POST UTME IGBINEDION UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If 75% of the scores fall below 70, what is the z-score corresponding to a score of 70?
A. 0.5
B. 1
C. 1.25
D. 1.5
Question 2
Find the sum of the first 5 terms of the geometric sequence ( 2, 6, 18, ... ).
A. ( 62 )
B. ( 64 )
C. ( 66 )
D. ( 68 )
Question 3
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \sin\( x \ \) = \frac{3}{5} ).
A. \( \frac{pi}{4} \)
B. \( \frac{pi}{3} \)
C. \( \frac{pi}{2} \)
D. \( \frac{pi}{6} \)
Question 4
Find the equation of the circle with center at (2, 3) and pas\sing through the point (4, 5).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
B. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 36 )
Question 5
Find the value of \( \log_{10} (100) \).
A. 1
B. 2
C. 3
D. 4
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \left\( - \infty, - \frac{3}{2} \right \) \cup \left\( \frac{1}{2}, \infty \right \)
B. \left\( - \infty, - \frac{3}{2} \right \) \cap \left\( \frac{1}{2}, \infty \right \)
C. \left\( - \infty, - \frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
D. \left\( - \infty, - \frac{1}{2} \right \) \cap \left\( \frac{3}{2}, \infty \right \)
Question 7
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{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )
Question 8
Let \( \vec{a} = \begin{bmatrix} 1 \\ 2 \end{bmatrix} \) and \( \vec{b} = \begin{bmatrix} 3 \\ 4 \end{bmatrix} \). Find the dot product of \( \vec{a} \) and \( \vec{b} \).
A. 11
B. 12
C. 13
D. 14
Question 9
Find the probability of drawing two hearts from a s\tandard deck of 52 cards.
A. \( \frac{1}{221} \)
B. \( \frac{1}{52} \)
C. \( \frac{1}{26} \)
D. \( \frac{1}{13} \)
Question 10
Find the area of the triangle with vertices (2, 3), (4, 5), and (6, 7).
A. 10
B. 20
C. 30
D. 40
Question 11
Find the sum of the first 10 terms of the arithmetic sequence ( 2, 5, 8, ldots ).
A. 50
B. 55
C. 60
D. 65
Question 12
Find the equation of the circle with centre ( (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 13
Solve the quadratic equation \( x^2 + 4x - 5 = 0 \).
A. \( x = -5, x = 1 \)
B. \( x = -1, x = 5 \)
C. \( x = -2, x = 2.5 \)
D. \( x = -1, x = 5 \)
Question 14
Find the determinant of the matrix \[ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \]
A. 0
B. 1
C. 2
D. 3
Question 15
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.8413
B. 0.8413
C. 0.8413
D. 0.8413

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