POST UTME OSUSTECH 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x > -1 \) or \( x < 3 \)
B. \( x > 1 \) or \( x < -3 \)
C. \( x > -3 \) or \( x < 1 \)
D. \( x > 3 \) or \( x < -1 \)
Question 2
Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = 2x$ and $f_Y(y) = 3y^2$ for $0 < x < 1$ and $0 < y < 1$, respectively. Find the probability that $X + Y < 1$.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 3
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 4
Solve the inequality $\frac{2x + 3}{x - 1} > 0$.
A. \( -\infty, -3 \) \cup \( 1, \infty \)
B. \( -\infty, -3 \) \cup (1, 2) \cup \( 2, \infty \)
C. \( -\infty, -3 \) \cup \( 1, \infty \)
D. \( -\infty, -3 \) \cup (1, 2]
Question 5
A particle moves in a straight line with its position given by ( s(t) = 2t^3 - 5t^2 + 3t + 1 ). Find the velocity of the particle at time \( t = 2 \) seconds.
A. 5
B. 10
C. 15
D. 20
Question 6
Find the sum of the first 5 terms of the geometric progression: \{2, 6, 18, 54, 162\}
A. 242
B. 242.5
C. 243
D. 243.5
Question 7
Solve the system of linear equations u\sing matrices: 2x + 3y = 7 and x - 2y = -3.
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 8
In a histogram, the class width is 5 and the number of classes is 6. If the total frequency is 30, what is the class frequency?
A. 5
B. 10
C. 15
D. 20
Question 9
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 10
Find the mean of the numbers 2, 4, 6, 8, 10.
A. 6
B. 7
C. 8
D. 9
Question 11
Solve the system of equations u\sing matrices: \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}
A. \text{Solution: } x = 3, y = 1
B. \text{Solution: } x = 1, y = 3
C. \text{Solution: } x = 2, y = 2
D. \text{Solution: } x = 4, y = 0
Question 12
Determine the mean of the following dataset: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?
A. 12
B. 14
C. 16
D. 18
Question 13
A histogram shows that the heights of 10 students are normally distributed with a mean of 160 cm and a s\tandard deviation of 10 cm. What is the probability that a randomly selected student is taller than 170 cm?
A. 0.1587
B. 0.3413
C. 0.5
D. 0.8413
Question 14
The mean of 5 numbers is 15. If one of the numbers is 10, what is the sum of the other 4 numbers?
A. 50
B. 60
C. 70
D. 80
Question 15
In a circle, the length of the major axis is 10 cm and the length of the minor axis is 8 cm. Find the area of the circle.
A. 50π
B. 75π
C. 100π
D. 125π

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