POST UTME BABCOCK UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. \( -1 \)
D. ( 2 )
Question 2
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 90.
A. 0.1587
B. 0.3413
C. 0.5
D. 0.8413
Question 3
A set of 5 points is chosen at random from the set of all points with integer coordinates in the interval [0, 10]. What is the probability that the 5 points form a convex quadrilateral?
A. \frac{1}{10}
B. \frac{1}{5}
C. \frac{1}{2}
D. \frac{2}{5}
Question 4
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).
A. ( 611 )
B. ( 621 )
C. ( 631 )
D. ( 641 )
Question 5
Solve the equation \( 2^x + 2^x = 128 \).
A. \( x = 7 \)
B. \( x = 6 \)
C. \( x = 5 \)
D. \( x = 4 \)
Question 6
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. 0
B. 1
C. 2
D. 3
Question 7
Find the value of $\int_0^1 x^2 dx$.
A. \frac{1}{3}
B. \frac{1}{2}
C. 1
D. \frac{2}{3}
Question 8
A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.
A. 8
B. 6
C. 4
D. 2
Question 9
Solve the inequality \( 2x^2 + 3x - 1 > 0 \) for ( x ).
A. \( x < -\frac{1}{2} \) or \( x > \frac{1}{2} \)
B. \( x < -\frac{1}{2} \) or \( x < \frac{1}{2} \)
C. \( x > -\frac{1}{2} \) or \( x < \frac{1}{2} \)
D. \( x > -\frac{1}{2} \) or \( x > \frac{1}{2} \)
Question 10
Find the value of $\frac{d}{dx}\left\( \frac{1}{x^2}\right \)$.
A. -\frac{2}{x^3}
B. +\frac{2}{x^3}
C. -\frac{1}{x^3}
D. +\frac{1}{x^3}
Question 11
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( x = \frac{pi}{4} \)
B. \( x = \frac{3pi}{4} \)
C. \( x = \frac{5pi}{4} \)
D. \( x = \frac{7pi}{4} \)
Question 12
A cone has a base radius of 4 cm and a height of 6 cm. Find the volume of the cone.
A. \( \frac{1}{3} pi r^2 h \)
B. \( \frac{1}{3} pi r h \)
C. \( \frac{1}{3} pi r^2 \)
D. \( \frac{1}{3} pi r \)
Question 13
A rec\tangular solid has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.
A. 72
B. 80
C. 88
D. 96
Question 14
A set of data is given by the following table. Find the mean of the data.
A. 25
B. 30
C. 35
D. 40
Question 15
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. \( x in \( -infty, -3 \ \) cup (2, infty) )
B. \( x in \( -infty, -3 \ \) cup (3, infty) )
C. \( x in \( -infty, 2 \ \) cup (3, infty) )
D. \( x in \( -infty, -3 \ \) cup (2, 3) )

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