POST UTME BOWEN UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details
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 View Details
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 View Details
Find the volume of the solid formed by revolving the region bounded by the curve (y = \(x^2\)\) and the line \(x = 2\\((y = x^2) and the line\) 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 View Details
A histogram of exam scores has a mean of 60 and a standard 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 View Details
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 View Details
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 View Details
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 View Details
Find the equation of the tangent line to the curve \(\frac{x^2}{a\\(tangent line to the curve (\)^2}\)\) + \(\frac{y^2}{b)^2}\)\) = 1 at the point \\()^2})\(a\sqrt{2}, b\).
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 View Details
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 View Details
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 View Details
Find the equation of the tangent line to the curve \(y = \frac{x^2}{x^2 + 1}\\(tangent line to the curve (y =\) 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 View Details
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 View Details
Find the area of the region bounded by the parabola (y = \(x^2\)\), the line \(x = 2\\((y = x^2), the line\), 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 View Details
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 View Details
Find the derivative of the function ( f(x) = \(\frac{x^2 + 1}{x^2 - 1}\)\)\) ) using 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 View Details
In the diagram below, the equation of the circle is given by \(x - 3 \\)^2 + \(y - 4)^\(2 = 25\) ). Find the equation of the \\\\((()^(2\) = 25\)\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 View Details
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 View Details
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 View Details
A curve is defined by the equation (y = \(\frac{1}{\(x^2 + 1}\)\)\). Find the area under the curve between the limits \\((y = frac{1}{x^2 + 1}\(x = 0\) 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 View Details
Two events, A and B, are independent. 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 View Details
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 View Details
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 View Details
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 View Details
Two events ( A ) and ( B ) are independent. 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 View Details
Find the equation of the line passing 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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