POST UTME AL-HIKMAH UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A geometric sequence has first term \( a = 2 \) and common ratio \( r = 3 \). Find the sum of the first five terms of the sequence.
A. 155
B. 160
C. 165
D. 170
Question 2
The volume of a sphere (V) is given by the formula V = \frac{4}{3}\pi r^3, where r is the radius of the sphere. If the radius of a sphere is increased by 20%, what is the percentage increase in its volume?
A. 10%
B. 20%
C. 30%
D. 520%
Question 3
Solve for x: \( 2^x = 16 \)
A. 2
B. 3
C. 4
D. 5
Question 4
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 6
B. 8
C. 12
D. 18
Question 5
Solve the quadratic equation: x^2 + 5x + 6 = 0
A. \left\( -3, -2 \right \)
B. \left\( -2, -3 \right \)
C. \left\( 1, 2 \right \)
D. \left\( 2, 1 \right \)
Question 6
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 = 9
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
Question 7
Solve for y: \( \sin^2 y + \cos^2 y = 1 \)
A. 0
B. π/2
C. π
D. 3π/2
Question 8
A polynomial function ( f(x) = x^3 - 2x^2 + 3x - 1 ) has a root at \( x = 1 \). Find the value of ( f(2) ).
A. 3
B. 5
C. 7
D. 9
Question 9
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x + 1
B. y = 2x - 1
C. y = -2x + 1
D. y = -2x - 1
Question 10
Find the value of x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \)
A. 1
B. -2
C. 3
D. -3
Question 11
A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, and P\( X = 3 \) = 0.3. If two indep\endent random variables X and Y have the same probability distribution, what is the probability that X + Y is greater than 4?
A. 0.4
B. 0.5
C. 0.6
D. 0.7
Question 12
Solve the inequality [ \frac{x^2 - 4}{x^2 - 9} > 0 ].
A. \( -3, -1 \) \cup (1, 3)
B. \( -3, -1 \) \cup (1, 3) \cup \( 3, \infty \)
C. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, -3 \) \cup \( 3, \infty \)
D. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, -3 \) \cup \( 3, \infty \) \cup (0, 1)
Question 13
A matrix A is given by \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}. Find the determinant of A.
A. -1
B. -2
C. 2
D. 4
Question 14
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.
A. 30
B. 40
C. 50
D. 60
Question 15
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].
A. -1
B. 1
C. 2
D. 3

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