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POST UTME UI 2021 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 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the value of $x$ in the equation $2^x + 3^x = 5^x$.

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 2

Find the equation of the line pas\sing through the points $(2,3)$ and $(4,5)$.

A. y = 1x + 1

Correct B. y = 2x + 1

C. y = 3x + 1

D. y = 4x + 1

Correct Answer: B

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Question 3

Solve the inequality $|x - 2| > 3$.

A. x < -1

Correct B. x > 5

C. x < 5

D. x > -1

Correct Answer: B

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Question 4

Find the area of the triangle with vertices $(0,0)$, $(3,0)$, and $(0,4)$.

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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Question 5

Solve the system of equations $x + y = 3$ and $x - y = 1$.

Correct A. x = 2, y = 1

B. x = 1, y = 2

C. x = 2, y = 2

D. x = 1, y = 1

Correct Answer: A

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Question 6

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. ( 4 )

D. ( 2 )

Correct Answer: A

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Question 7

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 ).

Correct A. ( 8 )

B. ( 6 )

C. ( 4 )

D. ( 2 )

Correct Answer: A

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Question 8

Find the derivative of ( f(x) = \sin$ x^2 $ ) u\sing the chain rule.

Correct A. $ 2x\cos\( x^2 \ $ )

B. $ \cos\( x^2 \ $ )

C. $ 2x\sin\( x^2 \ $ )

D. $ \sin\( x^2 \ $ )

Correct Answer: A

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Question 9

A sequence is defined by $ a_n = \frac{1}{n} $. Find the sum of the first 5 terms of the sequence.

A. ( 1.25 )

Correct B. ( 1.33 )

C. ( 1.45 )

D. ( 1.67 )

Correct Answer: B

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Question 10

Two events ( A ) and ( B ) are indep\endent. If ( P(A) = 0.3 ) and ( P(B) = 0.4 ), find ( P(A cap B) ).

Correct A. ( 0.12 )

B. ( 0.24 )

C. ( 0.36 )

D. ( 0.48 )

Correct Answer: A

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Question 11

Solve the inequality $ \frac{x}{x-2} > 1 $ for $ x > 2 $.

Correct A. $ x > 3 \ $

B. $ x < 3 \ $

C. $ x > 2 \ $

D. $ x < 2 \ $

Correct Answer: A

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Question 12

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If 80% of the scores lie between 60 and 90, what is the probability that a randomly selected score lies between 70 and 85?

A. 0.4

Correct B. 0.5

C. 0.6

D. 0.7

Correct Answer: B

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Question 13

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.

Correct A. $ \frac{16}{15} \pi \ $

B. $ \frac{32}{15} \pi \ $

C. $ \frac{64}{15} \pi \ $

D. $ \frac{128}{15} \pi \ $

Correct Answer: A

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Question 14

Solve the equation $ \sin^2 x + \cos^2 x = 1 \ $ for $ x \in [0, 2\pi] \ $.

A. $ x = \frac{\pi}{2} \ $

B. $ x = \frac{3\pi}{2} \ $

Correct C. $ x = \frac{\pi}{4} \ $ or $ x = \frac{5\pi}{4} \ $

D. $ x = \frac{\pi}{4} \ $ or $ x = \frac{3\pi}{4} \ $

Correct Answer: C

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Question 15

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

Correct 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} \)

Correct Answer: A

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Question 16

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

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 17

Solve the equation \frac{1}{2} \log_{10} $ x^2 $ = 4.

Correct A. 10^8

B. 10^4

C. 10^2

D. 10^0

Correct Answer: A

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Question 18

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

A. \frac{2x}{$ x^2 - 1 $^2}

Correct B. \frac{2x^3 - 2x}{$ x^2 - 1 $^2}

C. \frac{2x^3 + 2x}{$ x^2 - 1 $^2}

D. \frac{2x^3 - 2x^2}{$ x^2 - 1 $^2}

Correct Answer: B

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Question 19

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 20

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.

Correct A. 30

B. 60

C. 90

D. 120

Correct Answer: A

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Question 21

Find the area under the curve y = 2x^2 + 3x - 4 from x = 0 to x = 2.

A. 20

B. 22

Correct C. 24

D. 26

Correct Answer: C

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Question 22

Solve for x in the equation 2^x + 3^x = 5^x.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 23

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

Correct C. 0.70

D. 0.71

Correct Answer: C

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Question 24

Find the magnitude of the vector \begin{pmatrix} 3 \ 4 \end{pmatrix}.

Correct A. 5

B. 4

C. 3

D. 2

Correct Answer: A

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Question 25

Solve the equation \sin^2 x + \cos^2 x = 1 for x.

A. \frac{\pi}{2}

Correct B. \frac{\pi}{4}

C. \frac{\pi}{6}

D. \frac{\pi}{3}

Correct Answer: B

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