Exam Body

Year

Subject

Paper Type

POST UTME ABU 2024 Mathematics | Objective

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Question 1

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

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

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

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

A water \tank can hold 1000 liters of water. If 300 liters of water are already in the \tank, what \fraction of the \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

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

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

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

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

A histogram of exam scores has a mean of 60 and a s\tandard 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

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

A histogram of exam scores has a mean of 75 and a s\tandard 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

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

Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing 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

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

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

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

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

A car travels from City A to City B at an average speed of 60 km/h. If the dis\tance 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

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

Find the equation of the circle with center at ((2,3)) and pas\sing 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

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

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

Solve the system of equations u\sing 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

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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