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POST UTME NILE UNIVERSITY 2021 Mathematics | Objective

Are you preparing for POST UTME NILE 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.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \tan\( x \ \) = \frac{3}{4} ).

Correct A. \( \frac{pi}{6} \)

B. \( \frac{pi}{4} \)

C. \( \frac{pi}{3} \)

D. \( \frac{pi}{2} \)

Correct Answer: A

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Question 2

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 is between 60 and 90?

Correct A. 0.8413

B. 0.8413

C. 0.8413

D. 0.8413

Correct Answer: A

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Question 3

Solve for x in the equation \( 2^x + 2^{-x} = 3 \).

Correct A. \( \log_2\( 2 \ \) )

B. \( \log_2\( 3 \ \) )

C. \( \log_2\( 4 \ \) )

D. \( \log_2\( 5 \ \) )

Correct Answer: A

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Question 4

Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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Question 5

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 6

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 7

Solve the system of linear equations: \( \begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases} \).

Correct A. x = 1, y = 2

B. x = 2, y = 1

C. x = 3, y = 4

D. x = 4, y = 3

Correct Answer: A

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Question 8

Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 4 \ 3 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix} \).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 9

Sketch the graph of the function \( y = |x - 2| \).

Correct A. A graph with a \single vertex at (2, 0)

B. A graph with a \single vertex at (0, 2)

C. A graph with a \single vertex at (2, 2)

D. A graph with a \single vertex at (0, 0)

Correct Answer: A

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Question 10

Find the mean of the data set: \( \{ 2, 4, 6, 8, 10 \} \).

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 11

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

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

Solve the inequality \frac{x-2}{x+1} > 0.

Correct A. x < -1 \text{ or } x > 2

B. x < -1 \text{ or } x < 2

C. x > -1 \text{ or } x > 2

D. x > -1 \text{ or } x < 2

Correct Answer: A

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Question 13

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

A. 116

B. 118

Correct C. 120

D. 122

Correct Answer: C

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Question 14

Solve the equation \log_{10} x^2 = 4.

A. x = 10^2

Correct B. x = 10^4

C. x = 10^{-2}

D. x = 10^{-4}

Correct Answer: B

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Question 15

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

A. 12

B. 14

Correct C. 16

D. 18

Correct Answer: C

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Question 16

Let X and Y be indep\endent random variables with mean 0 and variance 1. What is the probability that X + Y is greater than 2?

A. 0.5

B. 0.25

Correct C. 0.75

D. 0.125

Correct Answer: C

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Question 17

Solve the system of linear equations u\sing the method of substitution: \begin{align*} x + 2y &= 6 \ 3x - 2y &= -3 \end{align*}

Correct A. x = 1, y = 2

B. x = 2, y = 1

C. x = 3, y = 2

D. x = 4, y = 3

Correct Answer: A

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Question 18

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the probability that a randomly selected score is greater than 70?

A. 0.25

B. 0.5

Correct C. 0.75

D. 0.9

Correct Answer: C

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Question 19

Solve the quadratic equation: \begin{align*} x^2 + 5x + 6 &= 0 \end{align*}

Correct A. x = -2, x = -3

B. x = 2, x = 3

C. x = -1, x = -6

D. x = 1, x = 6

Correct Answer: A

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Question 20

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

Correct A. y = 2x + 1

B. y = 2x - 1

C. y = x + 2

D. y = x - 2

Correct Answer: A

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Question 21

Let X be a random variable with probability density function f(x) = \( egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} \). Find the probability that X is greater than 0.5.

Correct A. 0.25

B. 0.5

C. 0.75

D. 1

Correct Answer: A

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Question 22

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

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 23

A binary operation \( * \) on the set of integers is defined as follows: \( a * b = a^2 + b^2 \). Find the value of \( 2 * 3 \).

A. 4

B. 5

C. 10

Correct D. 13

Correct Answer: D

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Question 24

In the diagram below, what is the value of x?

A. 30

B. 60

Correct C. 90

D. 120

Correct Answer: C

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Question 25

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( -∞, -3 \) ∪ (1, ∞)

B. \( -∞, -1 \) ∪ (3, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ \( -1, 1 \)

Correct Answer: A

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