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POST UTME WELLSPRING UNIVERSITY 2024 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 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.

Correct A. \frac{32\pi}{3}

B. \frac{64\pi}{3}

C. \frac{128\pi}{3}

D. \frac{256\pi}{3}

Correct Answer: A

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Question 2

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

A. \pm 10

Correct B. \pm 100

C. \pm 1000

D. \pm 10000

Correct Answer: B

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Question 3

Find the surface area of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.

Correct A. \frac{64\pi}{3}

B. \frac{128\pi}{3}

C. \frac{256\pi}{3}

D. \frac{512\pi}{3}

Correct Answer: A

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Question 4

Solve the system of equations \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*} u\sing matrices.

Correct A. \begin{pmatrix} 1 \ 2 \end{pmatrix}

B. \begin{pmatrix} 2 \ 1 \end{pmatrix}

C. \begin{pmatrix} 3 \ 4 \end{pmatrix}

D. \begin{pmatrix} 4 \ 3 \end{pmatrix}

Correct Answer: A

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Question 5

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

Correct A. -120

B. -240

C. -360

D. -480

Correct Answer: A

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Question 6

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 7

Solve the system of equations: \( egin{cases} x + y = 4 \ 2x - 3y = - 3 \end{cases} \).

A. \( -1, 5 \)

B. (1, 3)

Correct C. (2, 2)

D. (4, 0)

Correct Answer: C

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Question 8

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 = 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 9

Find the sum of the first 10 terms of the geometric series with first term \( a = 2 \) and common ratio \( r = 3 \).

Correct A. 3199

B. 3198

C. 3197

D. 3196

Correct Answer: A

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Question 10

Solve the inequality \( x^2 - 4x - 5 > 0 \).

Correct A. \( x < -1 \) or \( x > 5 \)

B. \( x < 1 \) or \( x > 5 \)

C. \( x < -1 \) or \( x < 5 \)

D. \( x > 1 \) or \( x > 5 \)

Correct Answer: A

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Question 11

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)

D. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \times 4 \)

Correct Answer: A

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Question 12

A fair six-sided die is rolled. If the number 5 is rolled, a second die is rolled. What is the probability that the sum of the numbers on the two dice is 10?

A. \( \frac{1}{6} \times \frac{1}{6} \)

Correct B. \( \frac{1}{6} \times \frac{5}{6} \)

C. \( \frac{1}{6} + \frac{1}{6} \)

D. \( \frac{1}{6} \times \frac{6}{6} \)

Correct Answer: B

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Question 13

Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).

Correct A. \( x = \frac{-5 pm \sqrt{25 + 24}}{4} \)

B. \( x = \frac{-5 pm \sqrt{25 - 24}}{4} \)

C. \( x = \frac{-5 pm \sqrt{25 + 24}}{2} \)

D. \( x = \frac{-5 pm \sqrt{25 - 24}}{2} \)

Correct Answer: A

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Question 14

Find the determinant of the matrix \( egin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} \).

Correct A. \( 2 \times 6 \times 10 - 3 \times 5 \times 10 - 4 \times 8 \times 6 \)

B. \( 2 \times 6 \times 10 + 3 \times 5 \times 10 - 4 \times 8 \times 6 \)

C. \( 2 \times 6 \times 10 - 3 \times 5 \times 10 + 4 \times 8 \times 6 \)

D. \( 2 \times 6 \times 10 + 3 \times 5 \times 10 + 4 \times 8 \times 6 \)

Correct Answer: A

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Question 15

A circle has a radius of 5 cm. Find the area of the circle.

Correct A. \( pi \times 5^2 \)

B. \( 2 pi \times 5 \)

C. \( pi \times 5 \)

D. \( 2 pi \times 5^2 \)

Correct Answer: A

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Question 16

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3/2.

Correct A. 2.488

B. 2.488

C. 2.488

D. 2.488

Correct Answer: A

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Question 17

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

Correct A. \( -\infty, -2 \) \cup \( 1, \infty \)

B. \( -\infty, -2 \) \cup \( 1, \infty \)

C. \( -\infty, -2 \) \cup \( 1, \infty \)

D. \( -\infty, -2 \) \cup \( 1, \infty \)

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. \( x-2 \)^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 19

Solve the system of equations \begin{align*} x+y+z &= 3 \ x+2y+3z &= 7 \ x+3y+6z &= 12 \end{align*}

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

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

C. \begin{align*} x &= 1 \ y &= 1 \ z &= 1 \end{align*}

D. \begin{align*} x &= 1 \ y &= 1 \ z &= 1 \end{align*}

Correct Answer: A

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Question 20

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

Correct A. 6

B. 6

C. 6

D. 6

Correct Answer: A

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Question 21

Determine the value of x in the equation \( \tan\( 2x \ \) = \sqrt{3} ) given that \( 0^circ leq x leq 90^circ \).

A. 45^circ

B. 30^circ

Correct C. 60^circ

D. 90^circ

Correct Answer: C

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Question 22

Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).

Correct A. 1

B. -1

C. 2

D. -2

Correct Answer: A

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Question 23

A random experiment consists of rolling a fair six-sided die. If the outcome is an even number, the experimenter wins a prize. If the outcome is an odd number, the experimenter loses a prize. What is the probability that the experimenter wins the prize?

Correct A. 1/2

B. 1/3

C. 2/3

D. 1/6

Correct Answer: A

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Question 24

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

A. 32\pi

B. 16\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 25

A histogram of the heights of students in a class has a mean of 170 cm and a s\tandard deviation of 10 cm. What is the probability that a randomly selected student is taller than 180 cm?

A. 0.1587

B. 0.3413

C. 0.5

Correct D. 0.8413

Correct Answer: D

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