POST UTME OSUSTECH 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A 3x3 matrix has the following elements: [1, 2, 3; 4, 5, 6; 7, 8, 9]. What is the value of the determinant of this matrix?
A. 0
B. 15
C. 30
D. 45
Question 2
A certain number base has the property that the number 1011 is equivalent to 11 in base 10. What is the value of the number base?
A. 5
B. 6
C. 7
D. 8
Question 3
Solve the inequality \( \frac{x}{2} + 3 > 5 \).
A. x > 2
B. x < 2
C. x > 4
D. x < 4
Question 4
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. \( \frac{1}{2} \)
B. \( \frac{2}{3} \)
C. \( \frac{3}{4} \)
D. \( \frac{4}{5} \)
Question 5
A polynomial function f(x) has a root at x = -2 and a root at x = 3. If f\( -1 \) = 6, what is the value of f(2)?
A. -2
B. 0
C. 2
D. 4
Question 6
Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.
A. 48\pi
B. 64\pi
C. 80\pi
D. 96\pi
Question 7
Find the value of \( \sqrt{16} + \sqrt{9} \).
A. 7
B. 8
C. 9
D. 10
Question 8
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. Calculate the coefficient of variation (CV) for the sample.
A. 16.8%
B. 17.4%
C. 18.0%
D. 18.6%
Question 9
A curve has the equation y = 2x^2 + 3x - 1. What is the area under the curve between x = 0 and x = 2?
A. 4
B. 6
C. 8
D. 10
Question 10
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. \( x = 2 \)
B. \( x = 3 \)
C. \( x = 4 \)
D. \( x = 5 \)
Question 11
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. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \times 4 \)
Question 12
A vector \( \vec{a} \) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of \( \vec{a} \).
A. 4.33 \hat{i} + 2.5 \hat{j}
B. 4.33 \hat{i} - 2.5 \hat{j}
C. 2.5 \hat{i} + 4.33 \hat{j}
D. 2.5 \hat{i} - 4.33 \hat{j}
Question 13
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If 75% of the scores are above 80, what is the value of the z-score for a score of 85?
A. 1.25
B. 1.5
C. 1.75
D. 2.0
Question 14
A particle moves in a circular path with a cons\tant speed of 5m/s. If the radius of the circle is 3m, find the magnitude of the acceleration of the particle.
A. 5\pi
B. 10\pi
C. 15\pi
D. 20\pi
Question 15
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

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