Exam Body

Year

Subject

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POST UTME UNILAG 2018 Mathematics | Objective

Are you preparing for POST UTME UNILAG 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.

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Question 1

Find the area under the curve $ y = \frac{1}{x^2} $ from $ x = 1 $ to $ x = 2 $.

Correct A. $ \frac{1}{2} $

B. $ \frac{1}{3} $

C. $ \frac{1}{4} $

D. $ \frac{1}{5} $

Correct Answer: A

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Question 2

A set ( A ) contains 5 elements, and a set ( B ) contains 3 elements. If ( A cap B ) contains 2 elements, find the number of elements in ( A cup B ).

A. 7

B. 8

Correct C. 9

D. 10

Correct Answer: C

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Question 3

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

Correct Answer: A

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Question 4

A sequence is defined by $ a_n = 2n + 1 $. Find the sum of the first 5 terms of the sequence.

A. 35

B. 40

Correct C. 45

D. 50

Correct Answer: C

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Question 5

A random experiment has 3 possible outcomes, each with a probability of $ \frac{1}{3} $. Find the probability that at least one of the outcomes occurs.

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

Correct B. $ \frac{2}{3} $

C. $ \frac{1}{2} $

D. $ \frac{2}{5} $

Correct Answer: B

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Question 6

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

Correct A. 27

B. 30

C. 33

D. 36

Correct Answer: A

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Question 7

A circle has a diameter of 10 cm. Find the area of the circle.

A. 50\pi

B. 75\pi

Correct C. 100\pi

D. 125\pi

Correct Answer: C

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Question 8

A line passes through the points (2, 3) and (4, 5). Find the equation of the line in slope-intercept form.

Correct A. y = x + 1

B. y = x - 1

C. y = -x + 1

D. y = x + 2

Correct Answer: A

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Question 9

Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A and B).

A. 0.2

Correct B. 0.24

C. 0.3

D. 0.36

Correct Answer: B

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Question 10

A vector \overrightarrow{a} has a magnitude of 5 units and makes an angle of 60 degrees with the positive x-axis. Find the x and y components of the vector.

Correct A. a_x = 2.5, a_y = 4.33

B. a_x = 4.33, a_y = 2.5

C. a_x = 3.54, a_y = 3.54

D. a_x = 4.33, a_y = 3.54

Correct Answer: A

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Question 11

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

A. \frac{-x}{$ x^2 + 1 $^{3/2}}

Correct B. \frac{x}{$ x^2 + 1 $^{3/2}}

C. \frac{1}{$ x^2 + 1 $^{3/2}}

D. \frac{-1}{$ x^2 + 1 $^{3/2}}

Correct Answer: B

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Question 12

Solve the inequality $ 2x^2 + 5x - 3 > 0 $ u\sing the quadratic formula.

Correct A. x < -1 or x > 3/2

B. x < 1 or x > -3/2

C. x < -3/2 or x > 1

D. x < 3/2 or x > -1

Correct Answer: A

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Question 13

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. 1/2

B. 1/3

Correct C. 2/5

D. 3/8

Correct Answer: C

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Question 14

Find the volume of the solid formed by revolving the region bounded by the curves $ y = x^2 $ and $ y = 2x $ about the x-axis.

Correct A. \frac{16\pi}{3}

B. \frac{32\pi}{3}

C. \frac{64\pi}{3}

D. \frac{128\pi}{3}

Correct Answer: A

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Question 15

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

A. 1/2

B. 1/3

Correct C. 2/3

D. 1/6

Correct Answer: C

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Question 16

Find the value of $\int_0^1 \frac{1}{x^2 + 2x + 2} dx$.

A. 1/2

Correct B. 1/3

C. 1/4

D. 1/5

Correct Answer: B

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Question 17

Solve the equation $\log_2 $ x + 1 $ + \log_2 $ x - 1 $ = 2$.

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 18

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 = 16

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

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

Correct Answer: A

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Question 19

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

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

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

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

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

Correct Answer: A

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Question 20

Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 2x$ about the x-axis.

Correct A. \frac{4}{3}\pi

B. \frac{2}{3}\pi

C. \frac{1}{3}\pi

D. \frac{1}{2}\pi

Correct Answer: A

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Question 21

Solve the equation $\tan^2 x + \tan x - 6 = 0$.

A. \tan x = 2

B. \tan x = -3

Correct C. \tan x = 3

D. \tan x = -2

Correct Answer: C

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Question 22

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 = x + 1

D. y = x - 5

Correct Answer: A

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Question 23

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

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: VIEW ANSWER

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Question 24

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 ) takes a value greater than 0.5.

A. 0.25

B. 0.5

Correct C. 0.75

D. 1

Correct Answer: C

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Question 25

Solve the equation $ \sin^2 x + \cos^2 x = 1 \ $ for $ x \ $ in the interval $ [0, \pi] \ $.

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

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

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

D. x = \pi

Correct Answer: A

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