POST UTME SUMMIT UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations: \[ \begin{cases} x + y + z = 6 \\ x + 2y + 3z = 14 \end{cases} \]
A. \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}
B. \begin{pmatrix} 2 \ 1 \ 3 \end{pmatrix}
C. \begin{pmatrix} 1 \ 3 \ 2 \end{pmatrix}
D. \begin{pmatrix} 3 \ 2 \ 1 \end{pmatrix}
Question 2
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \)
Question 3
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?
A. \frac{1}{2}
B. \frac{3}{5}
C. \frac{5}{8}
D. \frac{3}{8}
Question 4
A solid is formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the y-axis. Find the volume of the solid.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 5
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3/2.
A. 2\cdot\frac{1-\left\( \frac{3}{2}\right \)^{10}}{1-\frac{3}{2}}
B. 2\cdot\frac{1-\left\( \frac{3}{2}\right \)^{10}}{1-\frac{2}{3}}
C. 2\cdot\frac{1-\left\( \frac{2}{3}\right \)^{10}}{1-\frac{3}{2}}
D. 2\cdot\frac{1-\left\( \frac{2}{3}\right \)^{10}}{1-\frac{2}{3}}
Question 6
A vector has a magnitude of 5 units and makes an angle of 60 degrees with the positive x-axis. Find the x and y components of the vector.
A. 2.5 \hat{i} + 4.33 \hat{j}
B. 4.33 \hat{i} + 2.5 \hat{j}
C. 2.5 \hat{i} - 4.33 \hat{j}
D. 4.33 \hat{i} - 2.5 \hat{j}
Question 7
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10^4 \)
B. \( x = 10^2 \)
C. \( x = 10^{-2} \)
D. \( x = 10^{-4} \)
Question 8
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 = 4 )
C. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 4 )
Question 9
Solve the inequality \( x^2 - 6x + 8 > 0 \).
A. \( x < 2 \) or \( x > 4 \)
B. \( x > 2 \) and \( x < 4 \)
C. \( x < 2 \) and \( x > 4 \)
D. \( x = 2 \) or \( x = 4 \)
Question 10
A fair six-sided die is rolled. If the number on the die is even, a second die is rolled. What is the probability that the sum of the numbers on the two dice is 7?
A. 1/6
B. 1/12
C. 1/24
D. 1/36
Question 11
Solve the inequality \frac{x^2 - 4x - 5}{x + 1} > 0.
A. \( -\infty, -1 \) \cup \( 5, \infty \)
B. \( -\infty, -1 \) \cup \( -1, 5 \)
C. \( -\infty, 5 \) \cup \( 5, \infty \)
D. \( -\infty, -1 \) \cup \( 5, \infty \)
Question 12
A right-angled triangle has sides of length 3, 4, and 5. Find the area of the triangle.
A. \( \frac{1}{2} \times 3 \times 4 \)
B. \( \frac{1}{2} \times 3 \times 5 \)
C. \( \frac{1}{2} \times 4 \times 5 \)
D. \( \frac{1}{2} \times 3 \times 5 \)
Question 13
In the diagram below, a right-angled triangle has a hypotenuse of length 10 cm. If the ratio of the lengths of the two legs is 3:4, what is the area of the triangle in square centimeters?
A. 30
B. 40
C. 50
D. 60
Question 14
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 15
Find the area under the curve y = x^2 from x = 0 to x = 4.
A. \frac{64}{3}
B. \frac{32}{3}
C. \frac{16}{3}
D. \frac{8}{3}

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: