POST UTME AL-HIKMAH UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \( \log_{2} \( x^2 \ \) = 4 ).
A. 16
B. 32
C. 64
D. 128
Question 2
Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 64\pi cm^3
B. 128\pi cm^3
C. 192\pi cm^3
D. 256\pi cm^3
Question 3
Find the surface area of the sphere with radius \( r = 5 \) cm.
A. ( 50pi ) cm^2
B. ( 100pi ) cm^2
C. ( 150pi ) cm^2
D. ( 200pi ) cm^2
Question 4
In the diagram below, a circle with center O and radius 6 units intersects a line segment AB at point C. If angle AOB measures 60 degrees, what is the length of AC?
A. 4 units
B. 6 units
C. 8 units
D. 10 units
Question 5
A polynomial function has a degree of 4 and has zeros at \( x = -2, 1, 3 \). What is the polynomial function?
A. ( f(x) = \( x + 2 \)\( x - 1 \)\( x - 3 \)\( x + 1 \) )
B. ( f(x) = \( x + 2 \)\( x - 1 \)\( x - 3 \)\( x - 1 \) )
C. ( f(x) = \( x + 2 \)\( x - 1 \)\( x - 3 \)\( x + 3 \) )
D. ( f(x) = \( x + 2 \)\( x - 1 \)\( x - 3 \)\( x - 2 \) )
Question 6
Determine the mean of the data set {2, 4, 6, 8, 10} u\sing the formula for population mean.
A. \( \frac{2+4+6+8+10}{5} = 6 \)
B. \( \frac{2+4+6+8+10}{4} = 6.5 \)
C. \( \frac{2+4+6+8+10}{3} = 6.67 \)
D. \( \frac{2+4+6+8+10}{2} = 6 \)
Question 7
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \times 4 \)
Question 8
Find the area under the curve \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 2 \) u\sing integration.
A. \( int_{1}^{2} \frac{1}{x} dx = ln 2 - ln 1 \)
B. \( int_{1}^{2} \frac{1}{x} dx = ln 1 - ln 2 \)
C. \( int_{1}^{2} \frac{1}{x} dx = ln 2 + ln 1 \)
D. \( int_{1}^{2} \frac{1}{x} dx = ln 1 + ln 2 \)
Question 9
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \), where \( a_1 = 2 \). Find the sum of the first 5 terms of the sequence.
A. 2 + 7 + 17 + 37 + 79
B. 2 + 5 + 13 + 29 + 61
C. 2 + 4 + 12 + 28 + 60
D. 2 + 6 + 16 + 36 + 76
Question 10
A set of 5 numbers has a mean of 10. If the largest number is 20, find the sum of the remaining 4 numbers.
A. \( 4 \times 10 + 20 = 48 \)
B. \( 4 \times 10 - 20 = 28 \)
C. \( 4 \times 10 + 20 = 28 \)
D. \( 4 \times 10 - 20 = 48 \)
Question 11
A histogram has a mean of 25 and a s\tandard deviation of 5. If the histogram has a total of 20 bars, find the sum of the products of the heights and widths of the bars.
A. ( 500 )
B. ( 1000 )
C. ( 1500 )
D. ( 2000 )
Question 12
A histogram of exam scores is shown below. Find the mean score.
A. \( ar{x} = 75 \)
B. \( ar{x} = 80 \)
C. \( ar{x} = 85 \)
D. \( ar{x} = 90 \)
Question 13
A circle has an equation of the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). If the circle passes through the point ( (6, 8) ) and has a center at ( (3, 4) ), find the radius.
A. \( \sqrt{5} \)
B. \( \sqrt{10} \)
C. \( \sqrt{15} \)
D. \( \sqrt{20} \)
Question 14
A probability experiment has two indep\endent events, A and B, with probabilities 0.4 and 0.6, respectively. Find the probability that both events occur.
A. ( 0.2 )
B. ( 0.4 )
C. ( 0.6 )
D. ( 0.8 )
Question 15
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)
B. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)
C. \( x > \frac{5}{4} \) or \( x < -\frac{3}{2} \)
D. \( x < \frac{5}{4} \) or \( x > -\frac{3}{2} \)

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