POST UTME BOWEN UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In a geometric sequence, the first term is 2 and the common ratio is 3. Find the sum of the first five terms.
A. 2 + 6 + 18 + 54 + 162
B. 2 + 6 + 18 + 54 + 162 + 486
C. 2 + 6 + 18 + 54 + 162 + 486 + 1458
D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374
Question 2
Solve the inequality: [ 2x^2 + 3x - 1 > 0 ]
A. \( x < -1 \) or \( x > \frac{1}{2} \)
B. \( x < -1 \) or \( x < \frac{1}{2} \)
C. \( x > -1 \) or \( x < \frac{1}{2} \)
D. \( x > -1 \) or \( x > \frac{1}{2} \)
Question 3
A circle has a diameter of 10 cm. Find the area of the circle.
A. 25\pi
B. 50\pi
C. 75\pi
D. 100\pi
Question 4
A probability experiment consists of rolling a fair six-sided die. Find the probability of rolling a number greater than 4.
A. \frac{1}{3}
B. \frac{2}{3}
C. \frac{1}{2}
D. \frac{3}{4}
Question 5
Find the area of the region bounded by the parabola \( y = x^2 \), the line \( x = 2 \), and the x-axis.
A. \( \frac{8}{3} \)
B. \( \frac{16}{3} \)
C. \( \frac{32}{3} \)
D. \( \frac{64}{3} \)
Question 6
A set of numbers is defined as {1, 2, 3, 4, 5}. Find the number of subsets of this set.
A. 10
B. 20
C. 30
D. 40
Question 7
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. \( x in \( -infty, -3 \ \) cup (1, infty) )
B. \( x in \( -infty, -3 \ \) cup (1, 3) )
C. \( x in \( -infty, -3 \ \) cup (3, infty) )
D. \( x in \( -infty, 3 \ \) cup (3, infty) )
Question 8
Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 9
Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).
A. 1
B. -1
C. -2
D. 3
Question 10
Find the derivative of the function ( f(x) = \frac{x^2 + 1}{x^2 - 1} ) u\sing the quotient rule.
A. ( f'(x) = \frac{2x\( x^2 - 1 \) - \( x^2 + 1 \)(2x)}{\( x^2 - 1 \)^2} )
B. ( f'(x) = \frac{2x\( x^2 - 1 \) + \( x^2 + 1 \)(2x)}{\( x^2 - 1 \)^2} )
C. ( f'(x) = \frac{2x\( x^2 - 1 \) - \( x^2 + 1 \)(2x)}{\( x^2 - 1 \)^3} )
D. ( f'(x) = \frac{2x\( x^2 - 1 \) + \( x^2 + 1 \)(2x)}{\( x^2 - 1 \)^3} )
Question 11
Two events, A and B, are indep\endent. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. Find the probability that both events A and B occur.
A. 0.2
B. 0.3
C. 0.4
D. 0.5
Question 12
A binary operation ( odot ) is defined as \( a odot b = ab + 2 \). Find ( 2 odot 3 ).
A. 6
B. 8
C. 10
D. 12
Question 13
Solve the equation \log_{10} x^2 = 4.
A. 10^4
B. 10^8
C. 10^{-4}
D. 10^{-8}
Question 14
In the diagram below, the equation of the circle is given by \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 ). Find the equation of the \tangent line to the circle at the point ( (5, 3) ).
A. \( y = -x + 10 \)
B. \( y = x + 7 \)
C. \( y = -x + 7 \)
D. \( y = x - 3 \)
Question 15
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 1/3
C. 2/3
D. 3/5

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