Math Practice Problems Module 3

1. During the recent Olympics on 4-men relay team completed in a 1600-meter relay have the following individual speed, R₁ = 26 kph, R₂ = 27 kph, R₃=28 kph, R₄=29kph. What is the average speed of the team?

1. 25.43
2. 26.44
3. 27.45
4. 28.46

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

1. 15/11 days
2. 20/11 days
3. 30/11 days
4. 45/11 days

3. At what time between 7 and 8 o’clock are the hands of the clock, at right angles?

1. 7:22
2. 7:18
3. 7:15
4. 7:24

4. At what time between 7 and 8 o’clock are the hands of the clock, at 180⁰ apart?

1. 7:05
2. 7:10
3. 7:11
4. 7:30

5. At what time between 7 and 8o’clock are the hands of the clock together?

1. 7:38
2. 7:30
3. 7:45
4. 7:20

6. A man left his office for a business appointment one afternoon and noticed his watch at past 2 o’clock. Between two to three hours later, the man returned and noticed that the hands of the clock have exchanged places. What time did he leave and arrive?

1. 2:26.01 and 5:12.17
2. 2:15 and 5:30
3. 2:20 and 5:32
4. 2:23 and 5:40

7. A survey is made on the smoking habit of the male population above 18 years old of a certain community. The survey was on the three cigarettes A, B and C.

55% smoke S

40% smoke B

30% smoke C

20% smoke A and B

12% smoke B and C

10%smoke A and C

5% smoke all the three brands

How many % do not smoke?

1. 12
2. 15
3. 3
4. 10

8. Separate 132 into 2 such that the larger divided by the smaller, the quotient is 6 and the remainder is 13. Find the numbers.

1. 17 and 115
2. 20 and 112
3. 24 and 108
4. 30 and 102

9. A number of two digits divided by the sum of the digits, the quotient is 7 and the remainder is 6. If the digits of the number are interchanged the resulting number exceeds three times the sum of the digits by 5. What is the number?

1. 39
2. 48
3. 83
4. 72

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

1. 16.7
2. 15.6
3. 17.8
4. 18

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

1. 14 lbs. Silver
2. 15 lbs silver
3. 20 lbs silver
4. 30 lbs silver

12. A motorist is traveling from A to B at a constant rate of 30 kph and return from B to A at constant rate of 20 kph. What is his average velocity?

1. 8
2. 15
3. 30
4. 24

13. If log 2 = A and log3 = B, find the log (2.4)

1. 3A-B-1
2. 3A+B-1
3. 3A+B+1
4. 3A-B+1

14. If log_x2 +2log_x3 = 2 +log_x6, then x =

1. Ö3
2. Ö2
3. Ö5
4. Ö6

15. Solve logx²=(logx)²

1. 103
2. 102
3. 101
4. 100

16. If 2 = 10^0.3010 and 9 = 10^0.9542,then 4.5 = 10^x where x equals

1. 0.2552
2. 0.2553
3. 0.6322
4. 0.6532

17. If log_x (1/144)=-2, then x =

1. –11
2. 12
3. –4
4. 10

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

1. not equal to zero
2. equal to zero
3. equal to unity
4. infinite

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

1. complementary
2. dependent
3. independent
4. mutually exclusive

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

1. P(AandB)=

      P(A)·P9(B½A)

2. P(AandB)=P(A)·P(B)
3. P(A or B)=P(A)·(B½A)
4. P(A or B) = P(A)+P(B)

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

1. P(A and B) ¹0
2. P(A and B) = 0
3. P(A and B) >0
4. P(A and B)< 0

22. If P(A) is the probability of event A;P(B) is the probability of event B and P(A and B) is the probability of their joint occurrence, such that P(A and B)=P(A)·P(B), then A and B are said to be

1. complementary
2. disjoint
3. dependent
4. independent

23.Which of the following events are not mutually exclusive?

1. events “ACE” and HEART”
2. events ”ACE” and JACK”
3. events “2” and “odd”
4. events”1” and prime”

24. The probability that the Ginebra basketball team will win the championship is assessed as being 1/3. Find the odds that the team will win.

1. 1:2
2. 2:1
3. 1:3
4. 3:1

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

1. 0.80
2. 0.20
3. 0.25
4. 0.75

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

1. 0.25
2. 0.30
3. 0.35
4. 0.40

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

1. 0.55
2. 0.60
3. 0.65
4. 0.70

28.The mean deviation is a measure of

1. dispersion
2. distribution
3. central tendency
4. frequency

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

1. range
2. deviation
3. variance
4. interval

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

1. class boundary
2. class mark
3. class interval
4. class size

31. In statistics, which of the following is not considered as a continuous variable?

1. height
2. weight
3. number of accidents
4. temperature

32. The number of reviewees in a room is a

1. continuous variable
2. discrete variable
3. variate
4. statistic

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

1. 24
2. 25
3. 26
4. 23

34. It is a measure of central tendency, which depends upon the number of score and not on the magnitude of the scores.

1. mean
2. median
3. mode
4. geometric mean

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

1. 37.3
2. 38.3
3. 39.3
4. 36.3

36. Which of the following relations is true?

1. sin(-A) = sin A
2. tan(-A) = tan A
3. cos(-A) = cos A
4. csc(-A) = csc A

37. What is the period of y = 3sin(x2)?

1. 2p
2. 3p
3. 4p
4. 5p

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

1. sinAcosB = 1
2. sinAcosB = 0
3. sin²A-cos²B = 0
4. sin²A-cos²B = 1

39. If tanA = 2, then tan2A is equal to

1. 4/3
2. –4/3
3. ¾
4. -3/4

40. If sinx = cosy,then

1. xy = 90⁰
2. x+y = 90⁰
3. x-y = 90⁰
4. none of the above

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

1. sin60⁰
2. –sin60⁰
3. cos60⁰
4. –csc60⁰

42. Evaluate: 2sinx – 3 cotx = 0; 0 £x£2p

1. p/3, 5/3p
2. p/3, p/4
3. 5p/3, p/4
4. none of  these

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

1. I
2. II
3. III
4. IV

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

1. 27
2. 57
3. 114
4. 123

45. A man travels 4 miles north, 12 miles east and then 12 miles north. How far is he in miles from the starting point?

1. 17
2. 20
3. 21
4. 24

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

1. 60⁰
2. 90⁰
3. 100⁰
4. 110⁰

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

1. 16 and 26
2. 17 and 25
3. 18 and 24
4. 19 and 23

48. Find the value of (1+i)¹².

1. –36
2. –64
3. –36i
4. –64i

49. If sin60 +cos3q = 0, find 0 where 0⁰< q<360⁰.

1. 320⁰
2. 240⁰
3. 120⁰
4. 110⁰

50. Reduce (2cis60⁰)²(cis(-30⁰C))² to the form  a + bi.

1. 2+2Ö3i
2. 2-2Ö3i
3. 2+Ö3i
4. 2-Ö3i

Answers are found at the Answers section. Check out the Labels at the toolbar on the right hand side ->