POST UTME UNIPORT 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 2
Solve the system of equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix} \).
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 3 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 5 \end{bmatrix}
Question 3
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. 1/6
B. 1/3
C. 1/2
D. 2/3
Question 4
Find the derivative of the function f(x) = \frac{x^2 + 2x - 3}{x^2 - 4x + 3} u\sing the quotient rule.
A. \frac{2x + 2}{\( x^2 - 4x + 3 \)^2}
B. \frac{2x - 2}{\( x^2 - 4x + 3 \)^2}
C. \frac{2x + 4}{\( x^2 - 4x + 3 \)^2}
D. \frac{2x - 4}{\( x^2 - 4x + 3 \)^2}
Question 5
Find the equation of the circle with center at \( 2,-3 \ \)) and radius 4.
A. \( x-2 \ \)^2 + \( y+3 \)^2 = 16 )
B. \( x+2 \ \)^2 + \( y-3 \)^2 = 16 )
C. \( x-2 \ \)^2 + \( y+3 \)^2 = 32 )
D. \( x+2 \ \)^2 + \( y-3 \)^2 = 32 )
Question 6
Convert the \fraction \( \frac{3}{8} \) to a decimal.
A. 0.375
B. 0.3750
C. 0.37500
D. 0.375000
Question 7
A histogram of exam scores is shown below. What is the mean score?
A. 50
B. 60
C. 70
D. 80
Question 8
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = 2 \)
C. \( x = -1 \)
D. \( x = 1 \)
Question 9
Solve the inequality \( 2x^2 - 5x + 3 > 0 \).
A. \( x < -1 \) or \( x > 3 \)
B. \( x < 1 \) or \( x > 3 \)
C. \( x < -1 \) or \( x < 3 \)
D. \( x < 1 \) or \( x > 3 \)
Question 10
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} \)
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} \)
C. ( f'(x) = \frac{-x}{\( x^2 + 1 \)^2} \)
D. ( f'(x) = \frac{x}{\( x^2 + 1 \)^2} \)
Question 11
Find the determinant of the matrix \begin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix}.
A. 5
B. 6
C. 7
D. 8
Question 12
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. ( 20 )
B. ( 22 )
C. ( 24 )
D. ( 26 )
Question 13
Solve the inequality \frac{x^2 - 4x - 5}{x^2 - 4x + 4} > 0.
A. \left\( -\infty, -1\right \) \cup \left\( 1, \infty\right \)
B. \left\( -\infty, -1\right \) \cup \left\( 1, 2\right \)
C. \left\( -\infty, -1\right \) \cup \left\( 2, \infty\right \)
D. \left\( -\infty, 1\right \) \cup \left\( 2, \infty\right \)
Question 14
Solve the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) for x in the interval ( [0, 2pi] ).
A. \( x = \frac{\pi}{4} \ \)
B. \( x = \frac{\pi}{2} \ \)
C. \( x = \frac{3\pi}{4} \ \)
D. \( x = \frac{5\pi}{4} \ \)
Question 15
Evaluate the definite integral \int_0^1 x^2 \sin x dx.
A. -\frac{1}{2} + \frac{1}{3}
B. -\frac{1}{2} - \frac{1}{3}
C. \frac{1}{2} - \frac{1}{3}
D. \frac{1}{2} + \frac{1}{3}

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