POST UTME BOWEN UNIVERSITY 2020 Mathematics | Objective

Are you preparing for POST UTME BOWEN 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
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 5 \).
Correct A. 75
B. 100
C. 125
D. 150

Correct Answer: A

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Question 2
Solve the inequality \( |2x - 3| geq 7 \).
Correct A. x \leq -2 \text{ or } x \geq 5
B. x \leq 2 \text{ or } x \geq -3
C. x \leq -5 \text{ or } x \geq 2
D. x \leq 3 \text{ or } x \geq -2

Correct Answer: A

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Question 3
Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( x = 2 \) about the x-axis.
A. 32\pi
B. 64\pi
Correct C. 128\pi
D. 256\pi

Correct Answer: C

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Question 4
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If 5% of the scores are below 40, what is the value of the z-score corresponding to a score of 50?
A. 0.5
Correct B. 1
C. 1.5
D. 2

Correct Answer: B

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Question 5
A right circular cone has a height of 10 cm and a base radius of 5 cm. Find the volume of the cone.
A. 250\pi
Correct B. 500\pi
C. 750\pi
D. 1000\pi

Correct Answer: B

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Question 6
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
Correct B. 128\pi
C. 256\pi
D. 512\pi

Correct Answer: B

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Question 7
Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.
A. \( -3, -1 \) \cup (1, 3)
Correct B. \( -3, -1 \) \cup (1, 3) \cup \( 4, \infty \)
C. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, -4 \)
D. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, -4 \) \cup \( 4, \infty \)

Correct Answer: B

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Question 8
Find the equation of the \tangent line to the curve \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 at the point \( a\sqrt{2}, b \).
Correct A. y = \frac{b}{a}\sqrt{x - a}
B. y = \frac{b}{a}\sqrt{a - x}
C. y = \frac{b}{a}\sqrt{x + a}
D. y = \frac{b}{a}\sqrt{a + x}

Correct Answer: A

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Question 9
A circle has a diameter of 10 cm. Find the area of the circle.
A. 25\pi
B. 50\pi
Correct C. 100\pi
D. 200\pi

Correct Answer: C

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Question 10
Solve the equation \log_{10} x^2 = 4.
Correct A. 10^4
B. 10^8
C. 10^{-4}
D. 10^{-8}

Correct Answer: A

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Question 11
Find the equation of the \tangent line to the curve \( y = \frac{x^2}{x^2 + 1} \) at the point where \( x = 1 \).
Correct A. \( y = x - 1 \)
B. \( y = x + 1 \)
C. \( y = 2x - 1 \)
D. \( y = 2x + 1 \)

Correct Answer: A

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Question 12
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
Correct A. \( x in \( -infty, -3 \ \) cup (1, infty) )
B. \( x in \( -infty, -3 \ \) cup (1, 3) )
C. \( x in \( -infty, -3 \ \) cup (3, infty) )
D. \( x in \( -infty, 3 \ \) cup (3, infty) )

Correct Answer: A

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Question 13
Find the area of the region bounded by the parabola \( y = x^2 \), the line \( x = 2 \), and the x-axis.
A. \( \frac{8}{3} \)
Correct B. \( \frac{16}{3} \)
C. \( \frac{32}{3} \)
D. \( \frac{64}{3} \)

Correct Answer: B

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Question 14
A circle has a radius of 4 cm and passes through the points ( (0, 0) ) and ( (3, 4) ). Find the equation of the circle.
Correct A. \( x^2 + y^2 - 16x - 8y + 64 = 0 \)
B. \( x^2 + y^2 - 16x + 8y + 64 = 0 \)
C. \( x^2 + y^2 + 16x - 8y + 64 = 0 \)
D. \( x^2 + y^2 - 16x + 8y - 64 = 0 \)

Correct Answer: A

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Question 15
Find the derivative of the function ( f(x) = \frac{x^2 + 1}{x^2 - 1} ) u\sing the quotient rule.
Correct A. ( f'(x) = \frac{2x\( x^2 - 1 \) - \( x^2 + 1 \)(2x)}{\( x^2 - 1 \)^2} )
B. ( f'(x) = \frac{2x\( x^2 - 1 \) + \( x^2 + 1 \)(2x)}{\( x^2 - 1 \)^2} )
C. ( f'(x) = \frac{2x\( x^2 - 1 \) - \( x^2 + 1 \)(2x)}{\( x^2 - 1 \)^3} )
D. ( f'(x) = \frac{2x\( x^2 - 1 \) + \( x^2 + 1 \)(2x)}{\( x^2 - 1 \)^3} )

Correct Answer: A

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Question 16
In the diagram below, the equation of the circle is given by \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 ). Find the equation of the \tangent line to the circle at the point ( (5, 3) ).
Correct A. \( y = -x + 10 \)
B. \( y = x + 7 \)
C. \( y = -x + 7 \)
D. \( y = x - 3 \)

Correct Answer: A

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Question 17
A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. The ratio of whole wheat to white bread is 5:4. How many loaves of whole wheat bread are sold per day?
Correct A. 240
B. 320
C. 400
D. 480

Correct Answer: A

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Question 18
A right circular cone has a height of 15 cm and a base radius of 8 cm. Find the volume of the cone in cubic centimeters.
A. 3000
B. 4000
Correct C. 5000
D. 6000

Correct Answer: C

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Question 19
A curve is defined by the equation \( y = \frac{1}{x^2 + 1} \). Find the area under the curve between the limits \( x = 0 \) and \( x = 1 \).
Correct A. 0.5
B. 0.6
C. 0.7
D. 0.8

Correct Answer: A

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Question 20
Two events, A and B, are indep\endent. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. Find the probability that both events A and B occur.
A. 0.2
B. 0.3
Correct C. 0.4
D. 0.5

Correct Answer: C

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Question 21
Find the area under the curve \( y = \frac{1}{2}x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 4 \).
Correct A. 24
B. 30
C. 36
D. 48

Correct Answer: A

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Question 22
Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).
A. 1
Correct B. -1
C. -2
D. 3

Correct Answer: B

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Question 23
A binary operation ( odot ) is defined as \( a odot b = ab + 2 \). Find ( 2 odot 3 ).
A. 6
B. 8
Correct C. 10
D. 12

Correct Answer: C

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Question 24
Two events ( A ) and ( B ) are indep\endent. If ( P(A) = 0.4 ) and ( P(B) = 0.6 ), find \( P\( A \cap B \ \) ).
Correct A. 0.2
B. 0.3
C. 0.4
D. 0.6

Correct Answer: A

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Question 25
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
Correct A. y = x + 1
B. y = x - 1
C. y = x + 2
D. y = x - 2

Correct Answer: A

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