POST UTME UNIBEN 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A polynomial function has a degree of 4 and has zeros at \( x = -2 \), \( x = 1 \), and \( x = 3 \). Find the polynomial function.
A. \( x + 2 \)\( x - 1 \)\( x - 3 \ \) )
B. \( x + 2 \)\( x - 1 \)\( x - 3 \)\( x + 1 \ \) )
C. \( x + 2 \)\( x - 1 \)\( x - 3 \)\( x - 4 \ \) )
D. \( x + 2 \)\( x - 1 \)\( x - 3 \)\( x + 4 \ \) )
Question 2
Find the sum of the first 10 terms of the arithmetic progression ( 2, 5, 8, ldots ).
A. ( 55 )
B. ( 65 )
C. ( 75 )
D. ( 85 )
Question 3
Solve the inequality \( \frac{x}{x-2} > 0 \) for \( x in \( -infty, infty \ \) ).
A. \( -\infty, 2 \) \cup \( 2, \infty \)
B. \( -\infty, 2 \) \cap \( 2, \infty \)
C. \( -\infty, 2 \) \cup \( 2, \infty \)
D. \( -\infty, 2 \) \cap \( 2, \infty \)
Question 4
A set of 10 numbers has a mean of 20 and a s\tandard deviation of 5. What is the probability that a randomly selected number from this set will be greater than 25?
A. 0.25
B. 0.5
C. 0.75
D. 0.9
Question 5
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x = 1 - \cos^2 x \).
A. x = \frac{\pi}{4}
B. x = \frac{3\pi}{4}
C. x = \frac{\pi}{2}
D. x = \frac{5\pi}{4}
Question 6
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. What is the length of the other side?
A. 8
B. 6
C. 4
D. 2
Question 7
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 32
B. 64
C. 128
D. 256
Question 8
Simplify the expression \( \frac{2^3 \cdot 3^2}{2^2 \cdot 3^4} \).
A. \frac{1}{12}
B. \frac{1}{6}
C. \frac{1}{4}
D. \frac{1}{3}
Question 9
If ( f(x) = \sin x ), find ( f'(x) ).
A. \cos x
B. \sin x
C. \tan x
D. \csc x
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{1}{\( x^2 + 1 \)^2}
D. f'(x) = \frac{-1}{\( x^2 + 1 \)^2}
Question 11
Solve the matrix equation \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 7 \ 10 \end{bmatrix} \).
A. \begin{bmatrix} 3 \ 5 \end{bmatrix}
B. \begin{bmatrix} 5 \ 3 \end{bmatrix}
C. \begin{bmatrix} 7 \ 10 \end{bmatrix}
D. \begin{bmatrix} 10 \ 7 \end{bmatrix}
Question 12
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the z-score of a score of 70?
A. 0.5
B. 1.0
C. 1.5
D. 2.0
Question 13
Find the area under the curve of the function ( f(x) = \frac{1}{2}x^2 + 3x - 2 ) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \)
B. ( 3 )
C. ( 4 )
D. ( 6 )
Question 14
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).
A. \( 2 + 6 + 18 + ldots + 972 \)
B. \( 2 + 6 + 18 + ldots + 1024 \)
C. \( 2 + 6 + 18 + ldots + 1026 \)
D. \( 2 + 6 + 18 + ldots + 1028 \)
Question 15
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
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}

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