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POST UTME GREENFIELD UNIVERSITY 2023 Mathematics | Objective

Prepare for your exams with POST UTME GREENFIELD UNIVERSITY questions? Reviewing past/model 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.

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Question 1 View Details

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 View Details

A histogram of exam scores has a mean of 75 and a standard 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 View Details

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 View Details

Find the derivative of the function ( f(x) = \$\sin^2(x)$ ) using 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 View Details

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 View Details

Find the derivative of the function ( f(x) = $\frac{x^2 + 2x - 3}{x^2 - 4}$\)\) ) using 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 View Details

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

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 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of the function ( f(x) = $\frac{1}{2x^2 + 3x - 1}$\)\) ) using 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 View Details

Solve the system of equations using 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 View Details

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 View Details

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 View Details

Find the derivative of the function ( f(x) = \$\sin^2$ x ) using 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 View Details

Let ( X ) and ( Y ) be independent random variables with probability density functions (f_X x \\) = 2x ) for \$(f_X x \(0 < x < 1$ and $f_Y y \$$= \((3y^2$\)\) ) for $0 < y < 1\\((3y^2) ) for$. 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 View Details

Find the area under the curve $y = $1x \$ ) from $x = 0$ to $x = \frac{\pi}{2}$ using 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 View Details

Solve the system of equations using 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 View Details

Find the derivative of the function ( f(x) = $3x^2$ \sin(x) ) using 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 View Details

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 View Details

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 View Details

Solve for (x\) in the equation $\\((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 View Details

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 View Details

A histogram of exam scores has a mean of 75 and a standard 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 View Details

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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