POST UTME CALEB UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
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 2
Solve the system of linear equations \( \begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases} \). What is the value of ( x )?
A. 1
B. 2
C. 3
D. 4
Question 3
Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).
A. \( x = \frac{-5 pm \sqrt{25 + 24}}{4} \)
B. \( x = \frac{-5 pm \sqrt{25 - 24}}{4} \)
C. \( x = \frac{-5 pm \sqrt{25 + 24}}{2} \)
D. \( x = \frac{-5 pm \sqrt{25 - 24}}{2} \)
Question 4
Solve the trigonometric equation \( 2 \sin^2 x + 3 \cos x - 1 = 0 \).
A. \sin x = \frac{1}{2}
B. \cos x = \frac{1}{2}
C. \sin x = \frac{1}{3}
D. \cos x = \frac{1}{3}
Question 5
A particle moves in a straight line with its position given by ( s(t) = 2t^3 - 5t^2 + 3t + 1 ). Find the velocity and acceleration at time \( t = 1 \).
A. v(1) = 5, a(1) = -3
B. v(1) = 3, a(1) = 5
C. v(1) = -3, a(1) = 5
D. v(1) = 5, a(1) = -5
Question 6
Solve the inequality \( \frac{x}{x-2} > 2 \) for \( x > 2 \).
A. x > 4
B. x > 6
C. x < 4
D. x < 6
Question 7
Solve the matrix equation \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 3 \end{bmatrix}
C. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 4 \ 5 \end{bmatrix}
Question 8
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 9 )
Question 9
Solve the trigonometric equation [ 2 \sin^2 x + 3 \cos x - 1 = 0 ].
A. x = \frac{\pi}{6}
B. x = \frac{\pi}{4}
C. x = \frac{\pi}{3}
D. x = \frac{\pi}{2}
Question 10
Find the equation of the \tangent to the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) at the point where \( x = 1 \).
A. \( y = 2x - 1 \)
B. \( y = x + 2 \)
C. \( y = 2x + 1 \)
D. \( y = x - 2 \)
Question 11
Solve for $x$ in the equation [ \log_{10} \( x^2 \) = 4 ].
A. 10
B. 100
C. 1000
D. 10000
Question 12
A circle has a radius of 4 cm. What is the area of the circle?
A. 50.24 cm^2
B. 50.27 cm^2
C. 50.29 cm^2
D. 50.31 cm^2
Question 13
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 14
Find the equation of the circle with center ((2, 3)) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 4
C. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
D. \( x - 3 \)^2 + \( y - 2 \)^2 = 4
Question 15
A histogram of exam scores for a class of 50 students is shown below. Find the mean score.
A. 60
B. 70
C. 80
D. 90

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