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POST UTME PAN-ATLANTIC UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details

Find the area under the curve of ( f(x) = $\frac{1}{x^2}$\)\) ) from $x = 1$ to $x = 2$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 2 View Details

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

Correct A. $-∞, -1$ ∪ (3, ∞)

B. $-∞, 1$ ∪ (3, ∞)

C. $-∞, -1$ ∪ (1, 3)

D. $-∞, 1$ ∪ (3, ∞)

Correct Answer: A

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Question 3 View Details

Find the derivative of ( f(x) = $x^3 - 2x^2 + 3x - 1$ ) using the power rule.

Correct A. $3x^2 - 4x + 3$

B. $3x^2 - 2x + 1$

C. $2x^2 - 4x + 3$

D. $x^2 - 2x + 1$

Correct Answer: A

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Question 4 View Details

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

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 5 View Details

A set of numbers is defined as $S = \{x | x^2 - 4x + 3 = 0 \} \$. Find the elements of S.

Correct A. \{1, 3\}

B. \{-1, 3\}

C. \{1, -3\}

D. \{-1, -3\}

Correct Answer: A

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Question 6 View Details

Find the value of k such that the equation $x^2 + kx + 16 = 0$ has equal roots.

A. 8

Correct B. -8

C. 4

D. -4

Correct Answer: B

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Question 7 View Details

A histogram is constructed from the following data: 2, 4, 5, 7, 8, 9, 10. What is the class width of the histogram?

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 8 View Details

Find the equation of the circle with center $-2, 3$ and radius 4.

Correct A. \left$x + 2 \right$^2 + \left$y - 3 \right$^$2 = 16$

B. \left$x - 2 \right$^2 + \left$y + 3 \right$^$2 = 16$

C. \left$x + 2 \right$^2 + \left$y + 3 \right$^$2 = 16$

D. \left$x - 2 \right$^2 + \left$y - 3 \right$^$2 = 16$

Correct Answer: A

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Question 9 View Details

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

Correct A. \left$-\infty, -1 \right$ \cup \left$3, \infty \right$

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

C. \left$-\infty, -1 \right$ \cup \left$1, \infty \right$

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

Correct Answer: A

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Question 10 View Details

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

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 11 View Details

A set of 10 numbers has a mean of 20 and a standard deviation of 5. If a new number is added to the set, the mean increases by 2. What is the value of the new number?

A. 42

B. 45

Correct C. 48

D. 50

Correct Answer: C

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Question 12 View Details

Solve the equation $\frac{\sqrt{3}}{2} $1\left \frac{\pi}{6} \right$ + $\frac{1}{2}$\) \cos \left$\frac{\pi}{6} \right$ = $\frac{1}{2}$\)\)

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

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

C. $\frac{\pi}{4}$\)

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

Correct Answer: A

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Question 13 View Details

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

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

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

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

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

Correct Answer: B

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Question 14 View Details

A sequence is defined by (a_$n =$$\frac{1}{\(n^2}$\)\) for \$(a_n = frac{1}{n^2}\(n = 1, 2, 3, \ldots$. Find the sum of the first 10 terms of the sequence.

A. $\frac{1}{90}$\)

B. $\frac{1}{80}$\)

C. $\frac{1}{70}$\)

Correct D. $\frac{1}{60}$\)

Correct Answer: D

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Question 15 View Details

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

Correct A. 0.3413

B. 0.3415

C. 0.3417

D. 0.3419

Correct Answer: A

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Question 16 View Details

Find the area under the curve of ( f(x) = $2x^2 + 3x - 1$ ) from $x = 0$ to $x = 2$.

A. 10

B. 12

Correct C. 15

D. 18

Correct Answer: C

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Question 17 View Details

Solve the system of equations using matrices: $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix}$.

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ 3 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 5 \end{bmatrix}

Correct Answer: A

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Question 18 View Details

Find the mean and standard deviation of the data set: 2, 4, 6, 8, 10.

Correct A. \text{Mean}$= 6$, \text{Standard Deviation}$= 2$

B. \text{Mean}$= 5$, \text{Standard Deviation}$= 1$

C. \text{Mean}$= 4$, \text{Standard Deviation}$= 3$

D. \text{Mean}$= 3$, \text{Standard Deviation}$= 4$

Correct Answer: A

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Question 19 View Details

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

Correct A. \begin{bmatrix} -2 \ 2 \end{bmatrix}

B. \begin{bmatrix} -1 \ 1 \end{bmatrix}

C. \begin{bmatrix} 1 \ -1 \end{bmatrix}

D. \begin{bmatrix} 2 \ -2 \end{bmatrix}

Correct Answer: A

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Question 20 View Details

Find the area of the triangle with vertices (0, 0), (2, 0), and (0, 3).

A. 3

B. 6

Correct C. 9

D. 12

Correct Answer: C

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Question 21 View Details

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. 5 cm

Correct B. 7.5 cm

C. 10 cm

D. 12.5 cm

Correct Answer: B

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Question 22 View Details

A set of 10 consecutive integers has a median of 12. Find the sum of the integers.

A. 120

B. 150

Correct C. 180

D. 210

Correct Answer: C

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Question 23 View Details

A circle has a radius of 4 cm. Find the area of the circle.

A. 50.24 $cm^2$

B. 100.48 $cm^2$

C. 200.96 $cm^2$

Correct D. 314.16 $cm^2$

Correct Answer: D

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Question 24 View Details

A sequence is defined as: 1, 2, 4, 8, ... . Find the next term in the sequence.

A. 16

B. 32

C. 64

Correct D. 128

Correct Answer: D

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Question 25 View Details

A histogram shows the distribution of exam scores for a class of 20 students. The histogram has 5 bars, each representing a different score range. The heights of the bars are 2, 4, 5, 6, and 3, respectively. Find the mean score of the class.

A. 5.5

B. 6.5

Correct C. 7.5

D. 8.5

Correct Answer: C

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