POST UTME KSU 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \log_{10} \( x^2 \) = 4.
A. 10
B. 100
C. 1000
D. 10000
Question 2
A binary operation \( * \) is defined as \( a * b = a^2 + b^2 \). Find the value of \( 2 * 3 \).
A. 13
B. 14
C. 15
D. 16
Question 3
The volume of a sphere (V) varies with its radius (r) as V = \( 4/3 \)πr^3. If the radius of a sphere is increased from 2 cm to 4 cm, calculate the percentage increase in its volume.
A. 100%
B. 200%
C. 300%
D. 400%
Question 4
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 5
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula. What is the value of ( x )?
A. -2
B. -3
C. 2
D. 3
Question 6
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 7
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. -2/\( x^2 + 1 \)^2
D. 2/\( x^2 + 1 \)^2
Question 8
A histogram is constructed with 5 classes of equal width. The first class has a frequency of 10, the second class has a frequency of 15, the third class has a frequency of 20, the fourth class has a frequency of 25, and the fifth class has a frequency of 30. What is the mean of the histogram?
A. 20
B. 22
C. 24
D. 26
Question 9
A curve is defined by the equation y = x^2 + 2x - 3. Find the equation of the \tangent to the curve at the point where x = 1.
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 10
Solve the inequality $|2x-3| \geq 5$.
A. x \leq -4 \text{ or } x \geq 4
B. x \leq 1 \text{ or } x \geq 4
C. x \leq -1 \text{ or } x \geq 4
D. x \leq -4 \text{ or } x \geq 1
Question 11
A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?
A. ₦1250
B. ₦12500
C. ₦125000
D. ₦1250000
Question 12
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 13
Determine the value of $\frac{d}{dx}\left\( \frac{1}{x^2+1}\right \)$ u\sing the chain rule.
A. \frac{-2x}{\( x^2+1 \)^2}
B. \frac{2x}{\( x^2+1 \)^2}
C. \frac{2}{\( x^2+1 \)^2}
D. \frac{-2}{\( x^2+1 \)^2}
Question 14
Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{bmatrix} \).
A. -1
B. 1
C. 2
D. 3
Question 15
A cylindrical \tank with a radius of 5m and a height of 10m is filled with water. If the density of water is 1000 kg/m^3, calculate the volume of water in the \tank.
A. ( 500pi ) m^3
B. ( 1000pi ) m^3
C. ( 1500pi ) m^3
D. ( 2000pi ) m^3

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