POST UTME OAU 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = 2
C. x = -1
D. x = 1
Question 2
Solve for $x$: $\frac{\tan x}{\cos x} = \sqrt{3}$.
A. \frac{\pi}{3}
B. \frac{\pi}{6}
C. \frac{\pi}{2}
D. \frac{\pi}{4}
Question 3
Solve the inequality \( 2x - 5 > 3 \).
A. x > 4
B. x < 4
C. x > 2
D. x < 2
Question 4
A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?
A. 10
B. 12
C. 14
D. 16
Question 5
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} ) for \( x = 1, 2, 3 \). Find the expected value of ( X ).
A. 2
B. 3
C. 4
D. 5
Question 6
Find the area of the region bounded by $y = x^2 + 1$, $y = 2x + 1$, and the $y$-axis.
A. \frac{5}{2}
B. \frac{7}{2}
C. \frac{9}{2}
D. \frac{11}{2}
Question 7
In the diagram below, the circle with center A has a radius of 4cm. The circle with center B has a radius of 3cm. If the circles intersect at point C, what is the length of AB?
A. 5cm
B. 6cm
C. 7cm
D. 8cm
Question 8
Find the area under the curve $y = \frac{1}{x^2 + 1}$ from $x = 0$ to $x = 1.$
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{8}
D. \frac{\pi}{16}
Question 9
A quadratic equation has real roots. If the sum of the roots is 6 and the product of the roots is 12, find the equation.
A. x^2 - 6x + 12 = 0
B. x^2 + 6x + 12 = 0
C. x^2 - 6x - 12 = 0
D. x^2 + 6x - 12 = 0
Question 10
A random variable $X$ has a probability density function $f(x) = \begin{cases} \frac{1}{2} & \text{if } 0 < x < 2, \\ 0 & \text{otherwise}. \end{cases}$ Find $P\( 1 < X < 3 \).$
A. \frac{1}{2}
B. \frac{1}{4}
C. \frac{3}{4}
D. \frac{1}{8}
Question 11
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 70?
A. 0.25
B. 0.5
C. 0.75
D. 0.9
Question 12
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. If the population s\tandard deviation is 6.1 cm, calculate the 95% confidence interval for the population mean.
A. 168.3 cm, 182.7 cm
B. 170.1 cm, 180.9 cm
C. 172.9 cm, 178.1 cm
D. 169.5 cm, 181.5 cm
Question 13
A binary operation \(*\) on the set \{0, 1\} is defined as follows: \(0 * 0 = 0, 0 * 1 = 1, 1 * 0 = 1, 1 * 1 = 1\). Find the value of \(1 * \( 1 * 0)\ \).
A. 0
B. 1
C. 10
D. 11
Question 14
Find the value of \( \sin \( 2x \ \) ) given that \( \sin \( x \ \) = \frac{1}{2} ) and \( \cos \( x \ \) = \frac{\sqrt{3}}{2} ).
A. 1
B. √3
C. 2
D. √3/2
Question 15
A linear equation has a slope of 2 and a y-intercept of 3. What is the equation?
A. y = 2x + 3
B. y = 2x - 3
C. y = -2x + 3
D. y = -2x - 3

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