Quiz: Random Problems Set 3

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Quiz: Random Problems 03

Question 1

Which of the following is the value of x2 + 1/x2 when x + 1/x = 5?

25

27

24

23

Question 2

A decagon has how many diagonals?

10

15

35

25

Question 3

A product has a current selling price of P325. If its selling price is expected to decline at the rate of 10% per annum because of obsolescence, what will be its selling price four years hence?

P213.23

P202.75

P302.75

P156.00

Question 4

Convert the equation (3a + 2b)2 into a polynomial.

9a2 + 12ab + 4b2

(3a2 + 6ab + 4b2)

9a2 + 6ab + 4b

(a)2 + (3a)(2b) + (ab)2

Question 5

The ratio of two numbers is 6:7. If the large number is 42, what number is the smaller one?

6

7

36

18

Question 6

A circle with radius r has a circumference equal to the perimeter of a square whose side is S. Which of the following is true?

r = 2S/π

r = π/2S

r = πS/2

r2 = S

Question 7

Find C so that the line y = 4x + 3 is tangent to the curve y = x2 + C.

5

6

4

7

Question 8

Find x if the point (x, 2) is equidistant from (3, 2) and (7, 2).

4

5

1

2

Question 9

If three coins are tossed, how many possible ways are there of at least one coin showing tails?

6

8

5

7

Question 10

Circle a has circumference numerically equal to its area. If the certain square has the same area with the circle a, then what would be the length of its sides?

$\pi \sqrt{3}$

$\pi \sqrt{2}$

$4 \sqrt{\pi}$

$2 \sqrt{\pi}$

Question 11

An arch 18 m high has a form of a parabola with a vertical axis. The length of a horizontal beam placed across the arch 8 m from the top is 64 m. Find the width at the bottom.

76 m

86 m

106 m

96 m

Question 12

A highway has a gradient of 0.087. How many meters would an automobile rise vertically if it traveled 2 miles along the way?

297 m

254 m

264 m

279 m

Question 13

Find the equation of the line through (4, -7) parallel to the y-axis.

x = -7

y = -7

y = 4

x = 4

Question 14

A flywheel is brought from rest up to a speed of 1500 rpm in 1 minute. What is the average angular acceleration, α?

5.23 radians per second per second

2.617 radians per second per second

157 radians per second

333 radians per second

Question 15

Jojie was sent to the store to get 11 cans of spam. Jojie could carry only two cans at a time. How many trips would Jojie have to make?

4

5.5

5

6

Question 16

A large sewer system will cost P8,750,000 annually. There will be favorable consequences to the general public of P25,000,000 annually and adverse consequences to a small segment of the public of P2,500,000 annually. What is the benefit to cost ratio?

2.58

2.56

2.57

2.55

Question 17

In a company meeting, coffee and cake were served during the break. Of the 50 people who attended the meeting, 30 ate cake while 34 took coffee. If there were 22 people who had both cake and coffee, how many have neither coffee nor cake?

8

5

6

7

Question 18

What is the value of x in trigonometric substitution with an integrand involving (a2 - x2)?

a tan θ

a sin θ

a cos θ

a sec θ

Question 19

When an irregular shaped object is placed in a cylindrical vessel of water whose radius is 8 cm, the water rises 6 cm. What is the volume of the rock if it is completely submerged?

24π cm3

48π cm3

192π cm3

384π cm3

Question 20

The triangle defined by the points A(6, 1), B(2, 4), C(-2, 1) is…

Right

Obtuse

Isosceles

Equilateral

Question 21

Spherical degree is a unit of a spherical area taken as 1/720 of the surface of the sphere. How many spherical degrees hemispheres have?

180

360

270

720

Question 22

Point (3, 4) is the center of the circle that is tangent to the x-axis. What is the point of tangency?

(0, 4)

(0, 3)

(3, 0)

(4, 0)

Question 23

Find the equation of the line whose slope is -3 and the x-intercept is 5.

y = -3x + 5

3x + y = 15

x = -3y + 5

y = 3x + 15

Question 24

Ernie’s average in 6 subjects is 83. If his lowest grade is disregarded, his remaining subject is 84. What is his lowest grade?

79

76

78

77

Question 25

The front wheel of a bicycle has a diameter of 50 cm. Approximately how many times has the front wheel turned if the bicycle has traveled 1 km?

π/50

1000/π

2000/π

50/π