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POST UTME BSU 2018 Mathematics | Objective

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Question 1

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)

D. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \times 4 \)

Correct Answer: A

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Question 2

Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).

Correct A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )

B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )

C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )

D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 9 )

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.

Correct A. \( \frac{32}{3} pi \)

B. \( \frac{16}{3} pi \)

C. \( \frac{64}{3} pi \)

D. \( \frac{128}{3} pi \)

Correct Answer: A

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Question 4

Find the surface area of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( x = 2 \) about the x-axis.

Correct A. ( 32 pi )

B. ( 16 pi )

C. ( 64 pi )

D. ( 128 pi )

Correct Answer: A

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Question 5

Find the value of ( x ) in 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 random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the mean height of the population is 180 cm, what is the probability that the sample mean is less than 170 cm?

A. 0.01

Correct B. 0.05

C. 0.10

D. 0.20

Correct Answer: B

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Question 7

Solve for x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ).

Correct A. \( \sin\( x \ \) = 0 )

B. \( \cos\( x \ \) = 0 )

C. \( \tan\( x \ \) = 1 )

D. \( \tan\( x \ \) = -1 )

Correct Answer: A

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Question 8

A random experiment has two indep\endent events A and B. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. What is the probability that both events A and B occur?

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 9

Find the derivative of the function ( f(x) = 3x^2 \sin(x) ) u\sing the product rule.

Correct A. \( 6x \sin\( x \ \) + 3x^2 \cos(x) )

B. \( 6x \cos\( x \ \) - 3x^2 \sin(x) )

C. \( 6x \sin\( x \ \) - 3x^2 \cos(x) )

D. \( 6x \cos\( x \ \) + 3x^2 \sin(x) )

Correct Answer: A

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Question 10

Solve the system of equations u\sing matrices:

Correct A. \( x = 2, y = 3 \)

B. \( x = 3, y = 2 \)

C. \( x = 1, y = 4 \)

D. \( x = 4, y = 1 \)

Correct Answer: A

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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. 3,261

B. 3,261.25

C. 3,261.5

D. 3,261.75

Correct Answer: A

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Question 12

A particle moves along the x-axis with its position given by the equation x(t) = 2t^2 - 5t + 1. Find the velocity of the particle at t = 2.

Correct A. 1

B. -1

C. 3

D. -3

Correct Answer: A

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Question 13

A rec\tangular box has a length of 6 cm, a width of 4 cm, and a height of 2 cm. Find the volume of the box.

Correct A. 48

B. 50

C. 52

D. 54

Correct Answer: A

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Question 14

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

Correct A. \frac{1}{3}

B. \frac{1}{2}

C. \frac{2}{3}

D. \frac{3}{4}

Correct Answer: A

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Question 15

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

Correct A. x < -1 or x > \frac{3}{2}

B. x < -1 or x < \frac{3}{2}

C. x > -1 or x > \frac{3}{2}

D. x > -1 or x < \frac{3}{2}

Correct Answer: A

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Question 16

Let A be a 3x3 matrix with determinant 6. If A is transformed into B by multiplying each element by 2, what is the determinant of B?

A. 12

B. 24

Correct C. 48

D. 96

Correct Answer: C

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Question 17

A sequence is defined as: \( a_n = \frac{1}{n} + \frac{1}{n+1} \). Find the sum of the first 5 terms of the sequence.

A. 1.8

B. 2.1

Correct C. 2.4

D. 2.7

Correct Answer: C

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Question 18

In the diagram below, ( O ) is the center of the circle and ( AB ) is a chord. If \( OA = 5 \) and \( OB = 7 \), find the length of ( AB ).

Correct A. √(74)

B. √(50)

C. √(100)

D. √(200)

Correct Answer: A

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Question 19

A die is rolled twice. What is the probability that the sum of the two numbers is 7?

A. √\( 1/6 \)

Correct B. 1/6

C. 1/3

D. 1/2

Correct Answer: B

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Question 20

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).

A. 64

B. 128

Correct C. 256

D. 512

Correct Answer: C

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Question 21

In the diagram below, the graph of \( y = \frac{1}{2} \tan^{-1} x \) is shown. What is the value of ( x ) at the point where the graph intersects the line \( y = 1 \)?

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 22

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the sum of the first five terms of the sequence.

Correct A. 2 + 5 + 13 + 29 + 61

B. 2 + 5 + 13 + 29 + 57

C. 2 + 5 + 13 + 27 + 57

D. 2 + 5 + 13 + 27 + 61

Correct Answer: A

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Question 23

In the diagram below, the circle with center ( O ) has equation \( x^2 + y^2 = 4 \). What is the length of the chord ( AB )?

A. 2√3

Correct B. 2√2

C. 2√5

D. 2√6

Correct Answer: B

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Question 24

A right-angled triangle has sides of length 3, 4, and 5. What is the area of the triangle?

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 25

A function is defined by ( f(x) = \frac{1}{x^2 + 1} ). Find the value of \( f\( -1 \ \) ).

A. 0

B. 1

Correct C. 1/2

D. 1/4

Correct Answer: C

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