POST UTME OSUSTECH 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( x^2 - 4x + 3 > 0 \).
A. x < 1
B. x > 1
C. x < 3
D. x > 3
Question 2
Determine the volume of the frustum of a cone with a height of 6 units, a lower base radius of 4 units, and an upper base radius of 2 units.
A. 24π
B. 48π
C. 96π
D. 192π
Question 3
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 0 \) ∪ (1, ∞)
C. \( -∞, -2 \) ∪ (2, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 5
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times \frac{4^2}{2} - 2 \times 4 \)
Question 6
A set ( A ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( A ) that contain exactly two elements.
A. \( inom{5}{2} = 10 \)
B. \( inom{5}{3} = 10 \)
C. \( inom{5}{4} = 5 \)
D. \( inom{5}{1} = 5 \)
Question 7
A die is rolled twice. What is the probability that the sum of the two numbers is 7?
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{1}{2}
D. \frac{2}{3}
Question 8
Convert the binary number 1010 to decimal.
A. 2
B. 3
C. 4
D. 5
Question 9
A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a range of scores. The first bar represents scores from 0-20, the second bar represents scores from 21-40, the third bar represents scores from 41-60, the fourth bar represents scores from 61-80, and the fifth bar represents scores from 81-100. The heights of the bars are 2, 10, 15, 18, and 5, respectively. Find the mean score of the class.
A. 50
B. 60
C. 70
D. 80
Question 10
Find the derivative of the function \( f(x) = 3x^2 + 2x - 5 \) u\sing the power rule.
A. \( f'(x) = 6x + 2 \)
B. \( f'(x) = 3x^2 + 2 \)
C. \( f'(x) = 6x - 2 \)
D. \( f'(x) = 3x^2 - 2 \)
Question 11
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 90?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 12
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 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 13
A geometric sequence has a common ratio of 2 and the first term is 3. If the sum of the first four terms is 67, find the sum of the next three terms.
A. 336
B. 337
C. 338
D. 339
Question 14
Solve the system of linear equations u\sing matrices: \begin{align*} x + y + z &= 6 \ 2x + 3y - z &= 2 \ 3x - 2y + z &= 4 \end{align*}
A. \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}
B. \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix}
C. \begin{pmatrix} 3 \ 4 \ 5 \end{pmatrix}
D. \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}
Question 15
Solve the equation \( x^2 + 2x - 6 = 0 \) u\sing the quadratic formula.
A. x = -3
B. x = -2
C. x = 1
D. x = 2

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: