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POST UTME RSU 2017 Mathematics | Objective

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Question 1

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm. The slant height of the frustum is 8 cm.

Correct A. 48\pi cm^3

B. 64\pi cm^3

C. 80\pi cm^3

D. 96\pi cm^3

Correct Answer: A

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Question 2

Solve for x in the equation \( 2^x + 2^{x+1} = 3 \cdot 2^x \).

A. -1

B. 0

Correct C. 1

D. 2

Correct Answer: C

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Question 3

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

Correct B. 19

C. 20

D. 21

Correct Answer: B

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Question 4

Find the area of the region bounded by the parabola y = x^2, the line y = 4, and the x-axis.

A. 16

B. 32

Correct C. 48

D. 64

Correct Answer: C

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Question 5

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?

A. ₦1,250

Correct B. ₦1,500

C. ₦1,750

D. ₦2,000

Correct Answer: B

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Question 6

In the diagram below, the graph of \( y = \frac{1}{2} \sin \( 2x \ \) ) is shown. What is the amplitude of the function?

A. 1

Correct B. 0.5

C. 2

D. 4

Correct Answer: B

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Question 7

Solve for ( x ) in the equation \( \begin{vmatrix} 2 & 3 \ 1 & 4 \ \end{vmatrix} = 0 \)

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 8

Find the sum of the first 5 terms of the geometric progression \( 2, 6, 18, \ldots \)

Correct A. 62

B. 64

C. 66

D. 68

Correct Answer: A

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Question 9

In the diagram below, the circle with center ( C ) passes through the points ( A ) and ( B ). What is the equation of the circle?

Correct A. \( x^2 + y^2 - 4x - 6y + 9 = 0 \)

B. \( x^2 + y^2 - 4x - 6y + 11 = 0 \)

C. \( x^2 + y^2 - 4x - 6y + 13 = 0 \)

D. \( x^2 + y^2 - 4x - 6y + 15 = 0 \)

Correct Answer: A

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Question 10

Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 \)

A. 2

Correct B. 4

C. 6

D. 8

Correct Answer: B

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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. 24π cm³

Correct B. 48π cm³

C. 96π cm³

D. 192π cm³

Correct Answer: B

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Question 12

A circle passes through the points (2, 3), (4, 5), and (6, 7). Find the equation of the circle.

A. \( x - 4 \)² + \( y - 5 \)² = 9

B. \( x - 4 \)² + \( y - 5 \)² = 16

Correct C. \( x - 4 \)² + \( y - 5 \)² = 25

D. \( x - 4 \)² + \( y - 5 \)² = 36

Correct Answer: C

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Question 13

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

Correct A. 0.12

B. 0.24

C. 0.36

D. 0.48

Correct Answer: A

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Question 14

The mean of 5 numbers is 12. If one of the numbers is 15, find the sum of the remaining 4 numbers.

Correct A. 45

B. 50

C. 55

D. 60

Correct Answer: A

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Question 15

Solve the quadratic equation x² + 5x + 6 = 0.

Correct A. -2, -3

B. -3, -2

C. 2, 3

D. 3, 2

Correct Answer: A

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Question 16

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

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

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

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

D. \frac{2x}{\( 1 - x^2 \)^{3/2}}

Correct Answer: A

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Question 17

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = \frac{3}{4} \ \) for ( x ) in the interval \( [0, 2\pi] \).

A. \frac{\pi}{6}

B. \frac{\pi}{4}

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

D. \frac{\pi}{2}

Correct Answer: C

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Question 18

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is not blue?

A. \frac{1}{2}

B. \frac{2}{5}

Correct C. \frac{3}{5}

D. \frac{4}{5}

Correct Answer: C

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Question 19

Solve the polynomial equation \( x^3 - 6x^2 + 11x - 6 = 0 \) u\sing the rational root theorem.

A. x = 1

Correct B. x = 2

C. x = 3

D. x = 6

Correct Answer: B

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Question 20

Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

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Question 21

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

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

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

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

D. \( \frac{-1}{\( 1 - x^2 \ \)^{3/2}} )

Correct Answer: A

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Question 22

Solve the inequality \( \frac{2x - 1}{x + 1} > 0 \) u\sing the sign table method.

Correct A. \( x < -1 \) or \( x > \frac{1}{2} \)

B. \( x < -1 \) or \( x < \frac{1}{2} \)

C. \( x > -1 \) or \( x > \frac{1}{2} \)

D. \( x > -1 \) or \( x < \frac{1}{2} \)

Correct Answer: A

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Question 23

Find the equation of the \tangent line to the curve \( y = x^2 - 2x + 1 \) at the point ( (1, 0) ).

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 24

Solve the system of equations \( egin{cases} x + y = 2 \ 2x - y = 3 \end{cases} \) u\sing the method of substitution.

Correct A. \( x = 1, y = 1 \)

B. \( x = 1, y = 3 \)

C. \( x = 3, y = 1 \)

D. \( x = 3, y = 3 \)

Correct Answer: A

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Question 25

Find the value of \( \sin\( 2\theta \ \) ) if \( \cos\( \theta \ \) = \frac{3}{5} ) and \( \sin\( \theta \ \) = \frac{4}{5} ).

Correct A. \( \frac{24}{25} \)

B. \( \frac{24}{25} \)

C. \( \frac{24}{25} \)

D. \( \frac{24}{25} \)

Correct Answer: A

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