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POST UTME ABU 2024 Mathematics | Objective

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Question 1 View Details

Determine the value of \(\log_{10} \left \frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}} \right\)\).

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 2 View Details

A survey of 100 students found that 60 students preferred Mathematics, 30 preferred Science, and 10 preferred both. What is the probability that a randomly selected student prefers Mathematics or Science?

Correct A. 0.7

B. 0.8

C. 0.9

D. 1.0

Correct Answer: A

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Question 3 View Details

Solve for \(x\): \(\sqrt{2x + 5} - 3 = 2\).

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 4 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 5 View Details

A water tank can hold 1000 liters of water. If 300 liters of water are already in the \tank, what \fraction of the \\(tank can hold 1000 liters of water. If 300 liters of water are already in the tank, what \tank is still empty?

A. \(\frac{1}{4}\)\)

B. \(\frac{1}{3}\)\)

C. \(\frac{2}{3}\)\)

Correct D. \(\frac{3}{4}\)\)

Correct Answer: D

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Question 6 View Details

Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.

A. 64π cm³

Correct B. 128π cm³

C. 256π cm³

D. 512π cm³

Correct Answer: B

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Question 7 View Details

Determine the number of elements in the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} if the elements are selected such that the sum of the elements is 25.

A. 10

Correct B. 9

C. 8

D. 7

Correct Answer: B

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Question 8 View Details

Find the sum of the first 10 terms of the geometric progression 3, 6, 12, 24, ...

A. 1230

B. 1240

Correct C. 1250

D. 1260

Correct Answer: C

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Question 9 View Details

Solve for x in the equation \(2x + 5 = 11\).

Correct A. 3

B. 4

C. 5

D. 6

Correct Answer: A

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Question 10 View Details

A histogram of exam scores has a mean of 60 and a standard deviation of 10. What is the probability that a randomly selected score is 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 11 View Details

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

A. \(\frac{1}{2} \left[ \frac{x^3}{3} + \frac{3x^2}{2} - 2x \right]\)

Correct B. \(\frac{1}{2} \left[ \frac{4^3}{3} + \frac{3 \cdot 4^2}{2} - 2 \cdot 4 \right] - \frac{1}{2} \left[ \frac{1^3}{3} + \frac{3 \cdot 1^2}{2} - 2 \cdot 1 \right]\)

C. \(\frac{1}{2} \left[ \frac{4^3}{3} + \frac{3 \cdot 4^2}{2} - 2 \cdot 4 \right]\)

D. \(\frac{1}{2} \left[ \frac{1^3}{3} + \frac{3 \cdot 1^2}{2} - 2 \cdot 1 \right]\)

Correct Answer: B

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Question 12 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. 0.8413

Correct B. 0.6827

C. 0.6915

D. 0.9772

Correct Answer: B

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Question 13 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 - 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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Question 14 View Details

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

Correct A. ( f'\((x) =\)\(\frac{-2x}{x^2 + 1\) ^2}\)\) )

B. ( f'\((x) =\)\(\frac{2x}{x^2 + 1\) ^2}\)\) )

C. ( f'\((x) =\)\(\frac{2}{x^2 + 1\) ^2}\)\) )

D. ( f'\((x) =\)\(\frac{-2}{x^2 + 1\) ^2}\)\) )

Correct Answer: A

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Question 15 View Details

Find the vector ( mathbf{v} ) that is orthogonal to both \(\mathbf{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}\).

Correct A. \(\mathbf{v} = egin{pmatrix} -10 \ 15 \ -6 \end{pmatrix}\)

B. \(\mathbf{v} = egin{pmatrix} 10 \ -15 \ 6 \end{pmatrix}\)

C. \(\mathbf{v} = egin{pmatrix} -15 \ 10 \ 6 \end{pmatrix}\)

D. \(\mathbf{v} = egin{pmatrix} 15 \ -10 \ -6 \end{pmatrix}\)

Correct Answer: A

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Question 16 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 17 View Details

Solve for x in the equation: \(\sin^2 x \\) + \\(\cos^2(x)\)\(= 1 ).\)

A. 0

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

Correct C. \(\frac{\pi}{4}\)\)

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

Correct Answer: C

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Question 18 View Details

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, what is their total daily profit?

A. ₦1,250

B. ₦1,500

Correct C. ₦1,750

D. ₦2,000

Correct Answer: C

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Question 19 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. 8 hours

Correct Answer: B

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Question 20 View Details

A company has 500 employees, out of which 30% are engineers. How many engineers are there in the company?

A. 150

B. 200

Correct C. 250

D. 300

Correct Answer: C

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Question 21 View Details

Find the equation of the circle with center at ((2,3)) and passing through the point ((6,5)).

A. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 5\^2\) )

B. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 7\^2\) )

Correct C. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 9\^2\) )

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 11\^2\) )

Correct Answer: C

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Question 22 View Details

Solve for (x) in the equation \(2^x + 3^x = 5^x\).

Correct A. \(x = 1\)

B. \(x = 2\)

C. \(x = 3\)

D. \(x = 4\)

Correct Answer: A

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Question 23 View Details

Find the sum of the first 10 terms of the geometric series with first term \(a = 2\) and common ratio \(r = 3\).

Correct A. \(2 3^{10} - 1 \\) )

B. \(2 3^{10} + 1 \\) )

C. \(2 3^{10} - 2 \\) )

D. \(2 3^{10} + 2 \\) )

Correct Answer: A

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Question 24 View Details

Solve the system of equations using matrices: [ egin{cases} \(x + 2y = 6\) \\(3x - 2y = -3\)\end{cases} ].

Correct A. \(x = 3, y = 1.5\)

B. \(x = 1.5, y = 3\)

C. \(x = 2, y = 2\)

D. \(x = 4, y = 1\)

Correct Answer: A

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Question 25 View Details

Find the area of the triangle with vertices at ((0,0)), ((3,0)), and ((0,4)).

A. ( 6 )

B. ( 8 )

Correct C. ( 10 )

D. ( 12 )

Correct Answer: C

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