POST UTME UI 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation 2^x + 3^x = 5^x.
A. 1
B. 2
C. 3
D. 4
Question 2
Solve the equation \frac{1}{2} \log_{10} \( x^2 \) = 4.
A. 10^8
B. 10^4
C. 10^2
D. 10^0
Question 3
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} \) for \( x = 1, 2, 3, 4 \). Find the probability that ( X ) takes a value greater than 2.
A. \( \frac{1}{4} \ \)
B. \( \frac{1}{2} \ \)
C. \( \frac{3}{4} \ \)
D. \( \frac{7}{8} \ \)
Question 4
Solve the equation \( x^2 - 6x + 8 = 0 \) u\sing the quadratic formula.
A. \( x = 2 pm 2i \)
B. \( x = 2 pm 3i \)
C. \( x = 2 pm 4i \)
D. \( x = 2 pm 5i \)
Question 5
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. \( \frac{16}{15} \pi \ \)
B. \( \frac{32}{15} \pi \ \)
C. \( \frac{64}{15} \pi \ \)
D. \( \frac{128}{15} \pi \ \)
Question 6
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 7
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. \( \frac{8}{15} pi \)
B. \( \frac{16}{15} pi \)
C. \( \frac{32}{15} pi \)
D. \( \frac{64}{15} pi \)
Question 8
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 9
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 10
Solve the inequality $|x - 2| > 3$.
A. x < -1
B. x > 5
C. x < 5
D. x > -1
Question 11
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. \( 2 \sin x \cos x \)
B. \( \cos^2 x \)
C. \( \sin^2 x \)
D. \( \cos x \)
Question 12
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 13
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{-2}{\( x^2 + 1 \)^2} \)
D. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} \)
Question 14
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 15
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 )

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