POST UTME BELLS UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations \( x + y = 3 \) and \( x - y = 1 \).
A. x=2, y=1
B. x=1, y=2
C. x=2, y=2
D. x=1, y=1
Question 2
Solve the equation \( x^2 + 6x + 8 = 0 \) by factoring.
A. \( x + 4 \)\( x + 2 \) = 0
B. \( x + 2 \)\( x + 4 \) = 0
C. \( x - 2 \)\( x - 4 \) = 0
D. \( x - 4 \)\( x - 2 \) = 0
Question 3
A histogram is constructed with 5 classes of equal width. The first class has a frequency of 5, the second class has a frequency of 7, the third class has a frequency of 3, the fourth class has a frequency of 2, and the fifth class has a frequency of 4. What is the mean of the histogram?
A. 4
B. 5
C. 6
D. 7
Question 4
Solve the matrix equation \( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \).
A. x=1, y=2
B. x=2, y=1
C. x=1, y=1
D. x=2, y=2
Question 5
Find the surface area of a sphere with radius 5 cm.
A. 100\pi
B. 200\pi
C. 300\pi
D. 400\pi
Question 6
Solve the equation \( x^2 + 2x - 6 = 0 \) by factoring.
A. \( x + 3 \)\( x - 2 \) = 0
B. \( x + 2 \)\( x - 3 \) = 0
C. \( x - 3 \)\( x + 2 \) = 0
D. \( x - 2 \)\( x + 3 \) = 0
Question 7
Find the volume of a cylinder with radius 4 cm and height 6 cm.
A. 48\pi
B. 64\pi
C. 72\pi
D. 96\pi
Question 8
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \( \frac{-x}{\( x^2 + 1 \ \)^{3/2}} )
B. \( \frac{x}{\( x^2 + 1 \ \)^{3/2}} )
C. \( \frac{1}{\( x^2 + 1 \ \)^{3/2}} )
D. \( \frac{x^2}{\( x^2 + 1 \ \)^{3/2}} )
Question 9
Solve the inequality \( 2x - 5 > 3 \).
A. x > 4
B. x < 4
C. x > 2
D. x < 2
Question 10
Solve the inequality \( x^2 - 4x + 3 > 0 \) for ( x ).
A. x < 1
B. x > 1
C. x < 3
D. x > 3
Question 11
Find the area under the curve \( y = x^2 - 4x + 3 \) from \( x = 1 \) to \( x = 3 \).
A. \( \frac{2}{3} \)
B. \( \frac{4}{3} \)
C. \( \frac{6}{3} \)
D. \( \frac{8}{3} \)
Question 12
A particle moves along the x-axis with its position given by ( x(t) = 2t^3 - 5t^2 + 3t + 1 ). Find the velocity of the particle at time \( t = 2 \) seconds.
A. \( 12t^2 - 10t + 3 \)
B. \( 6t^2 - 10t + 3 \)
C. \( 12t^2 - 10t - 3 \)
D. \( 6t^2 - 10t - 3 \)
Question 13
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 14
Find the derivative of the function ( f(x) = \frac{1}{x^2} ) u\sing the chain rule.
A. f'(x) = -\frac{2}{x^3}
B. f'(x) = \frac{2}{x^3}
C. f'(x) = -\frac{1}{x^3}
D. f'(x) = \frac{1}{x^3}
Question 15
Find the area of the triangle with vertices (0,0), (2,0), and (1,2).
A. 1
B. 2
C. 3
D. 4

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