POST UTME UI 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
A circle with center ( C(2, 3) ) and radius \( r = 4 \) has a chord ( AB ) parallel to the x-axis. Find the length of ( AB ).
A. ( 8 )
B. ( 6 )
C. ( 4 )
D. ( 2 )
Question 3
Find the derivative of ( f(x) = \sin\( x^2 \) ) u\sing the chain rule.
A. \( 2x\cos\( x^2 \ \) )
B. \( \cos\( x^2 \ \) )
C. \( 2x\sin\( x^2 \ \) )
D. \( \sin\( x^2 \ \) )
Question 4
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.
A. 30
B. 60
C. 90
D. 120
Question 5
Determine the value of $x$ in the equation $2^x + 3^x = 5^x$.
A. 0
B. 1
C. 2
D. 3
Question 6
A histogram of exam scores is shown below. What is the mean score?
A. 20
B. 25
C. 30
D. 35
Question 7
Find the equation of the line pas\sing through the points $(2,3)$ and $(4,5)$.
A. y = 1x + 1
B. y = 2x + 1
C. y = 3x + 1
D. y = 4x + 1
Question 8
A population of 1000 bacteria grows at a rate of 20% per hour. Find the population after 3 hours.
A. \( 1000 \times 1.2^3 \)
B. \( 1000 \times 1.4^3 \)
C. \( 1000 \times 1.6^3 \)
D. \( 1000 \times 1.8^3 \)
Question 9
Find the magnitude of the vector \begin{pmatrix} 3 \ 4 \end{pmatrix}.
A. 5
B. 4
C. 3
D. 2
Question 10
A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 80?
A. 0.68
B. 0.69
C. 0.70
D. 0.71
Question 11
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \( \frac{-x}{\( x^2 + 1 \ \)^{3/2}} )
B. \( \frac{x}{\( x^2 + 1 \ \)^{3/2}} )
C. \( \frac{1}{\( x^2 + 1 \ \)^{3/2}} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^{3/2}} )
Question 12
Solve the inequality $|x - 2| > 3$.
A. x < -1
B. x > 5
C. x < 5
D. x > -1
Question 13
Solve the system of linear equations \( egin{cases} x + 2y - 3z = 7 \ 2x - 3y + z = -2 \ 3x + y + 2z = 5 \end{cases} \) u\sing the method of substitution.
A. \( x = 1, y = 2, z = 3 \)
B. \( x = 2, y = 1, z = 4 \)
C. \( x = 3, y = 4, z = 5 \)
D. \( x = 4, y = 3, z = 6 \)
Question 14
A circle has a radius of 5 cm. Find the area of the circle.
A. \( 10 \pi \ \) cm^2
B. \( 20 \pi \ \) cm^2
C. \( 25 \pi \ \) cm^2
D. \( 50 \pi \ \) cm^2
Question 15
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.
A. \( \frac{1}{\( 1 - x^2 \ \)^{\frac{3}{2}}} )
B. \( \frac{x}{\( 1 - x^2 \ \)^{\frac{3}{2}}} )
C. \( \frac{1}{\( 1 - x^2 \ \)^{\frac{1}{2}}} )
D. \( \frac{x^2}{\( 1 - x^2 \ \)^{\frac{3}{2}}} )

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