POST UTME OAU 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve y = x^3 - 6x^2 + 9x + 2 from x = 0 to x = 4.
A. 64
B. 128
C. 192
D. 256
Question 2
Determine the value of $\int_{0}^{\pi} \frac{\sin^2 x}{1 + \cos^2 x} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{8}
D. \frac{\pi}{16}
Question 3
Solve the system of linear equations u\sing matrices: \[ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 8 \end{bmatrix} \]
A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \\ 3 \end{bmatrix}
C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \\ 5 \end{bmatrix}
Question 4
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = -\frac{2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = -\frac{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
Question 5
Find the volume of the solid formed by rotating the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 6
A company produces two products, A and B. The profit from the sale of product A is $\frac{1}{2}$x + $\frac{1}{4}$y, and the profit from the sale of product B is $\frac{3}{4}$x - $\frac{1}{2}$y. If the company produces 100 units of product A and 50 units of product B, find the total profit.
A. $\frac{75}{2}$
B. $\frac{125}{2}$
C. $\frac{175}{2}$
D. $\frac{225}{2}
Question 7
A random variable X follows a normal distribution with mean \mu = 10 and s\tandard deviation \sigma = 2. Find the probability that X is less than 12.
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 8
A box contains 12 red balls, 16 blue balls, and 4 green balls. If a ball is drawn at random, what is the probability that it is either red or blue?
A. \frac{7}{12}
B. \frac{4}{5}
C. \frac{3}{4}
D. \frac{2}{3}
Question 9
A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is blue?
A. 0.2
B. 0.25
C. 0.3
D. 0.4
Question 10
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. -1
B. 0
C. 1
D. -2
Question 11
In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?
A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6915
Question 12
A rec\tangular solid has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the solid.
A. 30 cm^3
B. 40 cm^3
C. 50 cm^3
D. 60 cm^3
Question 13
Solve the system of equations \( x + y = 4 \) and \( xy = 5 \).
A. \( x = 1, y = 3 \)
B. \( x = 2, y = 2 \)
C. \( x = 3, y = 1 \)
D. \( x = 4, y = 0 \)
Question 14
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 = 16 )
C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
Question 15
A random variable X follows a binomial distribution with parameters n = 10 and p = 0.4. Find the probability that X is greater than 6.
A. 0.2
B. 0.3
C. 0.4
D. 0.5

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