POST UTME MADONNA UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)
C. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{5}{4} \) or \( x > \frac{3}{2} \)
Question 3
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 4
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 5
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. x < -1 or x > \frac{3}{2}
B. x < -1 or x < \frac{3}{2}
C. x > -1 or x < \frac{3}{2}
D. x > -1 or x > \frac{3}{2}
Question 7
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 8
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 9
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
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
Solve the equation \( x^2 + 2x - 6 = 0 \) u\sing the quadratic formula.
A. \frac{-2 \pm \sqrt{4 + 24}}{2}
B. \frac{-2 \pm \sqrt{28}}{2}
C. \frac{-2 \pm \sqrt{4 - 24}}{2}
D. \frac{-2 \pm \sqrt{28 - 4}}{2}
Question 12
A right triangle has legs of length 3 and 4. Find the length of the hypotenuse.
A. 5
B. 6
C. 7
D. 8
Question 13
A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is not blue?
A. 1/3
B. 2/3
C. 3/4
D. 4/5
Question 14
Find the value of \( \log_{10} \( 2^3 \).
A. 3
B. 6
C. 9
D. 12
Question 15
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

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