Exam Body

Year

Subject

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POST UTME NILE UNIVERSITY 2018 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 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the area under the curve $ y = \frac{1}{2}x^2 + 3x - 2 $ from $ x = 0 $ to $ x = 4 $.

Correct A. 24

B. 28

C. 30

D. 32

Correct Answer: A

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Question 2

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

A. 1

B. 2

C. 3

Correct D. 4

Correct Answer: D

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Question 3

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?

Correct A. 1/6

B. 1/3

C. 2/3

D. 5/6

Correct Answer: A

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Question 4

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

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

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

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

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

Correct Answer: B

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Question 5

A random variable ( X ) has a probability density function (pdf) given by ( f(x) = \frac{1}{2}e^{-|x|} ). Find the probability that ( X ) is greater than 1.

Correct A. 1/4

B. 1/2

C. 3/4

D. 1

Correct Answer: A

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Question 6

Find the equation of the line pas\sing through the points ((2,3)) and $ -1,4 \ $).

Correct A. $ y = -x + 5 $

B. $ y = x + 1 $

C. $ y = -2x + 7 $

D. $ y = 2x - 3 $

Correct Answer: A

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Question 7

A histogram of exam scores is shown below. What is the mean score of the exam?

A. 25

B. 30

Correct C. 35

D. 40

Correct Answer: C

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Question 8

Solve for ( x ) in the equation $ 2^x + 5^x = 7^x $.

A. $ x = 2 $

Correct B. $ x = 3 $

C. $ x = 4 $

D. $ x = 5 $

Correct Answer: B

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Question 9

Find the equation of the circle with center ( (3,4) ) and radius ( 5 ).

Correct A. $ x - 3 \ $^2 + $ y - 4 $^2 = 25 )

B. $ x - 4 \ $^2 + $ y - 3 $^2 = 25 )

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

D. $ x - 4 \ $^2 + $ y - 3 $^2 = 16 )

Correct Answer: A

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Question 10

A polynomial function is defined as ( f(x) = ax^3 + bx^2 + cx + d ). If $ f\( -1 \ $ = 2 ), ( f(1) = 4 ), and ( f(2) = 12 ), find the value of $ a + b + c + d $.

A. ( 10 )

B. ( 12 )

Correct C. ( 14 )

D. ( 16 )

Correct Answer: C

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Question 11

Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases}$ and $f_Y(y) = egin{cases} 3y^2 & 0 leq y leq 1 \ 0 & \text{otherwise} \end{cases}$. Find the probability that $X + Y leq 1$.

Correct A. \frac{1}{4}

B. \frac{1}{2}

C. \frac{3}{4}

D. \frac{5}{8}

Correct Answer: A

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Question 12

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 = 4

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

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

Correct Answer: A

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Question 13

If $f(x) = egin{cases} x^2 & x \geq 0 \ 0 & x < 0 \end{cases}$, find $f'(x)$.

Correct A. 2x

B. x^2

C. 0

D. x^3

Correct Answer: A

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Question 14

Solve the inequality $\frac{x^2 - 4}{x + 2} \geq 0$.

Correct A. $ -\infty, -2 $ \cup [0, \infty)

B. $ -\infty, -2 $ \cup $ 0, \infty $

C. $ -\infty, -2 $ \cup [2, \infty)

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

Correct Answer: A

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Question 15

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

Correct A. 4

B. 5

C. 6

D. 7

Correct Answer: A

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Question 16

Find the area under the curve $ y = \frac{1}{2}x^2 + 3x - 2 $ from $ x = 0 $ to $ x = 4 $.

A. 24

B. 30

Correct C. 36

D. 40

Correct Answer: C

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Question 17

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.

Correct A. 72

B. 80

C. 90

D. 100

Correct Answer: A

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Question 18

Find the derivative of the function $ y = \sqrt{x^2 + 1} $ u\sing the chain rule.

Correct A. \frac{x}{\sqrt{x^2 + 1}}

B. \frac{1}{2} \sqrt{x^2 + 1}

C. \frac{x^2}{\sqrt{x^2 + 1}}

D. \frac{1}{x^2 + 1}

Correct Answer: A

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Question 19

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

Correct A. $ -∞, -1 $ ∪ (3, ∞)

B. $ -∞, 1 $ ∪ (3, ∞)

C. $ -∞, -1 $ ∪ (1, ∞)

D. $ -∞, 3 $ ∪ (5, ∞)

Correct Answer: A

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Question 20

A circle has a radius of 4 cm. Find its circumference.

A. 8\pi

B. 10\pi

Correct C. 12\pi

D. 16\pi

Correct Answer: C

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Question 21

In a survey of 100 students, the mean height was 175 cm with a s\tandard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?

A. 0.1587

B. 0.3413

C. 0.5

Correct D. 0.8413

Correct Answer: D

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Question 22

A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. What is the volume of the prism in cubic centimeters?

Correct A. 400

B. 500

C. 600

D. 800

Correct Answer: A

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Question 23

Solve the quadratic equation $x^2 + 4x + 4 = 0$

Correct A. -2

B. 0

C. 2

D. 4

Correct Answer: A

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Question 24

A set of exam scores has a mean of 80 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be less than 70?

A. 0.1587

B. 0.3413

Correct C. 0.5

D. 0.8413

Correct Answer: C

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Question 25

A rec\tangular garden has a length of 15 m and a width of 8 m. If a path that is 2 m wide is built around the garden, what is the area of the path?

A. 48

B. 64

C. 80

Correct D. 96

Correct Answer: D

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