SET 1 (p. 3)

Question 1

1. A bag contains 3 white balls and 5 red balls. If 2 balls are drawn together, find the probability that all are the same color.

Answer 1

13/28 (p. 7)

Question 2

3. A bicycle tire has a diameter of 24 inches. From rest it accelerates at a constant rate of 2ft/sec². What is the angular velocity when it has traveled 1 mile?

Answer 2

145.33 rad/sec

Question 3

9: A water container has a square base 2 ft by 2 ft. A metal sphere is placed fully submerged inside the container causing water to rise 0.16 ft. What is the radius of the metal sphere?

Answer 3

0.53 ft

Question 4

11. Find the perimeter of a regular hexagon whose apothem is 15 cm.

Answer 4

103.92 cm (p. 9)

Question 5

12. The ellipse has its center at ( 0, 0 ), one end of minor axis at ( 5, 0 ) and distance between foci 6.633. Find the equation of the ellipse.

Answer 5

36x² + 25y² = 900 (p. 9)

Question 6

16. A hollow metal pipe is 30 cm long. The cross-section has an inner diameter of 2.5 cm and outer diameter of 3.2 cm. Find the volume of metal needed to make the pipe.

Answer 6

94 cm³ (p. 9)

Question 7

18. Find the equation of the circle with center at ( -3, 6 ) and touches the x-axis.

Answer 7

x^2 + y^2 + 6x -12y + 9 = 0

Question 8

23: A line was measured by a 20 m long tape. There are 2 tallies and 3 pins, and the distance of the last pin to the end of the line is 5.74 m. Find the length of the line.

Answer 8

465.74 m

Question 9

24. Assume that any distance of 100 ft can be taped with an error ±0.025 ft if certain techniques are employed. Determine the error in taping 4,000 ft using this skill.

Answer 9

±0.158 ft

Question 10

25. Find the equation of the line with x-intercept 5 and y-intercept of -3.

Answer 10

3x - 5y = 15

Question 11

26: The line with y = mx + 3 passes through (2, 1). Find the slope m.

Answer 11

-1

Question 12

27. Find the distance between the parallel lines 3x - 4y + 4 = 0 and 3x - 4y - 16 = 0.

Answer 12

4

Question 13

29: The total surface area of a cube is 34.56 cm². Find the volume of the cube.

Answer 13

13.824 cm³

Question 14

30. Given a triangular lot ABC with the following data:
    (p. 11)
    What is the measure of distance BC?

Answer 14

234.76 m (p. 11, 12)

Question 15

33. Which of the following statements is true about stemplots?
    A. Whether or not to provide a key depends on the relative importance of the data.
    B. Stemplots are useful both for quantitative and for categorical data sets.
    C. Stems should be skipped only if there is no data value for a particular stem.
    D. Stemplots can show symmetry, gaps, clusters, and outliers.

Answer 15

D

Question 16

34. Given the equation of the circle x² + y² - 8x - 12y + 2 = 0. Find the center of the circle.

Answer 16

( 4, 6 ) (p. 12)

Question 17

40: Consider a geometric sequence whose 3rd term is 18, and whose common ratio is 3/2. Find the 7th term.

Answer 17

729/8

Question 18

44. Find the diagonal of a rectangle with sides 6 cm by 10 cm.

Answer 18

11.66 cm

Question 19

45: 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 radius of the sphere.

Answer 19

14.05 cm

Question 20

49: A rectangular tank with base 1.2 m by 1.2 m square and a height of 1.6 m is filled water at the rate of 10 liters per minute. How long would it take to fill the tank?

Answer 20

3.84 hrs

Question 21

50: Find the value of x in the equation 2x^2 - 7x - 15 = 0.

Answer 21

5, -3/2

Question 22

53: The first quadrant area bounded by y²=8x and x=2 is revolved about the x-axis. Find the volume of the paraboloid generated.

Answer 22

16pi

Question 23

55: Jasper has a job offer of P288,000 salary on the first year, with his employer guaranteeing he will have a salary raise of P60,000 per year in the succeeding 5 years. Find his salary in the 4th year.

Answer 23

P468,000

Question 24

59: A differential leveling was conducted from BM1 to BM2 20 km apart. BM1 is at elevation 142.26 m. The backsight distances averages 150 m in length and the foresight distances averages 100 m. The recorded elevation of BM2 was 247.05 m. If the level used is out of adjustment such that when the bubble was centered the line of sight was inclined of 0.0025 m upward in distance of 100m. What would be the corrected elevation of BM2?

Answer 24

246.95 m

Question 25

61. Standard sign shape for STOP sign.

Answer 25

octagon

Question 26

63. The parabola y = x^2 + C has the line y = 2x + 4 as its tangent. Find the value of C.

Answer 26

5

Question 27

64. An open-topped rectangular box is to have a square cross-section and has a capacity of 12,000 cm^3. Find the height of the box that requires the minimum amount of material in making it.

Answer 27

14.42 cm (p. 16)

Question 28

68. Find the angle between the vectors 3i + 2j + 5k and -4i + j + 6k.

Answer 28

63.53°

Question 29

69. Lane line must not be continued on the following cases:
    I. Across signalized intersections. However, lane lines of low priority road must be discontinued at the intersection.
    II. Across side street entrances unless the street is one-way (going in only)
    III. Past the start of the taper at which a multilane road narrows down.
    IV. At approaches to widened or signalized intersection
    V. On divided roads

Answer 29

I, II, III only

Question 30

73. A point on the rim of the wheel has a linear speed of 12 cm/sec. If the radius of the wheel is 20 cm, what is the angular speed of the wheel in rad/sec?

Answer 30

0.60 rad/sec