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POST UTME UNIBEN 2024 Mathematics | Objective

Are you preparing for POST UTME UNIBEN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

Correct A. \frac{16\pi}{3}

B. \frac{32\pi}{3}

C. \frac{64\pi}{3}

D. \frac{128\pi}{3}

Correct Answer: A

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Question 2

Solve the inequality $\log_2 $ x^2 + 1 $ > 3$.

A. $ -\infty, -\sqrt{7}] \cup [\sqrt{7}, \infty $

B. $ -\infty, -\sqrt{7} $ \cup [\sqrt{7}, \infty)

Correct C. $ -\infty, -\sqrt{7}] \cup \( -\sqrt{7}, \sqrt{7} \ $ \cup [\sqrt{7}, \infty)

D. $ -\infty, -\sqrt{7} $ \cup $ -\sqrt{7}, \sqrt{7} $ \cup [\sqrt{7}, \infty)

Correct Answer: C

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Question 3

Find the area of the region bounded by the curves $y = x^2$ and $y = 4 - x^2$.

Correct A. \frac{16}{3}

B. \frac{32}{3}

C. \frac{64}{3}

D. \frac{128}{3}

Correct Answer: A

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Question 4

Solve the equation $\log_2 $ x^2 + 1 $ = 3$.

Correct A. x = \pm \sqrt{7}

B. x = \pm \sqrt{7} + 1

C. x = \pm \sqrt{7} - 1

D. x = \pm \sqrt{7} + 2

Correct Answer: A

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Question 5

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

Correct A. \frac{32\pi}{3}

B. \frac{64\pi}{3}

C. \frac{128\pi}{3}

D. \frac{256\pi}{3}

Correct Answer: A

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Question 6

Let ( f(x) = \frac{1}{x^2 + 1} ). Find the value of $ int_{0}^{1} f\( x \ $ , dx ).

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

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

C. $ \frac{\pi}{6} $

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

Correct Answer: A

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Question 7

A histogram of exam scores is shown below. If the mean score is 60, and the s\tandard deviation is 10, what is the value of ( x ) in the interval ( [x, 80] ) that corresponds to the 75th percentile?

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 8

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

Correct A. $ \frac{32}{3} \pi $

B. $ \frac{16}{3} \pi $

C. $ \frac{64}{3} \pi $

D. $ \frac{128}{3} \pi $

Correct Answer: A

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Question 9

Let $ \mathbf{a} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} $ and $ \mathbf{b} = \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} $. Find the value of $ \mathbf{a} \cdot \mathbf{b} $.

Correct A. 32

B. 40

C. 48

D. 56

Correct Answer: A

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Question 10

Find the sum of the infinite geometric series $ \sum_{n=1}^\infty \frac{1}{2^n} \ $.

A. 1

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

C. $ \frac{1}{4} $

D. $ \frac{1}{8} $

Correct Answer: B

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Question 11

Solve the inequality $ \frac{x}{x-2} > 0 $ for $ x in \( -infty, infty \ $ ).

Correct A. $ -2, 2 $ \cup $ 2, \infty $

B. $ -\infty, -2 $ \cup $ 2, \infty $

C. $ -\infty, 2 $ \cup $ 2, \infty $

D. $ -\infty, \infty $

Correct Answer: A

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Question 12

A rec\tangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. Find its volume.

Correct A. 120 cm^3

B. 160 cm^3

C. 200 cm^3

D. 240 cm^3

Correct Answer: A

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Question 13

A company produces two products, A and B. The profit from product A is $10 per unit, and the profit from product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. $1500

Correct B. $2000

C. $2500

D. $3000

Correct Answer: B

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Question 14

A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a different score range. The heights of the bars are 8, 12, 15, 10, and 5 units, respectively. What is the mean score?

A. 12

Correct B. 15

C. 18

D. 20

Correct Answer: B

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Question 15

A vector \overrightarrow{a} has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x-component of the vector.

Correct A. 4.33

B. 4.58

C. 4.83

D. 5.00

Correct Answer: A

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Question 16

Find the value of x in the equation $ \sin^2\( x \ $ + \cos^2(x) = 1 ), given that $ \sin\( x \ $ = \frac{3}{5} ).

A. 0

B. π/2

Correct C. π

D. 3π/2

Correct Answer: C

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Question 17

A circle has an equation of the form $ x - h \ $^2 + $ y - k $^2 = r^2 ). If the center of the circle is at (3, 4) and the radius is 5, find the equation of the circle.

Correct A. $ x - 3 \ $^2 + $ y - 4 $^2 = 25 )

B. $ x - 4 \ $^2 + $ y - 3 $^2 = 25 )

C. $ x - 3 \ $^2 + $ y - 4 $^2 = 9 )

D. $ x - 4 \ $^2 + $ y - 3 $^2 = 9 )

Correct Answer: A

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Question 18

A sequence is defined as $ a_n = 2n + 1 $. Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 19

A line passes through the points (2, 3) and (4, 5). Find the equation of the line in slope-intercept form.

Correct A. $ y = x + 1 $

B. $ y = x - 1 $

C. $ y = -x + 3 $

D. $ y = x - 3 $

Correct Answer: A

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Question 20

A quadratic equation is defined as $ x^2 + 4x + 4 = 0 $. Find the solutions to the equation.

Correct A. $ x = -2 $

B. $ x = -1 $

C. $ x = 0 $

D. $ x = 1 $

Correct Answer: A

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Question 21

Determine the value of $\int_{0}^{\pi} \frac{1}{1+\sin^2x} dx$.

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

B. \frac{\pi}{4}

C. \frac{\pi}{3}

D. \frac{\pi}{1}

Correct Answer: A

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Question 22

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

Correct A. $x < -1$ or $x > 5$

B. $x < 1$ or $x > 5$

C. $x < -1$ or $x > 2$

D. $x < 1$ or $x > 2$

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-2 $^2 + $ y+3 $^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 equation $\frac{x^2-4x+3}{x^2-4x+4} = \frac{x-1}{x-2}$.

A. x = 1

Correct B. x = 2

C. x = 3

D. x = 4

Correct Answer: B

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Question 25

Find the area of the region bounded by the curves $y = x^2$ and $y = 2x$.

Correct A. \frac{4}{3}

B. \frac{2}{3}

C. \frac{1}{3}

D. \frac{1}{2}

Correct Answer: A

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