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POST UTME COAL CITY UNIVERSITY 2020 Mathematics | Objective

Are you preparing for POST UTME COAL CITY UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Let ( f(x) = \frac{1}{x^2 + 1} ). Find $ int_{-\frac{pi}{2}}^{\frac{pi}{2}} f\( x \ $ , dx ).

A. 0

B. 1

Correct C. π

D. 2π

Correct Answer: C

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Question 2

Solve the system of equations: $ egin{cases} x + y + z = 6 \ 2x + 3y + z = 12 \ x + 2y + 3z = 9 \end{cases} $.

Correct A. [1, 2, 3]

B. [2, 1, 3]

C. [1, 3, 2]

D. [3, 2, 1]

Correct Answer: A

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Question 3

A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 7?

A. 1/6

Correct B. 1/12

C. 1/2

D. 5/6

Correct Answer: B

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Question 4

Find the area under the curve $ y = 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 5

Solve the equation $ x^3 - 6x^2 + 11x - 6 = 0 $.

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 6

In a certain number base, the value of the digit 5 is represented as $ overline{1011}_b $. If the base is denoted as ( b ), find the value of ( b ) in base 10.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 7

A polynomial ( P(x) ) is defined as ( P(x) = ax^3 + bx^2 + cx + d ). If ( P(1) = 4 ), ( P(2) = 12 ), and ( P(3) = 24 ), 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 8

Two events, ( A ) and ( B ), are indep\endent. If ( P(A) = 0.4 ) and ( P(B) = 0.6 ), find the probability that both events occur.

A. 0.2

Correct B. 0.24

C. 0.28

D. 0.32

Correct Answer: B

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Question 9

Find the determinant of the matrix $ egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} $.

Correct A. -1

B. 1

C. 3

D. 5

Correct Answer: A

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Question 10

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. 84

D. 90

Correct Answer: A

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Question 11

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 12

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

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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Question 13

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

A. x < -1 or x > 2

Correct B. x < 1 or x > 2

C. x < -1 or x < 2

D. x < 1 or x < 2

Correct Answer: B

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Question 14

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

A. 18

B. 20

Correct C. 22

D. 24

Correct Answer: C

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Question 15

A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?

A. 18

B. 20

Correct C. 22

D. 24

Correct Answer: C

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Question 16

Find the value of $\frac{d}{dx} \left$ \frac{1}{x^2 + 1} \right $$ u\sing the quotient rule.

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

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

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

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

Correct Answer: A

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Question 17

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

Correct A. $ -∞, -1 $ ∪ (4, ∞)

B. $ -∞, 1 $ ∪ (4, ∞)

C. $ -∞, -1 $ ∪ (1, 4)

D. $ -∞, 1 $ ∪ (1, 4)

Correct Answer: A

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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

Solve the matrix equation $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}$.

Correct A. x = 1, y = 2

B. x = 2, y = 1

C. x = 1, y = 1

D. x = 2, y = 2

Correct Answer: A

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Question 20

Find the value of $\int_0^1 x^2 dx$.

Correct A. 1/3

B. 1/2

C. 2/3

D. 1

Correct Answer: A

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Question 21

Find the value of x in the equation $ \log_{10} \( x^2 \ $ = 4 ).

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 22

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

Correct A. $ -∞, -1 $ ∪ (3, ∞)

B. $ -∞, -3 $ ∪ (1, ∞)

C. $ -∞, 1 $ ∪ (3, ∞)

D. $ -∞, -3 $ ∪ (1, ∞)

Correct Answer: A

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Question 23

Find the sum of the first 10 terms of the geometric series $ 2 + 6 + 18 + ldots $.

A. 1950

Correct B. 1960

C. 1970

D. 1980

Correct Answer: B

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Question 24

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 25

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

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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