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POST UTME WELLSPRING UNIVERSITY 2023 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 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \sin\( x \ \) = \frac{3}{5} ).

Correct A. \frac{4\sqrt{11}}{11}

B. \frac{3\sqrt{11}}{11}

C. \frac{4\sqrt{11}}{11}

D. \frac{3\sqrt{11}}{11}

Correct Answer: A

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Question 2

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

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

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

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

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

Correct Answer: B

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Question 3

A histogram of exam scores is shown below. What is the mean score of the exam?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 4

Solve the equation \( 2^x + 2^{-x} = 5 \).

Correct A. \log_2(3)

B. \log_2(2)

C. \log_2(3)

D. \log_2(2)

Correct Answer: A

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Question 5

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

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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Question 6

Determine the value of x in the equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix} \).

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 7

Solve for y in the equation \( \frac{dy}{dx} = \frac{2x}{y} \) where y(1) = 2.

Correct A. y = 2x^2

B. y = x^2

C. y = 2x

D. y = x

Correct Answer: A

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Question 8

A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } X = 1 \ 0.3 & \text{if } X = 2 \ 0.5 & \text{if } X = 3 \end{cases} ). Find the expected value of X.

A. 1.5

B. 2

Correct C. 2.5

D. 3

Correct Answer: C

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Question 9

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

A. f'(x) = -\frac{2x}{\( x^2 + 1 \)^2}

Correct B. f'(x) = \frac{2x}{\( x^2 + 1 \)^2}

C. f'(x) = -\frac{2}{\( x^2 + 1 \)^2}

D. f'(x) = \frac{2}{\( x^2 + 1 \)^2}

Correct Answer: B

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Question 10

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 85.

A. 0.1587

B. 0.3413

C. 0.5

Correct D. 0.8413

Correct Answer: D

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Question 11

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

Correct A. \boxed{\( x + 2 \)^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 12

If f(x) = 3x^2 + 2x - 5, find f'(x) u\sing the chain rule.

Correct A. \boxed{6x + 2}

B. 3x^2 + 2

C. 6x - 2

D. 3x^2 + 2x

Correct Answer: A

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Question 13

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

Correct A. \boxed{\( -\infty, -3 \) \cup \( 1, \infty \)}

B. \( -\infty, -3 \) \cup \( -1, \infty \)

C. \( -\infty, 1 \) \cup \( 3, \infty \)

D. \( -\infty, -1 \) \cup \( 3, \infty \)

Correct Answer: A

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Question 14

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

Correct A. \boxed{\frac{13}{3}}

B. \frac{11}{3}

C. \frac{15}{3}

D. \frac{17}{3}

Correct Answer: A

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Question 15

Find the vector projection of vector \mathbf{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} onto vector \mathbf{b} = \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}.

Correct A. \boxed{\begin{pmatrix} \frac{11}{14} \ \frac{13}{14} \ \frac{15}{14} \end{pmatrix}}

B. \begin{pmatrix} \frac{11}{14} \ \frac{13}{14} \ \frac{15}{14} \end{pmatrix}

C. \begin{pmatrix} \frac{13}{14} \ \frac{15}{14} \ \frac{17}{14} \end{pmatrix}

D. \begin{pmatrix} \frac{15}{14} \ \frac{17}{14} \ \frac{19}{14} \end{pmatrix}

Correct Answer: A

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Question 16

Determine the value of k in the equation \( 2x^2 + 5x + k = 0 \) if the sum of the roots is -2.

A. -1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 17

A survey of 100 students found that 60 students preferred Mathematics, 30 preferred Science, and 10 preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?

Correct A. 0.65

B. 0.7

C. 0.75

D. 0.8

Correct Answer: A

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Question 18

Find the volume of the solid formed by rotating the region bounded by \( y = x^2 \) and \( y = 4 \) about the x-axis.

A. 64π

B. 128π

Correct C. 256π

D. 512π

Correct Answer: C

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Question 19

A random variable X has a probability distribution given by \( P\( X = 1 \ \) = \frac{1}{2} ) and \( P\( X = 2 \ \) = \frac{1}{2} ). Find the expected value of X.

A. 1

Correct B. 1.5

C. 2

D. 2.5

Correct Answer: B

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Question 20

Solve the inequality \( \log_{10} \( x^2 \ \) > 4 ).

A. x > 10

B. x < -10

Correct C. x > 100

D. x < -100

Correct Answer: C

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Question 21

Let ( f(x) = \frac{x^2 - 4}{x^2 - 9} ). Find the value of \( lim_{x \to 3} f\( x \ \) ).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 22

In a triangle ABC, if \( \angle A = 30^\circ \) and \( \angle B = 60^\circ \), find the value of \( \sin C \).

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 23

Let \( A = \begin{pmatrix} 2 & 1 \ 3 & 4 \end{pmatrix} \) and \( B = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} \). Find the value of ( AB ).

Correct A. \begin{pmatrix} 5 & 6 \ 9 & 12 \end{pmatrix}

B. \begin{pmatrix} 3 & 4 \ 6 & 8 \end{pmatrix}

C. \begin{pmatrix} 4 & 5 \ 7 & 10 \end{pmatrix}

D. \begin{pmatrix} 6 & 7 \ 10 & 14 \end{pmatrix}

Correct Answer: A

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Question 24

Let ( f(x) = 2x^3 - 5x^2 + x - 1 ). Find the value of \( f\( -1 \ \) ).

Correct A. -9

B. -7

C. -5

D. -3

Correct Answer: A

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Question 25

Let \( A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} \) and \( B = \begin{pmatrix} 2 & 1 \ 3 & 4 \end{pmatrix} \). Find the value of \( A^2 \).

Correct A. \begin{pmatrix} 5 & 6 \ 9 & 12 \end{pmatrix}

B. \begin{pmatrix} 4 & 5 \ 7 & 10 \end{pmatrix}

C. \begin{pmatrix} 6 & 7 \ 10 & 14 \end{pmatrix}

D. \begin{pmatrix} 7 & 8 \ 11 & 16 \end{pmatrix}

Correct Answer: A

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