POST UTME OAU 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A histogram shows the distribution of exam scores of 20 students. The histogram has 5 equal-sized bins. The first bin has a frequency of 4, the second bin has a frequency of 5, the third bin has a frequency of 6, the fourth bin has a frequency of 3, and the fifth bin has a frequency of 2. What is the mean score of the students?
A. 15
B. 20
C. 25
D. 30
Question 2
Solve the following system of linear equations u\sing matrices:
A. \[ \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix} \]
B. \[ \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 2 \end{bmatrix} \]
C. \[ \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 1 \\ 4 \end{bmatrix} \]
D. \[ \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 4 \\ 1 \end{bmatrix} \]
Question 3
A set of 5 consecutive integers has a mean of 11. Find the sum of the integers.
A. 55
B. 60
C. 65
D. 70
Question 4
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = 2
C. x = -1
D. x = 1
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
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
Question 7
If $\begin{pmatrix} 2 & 1 \ 3 & 2 \end{pmatrix} \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 5 \ 8 \end{pmatrix}$, find the value of $x + y$.
A. 7
B. 8
C. 9
D. 10
Question 8
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 9
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 10
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 11
Solve the inequality \( 2x - 5 > 3 \).
A. x > 4
B. x < 4
C. x > 2
D. x < 2
Question 12
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 13
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 8
D. 16
Question 14
Find the vector product of \( vec{a} = 2hat{i} + 3hat{j} - hat{k} \) and \( vec{b} = hat{i} - 2hat{j} + 4hat{k} \).
A. -7hat{i} + 14hat{j} + 5hat{k}
B. 7hat{i} - 14hat{j} - 5hat{k}
C. -7hat{i} - 14hat{j} + 5hat{k}
D. 7hat{i} + 14hat{j} - 5hat{k}
Question 15
Find the value of x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \).
A. 1
B. -2
C. 3
D. -1

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