Exam Body

Year

Subject

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POST UTME WELLSPRING UNIVERSITY 2020 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 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the determinant of the matrix $ egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} $.

Correct A. 10

B. -1

C. 7

D. -7

Correct Answer: A

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Question 2

If ( f(x) = \frac{1}{x} ), find ( f'(x) ) u\sing the chain rule.

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

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

C. $ -\frac{1}{x} $

D. $ \frac{1}{x} $

Correct Answer: A

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Question 3

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its surface area.

Correct A. 104 cm^2

B. 96 cm^2

C. 112 cm^2

D. 120 cm^2

Correct Answer: A

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Question 4

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

Correct A. $ x = -2 $

B. $ x = -1 $

C. $ x = 1 $

D. $ x = 2 $

Correct Answer: A

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Question 5

A circle has a radius of 4 cm. Find its circumference.

Correct A. ( 8pi ) cm

B. ( 16pi ) cm

C. ( 32pi ) cm

D. ( 64pi ) cm

Correct Answer: A

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Question 6

A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the number on the die is even, the coin is flipped twice; otherwise, the coin is flipped only once. Let X be the number of heads obtained from the coin flips. What is E[X]?

A. 1

Correct B. 1.5

C. 2

D. 2.5

Correct Answer: B

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Question 7

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 8

A set of 10 points is chosen at random from a circle of radius 1. What is the probability that the dis\tance between the two closest points is greater than $ \frac{1}{2} $?

A. 0

B. \frac{1}{2}

Correct C. \frac{3}{4}

D. 1

Correct Answer: C

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Question 9

Find the sum of the infinite geometric series $ \sum_{n=1}^\infty \frac{1}{2^n} $

A. 1

B. \frac{1}{2}

Correct C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: C

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Question 10

A polynomial f(x) is defined as $ f(x) = x^3 + 2x^2 - 5x - 3 $. Find the value of f$ -1 $.

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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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

Solve the equation \[\sqrt{x + 5} + \sqrt{x - 3} = 7\] for x.

Correct A. \boxed{x = 16}

B. x = 10

C. x = 20

D. x = 22

Correct Answer: A

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Question 13

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

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

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

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

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

Correct Answer: A

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Question 14

Solve the system of equations \[\begin{cases} x + y = 4 \ 2x - 3y = -3 \end{cases}\] u\sing matrices.

Correct A. \boxed{\begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 1 \ 3 \end{pmatrix}}

B. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 2 \ 2 \end{pmatrix}

C. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 3 \ 1 \end{pmatrix}

D. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 4 \ 0 \end{pmatrix}

Correct Answer: A

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Question 15

Find the area of the triangle with vertices (1, 2), (3, 4), and (5, 6).

Correct A. \boxed{\frac{1}{2} \times 6 \times 4 = 12}

B. \frac{1}{2} \times 6 \times 5 = 15

C. \frac{1}{2} \times 4 \times 5 = 10

D. \frac{1}{2} \times 6 \times 3 = 9

Correct Answer: A

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Question 16

Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.

Correct A. \frac{16\pi}{3}

B. \frac{32\pi}{3}

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

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

Correct Answer: A

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Question 17

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

Correct A. $ 1, \infty $

B. $ -\infty, 1 $

C. (1, 2)

D. $ 2, \infty $

Correct Answer: A

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Question 18

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{2}{$ x^2 + 1 $^2}

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

Correct Answer: B

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Question 19

Evaluate the definite integral $\int_0^1 x^2 \sin x dx$.

Correct A. -\cos x + \sin x

B. \cos x - \sin x

C. -\sin x - \cos x

D. \sin x + \cos x

Correct Answer: A

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Question 20

Find the surface area of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 21

Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the quotient rule.

A. ( f'(x) = \frac{2x$ x - 2 $ - $ x^2 - 4 $}{$ x - 2 $^2} \)

B. ( f'(x) = \frac{2x$ x - 2 $ + $ x^2 - 4 $}{$ x - 2 $^2} \)

Correct C. ( f'(x) = \frac{2x$ x - 2 $ - $ x^2 - 4 $}{$ x - 2 $^2} \)

D. ( f'(x) = \frac{2x$ x - 2 $ + $ x^2 - 4 $}{$ x - 2 $^2} \)

Correct Answer: C

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Question 22

A set ( A ) contains the elements $ \{ 1, 2, 3, 4, 5 \} $. Find the number of subsets of ( A ) that contain exactly three elements.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 23

A sequence is defined by $ a_n = 2n + 1 $. Find the sum of the first five terms of the sequence.

A. 30

B. 35

C. 40

Correct D. 45

Correct Answer: D

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Question 24

A random experiment consists of rolling a fair six-sided die. Find the probability that the number rolled is greater than 4.

A. \frac{1}{6}

B. \frac{1}{3}

C. \frac{2}{3}

Correct D. \frac{5}{6}

Correct Answer: D

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Question 25

A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, with the heights of the bars being 8, 12, 15, 10, and 5. Find the mean of the exam scores.

A. 10

Correct B. 12

C. 15

D. 18

Correct Answer: B

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