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POST UTME GREENFIELD UNIVERSITY 2017 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 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).

A. 2 < x < 3

Correct B. x > 3

C. x < 2

D. x = 3

Correct Answer: B

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Question 2

Find the value of ( x ) in the quadratic equation \( x^2 + 5x + 6 = 0 \).

Correct A. x = -2

B. x = -3

C. x = 2

D. x = 3

Correct Answer: A

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Question 3

A sequence is defined by the formula \( a_n = 2n^2 - 3n + 1 \). Find the 5th term of the sequence.

A. a_5 = 21

B. a_5 = 25

Correct C. a_5 = 29

D. a_5 = 31

Correct Answer: C

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Question 4

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

Correct A. x = 1, y = 3

B. x = 2, y = 2

C. x = 3, y = 1

D. x = 4, y = 0

Correct Answer: A

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Question 5

Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} \).

A. det(A) = 0

B. det(A) = 1

Correct C. det(A) = 2

D. det(A) = 3

Correct Answer: C

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Question 6

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. 5 cm

Correct B. 5√3 cm

C. 10√3 cm

D. 20 cm

Correct Answer: B

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Question 7

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

Correct A. 50.24 cm²

B. 50.24 cm²

C. 50.24 cm²

D. 50.24 cm²

Correct Answer: A

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Question 8

Find the value of x in the equation 2^x + 2^x = 64.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 9

A sequence is defined by the formula an = 2n + 1. Find the sum of the first 5 terms of the sequence.

A. 15

Correct B. 21

C. 25

D. 30

Correct Answer: B

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Question 10

A histogram is shown below. Find the mean of the data.

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 11

Find the value of \( int_{0}^{1} \frac{1}{x^2 + 1} dx \) u\sing the method of substitution.

Correct A. π/2

B. π/4

C. π/3

D. π/6

Correct Answer: A

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Question 12

Solve the equation \( 2^x + 2^{-x} = 4 \) for ( x ).

A. 1

Correct B. 2

C. -1

D. -2

Correct Answer: B

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Question 13

A binary operation ( odot ) is defined as \( a odot b = a^2 + b^2 \). Find the value of ( 2 odot 3 ).

A. 13

B. 14

Correct C. 15

D. 16

Correct Answer: C

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Question 14

A circle has an equation of the form \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). If the center of the circle is at ( (3, 4) ) and the radius is 5, find the equation of the circle.

Correct A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25

B. \( x - 3 \)^2 + \( y - 4 \)^2 = 30

C. \( x - 3 \)^2 + \( y - 4 \)^2 = 35

D. \( x - 3 \)^2 + \( y - 4 \)^2 = 40

Correct Answer: A

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Question 15

A probability experiment consists of rolling a fair six-sided die. If the outcome is an even number, the experiment is repeated. If the outcome is an odd number, the experiment is stopped. What is the probability that the experiment will be stopped after exactly two rolls?

A. 1/6

Correct B. 1/3

C. 1/2

D. 2/3

Correct Answer: B

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Question 16

Let ( f(x) = \frac{1}{x^2 + 1} ). Find \( f^{-1}\( x \ \) ) u\sing the method of substitution.

A. \[ f^{-1}(x) = \frac{1}{x - 1} \]

B. \[ f^{-1}(x) = \frac{1}{x + 1} \]

Correct C. \[ f^{-1}(x) = \frac{1}{\sqrt{x} + 1} \]

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

Correct Answer: C

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Question 17

A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} \) for \( x = 1, 2, 3, 4 \). Find the probability that ( X ) is greater than 2.

A. 0.5

B. 0.75

C. 0.875

Correct D. 0.9375

Correct Answer: D

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Question 18

Let \( \mathbf{a} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \) and \( \mathbf{b} = \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} \). Find the cross product \( \mathbf{a} \times \mathbf{b} \).

Correct A. \[ \mathbf{a} \times \mathbf{b} = \begin{pmatrix} 5 \ 3 \ -7 \end{pmatrix} \]

B. \[ \mathbf{a} \times \mathbf{b} = \begin{pmatrix} 5 \ -3 \ 7 \end{pmatrix} \]

C. \[ \mathbf{a} \times \mathbf{b} = \begin{pmatrix} -5 \ 3 \ 7 \end{pmatrix} \]

D. \[ \mathbf{a} \times \mathbf{b} = \begin{pmatrix} 5 \ -3 \ -7 \end{pmatrix} \]

Correct Answer: A

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Question 19

A histogram of the heights of students in a class is shown below. If the mean height is 175 cm, find the median height.

A. 170 cm

Correct B. 175 cm

C. 180 cm

D. 185 cm

Correct Answer: B

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Question 20

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

A. \[ x = \frac{\pi}{2} \]

Correct B. \[ x = \frac{\pi}{4} \]

C. \[ x = \frac{3\pi}{4} \]

D. \[ x = \frac{5\pi}{4} \]

Correct Answer: B

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Question 21

Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{pmatrix} ].

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 22

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

Correct A. x = -2

B. x = -1

C. x = 1

D. x = 2

Correct Answer: A

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Question 23

Find the value of \( \log_{10} (1000) \).

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 24

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

Correct A. x > 4

B. x < 4

C. x > 2

D. x < 2

Correct Answer: A

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Question 25

Find the value of \( \sin \( 60^\circ \).

A. \frac{1}{2}

Correct B. \frac{\sqrt{3}}{2}

C. \frac{1}{\sqrt{2}}

D. \frac{\sqrt{2}}{2}

Correct Answer: B

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