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POST UTME GREENFIELD UNIVERSITY 2023 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 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the area under the curve $ y = \frac{1}{2}x^2 + 3x - 2 $ from $ x = 0 $ to $ x = 4 $.

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 2

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 5. If the scores are normally distributed, what is the probability that a randomly selected student scored above 85?

A. 0.2

B. 0.3

Correct C. 0.4

D. 0.5

Correct Answer: C

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Question 3

Solve the equation $ 2^x + 3^x = 5^x $ for ( x ).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 4

Find the derivative of the function ( f(x) = \sin^2(x) ) u\sing the chain rule.

Correct A. \cos^2(x)

B. -\cos^2(x)

C. \sin^2(x)

D. -\sin^2(x)

Correct Answer: A

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Question 5

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

Correct A. 50.24

B. 50.25

C. 50.26

D. 50.27

Correct Answer: A

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Question 6

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

A. \frac{2x$ x^2 - 4 $ - $ x^2 + 2x - 3 $(2x)}{$ x^2 - 4 $^2}

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

Correct C. \frac{2x$ x^2 - 4 $ - $ x^2 + 2x - 3 $(2x)}{$ x^2 - 4 $^2}

D. \frac{2x$ x^2 - 4 $ + $ x^2 + 2x - 3 $(2x)}{$ x^2 - 4 $^2}

Correct Answer: C

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Question 7

Solve the equation $ \sin^2 x + \cos^2 x = \frac{3}{4} \ $ for ( x ) in the interval $ [0, 2\pi] $.

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

B. \frac{\pi}{4}

C. \frac{\pi}{3}

D. \frac{\pi}{2}

Correct Answer: A

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Question 8

A histogram of exam scores is shown below. If the mean score is 75, what is the median score?

A. 75

Correct B. 80

C. 85

D. 90

Correct Answer: B

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Question 9

Solve the inequality $ \frac{x - 2}{x + 1} > 0 $ for ( x ).

Correct A. $ -\infty, -1 $ \cup $ 2, \infty $

B. $ -\infty, -1 $ \cup $ -1, 2 $

C. $ -\infty, 2 $ \cup $ 2, \infty $

D. $ -\infty, -1 $ \cup $ 2, \infty $

Correct Answer: A

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Question 10

Find the area of the triangle with vertices ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 2) ).

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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Question 11

Find the derivative of the function ( f(x) = \frac{1}{2x^2 + 3x - 1} ) u\sing the chain rule.

Correct A. ( f'(x) = \frac{-2x + 3}{$ 2x^2 + 3x - 1 $^2} )

B. ( f'(x) = \frac{2x + 1}{$ 2x^2 + 3x - 1 $^2} )

C. ( f'(x) = \frac{2x - 1}{$ 2x^2 + 3x - 1 $^2} )

D. ( f'(x) = \frac{-2x - 3}{$ 2x^2 + 3x - 1 $^2} )

Correct Answer: A

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Question 12

Solve the system of equations u\sing matrices: $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} $.

Correct A. $ egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix} $

B. $ egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 1 \end{bmatrix} $

C. $ egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} $

D. $ egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 3 \end{bmatrix} $

Correct Answer: A

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Question 13

Find the sum of the infinite geometric series $ sum_{n=1}^{infty} \frac{1}{2^n} $.

Correct A. $ \frac{1}{2} $

B. $ \frac{1}{3} $

C. $ \frac{1}{4} $

D. $ \frac{1}{5} $

Correct Answer: A

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Question 14

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

Correct A. $ x + 2 \ $^2 + $ y - 3 $^2 = 16 )

B. $ x - 2 \ $^2 + $ y + 3 $^2 = 16 )

C. $ x + 3 \ $^2 + $ y - 2 $^2 = 16 )

D. $ x - 3 \ $^2 + $ y + 2 $^2 = 16 )

Correct Answer: A

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Question 15

Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.

Correct A. ( f'(x) = 2 \sin x \cos x )

B. ( f'(x) = \sin x \cos x )

C. ( f'(x) = 2 \cos x )

D. ( f'(x) = \cos x )

Correct Answer: A

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Question 16

Let ( X ) and ( Y ) be indep\endent random variables with probability density functions $ f_X\( x \ $ = 2x ) for $ 0 < x < 1 $ and $ f_Y\( y \ $ = 3y^2 ) for $ 0 < y < 1 $. Find the probability that $ X + Y < 1 $.

Correct A. \frac{1}{2}

B. \frac{1}{3}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 17

Find the area under the curve $ y = \sin\( x \ $ ) from $ x = 0 $ to $ x = \frac{pi}{2} $ u\sing the definite integral.

Correct A. 1

B. \frac{1}{2}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 18

Solve the system of equations u\sing matrices: $ egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} $.

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ 3 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 5 \end{bmatrix}

Correct Answer: A

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Question 19

Find the derivative of the function ( f(x) = 3x^2 \sin(x) ) u\sing the product rule.

Correct A. 6x^2 \sin(x) + 3x^3 \cos(x)

B. 3x^2 \cos(x) - 3x \sin(x)

C. 3x^2 \cos(x) + 3x \sin(x)

D. 6x^2 \cos(x) - 3x \sin(x)

Correct Answer: A

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Question 20

Find the sum of the infinite geometric series $ sum_{n=1}^{infty} \frac{1}{2^n} $.

Correct A. 1

B. \frac{1}{2}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 21

Determine the value of $\int_{0}^{\pi} \frac{\sin^2 x}{1 + \cos^2 x} dx$.

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{8}

D. \frac{\pi}{16}

Correct Answer: A

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Question 22

Solve for $x$ in the equation $\log_{10} $ x^2 $ = 4$.

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 23

Find the equation of the circle with center $$ -2, 3 $$ and radius $4$.

Correct A. $ 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 24

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If 80% of the scores fall below 85, what is the value of the score that corresponds to the 80th percentile?

A. 80

Correct B. 85

C. 90

D. 95

Correct Answer: B

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Question 25

Solve the system of equations $\begin{cases} x + y = 4 \ x - 2y = -2 \end{cases}$.

Correct A. (2, 2)

B. (1, 3)

C. (3, 1)

D. (4, 0)

Correct Answer: A

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