Math Practice Problems Module 2

1. Evaluate the determinant

1 6 0

4 2 7

0 5 3

a. 011

b. 101

c. 001

d. 101

2. Find the value of a so that 1+a, 7+a, and 25+a forms ageometric progression

a. 3

b. 4

c. 2

d. 5

3. Mel gave Lea of her mystery books. Lea gave Benjie of the books she got form Mel. Benjie gave Badong ofthe books he got from Lea. Badong got only 4 books. Howmany books did Mel start with?

a. 8.5

b. 7.5

c. 8

d. 32

4. If the first and tenth terms of an arithmetic sequence are3 and 30 respectively, find the fiftieth term of the sequence.

a. 150

b. 75

c. 50

d. 100

5. What is the remainder if x55+3x47-5x31-8x24+2x18-4 isdivided by x + 1.

a. 10

b. 9

c. 9

d. 10

6. The equation y = am is equivalent to the equation

a. m = logya

b. m = logay

c. m = yloga

d. m = alogy

7. A chemical storeroom has a 90% acid solution and a40% acid solution. How many centiliters of solution must betaken from each to obtain 25 centiliters of a 50% acidsolution?

a. 6 and 19

b. 4 and 21

c. 5 and 20

d. 3 and 22

8. Find the sum of the sequence +1/4 + 1/8 +1/16 .

a. 2

b. 4

c. 1

d. 3

9. If you place one cent on the first square of thechessboard, two cents on the second square, four cents onthe third, and so on, continuing to double the amount untilall 64 squares are covered, how much money will there bein the last square board?

a. 9 x 1015

b. 9.22 x 1016

c. 9.22 x 1015

d. 9.22 x 1018

10. ________ is the set, which has no elements.

a. universal set

b. infinite set

c. empty set

d. finite set

11. There are 2n persons at a dinner dance party of whichthe number of males equals the number of females. If thetwo persons are selected at random, what is the probabilitythat the two persons selected at random are of oppositesex?

a. n2/2n-1

b. n/2n-1

c. n/n-1

d. n/2n+1

12. How many four-digit number can be written using thedigits 1, 2, 3, 4, 5, 6, 7, 8, 9 if no digit is repeated in anynumber?

a. 3020

b. 3022

c. 3024

d. 3042

13. How many cars can be given license plates having 5-digit number using the digit 1, 2, 3, 4, 5, 6, 7, 8, 9 with nodigit repeated in any license plate.

a. 15120

b. 15400

c. 16020

d. 15020

14. Find the number of permutation of the letters in theword ENGINEER?

a. 33600

b. 3360

c. 3860

d. 3630

15. How many three-digit numbers between 100 and 1000can be made with the digits 0, 1, 2, 3, and 4 if no digit isrepeated in any number?

a. 48

b. 49

c. 46

d. 45

16. How many of the arrangements of the letter of the wordVOLTAGE begins with a vowel and end with a consonant.

a. 1440

b. 1490

c. 1460

d. 1450

17. Find n if P(n+2, 2) = 5 P((n-1, 2)

a. 6

b. 9

c. 4

d. 3

18. How many different teams of 5 players can be chosenout of 12 applicants?

a. 730

b. 718

c. 792

d. 719

19. How many different committees of 5 members can beformed from 8 men and 6 women if each committee is tohave exactly 3 men?

a. 830

b. 840

c. 860

d. 820

20. In how many ways can 2 or more ties can be selectedout of 8 ties.

a. 235

b. 240

c. 247

d. 245

21. Find n if P(n, 3) = 6C(n,5).

a. 8

b. 9

c. 10

d. 7

22. A committee of three is to be chosen from a group of 5men and 4 women. If the selection is made at random, findthe probability that two are men.

a. 10/21

b. 9/10

c. 5/9

d. 11/21

23. A bag contains nine balls numbered 1 to 9. Two ballsare drawn at random. Find the probability that one is evenand the other is odd.

a. 5/9

b. 9/10

c. 10/21

d. 7/9

24. A bag contains nine balls numbered 1 to 9. Two ballsare drawn at random. Find the probability that both areeven.

a. 3/18

b. 5/18

c. 1/3

d. 7/18

25. A bag contains nine balls numbered 1 to 9. Two ballsare drawn at random. Find the probability that both areodd.

a. 3/18

b. 3/8

c. 1/3

d. 820

26. A bag contains 4 white and 5 black balls. If 4 balls aredrawn, what is the probability that the first two balls arewhite and the last two are black?

a. 4/5

b. 5/63

c. 4/53

d. 3/5

27. One bag contains 4 white and 6 black balls; a secondbag contains 2 white and 8 black balls; a third bag contains5 white and 5 black balls. One ball is drawn from each bag.Find the probability that all are white.

a. 1/25

b. 5/19

c. 3/19

d. 3/25

28. What is probability of throwing a 6 in single throw of twodice?

a. 1/6

b. 5/36

c. 9/51

d. 5/6

29. Find the probability of throwing a 4 with a die exactly 3times in 7 trials.

a. 0.00781

b. 0.781

c. 0.0781

d. 0.0871

30. A coin is tossed 6 times. Find the probability of getting4 heads.

a. 15/64

b. 3/8

c. 4/36

d. 13/64

31. A card is drawn from a deck of 52 cards. What is theprobability that the card drawn is a king or a heart?

a. 16/52

b. 4/52

c. 13/52

d. 15/52

32. Two person A and B work independently on a puzzle. Ifthe probability that A can solve the puzzle is 0.60 and thatB is 0.75. What is the probability that the puzzle will besolved?

a. 0.90

b. 0.80

c. 0.75

d. 0.65

33. There are three applicants A, B, and C to an EEposition in an electric firm. The odds that A will get theposition are 7:5 and the odds that B will get the sameposition are 1:3. What is the probability that either A or Bwill be employed?

a. 3/7

b. 5/6

c. 3/5

d. 2/7

34. What are the odds in favor of C in problem 33?

a. 1:5

b. 2:5

c. 3:5

d. 4:5

35. Six red blocks and 4 white blocks are placed at randomin a row. Find the probability that the two blocks in themiddle are of the same color.

a. 2/11

b. 1/5

c. 7/156

d. 4/15

36. In the series of nos. 2, 5, 8, 1141, the sum is

a. 301

b. 302

c. 303

d. 304

37. Johnny and Louie can clean a room in 3 hrs. Afterworking for 2 hrs., Johnny has his snack while Louiecleaned the room alone for 2 more hrs. How long Louietakes to clean the room alone?

a. 5 hrs

b. 6 hrs

c. 7 hrs

d. 8 hrs

38. Five times Greggys age is 10 more than hisgrandfathers age. If the sum of their ages is 86, what isgrandfathers age?

a. 50

b. 60

c. 70

d. 80

39. Seven times a number is 3 more that 5 times another. Ifthe sum of the numbers is 9, what are the numbers?

a. 2 and 7

b. 3 and 6

c. 4 and 5

d. 1 and 8

40. Train B is 5 mph faster than Train A and can travel adistance of 105 miles, hour faster than A. What are therates of the two trains?

a. 20 and 25

b. 30 and 35

c. 40 and 45

d. 50 and 55

41. The denominator of a fraction exceeds the numeratorby 4. If the numerator was tripled, the denominatordoubled, the resulting fractions denominator is 1 less thanthe numerator of the resulting fraction. What is the originalfraction?

a. 7/11

b. 8/12

c. 9/13

d. 10/14

42. Richard can finish off a gallon of ice cream in one hourwhile Philip can eat it in 45 mins. How long would it takeboth of them to consume the gallon of ice cream?

a. 15.51 min

b. 20.61 min

c. 25.71 min

d. 30.81 min

43. Annie, Betty, Carol and Dina can finish , , 1/8, and1/6 of a job respectively in one day. How many hours will ittake them to do the whole job if they work together?

a. 17.01 hrs

b. 19.02 hrs

c. 21.03 hrs

d. 23.04 hrs

44. In 5 years, a boy will be 7/6 times as old as his uncle. Ayear ago, he will be 4/13 times as old. How old is the boy?

a. 8

b. 9

c. 10

d. 11

45. A fraction becomes equal to 1 when 9 is added to thenumerator and becomes 1 when 16 is subtracted fromthe denominator. What is the fraction?

a. 35/44

b. 37/46

c. 39/48

d. 41/50

46. The sum of the digits of a 2-digit number is 17. if 9 isadded to the number, the order of the digits will bereversed. Find the number.

a. 69

b. 79

c. 89

d. 99

47. Barry can walk at a rate of 5 km/hr and his brother Alfiecan walk at a rate of 15 km/hr. How long would it take themto be 60 km apart if they are walking at oppositedirections?

a. 2 hrs

b. 3 hrs

c. 4 hrs

d. 5 hrs

48. Two pipes can fill a tank in 5 and 6 hours respectivelywhile another pipe can empty it in 6 hours. If the 3 pipeswere used at the same time, how many hours would it taketo fill the tank?

a. 2 hrs

b. 3 hrs

c. 4 hrs

d. 5 hrs

49. A woman divides P18, 000 among her 3 daughters in2:3:4 ratios. How much did each daughter receives?

a. P4, 000, P6, 000, P8, 000

b. P5, 000, P6, 000, P7, 000

c. P2, 000, P7, 000, P9, 000

d. P5, 000, P6, 000, P7, 000

50. A balcony section of a convention hall has 12 seats inthe 1st row, 14 in the 2nd, 16 in the 3rd, and so on. If thereare only 15 rows in the said balcony section, how manyseats are there in the 15th row?

a. 35

b. 40

c. 45

d. 50

Math Practice Problems Module 31. During the recent Olympics on 4-men relay teamcompleted in a 1600-meter relay have the followingindividual speed, R1 = 26 kph, R2 = 27 kph, R3=28kph, R4=29kph. What is the average speed of theteam?

a. 25.43

b. 26.44

c. 27.47d. 28.46

2. A garden can be cultivated by 8 boys in 5days. 5 men can do the same work in 6 days.How long would it take for 8 boys and 5 men tofinish the job?

a. 15/11 daysb. 20/11 daysc. 30/11 days

d. 45/11 days

3. At what time between 7 and 8 oclock are thehands of the clock, at right angles?

a. 7:22b. 7:18

c. 7:15

d. 7:24

4. At what time between 7 and 8 oclock are thehands of the clock, at 1800 apart?

a. 7:05b. 7:10

c. 7:11

d. 7:30

5. At what time between 7 and 8oclock are thehands of the clock together?

a. 7:38b. 7:30c. 7:45

d. 7:20

6. A man left his office for a businessappointment one afternoon and noticed hiswatch at past 2 oclock. Between two to threehours later, the man returned and noticed thatthe hands of the clock have exchanged places.What time did he leave and arrive?

a. 2:26.01 and 5:12.17b. 2:15 and 5:30

c. 2:20 and 5:32

d. 2:23 and 5:40

7. A survey is made on the smoking habit of themale population above 18 years old of a certaincommunity. The survey was on the threecigarettes A, B and C.55% smoke S40% smoke B30% smoke C20% smoke A and B12% smoke B and C10%smoke A and C5% smoke all the three brandsHow many % do not smoke?

a. 12b. 15

c. 3

d. 10

8. Separate 132 into 2 such that the largerdivided by the smaller, the quotient is 6 and theremainder is 13. Find the numbers.

a. 17 and 115b. 20 and 112

c. 24 and 108

d. 30 and 102

9. A number of two digits divided by the sum ofthe digits, the quotient is 7 and the remainder is6. If the digits of the number are interchangedthe resulting number exceeds three times thesum of the digits by 5. What is the number?

a. 39

b. 48

c. 83d. 72

10. The total tank of the car is filled with 50 litersof alcogas 25% of which is alcohol. How muchof the mixture must be drawn off which whenreplaced by pure alcohol will yield a 50-50%alcogas?

a. 16.7b. 15.6

c. 17.8

d. 18

11. An alloy contains of 25% silver and 10%copper. How much silver and how much coppermust be added to 20 lbs of the alloy to obtain analloy containing 38% silver and 36% copper?

a. 14 lbs. Silverb. 15 lbs silver

c. 20 lbs silver

d. 30 lbs silver

12. A motorist is traveling from A to B at aconstant rate of 30 kph and return from B to A atconstant rate of 20 kph. What is his averagevelocity?

a. 8

b. 15

c. 30d. 24

13. If log 2 = A and log3 = B, find the log (2.4)a. 3A-B-1b. 3A+B-1c. 3A+B+1

d. 3A-B+1

14. If logx2 +2logx3 = 2 +logx6, then x =a. 3b. 2c. 5d. 6

15. Solve logx2=(logx)2

a. 103

b. 102

c. 101d. 100

16. If 2 = 100.3010 and 9 = 100.9542,then 4.5 =10x where x equals

a. 0.2552

b. 0.2553

c. 0.6322d. 0.6532

17. If logx (1/144)=-2, then x =a. 11b. 12c. 4

d. 10

18. If A and B are not mutually exclusive events,then the probability of the joint occurrence of Aand B or P(A and B) is

a. not equal to zerob. equal to zero

c. equal to unity

d. infinite

19. When the occurrence or no occurrence ofevent A has no effect on the occurrence of eventB, then A and B are said to be

a. complementary

b. dependentc. independentd. mutually exclusive

20. Which of the following relations is true whenA and B are dependent events?

a. P(AandB)=P(A)P9(BA)b. P(AandB)=P(A)P(B)c. P(A or B)=P(A)(BA)d. P(A or B) = P(A)+P(B)

21. If A and B are mutually exclusive events,then

a. P(A and B) 0b. P(A and B) = 0c. P(A and B) >0

d. P(A and B)< 0

22. If P(A) is the probability of event A;P(B) isthe probability of event B and P(A and B) is the

probability of their joint occurrence, such thatP(A and B)=P(A)P(B), then A and B are said tobe

a. complementary

b. disjoint

c. dependentd. independent

23.Which of the following events are notmutually exclusive?

a. events ACE and HEARTb. events ACE and JACK

c. events 2 and odd

d. events1 and prime

24. The probability that the Ginebra basketballteam will win the championship is assessed asbeing 1/3. Find the odds that the team will win.

a. 1:2b. 2:1

c. 1:3

d. 3:1

25. The odds that a reviewee will not pass theboard exam are 1:4. Find the probability that thereviewee will not pass the exam.

a. 0.80b. 0.20c. 0.25

d. 0.75

26. An experiment consists of selecting arandom of three-television tubes form a lot of 5containing 2 defective. What is the probability ofgetting exactly two defective tubes?

a. 0.25

b. 0.30c. 0.35

d. 0.40

27. Out of 1, 000 ECE reviewees, the probabilitythat a reviewee picked at random is over 25years old is 0.25 and the probability that he isless than 20 years old is 0.15. What is theprobability that a reviewee picked at random isbetween 20 and 25 years old?

a. 0.55b. 0.60

c. 0.65

d. 0.70

28.The mean deviation is a measure ofa. dispersionb. distribution

c. central tendency

d. frequency

29. It is the highest score in a distribution minusthe lowest score in the distribution.

a. rangeb. deviation

c. variance

d. interval

30. It is halfway between the lower limit of oneclass and the upper limit of the preceding class.

a. class boundaryb. class mark

c. class interval

d. class size

31. In statistics, which of the following is notconsidered as a continuous variable?

a. height

b. weight

c. number of accidentsd. temperature

32. The number of reviewees in a room is aa. continuous variableb. discrete variablec. variate

d. statistic

33. Find the median of trhe following: 21, 43, 20,29, 50, 36, 17, 19.

a. 24b. 25c. 26

d. 23

34. It is a measure of central tendency, whichdepends upon the number of score and not onthe magnitude of the scores.

a. meanb. median

c. mode

d. geometric mean

35. A car travels from A and B at 30 kph, from Bto C at 40 kph and from C to A at 50 kph. If A, Band C are equidistant from each other,determine the average speed of the car for theentire trip by using the harmonic lean formula.

a. 37.3

b. 38.3c. 39.3

d. 36.3

36. Which of the following relations is true?a. sin(-A) = sin A

b. tan(-A) = tan A

c. cos(-A) = cos Ad. csc(-A) = csc A

37. What is the period of y = 3sin(x2)?a. 2b. 3c. 4d. 5

38. If A and B are complementary angles, thenwhich of the following is true?

a. sinAcosB = 1

b. sinAcosB = 0c. sin2A-cos2B = 0d. sin2A-cos2B = 1

39. If tanA = 2, then tan2A is equal toa. 4/3

b. 4/3c.

d. -3/4

40. If sinx = cosy,thena. xy = 900

b. x+y = 900

c. x-y = 900

d. none of the above

41. The value of csc 2400is equal to the value ofa. sin600

b. sin600

c. cos600

d. csc600

42. Evaluate: 2sinx 3 cotx = 0; 0 x2a. /3, 5/3b. /3, /4c. 5/3, /4d. none of these

43. cosx>0 and sin x< 0,then x is in quadranta. I

b. II

c. IIId. IV

44. If an angle is 9 degrees more than twice itssupplement then the number of degrees in theangle is

a. 27

b. 57

c. 114

d. 12345. A man travels 4 miles north, 12 miles eastand then 12 miles north. How far is he in milesfrom the starting point?

a. 17b. 20c. 21

d. 24

46. In a triangle, one angle is 3 times as big asthe other. If the sum of these angles is 1200.Find the measure of the third angle.

a. 600

b. 900

c. 1000

d. 1100

47. A triangle has sides of 4, 6, and 8 units long.If the shortest side of a similar triangle is 12units long, what are the lengths of the other twosides?

a. 16 and 26

b. 17 and 25

c. 18 and 24d. 19 and 23

48. Find the value of (1+i)12.

a. 36b. 64c. 36i

d. 64i

49. If sin60 +cos3 = 0, find 0 where 00<

9. A 90-degree arc on the earth is equal tohow many nautical miles in length?

a. 5, 600b. 5, 400c. 5, 200d. 5, 000

10. The plane of a small circle on asphere of radius 25 cm is 7 cm from thecenter of the sphere. Find the radius ofthe small circle.

a. 21b. 22c. 23d. 24

11. Find in kilometers the length of an arcof a great circle on the earth if its length is12.5 degrees.

a. 1389b. 1370c. 1352d. 1333

12. A spherical triangle has angles A, Band C, each of which is less than 180degrees. Which of the following is true?

a. A + B + C = 1800

b. A + B + C > 3600

c. A + B + C = 3600

d. A + B + C > 1800

13. Find the difference in longitudebetween two points A and B if A is inlongitudes 450 E and B in longitude1550W.

a. 1100

b. 1600

c. 1800

d. 2000

14. You are in latitude 400N. How far areyou from the equator in statute miles?

a. 2, 476.8b. 2, 674.8c. 2, 764.8d. 2, 467.8

15. If the radius of the earth is 6, 370 km,find the radius of a parallel of latitude 60degrees north.

a. 3, 185 kmb. 3, 158 kmc. 3, 518 kmd. 3, 581 km

16. Find the distance in nautical milesbetween A (40030N,600E) and B(80020S,600E).

a. 5,270b. 5,720c. 7,520d. 7250

17. Find the difference in longitudebetween New York (40043N, 740W) andSydney (33052S, 151013E).

a. 77013b. 134047c. 134087d. 77031

18. If A is 720 nautical miles south of theequator, find the latitude of A in degrees.

a. 140Sb. 120Sc. 100Sd. 130S

19. Find the area of a spherical trianglewith angles 34023, 119037and 38043on a sphere of radius 10.

a. 24.19b. 23.19c. 22.19d. 21.19

20. A spherical triangle, which contains atleast one side equal to a right angle, iscalled

a. a polar triangleb. a right trianglec. an isosceles triangled. a quadrantal triangle

21. A ship sails in latitude 320N due eastuntil it has made good a difference inlongitude of 2035. Find the departure.

a. 131.45 nmb. 141.35 nmc. 135.41 nmd. 145.31 nm

22. Using Napiers Rule, write a formula tofind angle A when angle B and side c aregiven.

a. tanA = cosc tanBb. cotA = cosc tanBc. tanA = tanc cosBd. cotA = tanc cosB

23. In a right spherical triangle whoseangles are A = 63015, B = 135034 and C= 900, find side b.

a. 134.10

b. 143.10

c. 131.40

d. 141.30

24. A ship leaves M (360N, 760W) andsailing on a great circle arc crosses theequator at 500W. Find the distancetraveled.

a. 2,601 nmb. 2,501 nmc. 2,401 nmd. 2,301 nm

25. Given a spherical triangle with A =74021, B = 83041 and C = 58039. Find c.

a. 54.930

b. 56.800

c. 55.730

d. 57.360

26. Given: a = 51031, b = 36047 and c =80012. Find A

a. 34.450

b. 34.550

c. 34035d. 34025

27. Given: a = 68027, b = 87032 and C =97053. Find c.

a. 94.410

b. 97.410

c. 96.410

d. 95.410

28. How long does it take to sail fromManila (14036N, 12105E) to Hong Kong(22018N, 114010E) at the rate of 18mph?

a. 1.5 daysb. 1.6 daysc. 1.7 daysd. 1.8 days

29. Express in hour, minutes and secondsthe time corresponding to 260034.a. 17h20m16sb. 17h21m16sc. 17h22m16sd. 17h23m16s30. In a quadrantal spherical trianglewhere a = 540, b = 380 and c = 900, findangle A.

a. 16.310

b. 17.310

c. 18.310

d. 19.310

31. An icosahedron is a regularpolyhedron having

a. 12 facesb. 16 facesc. 18 facesd. 20 faces

32. The perpendicular distance from thecenter of a regular polygon to a side iscalled the_________ of the polygon.

a. altitudeb. amplitudec. mediand. apothem

33. The angle formed by two intersectingplanes is called a

a. face angleb. vertical anglec. dihedral angle

d. central angle34. Find the area of a pentagon whoseapothem is 10 cm.

a. 336.72 cm2

b. 373.65 cm2

c. 327.36 cm2

d. 363.27 cm2

35. The radii of two spheres are in theratio 3:4 and the sum of their surface areais 2,500sq. cm. Find the radius of thesmaller sphere.

a. 15 cmb. 10 cmc. 20 cmd. 25 cm

36. The base of a pyramid is a regularhexagon whose apothem is 8.66 cm. Ifthe altitude of the pyramid is 6 cm, findthe volume of the pyramid rounded to 3significant figures.

a. 510 cu. Cmb. 515 cu. Cmc. 520 cu. Cmd. 525 cu. Cm

37. A face diagonal of a cube is 4 cm.Find the volume of the cube.

a. 22.63 cm3

b. 21.64 cm3

c. 23.62 cm3

d. 24.64 cm3

38. What is the distance in cm betweentwo vertices of a cube, which are farthestfrom each other, if an edge measures 5cm?

a. 52b. 53c. 54d. 55

39. The volume of a cube is reduced to_____ if all sides are halved.

a. b. c. 1/8

d. 1/1640. The sum of the angles of a polygon ofn sides equals.

a. 3600

b. 1800

c. (n-2) x1800

d. (n-2)(1800) / n41. Each exterior angles of a polygon of nsides is

a. 180/nb. 360/nc. (n-2)(1800) / nd. always 720

42. The median of a trapezoid equals_________ the sum of the bases.

a. 1/3b. c. d. 1/5

43. A pyramid has a base whose sidesare 10 m, 16 m and 18 m. if the altitude ofthe pyramid is 20 m, find the volume ofthe inscribed cone in m3.

a. 274.18b. 1715.36c. 325.1d. 376.57

44. The tangent and a secant are drawnto a circle from the same external point. Ifthe tangent is 6 inches and the externalsegment of the secant is 3 inches, thelength of the secant is _____inches.

a. 12b. 15c. 14d. 18

45. Two secants from a point outside thecircles are 24 and 32. If the externalsegment of the first is 8, the external ofthe second is:

a. 8b. 6c. 10

d. 1246. A trench is constructed so that itscross section is a trapezoid the area ofwhich is 21 square feet. If the shorterbase is 2 times its height and the longerbase is 5 ft longer than its height, find theheight of the trench.

a. 3 ftb. 4 ftc. 5 ftd. 6 ft

47. The second proposition of Pappusstates that the volume of a solid ofrevolution is equal to the generating areatimes the circumference of the circledescribed by the centroid of the area. Findthe volume of the solid formed byrevolving a circle around a line tangent toit. Let R be the radius of the circle.

a. 19.74 R3

b. 100R3

c. 18.85 R3

d. R3

48. If a circular cylindrical tank axishorizontal, diameter 1 meter, and length 2meters is filled with water up to a depth of0.75 meter, how much water is in thetank?

a. 2 m3

b. 1.51 m3

c. 1.2637 m3

d. 3.1415 m3

49. The diagonals of a rhombus are equalto 30 cm and 40 cm. Find the distancebetween the plane of the rhombus and apoint M if the latter is 20 cm distant fromeach of its sides.

a. 15 cmb. 16 cmc. 17 cmd. 18 cm

50. The angle at the vertex of an axialsection of a cone is a right one. The areaof the section is equal to 25 cm2. Find thearea of its base.

a. 25 cm2

b. 30 cm2c. 50 cm2d. 625 cm2

Math Practice Problems Module 51. The altitude of a cone is equal to half thediameter of the sphere circumscribed about it.How many times is the volume of the spheregreater than that of the cones?

a. b. 2c. 4d.

2. Determine the volume of the sphericalsegment given its altitude equal to 4 cm and theradius of the base circle equal to 8 cm.

a. 252/3 cm3

b. 342/3 cm3c. 342/3 cm3d. 416/3 cm3

3. A ball whose radius is equal to 30 cm isprovided with a cylindrical hole bored along itsdiameter. Compute the volume of the remainingportion if the radius of the cylindrical hole isequal to 18 cm.

a. 20, 582 cm3b. 15, 325 cm3c. 18, 432 cm3

d. 21, 153 cm34. The edge of a cube is equal to a. Find theradius of the circumscribed sphere.

a. 9/2b. 2ac. a3/2d. 42a

5. The perimeter of a rectangle is 22. If one ofthe rectangles is doubled and the other tripled,the perimeter would be 32 more than theperimeter of the original rectangle. What are thesides of the rectangle?

a. 6 and 5b. 8 and 7c. 10 and 9d. 12 and 11

6. if a polygon has 54 diagonals, then it musthave,

a. 12 sidesb. 10 sidesc. 11 sidesd. 13 sides

7. A trench is constructed so that its crosssection is a trapezoid the area of which is 21sq.ft. if the shorter base is 2 times its height andthe longer base is 5 ft longer than its height.Find the length of the shorter base.

a. 3b. 4c. 5d. 6

8. if the acute angles of a right triangle are in theratio 1:2, then the number of degrees in thesmall angles is:

a. 30b. 20c. 45d. 90

9. The length of a wire fence around a circularflowerbed is 10 feet. The area of the flowerbedin sq.ft is

a. 100b. 50c. 25d. 5

10. The perimeter of rectangle is 28m and itsdiagonal is 10 m. find the area of the rectangle.

a. 48 sq.mb. 38 sq.mc. 10 sq.md. 28 sq.m

11. This conic section may be defined as the lociof appoint that moves in a plane so that the sumof its distances from two fixed points of theplanes is a constant.

a. hyperbolab. circlec. parabolad. ellipse

12. The graph of r=a(1+cos) is aa. cardioidb. lemniscatec. limacon

d. rose13. The parabola y= 4-x2 opens

a. to the rightb. to the leftc. upwardd. downward

14. The equation r=a is the polar equation ofa. an ellipseb. a parabolac. a hyperbolad. circle

15. The graph of x3+y3-3axy = 0 is called thea. cycloidb. strophoidc. folium of Descartesd. cissoids of diocles

16. The intersection of the medians of a trianglewhose vertices are (-6, -8), (3, -5) and (4, -2) areat

a. (0, 0)b. (-1/3, -5)c. (-1/3, 5)d. 1/3, -5)

17. Find the equation of the line, which passesthrough the point (-2, 9) and the sum of itsintercepts equal to 10.

a. 2x+3y-23 = 0b. 3x+2y-12 = 0c. 3x-2y+24 = 0d. 2x-3y+31 = 0

18. A parabola may be defined as the set ofpoints that are equidistant from a fixed point anda fixed line. The fixed point is called the focusand the fixed line is called the

a. asymptoteb. latis rectumc. directrixd. tangent line

19. Find x if the lilneL1 through (-1, 3) and (-3, -2) is perpendicular to the line L2 through (-7, 4)and (x, 0).

a. 6b. 3c. 4d. 2

20. The general equation of the parabola whoseaxis is parallel to the y-axis is

a. Ax2+Cy2+Dx+Ey+F=0

b. Ax2+Dx+Ey+F=0c. Ax2+Cy2+Dx+Ey+F=0 whereA=C have the same signd. None of the above

21. The point P divides the line segment P1P2 inthe ratio r=P1P0/P1P2=3/10. if P0=(9, 2) and (6,8), find P2.

a. (15, -13)b. (16, -12)c. (17, -10)d. (18, -9)

22. The length of the latus rectum of4x2+9y2+24x+36y+36=0 is

a. 2.76b. 2.67c. 2.65d. 2.65

23. Find the angle from the line through (-2, -3)and 94, 3) to the line through (-1, 6) and (3, -2).

a. arctan(1/2)b. arctan(1/3)c. arctan 3d. arctan 2

24. The graph of y2=x isa. a parabolab. a pair of intersecting linesc. a pair of parallel linesd. none of the above

25. The slope of the line 3x-2y = 4 is equal toa. 3/2b. 2/3c. 3d. none of the above

26. If the eccentricity of a conic section isgreater than one, then it is

a. an ellipseb. a circlec. a hyperbolad. a parabola

27. If the lines L1 and L2 with slopes m12 andm2 respectively, are perpendicular to each other,then

a. m2=0b. m1=m2c. m1m2=-1d. m1 = -m2

28. The vertex of a parabola y2-4x+6y+13 = 0 isat

a. (-3, 1)b. (1, -3)c. (0, 0)d. (1, 1)

29. If a line sklants upward to the right, then itsslope is

a. zerob. positivec. negatived. infinity

30. The graph of 3x2 y = y2+6x isa. an ellipseb. a parabolac. a circled. a hyperbola

31. The lines 3x+4y-10 = 0 and 4x-3y-1 = 0 area. parallelb. coincidentc. bisectingd. perpendicular

32. The equation of the line passing through (2,2) and (4, 8) is y = ________

a. x-4b. 3x-4c. 3x+2d. x+2

33. Given the curve Ax2+By2+F=0, passesthrough the points (4, 0) and (0, 3). Find thevalue of A.

a. 9b. 3c. 4d. 5

34. The center of the circle 3x2+3y2-6x+10y+2 =0 is at

a. (1, 1)b. (2, 1/3)c. (1, -5/3)d. (0, 0)

35. The eccentricity of the ellipse x2/5 +y2/7 = 1is

a. 1/714b. 2/3c. 5/7d. 1

36. If the coefficient of the terms in x2 and y2 areunequal and of the same sign, then the conic is:

a. parabolab. hyperbolac. ellipsed. circle

37. _________is the locus of appoint theabsolute value of the difference of whosedistances from two distinct fixed points is apositive constant

a. ellipseb. parabolac. hyperbolad. circle

38. The slope of asymptotes of x2/a2 + y2/b2 = 1is

a. b/ab. a/bc. 1d. 1-b/a

39. The locus of the parabola (x-5)2 = -12(y-1) isa. (5, 1)b. (5, -2)c. (1, -2)d. (1, -1)

40. The straight line equation y = x-5 passesthrough the points

a. (6, 3)b. (3, 0)c. (2, 2)d. (0, -4)

41. The rectangular coordinates of a point are(3, 1). The polar coordinates of this point are

a. (4, /6)b. (2, /6)c. (4, /3)d. (3, 1)

42. The rectangular form of r=4 tan2sec isa. 4x3=y2

b. x3=4y2

c. 4x2=y3

d. x2=4y3

43. The equation of the line passing through (0,4) and parallel to the x-axis is

a. y=4b. 4x+y = 0c. y = x2+4d. 4y-2=x

44. The graphs of the equations y = 2x+3 and y=x2-x-1intersect at two point. The coordinates ofthese points are

a. (0, 3), (2, 1)b. (-1, 1), (4, 11)c. (-1, 1), (-6, 3)d. (1, 5), (2, 5)

45. The area of the triangle whose vertices are (-3, 8)(7, 4) and (5, -1) is

a. 40 sq. unitsb. 29 sq. unitsc. 30 sq. unitsd. 60 sq. units

46. The curve xy = a2 isa. hyperbolab. parabolac. circled. ellipse

47. The distance between two points P1(2, -1)and P2(6, 2) is

a. 4b. 5c. 6d. 3

48. The polar form of xy = 3(x+y) isa. r = 6csc20(cos+sin)b. r2=6scs4c. r=2sin2d. r2=3cos3

49. A quadrilateral whose four sides are equaland parallel with no angle equal to aright angleis called a

a. parallelogramb. parallelepipedc. trapezoidd. rhombus

50. The graph of an equation of the form r = a bcos is a limacon with a loop if

a. 1

b. a/b = 1

c. 0,

Math Practice Problems Module 6

1. If the equation r = () is unchangedwhen is replaced by 180 + of when r isreplaced by r, then the curve issymmetric with respect to

a. normal sizeb. polar axisc. poled. both axes

2. The curve whose general equation is r=a sin n of r=a cos n.

a. roseb. lemniscatec. cardoidd. spiral

3. An equilateral triangle is inscribed inthe parabola x2=8y with one vertex of thetriangle at the origin. Find the area of thetriangle.

a. 1923b. 1923/2c. 1923/4d. 1923/5

4. Find the area in the second quadrantbounded by the curve x2/9 +y2/9 = 1 andthe coordinates axes

a. 6b. 2.25c. 3d. 4

5. If P (x, y) is such that AP/PB = 7/6where A(2, 5) and B(5, -1), find x.

a. 43/13b. 54/13c. 47/13d. 51/13

6. If the line segment AB is parallel tothe line segment CD and A (4, -3), B(2, 0),C(4, 1), D(x,2), find x.

a. 11/3b. 10/3

c. 7/3d. 5/3

7. Which of the following curves issymmetric with respect to the x-axis?

a. y2=x3

b. y3=x2

c. y=x3

d. y=x2

8. Determine k so that the radius of thecircle x2+y2+3x-2y +k =0 is equal to 2.

a. 3/4b. c. 3/5d. 3/5

9. Find the eccentricity of 25x2+16y2 = 400a. 0.55b. 0.66c. 0.65d. 0.70

10. A power cable hangs in parabolic arcbetween two poles 100 ft apart. If thepoles are 40 ft and if the lowest point onthe suspended cable is 35 ft above theground, find the height of the cable at apoint 20 ft from the pole.

a. 34.8 ftb. 35.8 ftc. 36.8 ftd. 37.8 ft

11. Find the distance between (4, 3, 2)and (-3, -2, 1).

a. 33b. 43c. 53d. 63

12. Find the distance from the origin to (4,-3, 2).

a. 29b. 27c. 13d. 31

13. Find the radius of the sphere x2+y2+z2-2x+6y+2z-14 = 0.

a. a. 4b. 5c. 6d. 3

14. The triangle with vertices (3, 5, -4), (-1, 1, 2) and (-5, -5, -2) is

a. rightb. isoscelesc. equilaterald. scalene

15. Find the direction numbers of the linethrough P1 (-3, 2, 4) and P2 (2, 5, -2).

a. 5, 3, 6b. 5, -3, 6c. 5, 3, -6d. 5, 3, 6

16. Find the angle between the lineL1 with direction numbers 3, 4, 1 and theline L2 with direction numbers 5, 3, -6.

a. 60.410

b. 60.510

c. 60.610

d. 60.710

17. Find the angle A of the triangle whosevertices are A(4, 6, 1), B(6, 4, 0) and C(-2,3, 3).

a. 112.390

b. 113.290

c. 119.230

d. 112.930

18. If the angle between two lines withdirection numbers 1, 4, -8 and x, 3, -6 isarcos(62/63), find x.

a. 4b. 3c. 2d. 1

19. The direction numbers of two lines are2, -1, 4 and 3, y, 2. If the lines areperpendicular, find y.

a. 2

b. 3c. 4d. 5

20. Find the x-coordinate of the pointwhich is 10 units from the origin and hasdirection cosines cos = 1/3 and cos = -2/3.

a. 20/3b. 19/3c. 10/3d. 17/3

21. A triangle has a vertices at A(2, -1, 3),B(-4, -3, 1) and C(0, 5, -1). Find the lengthof the median from vertex A to the sideBC.

a. 27b. 28c. 29d. 30

22. Transform xy = 8 to cylindricalcoordinates.

a. r2sin2 = 8b. r2sin= 16c. rsin2=8d. rsin2=16

23. Transfrom psinsintan=5 50rectangular coordinates.

a. y=5xb. y2=5xc. y=5x2

d. xy=524. Transform p=6 to cylindricalcoordinates

a. r2+z2=2b. r2+z2=62c. r2+z2=36d. r2+z2=360

25. Give the equivalent sphericalcoordinate of (3, 4, 6).

a. (61, 53.130, 38.90)b. (61, 53.130, 39.810)c. (61, 51.330, 39.810)

d. (61, 53.310, 39.910)26. Find the equation of the plane whichpasses through (-1, -3, 6) and whichparallel to the plane 4x-9y+7z+2 = 0

a. 4x-9y+7z-65 = 0b. 4x-9y+5z-60 = 0c. 4x-9y-7z+65 = 0d. 4x-9y+5z-60 = 0

27. Find the distance from 2x +7y +4z 3= 0 to (2,3,3).

a. 32/69b. 33/69c. 35/69d. 34/69

28. Find the coordinates of thepoint whichdivides the line segment P1P2 where P1(2,5, -3) and P2(-4, 0, 1) in the ratio 2:3.

a. (-2/5, 3, -7/5)b. (/5, -3, -7/5)c. (2/5, -3, 7/5)d. 2/5, -3, 7/5)

29. If the angle between the planes 2x-3y+18 and 2x-y+kz = 12 is arcos(19/21),fin k.

a. 2b. 3c. 4d. 5

30. Find the angle between the line withdircton numbers 1, -1, -1 and the plane3x-4y+2z-5 = 0

a. 30.400

b. 31.410

c. 32.420

d. 33.430

31. Find the direction numbers of the line2x-y+3z+4 =m 0 and 3x+2y-z+7 = 0

a. [5, 11, -7]b. [-5, 11, 7]c. [5, -11, 7]d. [-5, -11, 7]

32. Find the equation of the planeperpendicular to the line joining (2, 5, -3)

and (4, -1, 0) and which passes through(1, 4, -7).

a. 2x-6y+3z-43 = 0b. 2x+6y+3z+43 = 0c. 2x-6y+3z+43 = 0d. 2x-6y-3z-43 = 0

33. If the acute angle between the planeskx-y+z = 7 and x+y+2z = 11 is 600, find k.

a. 1b. 2c. 3d. 4

34. The surface described by the equation4x2+y2+26z = 100 is

a. an elliptic hyperboloidb. an elliptic paraboloidc. an ellipsoidd. an elliptic cone

35. Find the Cartesian coordinates of thepoint having the cylindrical coordinates(3, /4, 5).

a. (0, 5, 3)b. (0, 3, 5)c. 5, 0, 3)d. (3, 0, 5)

36. Find the cylindrical coordinates of thepoint having the Cartesian coordinate (4,4, -2).

a. (42, /4, -2)b. (22, /6, -2)c. (3, /3, -2)d. (42, /2, -2)

37. Find the Cartesian coordinates of thepoint having the spherical coordinates(4, /6,/4)

a. (6, 2, 22)b. (3, 2, 23)c. (6, 3, 2)d. (3, 6, 22)

38. If an x = a, y

b. decreasesc. becomes infinited. becomes zero

39. If the 3rd derivative of a function in onevariable is equal to zero, then the functionis

a. quadraticb. cubicc. lineard. quartic

40. Find the maximum point of y = 4+3x-x3.

a. (0, 40b. 1, 2)c. (1, 6)d. (-2, 6)

41. A picture 2 m high is hanging on awall with the bottom of the picture 0.6 mabove the observers eye level. How farfrom the wall must be observer stand inorder that the angle subtended by thepicture be a maximum?

a. 1.23 mb. 1.25 mc. 1.27 md. 1.29 m

42. Evaluate

lim x3-x2-x+10x -2 x2+3x+2

a. 0b. c. 5d. 15

43. If the first derivative of a function is aconstant, then it is a, _______function.

a. linearb. quadraticc. logarithmicd. exponential

44. The function y = f(x) has a minimumvalue at x = 2 of f92) = 0 and if

a. f(2) = 0

b. f(2) 0c. f(2)0

45. How fast does the diagonal of a cubeincrease if each side of the cubeincreases at the constant rate of 5 cm/s?

a. 6.7 cm/sb. 7.6 cm/sc. 8.7 cm/sd. 7.8cm/s

46. At the minimum point, the slope of thetangent line is

a. zerob. positivec. negatived. infinity

47. At the inflection point where x = a,a. f(a) = 0b. f(a)>0c. f(a)

which the distance between them ischanging.

a. 60 kphb. 70 kphc. 50 kphd. 40 kph

Math Practice Problems Module 11.Which of the following quadraticequations will have two real and distinctroots?

a. 6x2-5x + 4 = 0b. 9x2-6x + 1 = 0c. 6x2-61x +143 = 0d. x2-22x + 121 = 0

2. Radicals can be added if they have thesame radicand and the same

a. coefficientb. b. exponentc. powerd. order

3. Drawing a card from a deck of cards iscalled

a. an eventb. an outcomec. a triald. an experiment

4. The set of integers does not satisfy theclosure property under the operation of

a. additionb. subtractionc. multiplicationd. division

5. A number which can be expressed asthe quotient of two integers is

a. rationalb. irrationalc. naturald. prime

6. All board reviewees are not more than25 years old. This statement implies thatthey are:

a. less than 25 years old

b. at least 25 years oldc. 25 years old or lessd. 25 years old or more

7. The roots of the equation 6x2 61x +143 = 0 are

a. real and distinctb. real and equalc. complex and distinctd. complex and unequal

8. A set of elements that is taken withoutregard to the order in which the elementsare arranged is called a:

a. permutationb. combinationc. progressiond. probability

9. If the value of the discriminant of aquadratic equation is 1.25, then the rootsof the equation are:

a. real and equalb. real and unequalc. complex and unequald. imaginary and distinct

10. Find the value of k that will make x2 28x +k a perfect square trinomial.

a. 196b. 169c. 144d. 121

11. In how many ways can a picture bepainted by using two or more of 7 differentcolors?

a. 120b. 110c. 128d. 131

12. What is the probability of getting anumber 4 thrice in five tosses of a die?

a. 0.0232b. 0.0322c. 0.3220d. 0.2330

13. In how many ways can 8 persons beseated at a round table if a certain 2 areto sit next to each other?

a. 1, 440b. 1,008c. 4, 140d. 5, 040

14. If x:y:z =4: - 3:2 and 2x+4y-3z = 20,find the value of x.

a. 6b. 4c. 8d. 7

15. At a Math Contest, the judgeseliminate 1/3 of the contestants after eachhalf hour. If 81 contestants were presentat the start, how many would be left after2 hours?

a. 18b. 12c. 16d. 10

16. Getting an odd number by throwing adie is called:

a. an experimentb. an outcomec. an eventd. a trail

17. Two prime numbers, which differ bytwo, are called prime twins. Which of thefollowing pairs of numbers are primetwins?

a. (1,3)b. (7,9)c. (13,15)d. (17,19)

18. The probability of As winning a gameagainst B is 1/3. What is the probabilitythat A will win at least two of a total of 3games?

a. 7/27b. 8/27c. 19/278

d. 15/2719. The probability of drawing a black jackand an ace is succession from a deck of52 cards

a. 0.0003b. 0.003c. 0.03d. none of the above

20. If P(n+1, 4) = 2P(n, 4)a. 4b. 7c. 10d. 7

21. What is probability of getting thenumber 1 thrice when a die is tossed 5times?

a. 0.0233b. 0.0223c. 0.0355d. 0.0322

22. In how many ways can 7 boys beseated in a row so that 3 boys are alwaysseated together?

a. 720b. 360c. 144d. 270

23. Find the 100th term of the sequence1.01, 1.00, 0.99,

a. 0.02b. 0.03c. 0.04d. 0.05

24. What is the probability of obtaining atleast 4 tails when a coin is tossed fivetimes?

a. 0.1857b. 0.1758c. 0.1785d. 0.1875

25. Mr. Diaz can finish a job in 9hrs. Afterworking for 5 hrs, he decided to take a

rest. Mr. Torres helped Mr. Diaz finishedthe job in 2 hrs and 20 minutes. How longwould it take Mr. Torres to do the jobalone?

a. 3 hrs and 5 minb. 4 hrs and 10 minc. 5 hrs and 15 mind. 6 hrs and 20 min

26. Find 2 numbers whose sum is 12 andthe sum of their squares is 74.

a. 3 and 9b. 4 and 8c. 6 and 6d. 7 and 5

27. Two jeepney start at the same pointbut are going in different directions. Ifjeepney A runs at the rate of 60 km/hr andjeepney B at 50 km/hr and both start atthe same time, when will the two jeepneybe 550 km apart?

a. 4 hrsb. 5 hrsc. 6 hrsd. 7 hrs

28. A man and a boy can dig a trench in20 days. It would take the boy 9 dayslonger to dig it alone than it would take theman. How long would it take the boy todig it alone?

a. 54 daysb. 45 daysc. 35 daysd. 36 days

29. The roots of the equation 2x2 3x +20 = 0 are

a. real and equalb. real and unequalc. complex and equald. complex and unequal

30. If x3+3x2+(5+k)x+2-k is divided by x+1and the remainder is 3, then the value of kis

a. 5b. 3c. 2d. 4

31. What is the sum of the prime numbersbetween 1 and 15?

a. 38b. 41c. 39d. 42

32. The sum of the integers that areexactly divisible by 15 between 288 and887 is

a. 21, 810b. 22, 815c. 23, 805d. 23, 700

33. If 16 is 4 more than 3x, find the valueof 2x-5.

a. 5b. 4c. 3d. 2

34. The 20th term of the progression 1, 4,7, 10, .is

a. 56b. 57c. 58d. 59

35. Which of the following quadratictrinomial is NOT factorable?

a. 6x2 + 5x - 4b. 6x2 - 7x - 343c. 6x2 - 52x - 60d. 6x2 61 x + 143

36. The value of k for which the roots of8x2+8kx+3k+2 = 0 are real and equal is

a. 3b. 1

c. 2d. 4

37. If the radius of a circle is diminishedby 20%, then its area is diminished by

a. 25%b. 46%c. 52%d. 36%

38. Which of the following is an irrationalnumber?

a. 1.363636.b. (16)3/4

c. 35d. 0.75

39. Which of the following numbers is nota prime number.

a. 2b. 5c. 9d. 7

40. If i2=-1, then i7-i6+i5=a. ib. Ic. 1d. 1

41. The degree of the polynomial f(x, y, z)= 7x3y2-4xz5+2x2y is

a. 5b. 6c. 3d. 4

42. Two sisters are 14 and 21 years oldrespectively. In how many years will theratio of their ages be 3:4?

a. 9b. 8c. 7d. 6

43. If (n+3)! / (n+1)! = 20, find n.a. 3b. 4c. 5d. 2

44. If x:6 = y:2 and x y = 12, find y.a. 8b. 2c. 4d. 6

45. Car A runs 30 km/hr less than Car B.Car A covers 250 km in the same time carB travels 400 km. Find the rate of each.

a. 50 km/hr and 80 kms/hrb. 60 kms/hr and 90 kms/hrc. 70 kms/hr and 100 kms/hrd. 809 kms/hr and 110 kms/hr

46. What is the probability of obtaining atleast 4 heads when a coin is tossed 5times?

a. 0.1857b. 0.1758c. 09.1785d. 0.1875

47. 2(2n+2)/2n+1-2n =a. 2b. 4c. 8d. 16

48. The product of two irrational numbersis

a. always irrationalb. sometimes irrationalc. never irrationald. rational

49. The least common multiple of (x-2)2 and x2+x-6 is

a. x-2b. (x-2)3(x+3)c. (x-2)2(x+3)d. (x+3)3

50. The length of a rectangle is increasedby 50%. By what percent would the widthhave to be decreased to maintain thesame area?

a. 33 1/3b. 50c. 66 2/3

d. 150