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POST UTME KSU 2022 Mathematics | Objective

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Question 1 View Details

Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using the quadratic formula. What is the value of ( x )?

Correct A. -2

B. -3

C. 2

D. 3

Correct Answer: A

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Question 2 View Details

A circle has a radius of 4 cm. If the center of the circle is at the point (2, 3), what is the equation of the circle in standard form?

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 3 View Details

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

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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Question 4 View Details

A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, with the first bar representing scores 0-10, the second bar representing scores 11-20, and so on. If the mean score is 25, what is the median score?

A. 20

Correct B. 25

C. 30

D. 35

Correct Answer: B

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Question 5 View Details

Find the equation of the line passing through the points (2, 3) and (4, 5).

Correct A. \(y = 2x - 1\)

B. \(y = 2x + 1\)

C. \(y = -2x + 1\)

D. \(y = -2x - 1\)

Correct Answer: A

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Question 6 View Details

A rectangular prism has a length of 10 cm, a width of 8 cm, and a height of 6 cm. Find the volume of the prism in cubic centimeters.

Correct A. 480

B. 640

C. 800

D. 960

Correct Answer: A

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Question 7 View Details

Solve for x in the equation: \(2x^2 + 5x - 3 = 0\)

Correct A. \(1/2\)

B. \(-1/2\)

C. \(3/2\)

D. \(-3/2\)

Correct Answer: A

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Question 8 View Details

A set of 5 consecutive integers has a median of 10. What is the sum of the integers?

A. 50

B. 60

Correct C. 70

D. 80

Correct Answer: C

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Question 9 View Details

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?

Correct A. ₦1250

B. ₦12500

C. ₦125000

D. ₦1250000

Correct Answer: A

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Question 10 View Details

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

A. \(1/2\)

B. \(1/3\)

Correct C. \(2/3\)

D. \(1/6\)

Correct Answer: C

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Question 11 View Details

A random variable X has a probability distribution given by P\(X = x\) = \(1/2\)^x for \(x = 0\), 1, 2, ... . Find the probability that X is greater than 2.

Correct A. \(1/4\)

B. \(1/2\)

C. \(3/4\)

D. 1

Correct Answer: A

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Question 12 View Details

The volume of a sphere (V) varies with its radius (r) as \(V = 4/3\)π\(r^3\). If the radius of a sphere is increased from 2 cm to 4 cm, calculate the percentage increase in its volume.

A. 100%

B. 200%

Correct C. 300%

D. 400%

Correct Answer: C

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Question 13 View Details

In a set of 8 distinct integers, 3 are odd and 5 are even. If 2 integers are randomly selected, what is the probability that the product of the two integers is even?

A. \(1/2\)

Correct B. \(2/3\)

C. \(3/4\)

D. \(4/5\)

Correct Answer: B

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Question 14 View Details

The sum of the first n terms of an arithmetic progression (AP) is given by \(Sn = n/2\)\) [2a + \(n-1\) d], where a is the first term and d is the common difference. If the sum of the first 10 terms of an AP is 110, and the first term is 2, find the common difference.

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 15 View Details

A curve is defined by the equation (y = x\^2 + 2x - 3\). Find the equation of the \\((y = x^2 + 2x - 3\tangent to the curve at the point where \(x = 1\).

Correct A. \(y = 2x - 1\)

B. \(y = 2x + 1\)

C. \(y = x - 1\)

D. \(y = x + 1\)

Correct Answer: A

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Question 16 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. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 17 View Details

Solve the matrix equation (AX = B\), where A = \begin{bmatrix} 1 & 2 \\\(((AX = B)\), where A = \\ 3 & 4 \end{bmatrix},\(X =\)\begin{bmatrix} x \\ y \end{bmatrix}, and B = \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 area under the curve \(y = x\^3\) from \(x = 0\) to \(x = 2\).

A. 8

Correct B. 16

C. 32

D. 64

Correct Answer: B

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Question 19 View Details

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 20 View Details

Find the surface area 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 21 View Details

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 22 View Details

A set A contains 5 elements. If 3 elements are randomly selected from set A, what is the probability that the selected elements are all distinct?

A. \(1/10\)

B. \(1/5\)

Correct C. \(3/10\)

D. \(1/2\)

Correct Answer: C

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Question 23 View Details

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

A. -2x/\(x^2 + 1\)^2

Correct B. 2x/\(x^2 + 1\)^2

C. -2/\(x^2 + 1\)^2

D. 2/\(x^2 + 1\)^2

Correct Answer: B

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Question 24 View Details

A sequence is defined by the recurrence relation \(a_n = 2a_{n-1} + 1\) with initial term \(a_1 = 3\). Find the value of \(a_{10}\).

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 25 View Details

A histogram is constructed with 5 classes of equal width. The first class has a frequency of 10, the second class has a frequency of 15, the third class has a frequency of 20, the fourth class has a frequency of 25, and the fifth class has a frequency of 30. What is the mean of the histogram?

A. 20

B. 22

Correct C. 24

D. 26

Correct Answer: C

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