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POST UTME RHEMA UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details

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

Correct A. ( 8 )

B. ( 16 )

C. ( 32 )

D. ( 64 )

Correct Answer: A

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Question 2 View Details

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

A. $x = 1$

Correct B. $x = 2$

C. $x = 3$

D. $x = 4$

Correct Answer: B

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Question 3 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. ( 0.9544 )

Correct B. ( 0.9772 )

C. ( 0.9987 )

D. ( 0.9999 )

Correct Answer: B

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Question 4 View Details

Find the determinant of the matrix $egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}$.

Correct A. $-1$

B. ( 0 )

C. ( 1 )

D. ( 2 )

Correct Answer: A

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Question 5 View Details

A vector ( mathbf{a} ) has a magnitude of 5 and makes an angle of 30° with the positive x-axis. Find the x-component of ( mathbf{a} ).

Correct A. ( 2.5 )

B. ( 3.5 )

C. ( 4.5 )

D. ( 5.5 )

Correct Answer: A

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Question 6 View Details

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

A. 0

Correct B. $\frac{\pi}{2}$\)

C. $\frac{\pi}{4}$\)

D. $\frac{\pi}{8}$\)

Correct Answer: B

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Question 7 View Details

Solve the matrix equation $\begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 4 \end{bmatrix}$ for \$4 end{bmatrix}\(x$ and $y$.

Correct A. $x = 1$, $y = 2$

B. $x = 2$, $y = 1$

C. $x = 1$, $y = 1$

D. $x = 2$, $y = 2$

Correct Answer: A

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Question 8 View Details

Find the derivative of $f(x) = \frac{1}{1+\sin^2 x}$ using the chain rule.

Correct A. $\frac{\cos^2$ x}{ 1+\$\sin^2$ x ^2}\)\)

B. $\frac{\sin^2$ x}{ 1+\$\sin^2$ x ^2}\)\)

C. $\frac{1}{1+\sin^2$ x ^2}\)\)

D. $\frac{$1x}{1+\sin^2$ x ^2}\)\)

Correct Answer: A

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Question 9 View Details

Solve the trigonometric equation $\sin^2 x + \cos^2 x = 1$ for $x$.

Correct A. $x =$$\frac{\pi}{4}$\)

B. $x =$$\frac{3\pi}{4}$\)

C. $x =$$\frac{\pi}{2}$\)

D. $x =$$\frac{5\pi}{4}$\)

Correct Answer: A

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Question 10 View Details

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

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 11 View Details

Find the volume of the solid formed by revolving the region bounded by the curves $y = x\^2$ and $y = 4 - x\^2$ about the x-axis.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 12 View Details

Solve 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 13 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 + $y-3$^$2 = 25$

C. $x-2$^2 + $y-3$^$2 = 36$

D. $x-2$^2 + $y-3$^$2 = 49$

Correct Answer: A

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Question 14 View Details

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

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

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

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

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

Correct Answer: A

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Question 15 View Details

Find the equation of the line passing through the points (1, 2) and (3, 4).

Correct A. $y = 2x + 2$

B. $y = 2x - 2$

C. $y = x + 2$

D. $y = x - 2$

Correct Answer: A

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Question 16 View Details

Solve the equation \$(x^2 + 4x + 4$$= 0.$\)

Correct A. $x = -2$

B. $x = -1$

C. $x = 1$

D. $x = 2$

Correct Answer: A

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Question 17 View Details

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

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 18 View Details

Solve the inequality \$(x^2 - 6x + 8$$> 0.$\)

Correct A. $-\infty, 2$ \cup $4, \infty$

B. $-\infty, 2$ \cup $4, \infty$

C. (2, 4)

D. (2, 4)

Correct Answer: A

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Question 19 View Details

Find the equation of the circle with center (1, 2) and radius 3.

A. $x-1$^2 + $y-2$^$2 = 9$

B. $x-1$^2 + $y-2$^$2 = 16$

C. $x-1$^2 + $y-2$^$2 = 25$

D. $x-1$^2 + $y-2$^$2 = 36$

Correct Answer: VIEW ANSWER

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Question 20 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 21 View Details

Solve the system of linear equations using the method of substitution: \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}

Correct A. \begin{align*} x &= 3 \ y &= 1 \end{align*}

B. \begin{align*} x &= 1 \ y &= 3 \end{align*}

C. \begin{align*} x &= 2 \ y &= 2 \end{align*}

D. \begin{align*} x &= 4 \ y &= 0 \end{align*}

Correct Answer: A

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Question 22 View Details

Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.

A. $\frac{16\pi}{3}$\)

B. $\frac{32\pi}{3}$\)

Correct C. $\frac{64\pi}{3}$\)

D. $\frac{128\pi}{3}$\)

Correct Answer: C

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Question 23 View Details

Solve the inequality $|x - 2| > 3$.

Correct A. \{x :$x < -1$\text{ or } $x > 5$\}

B. \{x :$x < -1$\text{ or } $x > 4$\}

C. \{x : $x < 1$ \text{ or } $x > 5$\}

D. \{x : $x < 1$ \text{ or } $x > 4$\}

Correct Answer: A

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Question 24 View Details

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

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

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

C. \left$x + 2\right$^2 + left$y + 3\right$^$2 = 16$

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

Correct Answer: A

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Question 25 View Details

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

Correct A. \$\cos^2$ x

B. \$\sin^2$ x

C. \$\tan^2$ x

D. \$\cot^2$ x

Correct Answer: A

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