POST UTME SUMMIT UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \( \tan^2 x + 2 \tan x - 6 = 0 \).
A. x = -2π/3, x = π/3
B. x = 2π/3, x = -π/3
C. x = π/3, x = -π/3
D. x = 2π/3, x = π/3
Question 2
In the number system with base 8, what is the value of the expression \( 5 \times 8^2 + 3 \times 8^1 + 2 \times 8^0 \)?
A. 42
B. 48
C. 52
D. 58
Question 3
Find the volume of the solid formed by rotating the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 4
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( x = 0, pi, 2pi \)
B. \( x = \frac{pi}{2}, \frac{3pi}{2} \)
C. \( x = \frac{pi}{4}, \frac{3pi}{4}, \frac{5pi}{4}, \frac{7pi}{4} \)
D. \( x = \frac{pi}{6}, \frac{5pi}{6}, \frac{7pi}{6}, \frac{11pi}{6} \)
Question 5
Find the value of y in the equation \( y = \frac{1}{2} left\( x + \frac{1}{x} \right \ \) ) when x = 2.
A. 3/2
B. 5/2
C. 7/2
D. 9/2
Question 6
Find the value of \sin 75^\circ in terms of \sin 15^\circ and \cos 15^\circ.
A. \sin 15^\circ + \cos 15^\circ
B. \sin 15^\circ - \cos 15^\circ
C. \sin 15^\circ \cos 15^\circ
D. \cos 15^\circ - \sin 15^\circ
Question 7
A function f(x) is defined as: f(x) = 2x^2 - 5x + 1. Find the derivative of the function.
A. 4x - 5
B. 2x - 1
C. x^2 - 5
D. x^2 + 5
Question 8
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
A. x < -3/2 or x > 1
B. x < -1 or x > 3
C. x < 1 or x > 3
D. x < -3/2 or x < 1
Question 9
Solve the equation 2x^2 + 5x - 3 = 0 u\sing the quadratic formula.
A. 1
B. -1
C. -2
D. 2
Question 10
A solid cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone.
A. 32π cm³
B. 64π cm³
C. 128π cm³
D. 256π cm³
Question 11
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for x.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{6}
D. \frac{\pi}{3}
Question 12
Find the mean of the data set: 2, 4, 6, 8, 10.
A. 6
B. 8
C. 10
D. 12
Question 13
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 10
D. 20
Question 14
Solve the system of equations x + y = 2 and x - y = 1.
A. x = 1, y = 1
B. x = 1, y = -1
C. x = -1, y = 1
D. x = -1, y = -1
Question 15
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 3.
A. 27
B. 30
C. 33
D. 36

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