POST UTME SUMMIT UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{5}{6} \)
Question 2
Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and (6, 7).
A. \[ \( x - 4 \)^2 + \( y - 5 \)^2 = 9 \]
B. \[ \( x - 3 \)^2 + \( y - 4 \)^2 = 16 \]
C. \[ \( x - 5 \)^2 + \( y - 6 \)^2 = 25 \]
D. \[ \( x - 6 \)^2 + \( y - 7 \)^2 = 36 \]
Question 3
A random variable X has a probability distribution given by P\( X = 1 \) = 1/4, P\( X = 2 \) = 1/2, P\( X = 3 \) = 1/4. Find the probability that X is greater than 2.
A. 1/2
B. 3/4
C. 1/4
D. 0
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, -3 \) \cup \( 3, \infty \)
Question 5
Find the value of $\lim_{x\to\infty} \left\( \frac{\ln\( x^2 + 1 \ \)}{x}\right)$.
A. 0
B. 1
C. \infty
D. undefined
Question 6
A histogram of the heights of 100 students is shown below. If the mean height is 170 cm, find the s\tandard deviation.
A. 10 cm
B. 15 cm
C. 20 cm
D. 25 cm
Question 7
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
Question 8
Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...
A. 300
B. 400
C. 500
D. 600
Question 9
A fair coin is tossed 5 times. What is the probability that exactly 3 heads appear?
A. \( \frac{10}{32} \)
B. \( \frac{15}{32} \)
C. \( \frac{20}{32} \)
D. \( \frac{25}{32} \)
Question 10
A quadratic equation has the form \( ax^2 + bx + c = 0 \) and has roots at \( x = 1 \) and \( x = -2 \). Find the equation.
A. x^2 - x - 4 = 0
B. x^2 + x - 4 = 0
C. x^2 - x + 4 = 0
D. x^2 + x + 4 = 0
Question 11
Find the value of x in the matrix equation \begin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 4 \ 7 \end{bmatrix}.
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 12
A probability experiment has two indep\endent events. The probability of event A occurring is 0.4 and the probability of event B occurring is 0.6. Find the probability that both events occur.
A. 0.24
B. 0.26
C. 0.28
D. 0.30
Question 13
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \), with initial term \( a_1 = 3 \). Find the 5th term of the sequence.
A. ( 31 )
B. ( 33 )
C. ( 35 )
D. ( 37 )
Question 14
Find the determinant of the matrix \[ \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \].
A. 0
B. 1
C. 2
D. 3
Question 15
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{1}{\( x^2 + 1 \)^2} )
D. ( f'(x) = -\frac{1}{\( x^2 + 1 \)^2} )

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