POST UTME ELIZADE UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \( \sin^2 x + \cos^2 x = 1 \ \) for ( x ) in the interval \( [0, 2\pi] \).
A. x = \frac{\pi}{4}
B. x = \frac{3\pi}{4}
C. x = \frac{5\pi}{4}
D. x = \frac{7\pi}{4}
Question 2
Find the value of ( x ) in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. x = 1
B. x = 2
C. x = 3
D. x = 4
Question 3
Solve the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. \( x = \frac{-5 \pm \sqrt{109}}{4} \)
B. \( x = \frac{-5 \pm \sqrt{121}}{4} \)
C. \( x = \frac{-5 \pm \sqrt{169}}{4} \)
D. \( x = \frac{-5 \pm \sqrt{225}}{4} \)
Question 4
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( x = \frac{pi}{4}, \frac{3pi}{4}, \frac{5pi}{4}, \frac{7pi}{4} \)
B. \( x = \frac{pi}{2}, \frac{3pi}{2} \)
C. \( x = \frac{pi}{4}, \frac{3pi}{4} \)
D. \( x = \frac{pi}{2}, \frac{3pi}{2}, \frac{5pi}{4}, \frac{7pi}{4} \)
Question 5
Find the derivative of the function ( f(x) = x^3 - 2x^2 + 5x - 1 ) u\sing the chain rule.
A. ( f'(x) = 3x^2 - 4x + 5 )
B. ( f'(x) = 3x^2 - 4x + 1 )
C. ( f'(x) = 3x^2 - 4x - 1 )
D. ( f'(x) = 3x^2 - 4x - 5 )
Question 6
Find the area under the curve \( y = \frac{1}{2} x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 112
Question 7
A rec\tangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. What is the volume of the prism?
A. 120 cm^3
B. 150 cm^3
C. 180 cm^3
D. 200 cm^3
Question 8
A solid cylinder has a height of 10 cm and a radius of 4 cm. Find the volume of the cylinder.
A. 800\pi
B. 1000\pi
C. 1200\pi
D. 1600\pi
Question 9
A binary number 1101 is converted to decimal. What is the decimal equivalent?
A. 13
B. 15
C. 17
D. 19
Question 10
A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:3, how many loaves of whole wheat bread are sold per day?
A. 240
B. 320
C. 400
D. 480
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > 3 \)
B. \( x < 1 \) or \( x > 3 \)
C. \( x < -3 \) or \( x > 1 \)
D. \( x < 3 \) or \( x > 1 \)
Question 12
Find the volume of the solid formed by revolving the region bounded by the parabola y = x^2, the x-axis, and the line x = 2 about the x-axis.
A. \( \frac{32\pi}{5} \)
B. \( \frac{64\pi}{5} \)
C. \( \frac{128\pi}{5} \)
D. \( \frac{256\pi}{5} \)
Question 13
A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } X = 1 \ 0.3 & \text{if } X = 2 \ 0.5 & \text{if } X = 3 \end{cases} ). Find the expected value of X.
A. ( E(X) = 1.5 )
B. ( E(X) = 2.5 )
C. ( E(X) = 3.5 )
D. ( E(X) = 4.5 )
Question 14
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 112
Question 15
Find the derivative of the function \( y = \sin^2 x \) u\sing the chain rule.
A. \cos 2x
B. \sin 2x
C. \cos x
D. \sin x

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