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POST UTME GREENFIELD UNIVERSITY 2024 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 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 - 4}} ) u\sing the chain rule.

Correct A. \( \frac{-2}{\( x^2 - 4 \ \)^{3/2}} )

B. \( \frac{2}{\( x^2 - 4 \ \)^{3/2}} )

C. \( \frac{1}{\( x^2 - 4 \ \)^{3/2}} )

D. \( \frac{-1}{\( x^2 - 4 \ \)^{3/2}} )

Correct Answer: A

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Question 2

A circle has a radius of 5 cm and a center at (0, 0). Find the equation of the circle in s\tandard form.

Correct A. \( x^2 + y^2 = 25 \)

B. \( x^2 + y^2 = 50 \)

C. \( x^2 - y^2 = 25 \)

D. \( x^2 + y^2 = 75 \)

Correct Answer: A

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Question 3

Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 4

Simplify the expression \( \frac{1}{2} \times \frac{3}{4} \times \frac{5}{6} \) u\sing the rules of \fractions.

Correct A. \( \frac{5}{24} \)

B. \( \frac{1}{24} \)

C. \( \frac{5}{12} \)

D. \( \frac{1}{12} \)

Correct Answer: A

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Question 5

A set of data has a mean of 25 and a s\tandard deviation of 3. Find the z-score of the value 32.

A. 1.33

B. 1.67

Correct C. 2.00

D. 2.33

Correct Answer: C

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Question 6

Determine the value of x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.

A. 1

B. -2

Correct C. 3

D. -4

Correct Answer: C

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Question 7

A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.

Correct A. 15

B. 20

C. 25

D. 30

Correct Answer: A

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Question 8

A polynomial function is defined as ( f(x) = x^3 - 2x^2 - 7x + 12 ). Find the value of x that makes f(x) = 0.

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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Question 9

A set of data is given as {1, 2, 3, 4, 5}. Find the mean and median of the data.

Correct A. 3, 3

B. 2, 3

C. 4, 4

D. 5, 5

Correct Answer: A

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Question 10

A matrix is given as \( egin{bmatrix} 1 & 2 \ 3 & 4 \ \end{bmatrix} \). Find the determinant of the matrix.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 11

Determine 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 12

Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, 54, ... ).

Correct A. 124

B. 126

C. 128

D. 130

Correct Answer: A

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Question 13

Solve for x in the equation \( 2^x + 2^x = 128 \).

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 14

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

A. 12

B. 14

Correct C. 16

D. 18

Correct Answer: C

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Question 15

Solve the system of equations \( x + y = 5 \) and \( x - y = 3 \).

Correct A. (2, 3)

B. (3, 2)

C. (4, 1)

D. (1, 4)

Correct Answer: A

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Question 16

Solve for x in the equation \( \frac{1}{x+2} + \frac{1}{x-3} = \frac{1}{2} \).

Correct A. \( x = -\frac{5}{2} \)

B. \( x = \frac{5}{2} \)

C. \( x = -\frac{1}{2} \)

D. \( x = \frac{1}{2} \)

Correct Answer: A

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Question 17

A particle moves in a straight line with its position given by the equation ( s(t) = 2t^3 - 5t^2 + 3t + 1 ). Find the velocity of the particle at time \( t = 2 \) seconds.

Correct A. ( v(2) = 14 ) m/s

B. ( v(2) = -14 ) m/s

C. ( v(2) = 0 ) m/s

D. ( v(2) = 21 ) m/s

Correct Answer: A

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Question 18

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

A. \( \frac{1}{6} \)

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

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

Correct D. \( \frac{5}{6} \)

Correct Answer: D

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Question 19

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

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

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

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

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

Correct Answer: A

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Question 20

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

Correct A. ( 16pi ) cm^2

B. ( 32pi ) cm^2

C. ( 64pi ) cm^2

D. ( 128pi ) cm^2

Correct Answer: A

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Question 21

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

Correct A. 24\pi

B. 48\pi

C. 96\pi

D. 192\pi

Correct Answer: A

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Question 22

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

Correct A. x \in \( -\infty, -1 \) \cup [3, \infty)

B. x \in \( -\infty, -3 \) \cup [1, \infty)

C. x \in \( -\infty, -3 \) \cup [1, 3]

D. x \in \( -\infty, -1 \) \cup [3, 1]

Correct Answer: A

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Question 23

A box contains 5 red balls, 4 blue balls, and 3 green balls. If a ball is drawn at random, what is the probability that it is either red or blue?

A. \frac{3}{6}

B. \frac{4}{6}

Correct C. \frac{5}{6}

D. \frac{2}{6}

Correct Answer: C

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Question 24

Solve for x in the equation \( 2^x + 2^{x+1} = 3 \cdot 2^x \).

Correct A. x = 1

B. x = 2

C. x = 3

D. x = 4

Correct Answer: A

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Question 25

Find the surface area of the sphere with radius 5 cm.

A. 100\pi

B. 200\pi

Correct C. 300\pi

D. 400\pi

Correct Answer: C

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