Exam Body

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Subject

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POST UTME WELLSPRING UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

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 View Details

If ( f(x) = $\frac{1}{x}$\) ), find ( f'(x) ) using 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 View Details

A rectangular 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 View Details

Solve the equation $x^2 + 4x + 4 = 0$ using 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 View Details

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 View Details

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 View Details

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 View Details

A set of 10 points is chosen at random from a circle of radius 1. What is the probability that the distance 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 View Details

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 View Details

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

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 11 View Details

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 View Details

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 View Details

Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$ using 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 View Details

Solve the system of equations $\begin{cases} x + y = 4 \ 2x - 3y = -3 \end{cases}$ using 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 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$ using 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 View Details

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

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 View Details

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 View Details

Let ( f(x) = $\frac{x^2 - 4}{x - 2}$\)\) ). Find the derivative of ( f(x) ) using 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 View Details

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 View Details

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 View Details

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 View Details

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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