POST UTME OSUSTECH 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 1022
B. 1023
C. 1024
D. 1025
Question 2
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 50 and 70?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 3
Find the equation of the \tangent line to the curve \( y = \frac{1}{x} \) at the point where \( x = 2 \).
A. \( y = -\frac{1}{2}x + 1 \)
B. \( y = \frac{1}{2}x + 1 \)
C. \( y = -\frac{1}{2}x - 1 \)
D. \( y = \frac{1}{2}x - 1 \)
Question 4
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{5}{6} \)
Question 5
A circle has a radius of 4 cm. Find the area of the circle.
A. 16\pi\text{ cm}^2
B. 32\pi\text{ cm}^2
C. 64\pi\text{ cm}^2
D. 128\pi\text{ cm}^2
Question 6
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. \( -1 \)
D. ( 2 )
Question 7
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 10
D. 20
Question 8
A box contains 5 red balls and 3 blue balls. If a ball is randomly selected, what is the probability that it is red?
A. \frac{1}{2}
B. \frac{2}{3}
C. \frac{3}{4}
D. \frac{4}{5}
Question 9
Determine the sum of the first 10 terms of the geometric series with first term 3 and common ratio 2.
A. \( 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 \)
B. \( 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 + 3072 \)
C. \( 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 - 3072 \)
D. \( 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 \)
Question 10
A histogram of exam scores for a class of 50 students is shown below. What is the mean score?
A. 25
B. 30
C. 35
D. 40
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 12
Determine the value of x in the equation \( \frac{x}{2} + 5 = 11 \).
A. 4
B. 6
C. 8
D. 10
Question 13
A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. What is the probability that a randomly selected number from this set is greater than 12?
A. \( \frac{1}{4} \)
B. \( \frac{1}{2} \)
C. \( \frac{3}{4} \)
D. \( \frac{3}{2} \)
Question 14
A curve is defined by the equation \( y = \frac{1}{2}x^2 + 3x - 2 \). Find the derivative of the curve at the point where \( x = 2 \).
A. ( 1 )
B. ( 2 )
C. ( 3 )
D. ( 4 )
Question 15
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?
A. 30
B. 40
C. 50
D. 60

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