POST UTME RSU 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let ( f(x) = \sin x ). Find the area under the curve \( y = f\( x \ \) ) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. \( \frac{1}{2} \ \)
B. \( \frac{pi}{2} \ \)
C. \( \frac{pi}{4} \ \)
D. \( \frac{pi}{6} \ \)
Question 2
Solve for x in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. 1
B. 2
C. 3
D. 4
Question 3
Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2
A. 13
B. 14
C. 15
D. 16
Question 4
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 5
A random variable ( X ) has a probability density function ( f(x) = \begin{cases} 2x & 0 < x < 1 \ 0 & \text{otherwise} \end{cases} \). Find the expected value of ( X ).
A. ( E(X) = \frac{1}{2} \)
B. ( E(X) = \frac{1}{4} \)
C. ( E(X) = \frac{1}{3} \)
D. ( E(X) = \frac{1}{6} \)
Question 6
Evaluate the definite integral \( int_{0}^{1} x^2 \sin\( x \ \) dx ).
A. -1
B. 0
C. 1
D. 2
Question 7
A solid cylinder has a radius of 4 cm and a height of 10 cm. Find its volume.
A. 800\pi
B. 1000\pi
C. 1200\pi
D. 1600\pi
Question 8
Solve for x in the equation \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2}
A. -1
B. 1
C. 2
D. 3
Question 9
Find the area under the curve \( y = \frac{1}{x^2 + 1} \ \) from \( x = 0 \ \) to \( x = 1 \ \).
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 10
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > 3/2
B. x < 1 or x > -3/2
C. x < -3/2 or x > 1
D. x < 3/2 or x > -1
Question 11
Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).
A. -1
B. 1
C. 2
D. 3
Question 12
Find the magnitude of the vector [2, 3, 4].
A. 5
B. 6
C. 7
D. 8
Question 13
Solve the equation \( x^4 - 6x^2 + 8 = 0 \ \).
A. \begin{cases} x = 2 \ x = -2 \end{cases}
B. \begin{cases} x = 1 \ x = -1 \end{cases}
C. \begin{cases} x = \sqrt{2} \ x = -\sqrt{2} \end{cases}
D. \begin{cases} x = 2 \ x = -2 \ x = \sqrt{2} \ x = -\sqrt{2} \end{cases}
Question 14
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 15
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 1/3
C. 2/5
D. 3/8

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