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POST UTME PAN-ATLANTIC UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

Determine the value of x in the equation $\frac{x}{2} + 5 = 11$.

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 2 View Details

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 View Details

A cylindrical \tank has a height of 10m and a radius of 4m. If the \tank is filled with water to a height of 6m, calculate the volume of water in the \tank.

A. 480π

Correct B. 600π

C. 720π

D. 960π

Correct Answer: B

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Question 4 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?

Correct A. 200

B. 250

C. 300

D. 350

Correct Answer: A

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Question 5 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 of the car for the entire trip?

A. 48 $km/h$

B. 50 $km/h$

Correct C. 52 $km/h$

D. 54 $km/h$

Correct Answer: C

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Question 6 View Details

Find the value of x in the equation $\frac{x}{2} + \frac{3}{4} = \frac{7}{8}$.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 7 View Details

Solve for y in the equation $y^2 - 6y + 8 = 0$.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 8 View Details

A circle with center (0, 0) and radius 4 passes through the point (12, 16). Find the equation of the circle.

Correct A. $x^2 + y^2 = 16$

B. $x^2 + y^2 = 64$

C. $x^2 + y^2 = 32$

D. $x^2 + y^2 = 48$

Correct Answer: A

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Question 9 View Details

A sequence is defined by the formula $a_n = 2n + 1$. 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 10 View Details

A set A has 5 elements and a set B has 3 elements. Find the number of elements in the union of sets A and B.

A. 6

Correct B. 7

C. 8

D. 9

Correct Answer: B

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Question 11 View Details

In a survey of 50 students, the heights of the students were recorded in centimeters. The mean height was 170 cm, and the standard deviation was 5 cm. If the heights of the students were normally distributed, what is the probability that a randomly selected student has a height between 165 cm and 175 cm?

Correct A. 0.9772

B. 0.6827

C. 0.3413

D. 0.1587

Correct Answer: A

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Question 12 View Details

Solve the inequality $\frac{x^2-4x-3}{x$^2-6x+8}\)\$) > 0.$

Correct A. \left$-\infty, 3 \right$ \cup \left$4, \infty \right$

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

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

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

Correct Answer: A

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Question 13 View Details

A rectangular box has a length of 6 cm, a width of 4 cm, and a height of 2 cm. What is the volume of the box in cubic centimeters?

Correct A. 48

B. 64

C. 72

D. 96

Correct Answer: A

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Question 14 View Details

A circle has a radius of 4 cm. What is the area of the circle in square centimeters?

A. 50.24

B. 100.48

C. 200.96

Correct D. 314.16

Correct Answer: D

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Question 15 View Details

A right triangle has a hypotenuse of 10 cm and one leg of 6 cm. What is the length of the other leg in centimeters?

Correct A. 8

B. 6

C. 4

D. 2

Correct Answer: A

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Question 16 View Details

Find the area under the curve $y = \frac{1}{2}x^2$ from $x = 0$ to $x = 4$.

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

B. ( 8 )

C. ( 4 )

D. ( 2 )

Correct Answer: A

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Question 17 View Details

Solve for ( x ) in the equation $\log_{10} x^2 \$$= 4 ).$

A. $x = 10^2$

Correct B. $x = 10^4$

C. $x = 10^{-2}$

D. $x = 10^{-4}$

Correct Answer: B

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Question 18 View Details

Find the value of $\(12\theta \$ ) given that 1\theta \\) = $\frac{3}{5}$\) ) and $$1\theta \$ = $\frac{4}{5}$\) ).

Correct A. $\frac{24}{25}$

B. $\frac{16}{25}$

C. $\frac{12}{25}$

D. $\frac{8}{25}$

Correct Answer: A

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Question 19 View Details

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

A. $\frac{1}{6}$

B. $\frac{1}{3}$

C. $\frac{2}{3}$

Correct D. $\frac{5}{6}$

Correct Answer: D

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Question 20 View Details

Find the vector ( mathbf{v} ) that satisfies the equation $\mathbf{v} \cdot \mathbf{i} = 3$ and $\mathbf{v} \cdot \mathbf{j} = 4$.

Correct A. $\mathbf{v} = 3\mathbf{i} + 4\mathbf{j}$

B. $\mathbf{v} = 4\mathbf{i} + 3\mathbf{j}$

C. $\mathbf{v} = 3\mathbf{i} - 4\mathbf{j}$

D. $\mathbf{v} = 4\mathbf{i} - 3\mathbf{j}$

Correct Answer: A

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Question 21 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pi $cm^3$

Correct B. 48\pi $cm^3$

C. 96\pi $cm^3$

D. 192\pi $cm^3$

Correct Answer: B

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Question 22 View Details

Solve for x in the equation $$1x = \frac{1}{\sqrt{3}}$.

Correct A. $\frac{\pi}{6}$\)

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

C. $\frac{\pi}{2}$\)

D. $\frac{5\pi}{6}$\)

Correct Answer: A

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Question 23 View Details

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

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

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

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

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

Correct Answer: B

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Question 24 View Details

Evaluate the definite integral $\int_0^1 x^2 dx$.

A. $\frac{1}{3}$\)

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

Correct C. 1

D. $\frac{2}{3}$\)

Correct Answer: C

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Question 25 View Details

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

Correct A. \boxed{-2}

B. \boxed{-1}

C. \boxed{2}

D. \boxed{1}

Correct Answer: A

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