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Subject

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POST UTME UNIOSUN 2022 Mathematics | Objective

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Question 1 View Details

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

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 2 View Details

A survey of 100 students found that 60 students preferred Mathematics, 30 preferred Science, and 10 preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?

A. 0.7

Correct B. 0.75

C. 0.8

D. 0.85

Correct Answer: B

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Question 3 View Details

The volume of a rectangular prism is given by $V = lwh$. If the length, width, and height of the prism are in the ratio 2:3:4, and the volume is 288 cubic units, find the length of the prism.

A. 6

Correct B. 8

C. 12

D. 16

Correct Answer: B

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Question 4 View Details

Solve the inequality $x^2 - 6x + 8 > 0$.

Correct A. $-∞, 2$ ∪ (4, ∞)

B. $-∞, 2$ ∪ (4, ∞)

C. $-∞, 2$ ∪ (4, ∞)

D. $-∞, 2$ ∪ (4, ∞)

Correct Answer: A

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Question 5 View Details

A company produces two products, A and B. The profit from the sale of one unit of product A is ₦100, and the profit from the sale of one unit of product B is ₦120. If the company produces 200 units of product A and 150 units of product B, what is the total profit?

A. ₦35,000

B. ₦40,000

C. ₦45,000

Correct D. ₦50,000

Correct Answer: D

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Question 6 View Details

In a set of consecutive integers, the sum of the first 5 terms is 15, and the sum of the next 5 terms is 25. What is the sum of the first 10 terms?

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 7 View Details

A sequence is defined by the recurrence relation $a_n = 2a_{n-1} + 3$, with initial term $a_1 = 2$. Find the sum of the first 5 terms of the sequence.

A. 35

B. 40

C. 45

Correct D. 50

Correct Answer: D

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Question 8 View Details

A histogram is constructed with 5 classes, each of width 2. The heights of the bars are 3, 5, 7, 9, and 11. What is the mean of the data?

A. 6

B. 7

Correct C. 8

D. 9

Correct Answer: C

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Question 9 View Details

A circle has equation $(x^2 + y^2$ = 16\). Find the equation of the \tangent line at point \$(x^2 + y^2 = 16). Find the equation of the \((4, 0)$.

Correct A. $y = -x + 4$

B. $y = x + 4$

C. $y = -x - 4$

D. $y = x - 4$

Correct Answer: A

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Question 10 View Details

Two events are independent if the occurrence of one does not affect the probability of the other. If event A has probability 0.4 and event B has probability 0.6, are events A and B independent?

A. Yes

B. No

C. Maybe

Correct D. Not enough information

Correct Answer: D

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Question 11 View Details

In a circle with center $C$ and radius $5$, a chord (AB\) is drawn such that $AC = 3\\((AB) is drawn such that$. Find the length of $AB$.

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 12 View Details

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

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 13 View Details

A function (f(x)\) is defined as $f(x) = \\((f(x)) is defined as \frac{x^2 - 4}{x - 2}$. Find the domain of $f(x)$.

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

B. $-\infty, 2$ \cup (2, 4]

C. $-\infty, 2$ \cup $4, \infty$

D. $-\infty, 4] \cup 4, \infty \$

Correct Answer: A

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Question 14 View Details

In a triangle $ABC$, $AB = 5$\), $BC = 6$, and \angle (B = 60\)^\circ. Find the length of \$(B = 60)^\(AC$.

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 15 View Details

A circle with center $O$ and radius $3$ is inscribed in a square with side length $6$. Find the area of the shaded region.

A. 12

Correct B. 18

C. 24

D. 36

Correct Answer: B

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Question 16 View Details

Find the derivative of ( f(x) = $\frac{1}${$\sqrt{x}$}\) ) using the chain rule.

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

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

C. ( f'$(x) = -$$\frac{1}{2}$\$)x^{-$$\frac{1}{2}$\)} )

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

Correct Answer: A

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Question 17 View Details

Solve for ( x ) in the equation $\sin^2 x \$ + \$\cos^2(x)$$= 1 ).$

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

B. $x = \frac{3\pi}{4}$

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

D. $x = \frac{5\pi}{4}$

Correct Answer: A

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Question 18 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. $\frac{32\pi}{3}$

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

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

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

Correct Answer: A

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Question 19 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 + $y-3$^$2 = 4$ )

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

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

Correct Answer: A

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Question 20 View Details

Find the area under the curve $y = x^2$ from $x = 0$ to $x = 4$.

Correct A. $\frac{64}{3}$

B. $\frac{128}{3}$

C. $\frac{256}{3}$

D. $\frac{512}{3}$

Correct Answer: A

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Question 21 View Details

Determine the value of x in the equation $\sin^2 x \$ + \$\cos^2(x)$ = 1 ) if $$1x \$$= 3 ).$

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

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

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

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

Correct Answer: A

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Question 22 View Details

Find the derivative of the function ( f(x) = $\frac{1}{x^2 + 1}$\)\) ) using 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 23 View Details

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

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 24 View Details

Determine the value of x in the equation $\log_{10} x \$$= 2 ).$

Correct A. $x = 100$

B. $x = 10$

C. $x = 1$

D. $x = 0.1$

Correct Answer: A

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Question 25 View Details

Find the mean of the data set {2, 4, 6, 8, 10}.

Correct A. $\frac{30}{5} = 6$

B. $\frac{20}{5} = 4$

C. $\frac{10}{5} = 2$

D. $\frac{40}{5} = 8$

Correct Answer: A

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