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POST UTME UNN 2022 Mathematics | Objective

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Question 1 View Details

Solve for x in the quadratic equation $x^2 + 5x + 6 = 0$.

A. $x = -2 \$

Correct B. $x = -3 \$

C. $x = 2 \$

D. $x = 3 \$

Correct Answer: B

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Question 2 View Details

A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:4, how many loaves of whole wheat bread are sold per day?

A. 120

B. 150

Correct C. 180

D. 200

Correct Answer: C

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Question 3 View Details

Find the determinant of the 3x3 matrix $\begin{bmatrix} 2 & 3 & 1 \\ 4 & 2 & 3 \\ 1 & 1 & 2 \end{bmatrix} \$.

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 4 View Details

A box contains 12 red balls and 8 blue balls. If 2 balls are drawn at random, what is the probability that both balls are blue?

A. $\frac{1}{5}$\)

Correct B. $\frac{1}{10}$\)

C. $\frac{1}{15}$\)

D. $\frac{1}{20}$\)

Correct Answer: B

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Question 5 View Details

Solve for x in the linear equation $2x + 5 = 11 \$.

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 6 View Details

Let ( f(x) = $\frac{x^2 - 4}{x - 2}$\)\) ). Find the derivative of ( f(x) ) using the chain rule.

A. 2x + 4

B. $x^2 + 4$

C. $x^2 - 4$

Correct D. $x^2 + 2x - 4$

Correct Answer: D

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Question 7 View Details

A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that both balls are blue?

A. $1/14$

Correct B. $1/7$

C. $1/2$

D. $3/7$

Correct Answer: B

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Question 8 View Details

Solve the equation $2^x + 2^y = 2^{x+y}$ for ( x ) and ( y ).

Correct A. $x = y$

B. $x = -y$

C. $x + y = 0$

D. $x - y = 0$

Correct Answer: A

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Question 9 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 10 View Details

A car travels from city A to city B at an average speed of 60 $(km/h$\). On the return trip, the car travels at an average speed of 40 $km/h\\((km/h). On the return trip, the car travels at an average speed of 40$. What is the average speed for the entire trip?

A. 45 $km/h$

B. 50 $km/h$

Correct C. 55 $km/h$

D. 60 $km/h$

Correct Answer: C

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Question 11 View Details

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. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 12 View Details

Solve the inequality $\frac{x^2 - 4}{x^2 - 9}$\)\$) > 0.$

Correct A. x < -3 or $x > 3$

B. -$3 < x$$< 3$

C. x < -3 or $x > 0$

D. $x > 0$

Correct Answer: A

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Question 13 View Details

Find the equation of the circle passing through the points (2, 3), (4, 5), and $-1, 2$.

Correct A. $x - 1$^2 + $y - 2$^$2 = 4$

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

C. $x + 1$^2 + $y - 2$^$2 = 4$

D. $x - 1$^2 + $y + 2$^$2 = 4$

Correct Answer: A

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Question 14 View Details

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

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

B. $\frac{2x}{x^2 + 1$ ^2}\)\)

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

D. $\frac{x}{x^2 + 1$ ^2}\)\)

Correct Answer: A

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Question 15 View Details

Solve the system of equations $x^2$ + \$(y^2$$= 4$\) and $x + y = 2$.

Correct A. $x = 1$, $y = 1$

B. $x = 2$, $y = 0$

C. $x = 0$, $y = 2$

D. $x = 1$, $y = 0$

Correct Answer: A

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Question 16 View Details

Determine the value of (x\) in the equation $\\((x) in the equation \begin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix} = 0$.

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 17 View Details

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

Correct A. 1.55

B. 1.65

C. 1.75

D. 1.85

Correct Answer: A

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Question 18 View Details

Solve the inequality $\frac{x-2}{x+1} > 0$.

Correct A. $-\infty, -1$ \cup $2, \infty$

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

C. $-\infty, 1$ \cup $2, \infty$

D. $-\infty, 1$ \cup $2, \infty$

Correct Answer: A

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Question 19 View Details

A histogram represents the distribution of exam scores. If the mean score is 60 and the standard deviation is 10, what is the probability that a randomly selected score is between 50 and 70?

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 20 View Details

In the diagram below, what is the value of $x$?

A. 30

B. 60

Correct C. 90

D. 120

Correct Answer: C

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Question 21 View Details

A random sample of 25 students from a university had a mean height of 175.5 cm with a standard deviation of 5.2 cm. Calculate the coefficient of variation (CV) of the sample.

A. 12.5%

Correct B. 15%

C. 18%

D. 20%

Correct Answer: B

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Question 22 View Details

If $\vec{a} = \begin{pmatrix} 2 \ 3 \end{pmatrix}$ and $\vec{b} = \begin{pmatrix} 4 \ 5 \end{pmatrix}$, find the magnitude of the cross product $\vec{a} \times \vec{b}$.

A. 10

B. 12

Correct C. 15

D. 20

Correct Answer: C

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Question 23 View Details

Solve the equation $x^2 + 4x + 4 = 0$ using the quadratic formula.

A. 0

Correct B. -2

C. -1

D. 1

Correct Answer: B

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Question 24 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. $1/3$

B. $1/2$

Correct C. $2/3$

D. 1

Correct Answer: C

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Question 25 View Details

Find the derivative of the function $f(x) = 3x^2 + 2x - 5$ using the power rule.

Correct A. 6x + 2

B. 3x + 2

C. 2x + 5

D. $x^2 + 2$

Correct Answer: A

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