Exam Body

Year

Subject

Paper Type

POST UTME MOUNTAIN TOP UNIVERSITY 2021 Mathematics | Objective

Prepare for your exams with POST UTME MOUNTAIN TOP UNIVERSITY questions? Reviewing past/model questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1 View Details

Solve the inequality $(2x^2 + 5x - 3$ > 0\) for ( x ) in the interval $-\\((2x^2 + 5x - 3 > 0) for ( x ) in the interval \infty, \infty \$ ).

Correct A. $x < -\frac{5}{4}$ or $x > \frac{3}{2}$

B. $x < -\frac{5}{4}$ or $x < \frac{3}{2}$

C. $x > -\frac{5}{4}$ or $x < \frac{3}{2}$

D. $x > -\frac{5}{4}$ or $x > \frac{3}{2}$

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 2 View Details

Find the value of ( x ) in the equation $\sin^2 x + \cos^2 x = 1$.

A. $x = \frac{\pi}{2}$

Correct B. $x = \frac{\pi}{4}$

C. $x = \frac{3\pi}{4}$

D. $x = \frac{5\pi}{4}$

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 3 View Details

In the circuit below, find the equivalent resistance.

A. ( 2 Omega )

B. ( 4 Omega )

Correct C. ( 6 Omega )

D. ( 8 Omega )

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 4 View Details

Find the sum of the first 5 terms of the geometric series $2x^2 + 3x + 4$.

A. $2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4$

B. $2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4$

Correct C. $2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4$

D. $2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4 + 2x^2 + 3x + 4$

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 5 View Details

Find the probability of drawing two hearts from a standard deck of 52 cards.

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

Correct B. $\frac{1}{52} \times \frac{1}{52}$

C. $\frac{1}{52} + \frac{1}{52}$

D. $\frac{1}{52} \times \frac{1}{52}$

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 6 View Details

Find the value of (x\) in the equation $2^x + 2^{x+1} = 3 \\((x) in the equation \cdot 2^{x+1}$.

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 7 View Details

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

A. x \in $-\infty, -2 \cup 1, \infty$\)

B. x \in $-\infty, -2 \cup [1, \infty)$

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

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

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 8 View Details

Find the sum of the first 10 terms of the geometric series $\sum_{n = 1}^{10} \frac{2}{3^n}$.

A. $\frac{63}{32}$

B. $\frac{127}{64}$

C. $\frac{255}{128}$

Correct D. $\frac{511}{256}$

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 9 View Details

In the diagram below, (ABCD\) is a rectangle with $AB = 6\\((ABCD) is a rectangle with$ and $BC = 8$. Find the area of the shaded region.

A. 24

B. 32

C. 40

Correct D. 48

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 10 View Details

Solve the quadratic equation $x^2 + 5x + 6 = 0$.

Correct A. $x = -2$

B. $x = -3$

C. $x = -1$

D. $x = 1$

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 11 View Details

Determine the mean of the following data set: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. If the mean is 12, what is the value of the missing number in the data set?

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 12 View Details

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 13 View Details

Find the determinant of the matrix $egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}$.

A. -2

Correct B. 2

C. 4

D. 6

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 14 View Details

Differentiate the function ( f(x) = $3x^2 + 2x - 5$ ) with respect to x.

A. 6x + 2

B. $6x^2 + 2x$

C. $6x^2 + 4x - 5$

Correct D. $6x^2 + 2x - 5$

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 15 View Details

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

Correct A. $-∞, -1$ ∪ (3, ∞)

B. $-∞, -3$ ∪ (1, ∞)

C. $-∞, -1$ ∪ (1, ∞)

D. $-∞, 1$ ∪ (3, ∞)

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 16 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 48\pi $cm^3$

B. 64\pi $cm^3$

Correct C. 80\pi $cm^3$

D. 96\pi $cm^3$

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 17 View Details

Solve for x in the equation $2^x + 3^x = 5^x$.

A. $x = 2$

Correct B. $x = 3$

C. $x = 4$

D. $x = 5$

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 18 View Details

Find the area of the region bounded by the parabola (y = x\^2\), the line \$(y = x^2\(y = 4$, and the x-axis.

A. 16

B. 32

Correct C. 48

D. 64

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 19 View Details

Solve the system of equations $x + y = 4$ and $xy = 5$.

Correct A. $x = 1$, $y = 3$

B. $x = 2$, $y = 2$

C. $x = 3$, $y = 1$

D. $x = 4$, $y = 0$

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

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. $x - 3$^2 + $y - 2$^$2 = 16$

C. $x - 4$^2 + $y - 3$^$2 = 16$

D. $x - 2$^2 + $y - 4$^$2 = 16$

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 21 View Details

Let $\mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}$ and $\mathbf{b} = egin{pmatrix} 4 \ 5 end{pmatrix}$. Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) using the formula $\\(end{pmatrix}). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) using the formula \mathrm{proj}_{\mathbf{a}} \mathbf{b} = \frac{\mathbf{a} \cdot \mathbf{b}}{| \mathbf{a} |^2} \mathbf{a}$.

Correct A. $egin{pmatrix} 0.8 \ 1.2 \end{pmatrix}$

B. $egin{pmatrix} 1.6 \ 2.4 \end{pmatrix}$

C. $egin{pmatrix} 2.4 \ 3.6 \end{pmatrix}$

D. $egin{pmatrix} 3.2 \ 4.8 \end{pmatrix}$

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 22 View Details

A random variable ( X ) has a probability distribution given by $P X = k \$ = $\frac{1}{2^k}$\)\) ) for $k = 1, 2, 3, ldots$. Find the expected value of ( X ).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 23 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 24 View Details

Find the derivative of the function ( f(x) = \$\sin^2$ x ) using the chain rule.

Correct A. $2 \(1x$1x\)

B. $2 $1x$

C. $2 $1x$

D. $2 \sin^2 x$

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 25 View Details

A binary operation ( ast ) is defined as $a ast b = a^2 + b^2$. Find the value of ( 2 ast 3 ).

A. 13

B. 17

C. 19

Correct D. 25

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows

Help others prepare! Share this practice hub:

Chat with Support