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POST UTME UNIBEN 2024 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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

A histogram of exam scores is shown below. If the mean score is 60, and the standard 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 View Details

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 View Details

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

Correct A. 32

B. 40

C. 48

D. 56

Correct Answer: A

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Question 10 View Details

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 View Details

Solve the inequality ($\frac{x}{x-2}\(> 0$\) for x in \$(frac{x}{x-2}\(> 0$$-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 View Details

A rectangular 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 View Details

A company produces two products, A and B. The profit from product A is 10 per unit, and the profit from product B is15 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 View Details

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 View Details

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 View Details

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

A. 0

B. π/2

Correct C. π

D. 3π/2

Correct Answer: C

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Question 17 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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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