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POST UTME COAL CITY UNIVERSITY 2019 Mathematics | Objective

Are you preparing for POST UTME COAL CITY UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

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

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

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

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

Let X be a random variable with probability density function f(x) = $ \frac{1}{2}x^2 $ for 0 ≤ 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

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

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

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

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

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

Correct Answer: A

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Question 8

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

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

Find the value of $ \sin\( 2x \ $) when x = $ \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

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

A. \frac{1}{4}

Correct B. \frac{1}{2}

C. 1

D. \frac{3}{4}

Correct Answer: B

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Question 12

Solve for $x$ 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

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

A. 5

B. 7

Correct C. 9

D. 11

Correct Answer: C

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Question 14

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

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

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

Solve the system of equations u\sing 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

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

Find the vector equation of the line pas\sing 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

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

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

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

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

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

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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