POST UTME MADONNA UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the trigonometric equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) for ( x ) in the interval \( [0, 2\pi] \).
A. 0
B. \frac{\pi}{2}
C. \pi
D. \frac{3\pi}{2}
Question 2
Solve for x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) u\sing the identity \( \sin^2\( x \ \) + \cos^2(x) = 1 ).
A. x = \frac{\pi}{4}
B. x = \frac{3\pi}{4}
C. x = \frac{5\pi}{4}
D. x = \frac{7\pi}{4}
Question 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 4
A right-angled triangle has a hypotenuse of length 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5\text{ cm}
B. 7.5\text{ cm}
C. 10\text{ cm}
D. 12.5\text{ cm}
Question 5
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?
A. \frac{2}{3}
B. \frac{3}{4}
C. \frac{4}{5}
D. \frac{5}{6}
Question 6
Find the volume of the frustum of a cone with height 15 cm, lower base radius 6 cm, and upper base radius 3 cm.
A. 450\pi\text{ cm}^3
B. 600\pi\text{ cm}^3
C. 750\pi\text{ cm}^3
D. 900\pi\text{ cm}^3
Question 7
A vector \( \vec{a} \) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of \( \vec{a} \).
A. (3, 4.33)
B. (4.33, 3)
C. (5, 0)
D. (0, 5)
Question 8
A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?
A. 18 days
B. 19 days
C. 20 days
D. 21 days
Question 9
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 64\pi cm^3
B. 96\pi cm^3
C. 128\pi cm^3
D. 192\pi cm^3
Question 10
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. \frac{-4 \pm \sqrt{16 - 16}}{2}
B. \frac{-4 \pm \sqrt{16 - 4}}{2}
C. \frac{-4 \pm \sqrt{16 + 4}}{2}
D. \frac{-4 \pm \sqrt{16 - 4}}{2}
Question 11
Find the area under the curve \( y = x^2 - 4x + 3 \) from \( x = 0 \) to \( x = 2 \).
A. 2
B. 4
C. 6
D. 8
Question 12
Find the derivative of the function \( f(x) = x^2 \sin(x) \) u\sing the product rule.
A. \sin(x) + x^2 \cos(x)
B. \cos(x) - x^2 \sin(x)
C. \sin(x) - x^2 \cos(x)
D. \cos(x) + x^2 \sin(x)
Question 13
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.
A. \frac{x}{\( 1 - x^2 \)^{3/2}}
B. \frac{1}{\( 1 - x^2 \)^{3/2}}
C. \frac{1}{\( 1 - x^2 \)^{1/2}}
D. \frac{-x}{\( 1 - x^2 \)^{3/2}}
Question 14
Find the value of \( \log_{10} \( 2^3 \).
A. 3
B. 6
C. 9
D. 12
Question 15
Find the volume of the solid formed by rotating the region bounded by the curves \( y = x^2 \) and \( y = 4x \) about the x-axis.
A. \( \frac{32}{3} pi \)
B. \( \frac{64}{3} pi \)
C. \( \frac{128}{3} pi \)
D. \( \frac{256}{3} pi \)

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