POST UTME SUMMIT UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 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
Solve the system of equations u\sing matrices: \( egin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases} \).
A. [1, 2]
B. [2, 1]
C. [3, -1]
D. [-1, 3]
Question 4
Find the equation of the circle with center at \( -2, 3 \) and pas\sing through the point (1, 2).
A. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 5
B. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 10
C. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 15
D. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 20
Question 5
Find the derivative of the function \[ f(x) = \frac{1}{x^2 + 1} \].
A. \[ f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} \]
B. \[ f'(x) = \frac{2x}{\( x^2 + 1 \)^2} \]
C. \[ f'(x) = \frac{x}{\( x^2 + 1 \)^2} \]
D. \[ f'(x) = \frac{1}{\( x^2 + 1 \)^2} \]
Question 6
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. -2x/\( x^2 + 1 \)^2
B. 2x/\( x^2 + 1 \)^2
C. -1/\( x^2 + 1 \)^2
D. 1/\( x^2 + 1 \)^2
Question 7
A geometric series has first term \( a = 2 \) and common ratio \( r = \frac{1}{2} \). Find the sum of the first 5 terms.
A. \( \frac{63}{32} \)
B. \( \frac{127}{64} \)
C. \( \frac{255}{128} \)
D. \( \frac{511}{256} \)
Question 8
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 9
A polynomial function has degree 3 and has zeros at \( x = -1 \) and \( x = 2 \). Find the polynomial function.
A. f(x) = \( x + 1 \)\( x - 2 \)\( x - 3 \)
B. f(x) = \( x + 1 \)\( x - 2 \)\( x + 3 \)
C. f(x) = \( x + 1 \)\( x - 2 \)\( x - 3 \)
D. f(x) = \( x + 1 \)\( x - 2 \)\( x + 2 \)
Question 10
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + cdots \).
A. 1048576
B. 1048575
C. 1048574
D. 1048573
Question 11
In a set of consecutive integers, the sum of the first and last term is 56. If the sum of the second and second last term is 34, find the sum of the first and second term.
A. 10
B. 12
C. 14
D. 16
Question 12
Solve the matrix equation AX = B, where A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}, X = egin{bmatrix} x \ y \end{bmatrix}, and B = egin{bmatrix} 5 \ 6 \end{bmatrix}.
A. X = egin{bmatrix} 1 \ 2 \end{bmatrix}
B. X = egin{bmatrix} 2 \ 1 \end{bmatrix}
C. X = egin{bmatrix} 3 \ 4 \end{bmatrix}
D. X = egin{bmatrix} 4 \ 3 \end{bmatrix}
Question 13
Solve the inequality \[ 2x^2 + 5x - 3 \geq 0 \].
A. \[ x \leq -1 \text{ or } x \geq \frac{3}{2} \]
B. \[ x \leq -2 \text{ or } x \geq 1 \]
C. \[ x \leq -3 \text{ or } x \geq 2 \]
D. \[ x \leq -4 \text{ or } x \geq 3 \]
Question 14
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 15
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. ( f'(x) = 2 \sin x \cos x )
B. ( f'(x) = -2 \sin x \cos x )
C. ( f'(x) = \cos^2 x )
D. ( f'(x) = \sin^2 x )

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: