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POST UTME COAL CITY UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

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

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

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

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

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

Correct Answer: A

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Question 2 View Details

A cylindrical \tank with a radius of 4m and a height of 6m is filled with water. Find the volume of water in the \tank.

A. ( 96pi ) cubic meters

B. ( 192pi ) cubic meters

Correct C. ( 384pi ) cubic meters

D. ( 576pi ) cubic meters

Correct Answer: C

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Question 3 View Details

Find the equation of the circle with center $-2, 3 \$ ) and radius 5.

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

B. $x - 2 \$^2 + $y + 3$^$2 = 25$ )

C. $x + 2 \$^2 + $y + 3$^$2 = 25$ )

D. $x - 2 \$^2 + $y - 3$^$2 = 25$ )

Correct Answer: A

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Question 4 View Details

Solve the inequality $2x^2 - 5x - 3 > 0$.

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

B. $x < -1$ or $x < \frac{3}{2}$

C. $x > -1$ or $x < \frac{3}{2}$

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

Correct Answer: A

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Question 5 View Details

A polynomial function has a degree of 4 and has zeros at $x = -2, 1, 3$. Find the polynomial function.

Correct A. $x + 2$, x - 1\)$x - 3$, x + 1 \\) )

B. $x - 2$, x + 1\)$x - 3$, x + 3 \\) )

C. $x + 2$, x - 1\)$x + 3$, x - 3 \\) )

D. $x - 2$, x + 1\)$x - 3$, x + 1 \\) )

Correct Answer: A

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Question 6 View Details

Let X be a random variable with probability density function f(x) = ($\frac{1}{2}\\()x^2$\) for \$(frac{1}{2}x^2\(0 \le x$ ≤ 2. Find the probability that X is greater than 1.

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

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

C. $\frac{3}{4}$

D. $\frac{5}{8}$

Correct Answer: B

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Question 7 View Details

Find the area under the curve y = $\sin^2 x \$) from 0 to $\frac{\pi}{2}$ using integration by substitution.

Correct A. $\frac{\pi}{4}$

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

C. $\frac{3\pi}{4}$

D. $\frac{5\pi}{4}$

Correct Answer: A

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Question 8 View Details

Solve the differential equation $\frac{dy}{dx} = \frac{y}{x}$ with the initial condition y(1) = 1.

A. $y =$$\ln|x|$

Correct B. $y =$$\frac{1}{x}$

C. $y =$$\frac{1}{x^2}$

D. $y =$$\frac{1}{x^3}$

Correct Answer: B

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Question 9 View Details

Use the chain rule to find the derivative of the function f(x) = $2x + 1 \$^3).

Correct A. f'$(x) = 6$$2x + 1$^2

B. f'$(x) = 6$$2x + 1$

C. f'$(x) = 12$$2x + 1$

D. f'$(x) = 24$$2x + 1$

Correct Answer: A

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Question 10 View Details

Find the value of ($12x \$) when x = \$($12x $\frac{\pi}{6}$.

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

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

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

D. $\frac{\sqrt{3}}{\sqrt{2}}$

Correct Answer: B

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Question 11 View Details

Determine the value of $\int_0^1 x^2 $1x \, dx$.

A. $\frac{1}{4}$\)

Correct B. $\frac{1}{2}$\)

C. 1

D. $\frac{3}{4}$\)

Correct Answer: B

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Question 12 View Details

Solve for (x\) in the equation $\\((x) in the equation \log_2 x^2 + 1$$= 3$\).

A. $\sqrt{7}$

B. $\sqrt{8}$

Correct C. $\sqrt{9}$

D. $\sqrt{10}$

Correct Answer: C

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Question 13 View Details

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

A. 5

B. 7

Correct C. 9

D. 11

Correct Answer: C

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Question 14 View Details

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experiment is repeated. If the number rolled is odd, the experiment is terminated. What is the probability that the experiment will be terminated on the first roll?

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

B. $\frac{2}{3}$\)

C. $\frac{3}{4}$\)

D. $\frac{4}{5}$\)

Correct Answer: A

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Question 15 View Details

Find the area under the curve $y = x^2$ from $x = 0$ to $x = 2$.

A. 2

B. 4

Correct C. 6

D. 8

Correct Answer: C

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Question 16 View Details

Find the area under the curve $y = x\^2 + 2x + 1$ from $x = 0$ to $x = 3$.

Correct A. 27

B. 30

C. 33

D. 36

Correct Answer: A

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Question 17 View Details

Solve the system of equations using matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 8 \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 18 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. $x - 3$^2 + $y - 2$^$2 = 16$

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

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

Correct Answer: A

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Question 19 View Details

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

Correct A. $\vec{r} = \begin{bmatrix} 1 \\ 2 \end{bmatrix} + t \begin{bmatrix} 1 \\ 1 \end{bmatrix}$

B. $\vec{r} = \begin{bmatrix} 1 \\ 2 \end{bmatrix} + t \begin{bmatrix} 2 \\ 3 \end{bmatrix}$

C. $\vec{r} = \begin{bmatrix} 1 \\ 2 \end{bmatrix} + t \begin{bmatrix} 3 \\ 4 \end{bmatrix}$

D. $\vec{r} = \begin{bmatrix} 1 \\ 2 \end{bmatrix} + t \begin{bmatrix} 4 \\ 5 \end{bmatrix}$

Correct Answer: A

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Question 20 View Details

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

Correct A. $-∞, -1$ ∪ (3, ∞)

B. $-∞, -3$ ∪ (1, ∞)

C. $-∞, -2$ ∪ (2, ∞)

D. $-∞, -4$ ∪ (4, ∞)

Correct Answer: A

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Question 21 View Details

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is 6, what is the sum of the data set?

A. 20

Correct B. 30

C. 40

D. 50

Correct Answer: B

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Question 22 View Details

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

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 23 View Details

Find the value of x in the quadratic equation $x^2 + 4x + 4 = 0$.

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 24 View Details

A histogram is shown below. What is the mean of the data set?

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 25 View Details

Solve the system of linear equations $egin{cases} 2x + 3y = 7 \ x - 2y = -3 \end{cases}$.

Correct A. (1, 2)

B. (2, 1)

C. (3, 4)

D. (4, 5)

Correct Answer: A

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