1. The profits of a business are shared among three stockholders. The first stockholder receives twice as much as the second, and the second receives three times as much as the third. If the profits for last year were Php 264,000, how much did each stockholder receive?

2. Abi invested some money at 3% and $4000 less than that amount at 5%. The two investments produced a total of $200 interestin a year. How much was invested at each rate?

3. With income earned by selling the rights to her life story, Mystica invests some of the money at 3% and $30,000 more than twice as much at 4%. The total annual interest earned from the two investments is $5,800. How much is invested at each rate?

4. A man has Php1,000,000 invested at 7.4%. How much can he invest at 5% in order to make 6.6 percent on his total investment?

5. Jane has Php 180,000 invested and gets an income of Php 14,700. Part of the investment pays 10% and the remainder pays 7%. How much is invested at each rate?

6. I invested Php 24,000 in the common stock of one company and Php 12,800 in the stock of another. The price per share of the second was four-fifths of the price per share of the first. The next day, the price of the more expensive stock advanced Php 15 per share, the price of the other declined Php 7.50 per share and as a result, the value of my investment increased Php 300. Find the price per share of the more expensive stock.

7. A woman invested Php 250,000 in two business ventures. Last year she made a profit of 15% from the first venture but lost 5% from the second venture. If last year’s income from the two investments was equivalent to a return 8% on the entire amount invested, how much has she invested in each venture?

8. An investor wishes to realize a return of 12% on a total of two investments. If he has Php 100,000 invested at 10%, how much additional money should be invested at 16%?

9. A retail merchant invested Php 6.5 million in three kinds of cameras. The profit on the sales of Camera A was 25%, on the sales of Camera B the profit was 12% and there was a loss of 1% on Camera C. If the merchant invested an equal amount in cameras A and B, and the overall profit on the total investment was 14%, how much was invested in each kind of cameras?

10. Maria invested a portion of Php 31,750 at 9% and the remainder at 10%. If the total income from the money is Php 3020, how much did she invest at each rate?

11. Pedro has an income of Php 300,000 from the business he inherited. He pays a total income tax of 28% and invests part of the amount left at 10% and the remainder at 12%. How much was invested at each rate if the total income from these two investments is Php 23,600?

12. One alloy contains 80% gold (by weight) and another alloy contains 55% gold. How many grams of each alloy should be combined to make of an alloy that contains 70% gold?

13. A radiator contains 25 quarts of a water and anti-freeze solution of which 60% (by volume) is anti-freeze. How much of this solution must be drained and replaced with water for the new solution to be 40% anti-freeze?

14. How much water is required to dilute 15 liters of a solution that is 12% dye solution so that a 5% dye solution is obtained?

15. How much water must be evaporated from the 15 liters of the 12% dye solution in the previous item to obtain a solution that is 20% dye? Assume that the process of evaporation does not affect the total amount of pure dye.

16. A gardener has of a mixture of a fertilizer and weed killer. If one kilo of the mixture is replaced by weed killer the result is a mixture that is 5% weed killer. What percent of the original mixture was weed killer?

17. A tank contains 20 gallons of a mixture of alcohol and water that is 40% alcohol by volume. How much of the mixture should be removed and replaced by an equal volume of water so that the resulting solution will be 25% alcohol by volume?

18. What weight of water must be evaporated from of a 20% salt solution to produce a 50% solution? All percentages are by weight.

19. How many quarts of a 60% alcohol must be added to 40 quarts fo a 20% alcohol solution to obtain a mixture which is 30% alcohol. All percentages are by volume.

20. Two unblended manganese ores contain 40% and 25% of manganese, respectively. How many tons of each must be mixed with to give 100 tons of blended ore containing 35% of manganese? All percentages are by weight.

21. What weight of water must be added to of a 36% sulfuric acid solution to yield a 20% solution? All percentages are by weight.

22. How many quarts of pure alcohol must be added to 10 quarts of a 15% alcohol solution to obtain a mixture that is 25% alcohol? All percentages are by volume.

23. The radiator of a jeep has a capacity of 4 gallons. It is filled with an anti-freeze solution of water and glycol that analyzes 10% gycol. What volume of the mixture must be drawn off and replaced with glycol to obtain a 25% glycol solution? All percentages are by volume.

24. One thousand quarts of milk testing 4% butterfat are to be reduced to 3%. How many quarts of cream testing 23% butterfat must be separated from the milk to produce the required result? All percentages are by volume.

25. A 42-year old has a son 12 years old. In how many years will the father be twice as old as his son?

26. The tens digit of a number is 3 less than the units digit. If the number is divided by the sum of the digits, the quotient is 4 and the remainder is 3. What is the original number?

27. A man left of his money to his wife, to his daughter and the remainder, an

amount of Php to his son. How much money did he leave?

28. Person A can do a certain job in 3 hours, while the same job takes Person B in 4 hours. How long will it take both to finish the job if they work together?

29. whe Harry Potter opened his math book, two pages faced him. The sum of the page numbers was 153. On what page did he open his book?

30. In the mini-zoo of the community, one-half of the animals are mammals, one-eight are amphibians, one-sixteenth are birds, one-fourth are reptiles and 32 are fish. How many animals are there?

31. The width of the rectangle is 2 centimeters more than one-half its length and its perimeter is 40 centimeters, what are the dimensions of the rectangle?

32. Admission tickets to a motion picture theater cost $2 for adults and $1.50 for students. If 810 tickets were sold and the total receipts was $1426.50, how many of each type of tickets were sold?

33. How many gallons of a solution containing 55% glycerine should be added to 25 gallons of a solution that contains 28% glycerine to give a solution that contains 35% glycerine?

34. A little boy held two ants 150 cm apart on a table. One ant traveled at the rate of 10 cm per minute. After how long will the two ants meet?

35. There are four times as many men as women in a conference. When 18 more women and 12 more men arrive, there are twice as many men as women. How many men in all are there in the conference?

36. Before midnight during a New Year’s eve masquerade ball, a girl asked her partner his age. He said if she subtracted 4 from his age and mulitplied the difference by 4, she would have his age plus twice the day’s date. How old was the partner?

37. A man goes on a trip in a car. Ten minutes later, his son finds out he left some important documents and proceeds to catch his father. Knowing that his father drive at an average speed of 50 km per hour and he will drive at 70 km per hour, how long will it take before he overtakes his father?

1. True or Falsea. The value of is always nonnegative for all .b. For any .c. The modulus of is always equal to for any .d. If is the polar form of a nonzero complex number , then e. The set of purely imaginary numbers is closed under multiplication.

2. If , then the value of is ___________.

3. The exact value of is ___________.

4. In the form , the complex conjugate of is ____________.

5. If , then the rectangular form of is ___________.

6. There is/are _________ triangle(s) that can be solved in an oblique properly labeled if .

7. Evaluate:

8. For the function :

a. Determine the amplitude, period and phase shift of the graph of .b. Obtain the zeroes of on the interval c. Sketch one cycle of the graph of .

9. Simplify the following in the form .

a. , given and

b.

10. solve the following equations for .a.

b.

c. (express solutions in rectangular form)

11. Meowth is on top of a tree high. From there, he can see the feet of Jessie, standing at a distance from and on the same level ground as the tree, has an angle of depression of . Also from the top of the tree, Meowth sees the air balloon of James, hovering directly above Jessie, at an angle of elevation of from the top of the tree. How high above the ground is James’s balloon flying?

12. In a park somewhere in Emerald City, Ash is seated directly north of Brock and from Missy, while Missy is seated from Brock. If Pikachu walks from Brock

to Missy and covered , how far will Pikachu walk from Missy to Ash?

13. In what quadrant will lie if and ?A. I B. II C. III D. IV

14. If the point is on the terminal side of an angle in standard position, then the value of is

A. B. C. D.

15. Which of the following is correct?

A. C.

B. D.

16. The following are equal to except

A. C.

B. D.

17. Which of the following is always equal to ?

A. C.

B. D.

18. Which of the following statements is true?A. If , then the point cannot be in the third quadrant.

B. Given that and is the reference angle of , then .

C. If , then .D. The secant function is an odd function.

19. An angle measuring revolutions is the same as an angle measuring ________

radians and _______ degreees.

20. The radius of a circle whose central angle of subtends an arc of length is _________.

21. If and , then is equal to _________.

22. Given and , then is equal to _____.

23. The exact value of is _______.

24. Find the exact values of the following:

a.

b.

c.

d.

25. Given , and . Compute for the following.

a.

b.

c.

26. Prove the following identities.

a.

b.

27. Given: . Find

28. Given:

Find:

29. A triangle has sides of length , and . Find the measure of the largest angle of the triangle.

30. At a point P, the angle of elevation of the top of a hill is . At a point Q on the same horizontal line as P and the foot of the hill and from P, the angle of elevation is . Find the height of the hill.

31. The leaning tower of Pisa was originally perpendicualr to the ground and tall. Because of sinking into the earth, it now leans at a certain angle from the perpendicular. When the top of the tower is viewed from a point from the center of its base, the angle of elevation is . Find .

32. A flagpole is situated at the top of the building tall. From a point in the same horizontal plane as the base of the building the angles of elevation of the top and bottom of the flagpole are and , respectively. How tall is the flagpole?

33. A building is located at the end of the street that is inclined at an angle of with the horizontal. At a point P, down the street from the building, the angle subtended by the building is . How tall is the building?

34. A parallelogram has sides of lengths and and one angle of measure . What is the measure of the longer diagonal?

35. From a lookout tower high, a man observes from a position below the top of the tower that the angle of elevation of the top of a certain tree is and that the angle of depression of its base is . If the base of the tower and tree are at the same level, what is the height of the tree?

36. A vertical pole tall stands on a hillside that makes an angle of with the horizontal. What is the minimal length of cable that will reach from the top of the pole to a point downhill from the base of the pole?

37. A ladder long is leaning against an embankment inclined to the horizontal. If the bottom of the ladder is from the embankment, what is the distance from the top of the ladder down the embankment to the ground?

38. From the top of a building high, the angle of elevation of the top of a pole is . At the bottom of the building the angle of elevation of the top of the pole is . Find

the height of the pole.

39. A tunnel for a new highway is to be cut through a mountain that is high. At a distance of from the base of the mountain, the angle of elevation is . From a distance of on the other side, the angle of elevation is . What is the length of the tunnel?

40. Find the exact values:

a.

b.

c.

d.

e.

f. If , then

g. If , then

h.

41. Given is on the line segment joining the origin and the point while is on the line segment joining the origin and the point , find

a.

b.

42. Given and . Neither nor is in . Find

a. sinb.

c.

43. Prove the following identities.

a.

b.

c.

44. Write True if the statement is always true; otherwise, write False.a. b. If , c.

d. If and sin

19

85cos

, then

e.

45. Find the numerical value of the following:

a.

b.

c.

46. Given and . Find the numerical value of the

following:a. b.

c.

d.

e.

47. Find the numerical value of the following:

a.

b.

48. Prove the following identities:

a.

b.

49. lies in what quadrant?

a. c. b. d.

50. Which of the following is true?a. c. b. d.

51. is equivalent to

a. c.

b. d.

52. If , then

a. 125.0 c. b. d.

53. If , find the value of

a. c.

b. d.

54. Which of the following is/are false?

a. c.

b. d.

55. Which of the following is/are true?a. In , the sine function and cosine function are decreasing.b. The tangent function has period .c. In , the values of sine are negative while the values of cosine are positive.d. The domain of secant function are all rela numbers except where is an

integer.

56. The length of the chord in a unit circle if the length of the corresponding arc is

will be:a. c. b. d.

57. In terms of , isa. c.

b. d.

58. If and , is equal to

a. c.

b. d.

59. Find the exact value of

60. Find the exact value of

61. If 34

tan

and P is not in QI ,

a. Find the exact value of

b. Find the exact value of

62. Solve for

63. Prove the following identities:a.

b.

64. Prove:

65. Determine which of the following

<Periodical Exam>I. Morse Type. Write A if only statement A is true. Write B if only statement B is true. Write C if both statements are true. Write D if both statements are false.

1. A. Of the six trigonometric function, only the cosine and secant functions are even.B. For any angle and , .

2. Given that the approximate value of is 0.643.A. The approximate value of is 0.643.B. The approximate value of is 0.643.

3. A. The equation is an identity for .

B. The equation is an identity for .

4. A. For any B. For any

5. A. The function is increasing in quadrants I and III.B. The function is decreasing in quadrants III and IV.

6. A. The domain of is the set of real numbers.

B. The range of is

7. Given:

A. The graph of is displaced units to the right.

B. The graph of is displaced units up.

8. A. The graph of intersects the at the origin.

B. The graph of is asymptotic to the lines , where .

9. Given a triangle with sides , and .A. Its perimeter is .B. Its area is .

10. A. If a triangle is not a right triangle, then it is an oblique triangle.

B. If is an oblique triangle, then

II. Mulitple Choice. Write the letter corresponding to the best answer on your answer sheet. If the answer is not found among the choices, write E.

1. A. B. C. D.

For numbers 2 and 3, given and is in quadrant II.

2.

A. B. C. D.

3.

A. B. C. D.

4.