^2 - 4 \)(1)}{\( x + 2 \)^2}
B. \frac{2x\( x + 2 \) + \( x^2 - 4 \)(1)}{\( x + 2 \)^2}
C. \frac{2x\( x + 2 \) - \( x^2 - 4 \)(1)}{\( x + 2 \)^2}
D. \frac{2x\( x + 2 \) + \( x^2 - 4 \)(1)}{\( x + 2 \)^2}
Question 8
A histogram of the scores of 50 students in a mathematics test is shown below. If the mean score is 60, what is the median score?
A. 60
B. 62
C. 64
D. 66
Question 9
Solve for y in the equation \( y = \frac{1}{2} \left\( x + \frac{1}{x} \right \ \) ).
A. \frac{x^2 + 1}{2x}
B. \frac{x^2 - 1}{2x}
C. \frac{x^2 + 2}{2x}
D. \frac{x^2 - 2}{2x}
Question 10
A particle moves in a straight line with its position given by the equation s(t) = 2t^3 - 5t^2 + 3t + 1. Find the velocity of the particle at time t = 2.
A. 4
B. 6
C. 8
D. 10
Question 11
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. Find the probability that a randomly selected score is between 50 and 70.
A. ( 0.5 )
B. ( 0.6 )
C. ( 0.7 )
D. ( 0.8 )
Question 12
A company produces two products, A and B. The profit from product A is $₦100 per unit, and the profit from product B is $₦150 per unit. If the company produces 50 units of product A and 30 units of product B, what is the total profit?
A. ₦15000
B. ₦18000
C. ₦20000
D. ₦22000
Question 13
Determine the value of $\int_{0}^{\pi} \frac{1}{1 + \sin^2 x} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{1}
Question 14
Solve the inequality 3x^2 - 2x - 5 > 0.
A. \( -∞, -1 \) ∪ (5, ∞)
B. \( -∞, 1 \) ∪ (5, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 1 \) ∪ (5, ∞)
Question 15
Find the area under the curve y = x^3 - 6x^2 + 9x + 2 from x = 0 to x = 4.
A. 120
B. 150
C. 180
D. 200

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