Exam Body

Year

Subject

Paper Type

POST UTME IMS U 2023 Mathematics | Objective

Are you preparing for POST UTME IMS U exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the value of x in the equation $ \log_{10} \( x^2 \ $ = 4 )

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 2

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 3

In the diagram below, find the value of x.

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 4

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

A. x = 0

Correct B. x = π/2

C. x = π

D. x = 2π

Correct Answer: B

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Question 5

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 6

Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = 2x$ for $0 < x < 1$ and $f_Y(y) = 3y^2$ for $0 < y < 1$. Find the probability that $X + Y < 1$.

Correct A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 7

Solve the inequality $\frac{x^2 - 4x + 3}{x^2 - 2x - 3} > 0$.

Correct A. $ -\infty, -1 $ \cup $ 3, \infty $

B. $ -\infty, -3 $ \cup $ 1, \infty $

C. $ -\infty, -3 $ \cup $ -1, 1 $ \cup $ 3, \infty $

D. $ -\infty, -3 $ \cup (1, 3)

Correct Answer: A

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Question 8

Find the area under the curve $y = \frac{1}{x^2 + 1}$ from $x = 0$ to $x = 1$.

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

B. \frac{\pi}{2}

C. \frac{\pi}{6}

D. \frac{\pi}{8}

Correct Answer: A

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Question 9

Let $a_n = \frac{1}{n^2}$ for $n = 1, 2, 3, \dots$. Find the sum of the series $\sum_{n=1}^\infty a_n$.

Correct A. \frac{\pi^2}{6}

B. \frac{\pi^2}{12}

C. \frac{\pi^2}{24}

D. \frac{\pi^2}{36}

Correct Answer: A

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Question 10

Solve the equation $\tan^2 x + 2 \tan x - 1 = 0$ for $x$ in the interval $[0, \pi]$.

A. \frac{\pi}{4}

Correct B. \frac{\pi}{3}

C. \frac{\pi}{2}

D. \frac{2\pi}{3}

Correct Answer: B

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Question 11

In a survey of 100 students, 60 students preferred Mathematics, 30 students preferred Science, and 10 students preferred both Mathematics and Science. What is the probability that a student chosen at random from the survey prefers either Mathematics or Science?

Correct A. $ \frac{19}{20} $

B. $ \frac{1}{2} $

C. $ \frac{3}{5} $

D. $ \frac{7}{10} $

Correct Answer: A

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Question 12

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

Correct A. $ x = 16 $

B. $ x = 8 $

C. $ x = 4 $

D. $ x = 2 $

Correct Answer: A

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Question 13

Find the volume of the solid formed by revolving the region bounded by the curves $ y = x^2 $ and $ y = 4 - x $ about the x-axis.

Correct A. $ \frac{256}{15} pi $

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

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

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

Correct Answer: A

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Question 14

A circle with radius 6 cm is inscribed in a square. What is the area of the square?

A. ( 36 pi )

Correct B. ( 72 pi )

C. ( 144 pi )

D. ( 216 pi )

Correct Answer: B

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Question 15

Solve the inequality $ 2x^2 + 5x - 3 > 0 $.

Correct A. $ x < -\frac{3}{2} $ or $ x > \frac{1}{2} $

B. $ x < -\frac{1}{2} $ or $ x > \frac{3}{2} $

C. $ x < -\frac{3}{2} $ or $ x < \frac{1}{2} $

D. $ x > -\frac{3}{2} $ or $ x < \frac{1}{2} $

Correct Answer: A

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Question 16

Determine the value of 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 17

Solve the quadratic equation $ x^2 + 5x + 6 = 0 $ u\sing the quadratic formula.

Correct A. -2

B. -3

C. 2

D. 3

Correct Answer: A

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Question 18

A binary operation ( odot ) is defined as $ a odot b = ab + 2 $. Find the value of ( 3 odot 4 ).

A. 14

B. 16

Correct C. 18

D. 20

Correct Answer: C

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Question 19

In the diagram below, ( ABC ) is a right-angled triangle with $ AB = 3 $ and $ BC = 4 $. Find the length of ( AC ).

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 20

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

Correct A. 1/2

B. 1/3

C. 2/5

D. 3/8

Correct Answer: A

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Question 21

Find the volume of the solid formed by revolving the region bounded by y = x^2, x = 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 22

Solve the system of equations u\sing matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 8 \end{bmatrix}

Correct A. \\begin{bmatrix} 1 \\\\ 2 \\end{bmatrix}

B. \\begin{bmatrix} 2 \\\\ 3 \\end{bmatrix}

C. \\begin{bmatrix} 3 \\\\ 4 \\end{bmatrix}

D. \\begin{bmatrix} 4 \\\\ 5 \\end{bmatrix}

Correct Answer: A

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Question 23

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 + 2 $^2 + $ y - 3 $^2 = 16

D. $ x - 2 $^2 + $ y + 3 $^2 = 16

Correct Answer: A

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Question 24

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

Correct A. $ -\\infty, -1 $ \\cup $ 3, \\infty $

B. $ -\\infty, 1 $ \\cup $ 3, \\infty $

C. $ -\\infty, -3 $ \\cup $ 1, \\infty $

D. $ -\\infty, 3 $ \\cup $ 1, \\infty $

Correct Answer: A

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Question 25

Find the area of the triangle with vertices (0, 0), (2, 0), and (0, 3).

A. 3

Correct B. 6

C. 9

D. 12

Correct Answer: B

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