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POST UTME MOUNTAIN TOP UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details

Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].

A. -120

B. 120

Correct C. 0

D. 180

Correct Answer: C

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Question 2 View Details

Solve the equation [ \$\sin^2$ x + \$\cos^2$ $x = 1$ ].

Correct A. $x =$$\frac{\pi}{4}$\)

B. $x =$$\frac{\pi}{2}$\)

C. $x =$$\frac{\pi}{3}$\)

D. $x =$$\frac{\pi}{6}$\)

Correct Answer: A

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Question 3 View Details

Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...

A. 1040

Correct B. 1080

C. 1100

D. 1120

Correct Answer: B

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Question 4 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. $\frac{1}{x^2 + 1$ ^2}\)\)

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

Correct Answer: A

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Question 5 View Details

Solve the inequality [ \$(2x^2 - 5x - 3$$> 0$\) \].

Correct A. x < -1 or x > $\frac{3}{2}$\)

B. x < -1 or x < $\frac{3}{2}$\)

C. x > -1 or x < $\frac{3}{2}$\)

D. x > -1 or x > $\frac{3}{2}$\)

Correct Answer: A

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Question 6 View Details

Determine the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 50\pi $cm^3$

B. 75\pi $cm^3$

Correct C. 100\pi $cm^3$

D. 125\pi $cm^3$

Correct Answer: C

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Question 7 View Details

A particle moves in a straight line with initial velocity 5 $m/s$ and acceleration 2 $m/s\^2$. Find its velocity after 4 seconds.

A. 10 $m/s$

B. 12 $m/s$

Correct C. 14 $m/s$

D. 16 $m/s$

Correct Answer: C

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Question 8 View Details

Solve the inequality $2x^2 + 5x - 3 \geq 0$.

Correct A. x \in $-\infty, -1$ \cup [3, \infty)

B. x \in $-\infty, -3$ \cup [1, \infty)

C. x \in $-\infty, -3$ \cup [1, \infty)

D. x \in $-\infty, -1$ \cup [3, \infty)

Correct Answer: A

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Question 9 View Details

Find the area under the curve $y = 2x^2 + 3x - 1$ from $x = 0$ to $x = 2$.

A. 13

B. 15

Correct C. 17

D. 19

Correct Answer: C

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Question 10 View Details

A right-angled triangle has sides 3 cm, 4 cm, and 5 cm. Find the area of the triangle.

Correct A. 6 $cm^2$

B. 8 $cm^2$

C. 10 $cm^2$

D. 12 $cm^2$

Correct Answer: A

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Question 11 View Details

Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.

A. 64\pi $cm^3$

Correct B. 128\pi $cm^3$

C. 256\pi $cm^3$

D. 512\pi $cm^3$

Correct Answer: B

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Question 12 View Details

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

Correct A. \pm 2

B. \pm 4

C. \pm 8

D. \pm 16

Correct Answer: A

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Question 13 View Details

A particle moves along the curve (y = $x^2 + 2x + 1$\) with a velocity of $2m/s\\((y = x^2 + 2x + 1) with a velocity of$. Find the acceleration at the point where $x = 1$.

Correct A. -4 $m/s\^2$

B. -2 $m/s\^2$

C. 2 $m/s\^2$

D. 4 $m/s\^2$

Correct Answer: A

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Question 14 View Details

Find the equation of the tangent to the curve $y = x^3 - 6x^2 + 9x + 2$ at the point where \$tangent to the curve (y = x^3 - 6x^2 + 9x + 2\(x = 2$.

Correct A. $y = 3x - 5$

B. $y = 3x + 5$

C. $y = -3x + 5$

D. $y = -3x - 5$

Correct Answer: A

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Question 15 View Details

A company produces two products, A and B. The profit from the sale of product A is 10 per unit, and the profit from the sale of product B is15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?

A. $1500

Correct B. $2000

C. $2500

D. $3000

Correct Answer: B

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Question 16 View Details

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

Correct A. f'$(x) =$$\frac{-x}${ $x^2 + 1$ \)^{$3/2$}}\)

B. f'$(x) =$$\frac{x}${ $x^2 + 1$ \)^{$3/2$}}\)

C. f'$(x) =$$\frac{1}${ $x^2 + 1$ \)^{$3/2$}}\)

D. f'$(x) =$$\frac{-1}${ $x^2 + 1$ \)^{$3/2$}}\)

Correct Answer: A

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Question 17 View Details

Solve the inequality $2x^2 - 5x - 3 > 0$ using the quadratic formula.

Correct A. $x <$$\frac{3}{2}$\) \text{ or } $x > 1$

B. $x < -1$\text{ or }$x >$$\frac{3}{2}$\)

C. $x < -1$\text{ or }$x <$$\frac{3}{2}$\)

D. $x > -1$\text{ or }$x <$$\frac{3}{2}$\)

Correct Answer: A

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Question 18 View Details

Find the sum of the first 10 terms of the geometric series $2 + 6 + 18 + \cdots$.

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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Question 19 View Details

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. 2

D. 3

Correct Answer: A

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Question 20 View Details

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 21 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. $\frac{1}{3}$\)

B. $\frac{1}{2}$\)

C. $\frac{2}{3}$\)

Correct D. $\frac{5}{6}$\)

Correct Answer: D

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Question 22 View Details

A set of 5 cards is drawn from a standard deck of 52 cards. What is the probability that the set contains at least one ace?

A. $\frac{1}{52}$\)

B. $\frac{1}{26}$\)

C. $\frac{1}{13}$\)

Correct D. $\frac{51}{52}$\)

Correct Answer: D

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Question 23 View Details

A box contains 3 red balls and 2 blue balls. If a ball is drawn at random, what is the probability that it is blue?

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

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

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

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

Correct Answer: B

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Question 24 View Details

A set of 4 cards is drawn from a standard deck of 52 cards. What is the probability that the set contains at least one pair?

A. $\frac{1}{52}$\)

B. $\frac{1}{26}$\)

C. $\frac{1}{13}$\)

D. $\frac{48}{52}$\)

Correct Answer: VIEW ANSWER

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Question 25 View Details

Determine the mean of the data set {2, 4, 6, 8, 10} using the formula for the mean.

Correct A. $\frac{2+4+6+8+10}{5}$

B. $\frac{2+4+6+8+10}{4}$

C. $\frac{2+4+6+8+10}{3}$

D. $\frac{2+4+6+8+10}{2}$

Correct Answer: A

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