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POST UTME ABU 2017 Mathematics | Objective

Are you preparing for POST UTME ABU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the volume of the solid formed by revolving the region bounded by the parabola y = x^2, the x-axis, and the line 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 2

A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. Find the probability that a randomly selected number from this set is greater than 12.

A. 0.25

B. 0.5

Correct C. 0.75

D. 0.9

Correct Answer: C

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Question 3

In a geometric sequence, the first term is 2 and the common ratio is 3. Find the sum of the first 5 terms of this sequence.

Correct A. 731

B. 7311

C. 73111

D. 731111

Correct Answer: A

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Question 4

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

Correct A. 50.24

B. 100.48

C. 200.96

D. 201.06

Correct Answer: A

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Question 5

A set of 3 numbers has a median of 5 and a mode of 3. Find the mean of this set.

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 6

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

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 7

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, -1 \) ∪ (1, ∞)

D. \( -∞, 1 \) ∪ (3, ∞)

Correct Answer: A

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Question 8

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

Correct A. 126

B. 128

C. 130

D. 132

Correct Answer: A

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Question 9

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 10

Determine the value of y in the equation \( y = 2x^2 + 5x - 3 \) when x = -1.

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 11

In a survey of 100 students, the mean height was 175 cm with a s\tandard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will have a height between 170 cm and 180 cm?

Correct A. 0.68

B. 0.95

C. 0.99

D. 0.999

Correct Answer: A

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Question 12

Solve for x in the equation \( x^2 + 4x + 4 = 0 \)

Correct A. -2

B. 0

C. 2

D. 4

Correct Answer: A

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Question 13

A circle has a radius of 4 cm. If the area of the circle is 50.24 cm^2, what is the circumference of the circle?

Correct A. 12.56 cm

B. 25.12 cm

C. 50.24 cm

D. 100.48 cm

Correct Answer: A

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Question 14

A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed of the car for the entire trip?

A. 48 km/h

B. 50 km/h

Correct C. 52 km/h

D. 54 km/h

Correct Answer: C

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Question 15

A water \tank can hold 2000 liters of water. If 3/4 of the \tank is already filled, how many more liters of water can be added?

Correct A. 1000 liters

B. 1200 liters

C. 1500 liters

D. 2000 liters

Correct Answer: A

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Question 16

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

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 17

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 18

Find the area under the curve \( y = x^2 \) from x = 0 to x = 2.

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 19

Solve the system of equations \( egin{cases} x + y = 2 \ x - y = 1 \end{cases} \).

Correct A. x = 1, y = 1

B. x = 1, y = -1

C. x = -1, y = 1

D. x = -1, y = -1

Correct Answer: A

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Question 20

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 21

Find the derivative of the function ( f(x) = x^3 - 2x^2 + x - 1 ).

Correct A. ( f'(x) = 3x^2 - 4x + 1 )

B. ( f'(x) = 3x^2 - 4x - 1 )

C. ( f'(x) = 3x^2 + 4x - 1 )

D. ( f'(x) = 3x^2 + 4x + 1 )

Correct Answer: A

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Question 22

Find the integral of the function ( f(x) = x^2 \sin x ).

Correct A. ( int f(x) dx = -x^2 \cos x - 2x \sin x + 2 \cos x + C )

B. ( int f(x) dx = -x^2 \cos x + 2x \sin x - 2 \cos x + C )

C. ( int f(x) dx = x^2 \cos x + 2x \sin x + 2 \cos x + C )

D. ( int f(x) dx = x^2 \cos x - 2x \sin x + 2 \cos x + C )

Correct Answer: A

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Question 23

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

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

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

C. \( x = 1, y = 3 \)

D. \( x = 3, y = 1 \)

Correct Answer: VIEW ANSWER

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Question 24

Find the volume of the solid formed by revolving the region bounded by the curve \( y = \frac{1}{2}x^2 \) and the line \( x = 2 \) about the x-axis.

A. 8π

B. 16π

Correct C. 32π

D. 64π

Correct Answer: C

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Question 25

Solve the inequality \( \frac{x}{x-1} > 0 \) for ( x in mathbb{R} ).

Correct A. \( x < 0 \) or \( x > 1 \)

B. \( x < 0 \) or \( 0 < x < 1 \)

C. \( x > 0 \) and \( x < 1 \)

D. \( x > 1 \)

Correct Answer: A

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