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POST UTME MOUNTAIN TOP UNIVERSITY 2021 Mathematics | Objective

Are you preparing for POST UTME MOUNTAIN TOP UNIVERSITY exams? Reviewing past 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.

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Question 1

Solve the inequality $ 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

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Question 2

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{3pi}{4} $

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

Correct Answer: B

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Question 3

In the circuit below, find the equivalent resis\tance.

A. ( 2 Omega )

B. ( 4 Omega )

Correct C. ( 6 Omega )

D. ( 8 Omega )

Correct Answer: C

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Question 4

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

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Question 5

Find the probability of drawing two hearts from a s\tandard 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

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Question 6

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

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 7

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

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Question 8

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

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Question 9

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

A. 24

B. 32

C. 40

Correct D. 48

Correct Answer: D

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Question 10

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

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Question 11

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 mis\sing number in the data set?

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 12

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 13

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

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Question 14

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

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Question 15

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

Correct A. $ -∞, -1 $ ∪ (3, ∞)

B. $ -∞, -3 $ ∪ (1, ∞)

C. $ -∞, -1 $ ∪ (1, ∞)

D. $ -∞, 1 $ ∪ (3, ∞)

Correct Answer: A

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Question 16

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

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Question 17

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

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Question 18

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

A. 16

B. 32

Correct C. 48

D. 64

Correct Answer: C

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Question 19

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

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Question 20

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

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Question 21

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} ) u\sing 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

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Question 22

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

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Question 23

A histogram of exam scores has a mean of 75 and a s\tandard 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

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Question 24

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

Correct A. $ 2 \sin x \cos x $

B. $ 2 \sin x $

C. $ 2 \cos x $

D. $ 2 \sin^2 x $

Correct Answer: A

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Question 25

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

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