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POST UTME UI 2022 Mathematics | Objective

Are you preparing for POST UTME UI exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).

Correct A. \boxed{x^2 + y^2 - 5x + 7y - 12 = 0}

B. \boxed{x^2 + y^2 - 3x - 5y + 4 = 0}

C. \boxed{x^2 + y^2 + 3x - 7y + 2 = 0}

D. \boxed{x^2 + y^2 - x + 3y - 6 = 0}

Correct Answer: A

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Question 2

Solve the equation \( 2x^3 - 5x^2 + 3x - 1 = 0 \) u\sing the Rational Root Theorem.

Correct A. \boxed{r = \pm 1}

B. \boxed{r = \pm 2}

C. \boxed{r = \pm 3}

D. \boxed{r = \pm 1/2}

Correct Answer: A

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Question 3

Find the derivative of the function \( f(x) = \frac{x^2 + 3x - 2}{x + 1} \) u\sing the Quotient Rule.

Correct A. \boxed{f'(x) = \frac{2x + 3}{\( x + 1 \)^2}}

B. \boxed{f'(x) = \frac{2x - 3}{\( x + 1 \)^2}}

C. \boxed{f'(x) = \frac{2x + 2}{\( x + 1 \)^2}}

D. \boxed{f'(x) = \frac{2x - 2}{\( x + 1 \)^2}}

Correct Answer: A

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Question 4

Solve the system of equations \( x + y = 2 \) and \( x - y = 1 \) u\sing the method of substitution.

Correct A. \boxed{x = 1, y = 1}

B. \boxed{x = 2, y = 0}

C. \boxed{x = 0, y = 2}

D. \boxed{x = 1, y = 2}

Correct Answer: A

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Question 5

Find the equation of the line pas\sing through the points (1, 2) and (3, 4).

Correct A. \boxed{y = x + 1}

B. \boxed{y = x - 1}

C. \boxed{y = -x + 2}

D. \boxed{y = x - 2}

Correct Answer: A

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Question 6

Find the equation of the circle with center at (2, 3) and radius 4.

Correct A. \text{Equation: } \( x - 2 \)^2 + \( y - 3 \)^2 = 16

B. \text{Equation: } \( x + 2 \)^2 + \( y - 3 \)^2 = 16

C. \text{Equation: } \( x - 2 \)^2 + \( y + 3 \)^2 = 16

D. \text{Equation: } \( x + 2 \)^2 + \( y + 3 \)^2 = 16

Correct Answer: A

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Question 7

Solve for x in the equation \(\log_{10} \( x^2 \) = 4\).

Correct A. x = 10^4

B. x = 10^2

C. x = 10^8

D. x = 10^6

Correct Answer: A

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Question 8

Find the derivative of the function \(f(x) = \frac{1}{x^2 + 1}\).

A. \frac{-2x}{\( x^2 + 1 \)^2}

Correct B. \frac{2x}{\( x^2 + 1 \)^2}

C. \frac{1}{\( x^2 + 1 \)^2}

D. \frac{-1}{\( x^2 + 1 \)^2}

Correct Answer: B

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Question 9

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \frac{1}{6}

B. \frac{2}{6}

C. \frac{3}{6}

Correct D. \frac{4}{6}

Correct Answer: D

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Question 10

Find the vector \(\mathbf{a} \cdot \mathbf{b}\) given \(\mathbf{a} = \begin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = \begin{pmatrix} 4 \ 5 \end{pmatrix}\).

A. 23

Correct B. 29

C. 31

D. 37

Correct Answer: B

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Question 11

Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 12

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24π cm^3

B. 48π cm^3

Correct C. 72π cm^3

D. 96π cm^3

Correct Answer: C

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Question 13

If ( f(x) = \frac{x^2 - 4}{x - 2} ), find \( f\( -2 \ \) ).

A. 0

Correct B. 2

C. 4

D. 6

Correct Answer: B

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Question 14

A particle moves along the x-axis with its position given by ( s(t) = 2t^3 - 5t^2 + 3t + 1 ). Find the velocity of the particle at time t = 2 s.

A. 10 m/s

B. 20 m/s

Correct C. 30 m/s

D. 40 m/s

Correct Answer: C

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Question 15

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 16

Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{16}{3} \)

B. ( 8 )

C. ( 12 )

D. ( 16 )

Correct Answer: A

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Question 17

Solve the system of linear equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} \).

Correct A. \( x = 1, y = 2 \)

B. \( x = 2, y = 1 \)

C. \( x = 3, y = 4 \)

D. \( x = 4, y = 3 \)

Correct Answer: A

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Question 18

Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).

Correct A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )

B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )

C. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 16 )

D. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 16 )

Correct Answer: A

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Question 19

Solve the inequality \( x^2 - 4x + 3 > 0 \).

Correct A. \( x < -1 \) or \( x > 3 \)

B. \( x < 1 \) or \( x > 3 \)

C. \( x < -3 \) or \( x > 1 \)

D. \( x < 3 \) or \( x > 1 \)

Correct Answer: A

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Question 20

Find the mean of the data set: ( 2, 4, 6, 8, 10 ).

Correct A. ( 6 )

B. ( 8 )

C. ( 10 )

D. ( 12 )

Correct Answer: A

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Question 21

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.

Correct 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}} )

Correct Answer: A

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Question 22

A histogram of exam scores has a mean of 75 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 90?

Correct A. 0.8413

B. 0.8413

C. 0.8413

D. 0.8413

Correct Answer: A

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Question 23

Solve for x in the equation \( 2^x + 2^{x+1} = 2^{x+2} + 2^{x+3} \).

A. -2

Correct B. -1

C. 0

D. 1

Correct Answer: B

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Question 24

Find the vector projection of \( vec{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \) onto \( vec{b} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} \).

Correct A. \( egin{pmatrix} 0.8 \ 1 \ 1.2 \end{pmatrix} \)

B. \( egin{pmatrix} 1 \ 1.2 \ 1.6 \end{pmatrix} \)

C. \( egin{pmatrix} 1.2 \ 1.6 \ 2 \end{pmatrix} \)

D. \( egin{pmatrix} 1.6 \ 2 \ 2.4 \end{pmatrix} \)

Correct Answer: A

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Question 25

A set ( S ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( S ) that contain exactly two elements.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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