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POST UTME MADONNA UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details

Find the value of x in the equation $2^x + 5^x = 3^x$.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 2 View Details

Solve for y in the equation $y = \frac{1}{2} \log_{10} x^2 \$ ).

A. \log_{10} (x)

Correct B. $\frac{1}{2}$\) \log_{10} (x)

C. \log_{10} $x^2$

D. 2 \log_{10} (x)

Correct Answer: B

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Question 3 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 4 View Details

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

Correct A. $x < -1$ or $x > \frac{3}{2}$

B. $x < -\frac{3}{2}$ or $x > 1$

C. $x < -\frac{1}{2}$ or $x > 3$

D. $x < 1$ or $x > -\frac{3}{2}$

Correct Answer: A

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Question 5 View Details

Find the value of x in the equation $$12x \$ = $\frac{1}{2}$\) ).

Correct A. $x = \frac{\pi}{6}$

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

C. $x = \frac{\pi}{3}$

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

Correct Answer: A

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Question 6 View Details

Determine the mean of the following dataset: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

A. 5

Correct B. 6

C. 7

D. 10

Correct Answer: B

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Question 7 View Details

A histogram is a graphical representation of a dataset. What is the primary purpose of a histogram?

Correct A. To show the distribution of data

B. To calculate the mean of a dataset

C. To determine the median of a dataset

D. To create a scatter plot

Correct Answer: A

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Question 8 View Details

Given the vectors α = ¯(1, 2) and β = ¯(3, 4), find the magnitude of the vector α + β.

A. $√10$

B. $√14$

Correct C. $√18$

D. $√22$

Correct Answer: C

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Question 9 View Details

Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?

A. 0.2

Correct B. 0.4

C. 0.6

D. 0.8

Correct Answer: B

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Question 10 View Details

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

A. 16

B. 32

Correct C. 64

D. 128

Correct Answer: C

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Question 11 View Details

Find the area under the curve $y = \frac{1}{2}x^2 + 3x - 2$ from $x = 0$ to $x = 4$.

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 12 View Details

Solve the equation $$1x = \frac{1}{3} \$ for ( x ) in the interval $\left[ \frac{\pi}{2}, \frac{5\pi}{2} \right]$.

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

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

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

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

Correct Answer: D

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Question 13 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 14 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$x - 3 \right$^2 + \left$y - 2 \right$^$2 = 16$

C. \left$x - 4 \right$^2 + \left$y - 3 \right$^$2 = 16$

D. \left$x - 2 \right$^2 + \left$y - 4 \right$^$2 = 16$

Correct Answer: A

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Question 15 View Details

Solve the system of equations using matrices:

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

B. \begin{bmatrix} 2 \ 1 \end{bmatrix}

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

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

Correct Answer: A

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Question 16 View Details

Determine the sum of the infinite geometric series - 3 + 6 + 12 + …, where the first term is - 3 and the common ratio is 2.

Correct A. 9

B. -3

C. -9

D. 27

Correct Answer: A

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Question 17 View Details

A solid cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone.

A. 256\pi

B. 512\pi

Correct C. 1024\pi

D. 2048\pi

Correct Answer: C

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Question 18 View Details

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

Correct A. 6x + 2

B. $6x^2 + 2x - 5$

C. 6x + 2x - 5

D. $6x^2 + 2$

Correct Answer: A

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Question 19 View Details

Solve the system of linear equations using the method of substitution: $2x + 3y = 7$ and x - 2y = -3.

Correct A. $x = 2$, $y = 1$

B. $x = 1$, $y = 2$

C. $x = -1$, $y = 2$

D. $x = 2$,$y = -1$

Correct Answer: A

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Question 20 View Details

A vector ℓ has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x and y components of the vector.

Correct A. $x = 4$, $y = 3$

B. $x = 3$, $y = 4$

C. $x = 4$,$y = -3$

D. $x = -3$, $y = 4$

Correct Answer: A

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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.

Correct A. 5 cm

B. 10 cm

C. 15 cm

D. 20 cm

Correct Answer: A

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Question 22 View Details

A vector \overrightarrow{a} has a magnitude of 6 units and makes an angle of 60° with the positive x-axis. Find the x and y components of the vector.

Correct A. $x = 3$, $y = 3$$\sqrt{3}$

B. $x = 3$, $y = 3$

C. $x = 6$, $y = 6$

D. $x = 6$, $y = 6$$\sqrt{3}$

Correct Answer: A

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Question 23 View Details

A histogram is shown below. Find the mean of the data.

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 24 View Details

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

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 25 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

A. 15

Correct B. 30

C. 45

D. 60

Correct Answer: B

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