SET 2 (p. 18)

Question 1

2. In a car race, the rate of one car is 120 km/hr and the rate of another is 105 km/hr. If the faster car finished the race 20 minutes before the slower one, what was the distance of the race?

Answer 1

280 km (p. 22)

Question 2

3: The area of a cross-section of a right circular cone is 20, and the area of the base is 45. If the altitude of the cone is 6, how far from the base is the cross-section?

Answer 2

2 (p. 23)

Question 3

4. Find the altitude of the right prism for which the area of the lateral surface is 143, and the perimeter of the base is 11.

Answer 3

13

Question 4

8. These are signs that instruct road users to meet certain traffic rule requirements or road condition.

Answer 4

Special instruction signs

Question 5

10. Jack’s beanstalk has a growth pattern stated as follows: “On the first day it increased its height by 1/2, on the second day by 1/3, on the third day by 1/4, and so on”. How long will it take to achieve its maximum height if it is 100 times its original height?

Answer 5

198 days (p. 24)

Question 6

11. It is a type of thermoplastic lane marking designed to aid and provide motorists with visual, audio, and motion warning on the road.

Answer 6

Rumble strips

Question 7

12: A long cylinder driven into the soil that extends deep into the ground to support a structure by transferring loads to a deeper and stronger layer of soil or rock.

Answer 7

Pile

Question 8

13. Melissa can mow the lawn in 4 hours, while her husband, George, can mow the lawn in 3 hours. They agreed to mow the lawn together. How long will it take them to mow the lawn together?

Answer 8

1.7 hours

Question 9

14. Find the area which is inside the circle r = 3sin⁡θ and outside the cardioid r = 1 + sin⁡θ.

Answer 9

π sq. units

Question 10

15: A company wishes to accumulate P350,000 over a period of 5 years needed for building expansion. To have this amount, quarterly payments at the end of each quarter will be made into a savings account that earns 10% compounded quarterly. How much must each payment be?

Answer 10

P13,701.50

Question 11

18. A coin purse contains 5 centavo, 10 centavo, and 25 centavo coins, 30 coins in all. The total amount of all coins is P 4.40. Find the total amount of all 10 centavo coins.

Answer 11

P 1.40 (p. 25)

Question 12

19. Find the angle of the sector that should be removed from a circular piece of canvas of radius 12 ft so that the conical tent made from the remaining piece will have a height of 7 ft.

Answer 12

67.60°

Question 13

20. It is used to test the relative consistency of concrete.

Answer 13

Slump test

Question 14

32. What is the measure of an interior angle of a regular dodecagon?

Answer 14

150°

Question 15

34: These are joints provided wherever concrete cement pavement work is suspended.

Answer 15

Construction joint

Question 16

35: Find the equation of the line through (3,-1) and parallel to the line x-3y+6=0.

Answer 16

x-3y=6

Question 17

40. Find the area of a cyclic quadrilateral whose sides are 5 cm, 7 cm, 10 cm, and 16 cm.

Answer 17

67.35 cm^2

Question 18

41. Given a triangular lot ABC with the following data:
    (p. 11)
    What is the bearing of side CA?

Answer 18

N 58.92° W

Question 19

42. The area bounded by the water line of a reservoir and the contours with a contour interval of 2 m are as follows: A1 = 12,340 m², A2 = 10,530 m², A3 = 9,180 m², A4 = 7,720 m², A5 = 5,520 m², A6 = 3,870 m². Determine the capacity of the reservoir using End Area Method.

Answer 19

82,110 m³

Question 20

43. The table below displays the results of a survey regarding the number of study hours each student in a class. The average number of study hours in this class is 1.25. Find the value of k.

Answer 20

7

Question 21

44. A man 1.8 m tall standing on one bank of a river can just see the top of a 41.27 m-high tower standing on the opposite bank of the river. Considering the effect of curvature and refraction, how wide should the river be?

Answer 21

30 km

Question 22

45: P200,000 was deposited at an interest rate of 24% compounded semiannually. How many years will the sum be P621,170?

Answer 22

5

Question 23

46: Two secants PAB and PCD are drawn to a circle from external point P and intersect the circle at A, B, C, and D, with A and C nearer to P. Angle PBC = 42°, angle BPC = 30°, BC is the diameter of the circle, and PA = 25 cm. Compute the measure of angle CAD.

Answer 23

18°

Question 24

48. An existing machine in a factory has an annual maintenance cost of P 90,000. A new production methodology needs the purchase of a new and more efficient machine which will require an investment of P 250,000 and is estimated to have a salvage value of P 20,000 at the end of its 10 - year life. Annual maintenance for the new machine will total to P 30,000. If the company expects to earn 12% on its investment, what will be the rate of return on investment of the new machine?

Answer 24

19% (p. 31)

Question 25

49. An airplane flew from Sydney ( 151°12' E, 33°52' S ) on a course N 40° W maintaining a uniform altitude. At what longitude will it crosses the equator?

Answer 25

126°08'

Question 26

51. Given 2 independent random variables x and y with mean and variance as follows: E(x) = 640, σ(x) = 6, E(y) = 280, σ(y) = 8. Find the standard deviation of the random variable ( x + y ).

Answer 26

10

Question 27

52. A frustum of a sphere has diameters of the bases 10.8 cm and 24.4 cm. The thickness of the frustum is 6 cm. Find the volume of the frustum.

Answer 27

1791 cm^3

Question 28

54: Determine the required length of spiral with a design speed of 80 kph if the central circular curve has a degree of 5.

Answer 28

80 m

Question 29

55: Data on traffic accident recorded on a certain section of a highway for the past 5 years shows 4,684 total accidents. If the average daily traffic is 482, what is the accident rate per million entering vehicles?

Answer 29

5,325

Question 30

64. Joan has some coins in his pocket consisting of dimes, nickels, and pennies. She has two more nickels than dimes and three times as many pennies as nickels. How many coins are there if the total value is 52 cents?

Answer 30

18

Question 31

65: The area of a regular hexagon is 300 square units. Find its apothem.

Answer 31

9.3