POST UTME UNIPORT 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 \( x > 3 \)
B. \( x < 1 \) or \( x > 3 \)
C. \( x < -1 \) or \( x < 3 \)
D. \( x < 1 \) or \( x > 3 \)
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
Solve the system of equations u\sing matrices:
A. \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \)
B. \( egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} \)
C. \( egin{bmatrix} 1 & 3 \ 2 & 4 \end{bmatrix} \)
D. \( egin{bmatrix} 3 & 1 \ 2 & 4 \end{bmatrix} \)
Question 5
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 6
Find the area of the triangle with vertices at ((0,0)), ((3,0)), and ((0,4)).
A. ( 6 )
B. ( 8 )
C. ( 10 )
D. ( 12 )
Question 7
A circle with a radius of 5 cm is inscribed in a square. Find the area of the square.
A. 25 cm²
B. 50 cm²
C. 75 cm²
D. 100 cm²
Question 8
Convert the \fraction \( \frac{3}{8} \) to a decimal.
A. 0.375
B. 0.3750
C. 0.37500
D. 0.375000
Question 9
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = 2
C. x = -1
D. x = 1
Question 10
Find the mean of the data set: 2, 4, 6, 8, 10.
A. 5
B. 6
C. 7
D. 8
Question 11
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 50\pi cm^3
B. 75\pi cm^3
C. 100\pi cm^3
D. 125\pi cm^3
Question 12
Find the value of \( \sin 2x \) if \( \sin x = \frac{1}{3} \) and ( x ) is in the first quadrant.
A. \( \frac{2}{3} \)
B. \( \frac{4}{9} \)
C. \( \frac{8}{9} \)
D. \( \frac{16}{27} \)
Question 13
Solve for x in the equation \frac{1}{2}x^2 + 3x - 2 = 0.
A. x = -4
B. x = -2
C. x = 1
D. x = 4
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 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 15
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} \)

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