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POST UTME WELLSPRING UNIVERSITY 2018 Mathematics | Objective

Are you preparing for POST UTME WELLSPRING UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Determine the area under the curve of the function ( f(x) = \frac{1}{x^2 + 1} ) from $ x = 0 $ to $ x = 1 $.

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

B. $ \frac{pi}{4} $

C. $ \frac{pi}{6} $

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

Correct Answer: A

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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 score is between 70 and 80?

Correct A. 0.3413

B. 0.3415

C. 0.3417

D. 0.3419

Correct Answer: A

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Question 3

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

A. 10

B. 100

Correct C. 1000

D. 10000

Correct Answer: C

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Question 4

Find the equation of the circle with center ( (3, 4) ) and radius 5.

Correct A. $ x - 3 \ $^2 + $ y - 4 $^2 = 25 )

B. $ x - 4 \ $^2 + $ y - 3 $^2 = 25 )

C. $ x - 3 \ $^2 + $ y - 4 $^2 = 30 )

D. $ x - 4 \ $^2 + $ y - 3 $^2 = 30 )

Correct Answer: A

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Question 5

In the circuit below, what is the equivalent resis\tance between points A and B?

Correct A. $ \frac{R1 cdot R2}{R1 + R2} $

B. $ R1 + R2 $

C. $ \frac{R1 + R2}{R1 cdot R2} $

D. $ \frac{R1 cdot R2}{R1 - R2} $

Correct Answer: A

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Question 6

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 7

Find the determinant of the matrix $\begin{bmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{bmatrix}$.

Correct A. 4

B. 6

C. 8

D. 10

Correct Answer: A

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Question 8

Solve the inequality $\log_2 $ x^2 + 1 $ > 3$.

Correct A. \left$ \frac{1}{2}, \infty \right $

B. \left$ -\infty, -\frac{1}{2} \right $

C. \left$ -\frac{1}{2}, \frac{1}{2} \right $

D. \left$ -\infty, \infty \right $

Correct Answer: A

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Question 9

Find the equation of the circle with center $\left$ \frac{3}{2}, \frac{1}{2} \right $$ and radius $\frac{1}{2}$.

Correct A. \left$ x - \frac{3}{2} \right $^2 + \left$ y - \frac{1}{2} \right $^2 = \frac{1}{4}

B. \left$ x - \frac{1}{2} \right $^2 + \left$ y - \frac{3}{2} \right $^2 = \frac{1}{4}

C. \left$ x - \frac{1}{2} \right $^2 + \left$ y - \frac{1}{2} \right $^2 = \frac{1}{4}

D. \left$ x - \frac{3}{2} \right $^2 + \left$ y - \frac{3}{2} \right $^2 = \frac{1}{4}

Correct Answer: A

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Question 10

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

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

Correct B. \frac{2x^3 + 2x}{$ x^2 - 1 $^2}

C. \frac{2x^3 - 2x}{$ x^2 - 1 $^2}

D. \frac{2x^3 + 2}{$ x^2 - 1 $^2}

Correct Answer: B

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Question 11

Solve for x in the equation $ \sin^2\( x \ $ + \cos^2(x) = 1 ), given that $ \sin\( x \ $ = \frac{3}{5} ).

A. x = \frac{\pi}{4}

Correct B. x = \frac{3\pi}{4}

C. x = \frac{5\pi}{4}

D. x = \frac{7\pi}{4}

Correct Answer: B

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Question 12

A random variable X has a probability distribution given by $ P\( X = x \ $ = \frac{1}{2} \) for $ x = 1, 2, 3 $. Find the probability that X is greater than 2.

A. \frac{1}{4}

B. \frac{1}{2}

Correct C. \frac{3}{4}

D. \frac{5}{8}

Correct Answer: C

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Question 13

Solve the equation $ x^2 + 4x + 4 = 0 $ u\sing the quadratic formula.

Correct A. x = -2 \pm \sqrt{3}

B. x = -2 \pm \sqrt{2}

C. x = -2 \pm \sqrt{1}

D. x = -2 \pm \sqrt{0}

Correct Answer: A

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Question 14

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

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 15

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

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

B. x < 1 \text{ or } x > 5

C. x < -1 \text{ or } x > 2

D. x < 1 \text{ or } x > 2

Correct Answer: A

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Question 16

Find the value of x in the equation $ \frac{1}{x} + \frac{1}{3} = \frac{1}{2} $.

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 17

Solve for y in the equation $ y^2 + 4y + 4 = 0 $.

A. 0

Correct B. -2

C. 2

D. -4

Correct Answer: B

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Question 18

Find the determinant of the matrix $ egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} $.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 19

Find the mean of the data set { 2, 4, 6, 8, 10 }.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 20

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

Correct A. 2

B. -2

C. 1

D. -1

Correct Answer: A

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Question 21

In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the distribution of heights is approximately normal, what is the probability that a randomly selected student will be taller than 180 cm?

A. 0.1587

B. 0.3413

C. 0.5

Correct D. 0.8413

Correct Answer: D

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Question 22

A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. What is the surface area of the prism?

A. 240

B. 260

Correct C. 280

D. 300

Correct Answer: C

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Question 23

Solve the equation $ x^3 - 6x^2 + 11x - 6 = 0 $ by factoring.

Correct A. \left$ x-1\right)\left\( x-2\right)\left(x-3\right \ $=0

B. \left$ x-1\right)\left\( x-2\right)\left(x+3\right \ $=0

C. \left$ x-1\right)\left\( x-2\right)\left(x-6\right \ $=0

D. \left$ x-1\right)\left\( x-2\right)\left(x-9\right \ $=0

Correct Answer: A

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Question 24

A company has two factories, A and B, producing a total of 1000 units of a product per day. Factory A produces 60% of the total units, while factory B produces the remaining 40%. If factory A produces x units per day, how many units does factory B produce per day?

Correct A. 400

B. 600

C. 800

D. 1000

Correct Answer: A

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Question 25

Find the determinant of the matrix \[\begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}\].

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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