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POST UTME GREENFIELD UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME GREENFIELD UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2025 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the volume of the frustum of a cone with a height of 10 cm, a lower base radius of 4 cm, and an upper base radius of 6 cm.

A. 100π cm³

Correct B. 150π cm³

C. 200π cm³

D. 250π cm³

Correct Answer: B

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Question 2

Solve for x in the equation \( \frac{1}{2} \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 3

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).

A. 32

B. 64

Correct C. 128

D. 256

Correct Answer: C

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Question 4

In the circuit below, determine the current flowing through the 2 Ω resistor.

A. 0.5 A

Correct B. 1 A

C. 2 A

D. 4 A

Correct Answer: B

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Question 5

Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases} \).

A. (1, 3)

Correct B. (2, 2)

C. (3, 1)

D. (4, 0)

Correct Answer: B

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Question 6

Determine the equation of the circle pas\sing through the points (2,3), (4,5), and (6,7).

Correct A. \( x^2 + y^2 - 12x - 6y + 36 = 0 \)

B. \( x^2 + y^2 - 10x - 4y + 20 = 0 \)

C. \( x^2 + y^2 - 14x - 8y + 56 = 0 \)

D. \( x^2 + y^2 - 16x - 10y + 80 = 0 \)

Correct Answer: A

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Question 7

A cylindrical \tank with a radius of 3m and a height of 5m is filled with water. Find the volume of water in the \tank.

A. ( 150pi ) cubic meters

B. ( 300pi ) cubic meters

Correct C. ( 450pi ) cubic meters

D. ( 600pi ) cubic meters

Correct Answer: C

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Question 8

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

Correct A. \( x < -1 \) or \( x > \frac{3}{2} \)

B. \( x < -\frac{1}{2} \) or \( x > 3 \)

C. \( x < -3 \) or \( x > \frac{1}{2} \)

D. \( x < 3 \) or \( x > -\frac{1}{2} \)

Correct Answer: A

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Question 9

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

Correct A. \( y = \frac{1}{2}x + \frac{1}{2} \)

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

C. \( y = \frac{1}{4}x + \frac{5}{4} \)

D. \( y = x - 1 \)

Correct Answer: A

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Question 10

A right-angled triangle has a hypotenuse of length 10cm and one of the other sides is 6cm. Find the length of the third side.

Correct A. ( 8cm )

B. ( 6cm )

C. ( 4cm )

D. ( 12cm )

Correct Answer: A

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Question 11

A random sample of 25 students from a university had a mean height of 170 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is 3 cm, calculate the s\tandard error of the mean.

Correct A. 1.67

B. 2.5

C. 3.33

D. 4.17

Correct Answer: A

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Question 12

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

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 13

A histogram of exam scores is shown below. If the mean score is 60 and the s\tandard deviation is 10, calculate the range of scores.

A. 40-80

B. 50-70

Correct C. 60-80

D. 70-90

Correct Answer: C

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Question 14

Solve the equation \( \sin(x) = \frac{1}{2} \) for x in the interval \( [0, 2\pi] \).

Correct A. \frac{\pi}{6}

B. \frac{\pi}{3}

C. \frac{\pi}{2}

D. \frac{5\pi}{6}

Correct Answer: A

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Question 15

A polynomial function is defined as \( f(x) = x^3 - 6x^2 + 9x + 2 \). Find the value of \( f\( -1 \).

Correct A. -8

B. -6

C. -4

D. 2

Correct Answer: A

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Question 16

Find the equation of the circle with center \( -2, 3 \) and radius 4.

Correct A. \boxed{\( x + 2 \)^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 17

Solve for x: \[\log_{10} \( x^2 \) = 4\]

A. x = 10^2

Correct B. x = 10^4

C. x = 10^8

D. x = 10^12

Correct Answer: B

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Question 18

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

Correct A. \boxed{\frac{1}{3}}

B. \frac{1}{2}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 19

Find the derivative of the function f(x) = 3x^2 + 2x - 5 u\sing the chain rule.

Correct A. f'(x) = 6x + 2

B. f'(x) = 6x - 2

C. f'(x) = 3x^2 + 2x - 5

D. f'(x) = 3x^2 - 2x - 5

Correct Answer: A

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Question 20

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is its volume?

Correct A. V = 72 cm^3

B. V = 48 cm^3

C. V = 36 cm^3

D. V = 24 cm^3

Correct Answer: A

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Question 21

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

A. \frac{-x}{\( 1 + x^2 \)^{3/2}}

Correct B. \frac{x}{\( 1 + x^2 \)^{3/2}}

C. \frac{1}{\( 1 + x^2 \)^{3/2}}

D. \frac{-1}{\( 1 + x^2 \)^{3/2}}

Correct Answer: B

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Question 22

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

Correct A. x < -1.5 or x > 1

B. x < -1 or x > 1

C. x < -1.5 or x < 1

D. x > -1.5 or x > 1

Correct Answer: A

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Question 23

Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).

Correct A. 3120

B. 3124

C. 3128

D. 3132

Correct Answer: A

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Question 24

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).

A. x = 0, \\pi/2, \\pi, 3\\pi/2

Correct B. x = 0, \pi/2, \pi, 3\pi/2, 2\pi

C. x = \\pi/2, \\pi, 3\\pi/2

D. x = 0, \pi

Correct Answer: B

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Question 25

A set of 5 numbers has a mean of 10. Find the sum of the numbers.

Correct A. 50

B. 100

C. 150

D. 200

Correct Answer: A

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