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POST UTME UNIOSUN 2018 Mathematics | Objective

Are you preparing for POST UTME UNIOSUN 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 derivative of ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the chain rule.

Correct A. $ \frac{2x\( x^2 + 1 \ $ - 2x^3}{$ x^2 + 1 $^2} )

B. $ \frac{2x^2 - 2x^3}{\( x^2 + 1 \ $^2} )

C. $ \frac{2x^3 - 2x}{\( x^2 + 1 \ $^2} )

D. $ \frac{2x^2 + 2x^3}{\( x^2 + 1 \ $^2} )

Correct Answer: A

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Question 2

A set of 10 students scored the following marks in a mathematics test: 85, 90, 78, 92, 88, 76, 95, 89, 91, 84. Calculate the mean and s\tandard deviation of the scores.

Correct A. Mean: 87.5, S\tandard Deviation: 5.5

B. Mean: 88.5, S\tandard Deviation: 6.5

C. Mean: 89.5, S\tandard Deviation: 7.5

D. Mean: 90.5, S\tandard Deviation: 8.5

Correct Answer: A

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Question 3

Solve the inequality $ \frac{x^2 - 4}{x^2 - 9} > 0 $.

Correct A. $ x in \( -infty, -3 \ $ cup $ -3, 2 $ cup (2, infty) )

B. $ x in \( -infty, -3 \ $ cup (2, infty) )

C. $ x in \( -3, 2 \ $ )

D. $ x in \( -infty, -3 \ $ cup (2, infty) )

Correct Answer: A

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Question 4

A geometric sequence has first term $ a = 2 $ and common ratio $ r = 3 $. Find the sum of the first 5 terms.

Correct A. $ 2 + 6 + 18 + 54 + 162 = 242 $

B. $ 2 + 6 + 18 + 54 + 162 = 242 $

C. $ 2 + 6 + 18 + 54 + 162 = 242 $

D. $ 2 + 6 + 18 + 54 + 162 = 242 $

Correct Answer: A

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Question 5

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

Correct A. 60

B. 70

C. 80

D. 90

Correct Answer: A

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Question 6

Find the value of $\frac{d}{dx}\left$ \frac{1}{x^2}\right $$.

Correct A. -\frac{2}{x^3}

B. \frac{2}{x^3}

C. -\frac{1}{x^3}

D. \frac{1}{x^3}

Correct Answer: A

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Question 7

Solve the inequality $\log_2$ x-1 $ > 2$.

Correct A. $ 4, \infty $

B. $ 2, \infty $

C. $ 1, \infty $

D. $ 0, \infty $

Correct Answer: A

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Question 8

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 9

A set $A$ contains $5$ elements, and a set $B$ contains $3$ elements. What is the number of elements in the set $A \cup B$?

A. 8

Correct B. 7

C. 6

D. 5

Correct Answer: B

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Question 10

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

A. 30

Correct B. 35

C. 40

D. 45

Correct Answer: B

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Question 11

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

Correct A. 104,783

B. 104,783

C. 104,783

D. 104,783

Correct Answer: A

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Question 12

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

Correct A. $ -\infty, -2 $ \cup $ 2, \infty $

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

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

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

Correct Answer: A

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Question 13

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 = 25

C. $ x - 2 $^2 + $ y - 3 $^2 = 36

D. $ x - 2 $^2 + $ y - 3 $^2 = 49

Correct Answer: A

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Question 14

Evaluate the definite integral \int_0^1 x^2 dx.

Correct A. \frac{1}{3}

B. \frac{1}{3}

C. \frac{1}{3}

D. \frac{1}{3}

Correct Answer: A

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Question 15

Find the derivative of the function f(x) = 3x^2 + 2x - 5.

Correct A. 6x + 2

B. 6x + 2

C. 6x + 2

D. 6x + 2

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 $.

Correct A. \frac{1}{6}$ 4^3 + 12 cdot 4^2 - 8 cdot 4 $ + 3 cdot 4^2 - 2 cdot 4

B. \frac{1}{6}$ 4^3 + 12 cdot 4^2 - 8 cdot 4 $ + 3 cdot 4^2 - 2 cdot 4 + 2

C. \frac{1}{6}$ 4^3 + 12 cdot 4^2 - 8 cdot 4 $ + 3 cdot 4^2 - 2 cdot 4 - 2

D. \frac{1}{6}$ 4^3 + 12 cdot 4^2 - 8 cdot 4 $ + 3 cdot 4^2 - 2 cdot 4 + 4

Correct Answer: A

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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. 6 cdot 4 cdot 3

B. 6 cdot 4 cdot 3 + 2

C. 6 cdot 4 cdot 3 - 2

D. 6 cdot 4 cdot 3 + 4

Correct Answer: A

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Question 18

Solve the inequality $ |x - 2| geq 3 $.

Correct A. x leq -1 \text{ or } x geq 5

B. x leq 1 \text{ or } x geq 5

C. x leq -1 \text{ or } x geq 4

D. x leq -1 \text{ or } x geq 3

Correct Answer: A

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Question 19

Find the determinant of the matrix [egin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{pmatrix}].

Correct A. 2 cdot $ 2 cdot 2 - 1 cdot 1 $ - 1 cdot $ 4 cdot 2 - 1 cdot 3 $ + 3 cdot $ 4 cdot 1 - 2 cdot 3 $

B. 2 cdot $ 2 cdot 2 - 1 cdot 1 $ - 1 cdot $ 4 cdot 2 - 1 cdot 3 $ - 3 cdot $ 4 cdot 1 - 2 cdot 3 $

C. 2 cdot $ 2 cdot 2 - 1 cdot 1 $ + 1 cdot $ 4 cdot 2 - 1 cdot 3 $ + 3 cdot $ 4 cdot 1 - 2 cdot 3 $

D. 2 cdot $ 2 cdot 2 - 1 cdot 1 $ + 1 cdot $ 4 cdot 2 - 1 cdot 3 $ - 3 cdot $ 4 cdot 1 - 2 cdot 3 $

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 - 2 $^2 + $ y - 3 $^2 = 4

C. $ x - 2 $^2 + $ y - 3 $^2 = 9

D. $ x - 2 $^2 + $ y - 3 $^2 = 25

Correct Answer: A

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Question 21

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. 24\pi cm^3

Correct B. 48\pi cm^3

C. 64\pi cm^3

D. 96\pi cm^3

Correct Answer: B

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Question 22

A circle passes through the points (2, 3) and (4, 5). Find the equation of the circle.

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

Correct B. $ x - 2 $^2 + $ y - 3 $^2 = 25

C. $ x - 4 $^2 + $ y - 5 $^2 = 25

D. $ x - 3 $^2 + $ y - 5 $^2 = 25

Correct Answer: B

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Question 23

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

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

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

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

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

Correct Answer: A

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Question 24

Find the mean of the following data: 2, 4, 6, 8, 10.

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 25

A polynomial function f(x) has zeros at x = -2, x = 1, and x = 3. Write the function in factored form.

A. f(x) = $ x + 2 $$ x - 1 $$ x - 3 $

Correct B. f(x) = a$ x + 2 $$ x - 1 $$ x - 3 $

C. f(x) = $ x + 2 $$ x - 1 $$ x - 3 $ + 2

D. f(x) = a$ x + 2 $$ x - 1 $$ x - 3 $ + 2

Correct Answer: B

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