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POST UTME AFE BABALOLA UNIVERSITY 2023 Mathematics | Objective

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Question 1 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 2 View Details

Solve the matrix equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}\).

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

B. \(x = 2\), \(y = 3\)

C. \(x = 3\), \(y = 4\)

D. \(x = 4\), \(y = 5\)

Correct Answer: A

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Question 3 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}\).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 4 View Details

A car travels from city A to city B at an average speed of 60 \(km/h\). If the distance between the two cities is 240 km, how long does the journey take?

A. 4 hours

Correct B. 5 hours

C. 6 hours

D. 7 hours

Correct Answer: B

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Question 5 View Details

A bakery sells 250 loaves of bread per day. If each loaf \costs ₦120, how much money does the bakery make in a day?

A. ₦30,000

B. ₦30,500

Correct C. ₦31,000

D. ₦31,500

Correct Answer: C

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Question 6 View Details

In a geometric sequence with first term (a) and common ratio (r), find the sum of the first 5 terms if \(a = 2\) and \(r = 3\).

Correct A. 2\(3^5 - 1\)/\(3 - 1\)

B. 2\(3^5 - 1\)/\(3 + 1\)

C. 2\(3^5 + 1\)/\(3 - 1\)

D. 2\(3^5 + 1\)/\(3 + 1\)

Correct Answer: A

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Question 7 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. -\(\frac{1}{x^2 + 1\) ^2}\)\)

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

Correct Answer: A

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Question 8 View Details

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

Correct A. 30

B. 50

C. 60

D. 70

Correct Answer: A

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Question 9 View Details

Solve the system of equations using matrices: \begin{align*} x + y &= 4 \ 2x - y &= 3 \end{align*}

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 10 View Details

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is drawn at random, what is the probability that it is blue?

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

B. \(\frac{1}{10}\)\)

Correct C. \(\frac{3}{10}\)\)

D. \(\frac{3}{5}\)\)

Correct Answer: C

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Question 11 View Details

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 12 View Details

Solve for x in the equation \(\frac{x}{2} + 3 = 7\).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 13 View Details

Find the sum of the first 5 terms of the geometric sequence 2, 6, 18, ...

A. 62

B. 64

Correct C. 66

D. 68

Correct Answer: C

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Question 14 View Details

In the matrix \(egin{bmatrix} 2 & 4 \ 6 & 8 \end{bmatrix}\), find the determinant.

Correct A. -20

B. -16

C. -12

D. -8

Correct Answer: A

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Question 15 View Details

Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\).

Correct A. \(x =\)\(\frac{\pi}{4}\)\)

B. \(x =\)\(\frac{\pi}{2}\)\)

C. \(x =\)\(\frac{3\pi}{4}\)\)

D. \(x =\)\(\frac{5\pi}{4}\)\)

Correct Answer: A

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Question 16 View Details

Find the equation of the line passing through the points (2,3) and (4,5) in the form \(y = mx + c\), where m is the slope and c is the y-intercept.

A. \(y = 1x + 1\)

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

C. \(y = 3x + 2\)

D. \(y = 4x - 3\)

Correct Answer: B

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Question 17 View Details

Solve the system of equations using matrices: \nbegin{align*} \n 2x + 3y &= 7 \n 4x - 2y &= -3 \nend{align*}

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

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

C. \(x = 3\), \(y = 4\)

D. \(x = 4\), \(y = 3\)

Correct Answer: A

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Question 18 View Details

Find the area under the curve \(y = x\^2 + 2x - 3\) from \(x = 0\) to \(x = 3\) using integration.

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 19 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 will be between 50 and 70?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 20 View Details

Find the equation of the circle with center (2,3) and radius 4 in the form \(x - h\)^2 + \(y - k\)^\(2 = r\^2\).

Correct A. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\)

B. \(x - 3\)^2 + \(y - 2\)^\(2 = 16\)

C. \(x - 4\)^2 + \(y - 3\)^\(2 = 16\)

D. \(x - 2\)^2 + \(y - 4\)^\(2 = 16\)

Correct Answer: A

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