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POST UTME BELLS UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

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

Correct A. 2 \cdot $\frac{3^{10} - 1}{3 - 1}$\)

B. 2 \cdot $\frac{3^{11} - 1}{3 - 1}$\)

C. 2 \cdot $\frac{3^{12} - 1}{3 - 1}$\)

D. 2 \cdot $\frac{3^{13} - 1}{3 - 1}$\)

Correct Answer: A

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Question 2 View Details

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

Correct A. $x = -2$

B. $x = 2$

C. $x = -1$

D. $x = 1$

Correct Answer: A

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Question 3 View Details

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

Correct A. $1/2$

B. $1/3$

C. $2/5$

D. $3/8$

Correct Answer: A

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Question 4 View Details

Find the equation of the line passing through the points (2, 3) and (4, 5).

Correct A. $y = x + 1$

B. $y = x - 1$

C. $y = -x + 3$

D. $y = x + 3$

Correct Answer: A

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Question 5 View Details

A company produces x units of a product and incurs a fixed \cost of ₦5000 and a variable \cost of ₦200 per unit. If the selling price is ₦300 per unit, find the break-even point.

Correct A. $x = 20$

B. $x = 25$

C. $x = 30$

D. $x = 35$

Correct Answer: A

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Question 6 View Details

Solve for x in the equation $\frac{x}{2} + 5 = 11$.

Correct A. 6

B. 12

C. 18

D. 24

Correct Answer: A

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Question 7 View Details

A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:4, how many loaves of whole wheat bread are sold per day?

A. 100

Correct B. 120

C. 150

D. 200

Correct Answer: B

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Question 8 View Details

Find the derivative of the function ( f(x) = $3x^2 + 2x - 5$ ) using the power rule.

Correct A. 6x + 2

B. 6x - 2

C. $3x^2 + 2$

D. $3x^2 - 2$

Correct Answer: A

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Question 9 View Details

A box contains 12 red balls and 8 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. $1/3$

Correct B. $1/4$

C. $2/5$

D. $3/5$

Correct Answer: B

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Question 10 View Details

Solve the inequality $2x - 5 > 3x + 2$.

Correct A. $x < -1$

B. $x > -1$

C. $x < 1$

D. $x > 1$

Correct Answer: A

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Question 11 View Details

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

Correct A. $\frac{32\pi}{15}$\)

B. $\frac{16\pi}{3}$\)

C. $\frac{32\pi}{5}$\)

D. $\frac{64\pi}{3}$\)

Correct Answer: A

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Question 12 View Details

Find the equation of the tangent line to the curve $y = \frac{1}{x}\\(tangent line to the curve (y =$ at the point $2, \frac{1}{2}$\).

A. $y = -$$\frac{1}{4}$\) x + 1

Correct B. $y = -$$\frac{1}{4}$\) x + $\frac{1}{2}$\)

C. $y =$$\frac{1}{4}$\) x + 1

D. $y =$$\frac{1}{4}$\) x + $\frac{1}{2}$\)

Correct Answer: B

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Question 13 View Details

A histogram of the heights of students in a class is shown below. If the class has 50 students, what is the probability that a randomly selected student is between 165 and 170 cm tall?

A. $\frac{1}{5}$\)

B. $\frac{2}{5}$\)

Correct C. $\frac{3}{5}$\)

D. $\frac{4}{5}$\)

Correct Answer: C

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Question 14 View Details

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

Correct A. $-\infty, -1$ \cup $4, \infty$

B. $-\infty, 1$ \cup $4, \infty$

C. $-\infty, -1$ \cup $1, \infty$

D. $-\infty, 1$ \cup $2, \infty$

Correct Answer: A

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Question 15 View Details

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

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

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

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

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

Correct Answer: A

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Question 16 View Details

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

Correct A. $\frac{-x}{1 - x^2 \$^{$3/2$}} )

B. $\frac{x}{1 - x^2 \$^{$3/2$}} )

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

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

Correct Answer: A

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Question 17 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. What is the probability that a randomly selected score is between 60 and 90?

A. 0.68

Correct B. 0.84

C. 0.95

D. 0.99

Correct Answer: B

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Question 18 View Details

Evaluate the definite integral $int_{0}^{1} x^2 $1x , dx$ using integration by parts.

Correct A. $-\(1x + x^2$1x\)

B. $\(1x - x^2$1x\)

C. $-\(1x - x^2$1x\)

D. $\(1x + x^2$1x\)

Correct Answer: A

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Question 19 View Details

Solve the equation $2^x + 2^{-x} = 10$ for ( x ).

Correct A. $x = \log_2 3$

B. $x = -\log_2 3$

C. $x = \log_2 5$

D. $x = -\log_2 5$

Correct Answer: A

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Question 20 View Details

A circle has a radius of 4 cm. Find the area of the circle using the formula $A = \pi r^2$.

Correct A. ( 16pi ) $cm^2$

B. ( 32pi ) $cm^2$

C. ( 64pi ) $cm^2$

D. ( 128pi ) $cm^2$

Correct Answer: A

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Question 21 View Details

Find the area under the curve $y = \frac{1}{2}x^2$ from $x = 0$ to $x = 4$.

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 22 View Details

Solve for ( x ) in the equation $2x + 5 = 11$.

Correct A. 3

B. 4

C. 5

D. 6

Correct Answer: A

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Question 23 View Details

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

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 24 View Details

Solve the inequality $2x - 5 > 3$.

Correct A. $x > 4$

B. $x < 4$

C. $x > 3$

D. $x < 3$

Correct Answer: A

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Question 25 View Details

Find the equation of the line passing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. $y = 1x + 1$

B. $y = 2x + 2$

C. $y = 3x + 3$

D. $y = 4x + 4$

Correct Answer: A

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