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reaY eht fo naicitamehtaM > Algebra > Flashcards

Algebra Flashcards

1
Q

Set 1 Problem 40: Consider a geometric sequence whose 3rd term is 18, and whose common ratio is 3/2. Find the 7th term.

A

729/8 (p. 13)

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2
Q

Set 1 Problem 50: Find the value of x in the equation 2x^2-7x-15=0.

A

5, -3/2 (p.14)

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3
Q

Set 1 Problem 54: The 5th term of a harmonic progression is 10 and 11th term is is 5. Find the 9th term.

A

6 (p.15)

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4
Q

Set 1 Problem 56: Find the sum of the exponents of all the terms in the expansion of (3x-2)^5.

A

15 (p.15)

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5
Q

Set 2 Problem 6: Three numbers whose sum is 91 form a geometric progression. If the first decreases by 2, the second by 3, and the third by 5, the resulting numbers from an arithmetic progression. Find the common ratio of the geometric progression.

A

5/6 and 6/5 (p.23)

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6
Q

Set 2 Problem 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?

A

198 days (p. 24)

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7
Q

Set 2 Problem 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?

A

1.7 hours

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8
Q

Set 2 Problem 17: A road concreting project can be done by 24 men in 68 days. At the start of the work, all 24 men are working but the number of men decreases by 2 every end of each 12-day period. How long will it takes to finish the project?

A

96 (p.25)

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9
Q

Set 2 Problem 29: How many quarts of pure sulfuric acid should be added to 5 quarts of water to obtain a 40% sulfuric acid solution?

A

3-1/3

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10
Q

Set 2 Problem 30: Art and Bob complete a certain job if they work together for 6 days, or if Art works for 12 days and Bob for 3 days. How long would it take Art alone to complete the job?

A

18 days (p.28)

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11
Q

Set 2 Problem 53: A firm producing poultry feeds finds that a new production method needs to purchase an equipment costing P36,000 and the cost of each feed is P792 and the management plans to charge P1,260 per unit for the feed. How many units of feeds must be sold for the firm to break even?

A

77 (p.31)

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12
Q

Set 2 Problem 59: Mr. Cruz purchases a selection of screws for his shop. He buys the same number of PHP1.50 and PHP2.50 screws, and half that many of PHP4 screws. The number of PHP3 screws is one more than the number of PHP4 screws. If his total bill is P78, how many PHP4 screws did he purchase?

A

5 (p.32)

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13
Q

Set 2 Problem 63: Find the nth term of the sequence 6, 2, -2, … .

A

-4n+10 (p.33)

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14
Q

Set 2 Problem 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?

A

18 (p.33)

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15
Q

Set 2 Problem 70: If an alloy containing 30% silver is mixed with a 55% silver alloy to get 800 pounds of 40% alloy, how much of the 55% silver alloy must be used?

A

320 pounds (p.36)

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16
Q

Set 3 Problem 1: Mr. Jones walks up a stalled 18m long escalator in 120 sec. When standing on the same escalator now moving, he is carried up in 80 sec. How much time would it take Mr. Jones to walk up the moving escalator?

A

48 seconds (p.41)

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17
Q

Set 3 Problem 9: Solve for y from the systems of equations: xy=10, yz=12, xz=30

A

2 (p.42)

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18
Q

Set 3 Problem 39: It takes Alex 60 seconds to run around a 440-yard track. How long does it take Rubin to run around the track if he and Alex meet in 32 seconds after they start together in a race around the track in opposite direction?

A

72.57 sec (p.48)

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19
Q

Set 3 Problem 40: At how many minutes after 3 P.M. will the minute hand of the clock overtakes the hour hand?

A

16.364 (p. 48)

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20
Q

Set 3 Problem 41: A motorboat that can travel 20 mph in still water, takes 3/5 as long to travel downstream on a river from A to B, as to return. Find the rate of current.

A

5 mph (p. 49)

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21
Q

Set 3 Problem 60: A ball is dropped from a height of 1.2 m and each time it strikes the ground it rebounds back to a height of three-fourths of the height from which it fell. Determine the total distance traveled by the ball before it comes to rest.

A

8.40 m (p.60)

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22
Q

Set 3 Problem 69: Charlie bought two cars, one for P600,000 and the other for P400,000. He sold the first at a gain of 12% and the second at a loss of 10%. What was his total percentage, gain or loss?

A

3.2% gain (p.54)

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23
Q

Set 4 Problem 16: What is the total value of x in log_x(625)=4?

A

5 (p.62)

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24
Q

Set 4 Problem 24: Find the sum to infinity of the series 4, 4/3, 4/9,…..

A

6 (p. 63)

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25
Q

Set 4 Problem 25: An arithmetic progression has its 4th term 24 and 11th term 102. Find the common difference.

A

78/7 (p.63)

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26
Q

Set 4 Problem 33: What is the remainder when (9-3x+5x^2+6x^3) is divided by (3x-2)?

A

11 (p.64)

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27
Q

Set 4 Problem 34: A job can be done in 15 days by a crew 12 men working 7 hours a day. How long will a crew of 9 men working 7 hours a day take to finish the same job?

A

20 (p.65)

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28
Q

A closed traverse has the following data in Table 4.1.
Set 4 Problem 38: Compute the distance CD in meters.

A

77.60 m (p.65)

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29
Q

A closed traverse has the following data in Table 4.1.
Set 4 Problem 39: Compute the distance DA in meters.

A

75.02 m (p.66)

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30
Q

A closed traverse has the following data in Table 4.1.
Set 4 Problem 40: Compute the area of the lot ABCD in square meters.

A

1,315.74 m^2 (p.66)

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31
Q

Set 4 Problem 44.:Given the inequality 3<x<7 and 6>x>2. What are the possible values of x?

A

3<x<6 (p.66)

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32
Q

Set 4 Problem 45: How many integers do the solutions of the inequalities 3x-5>7 and x≤18-x share?

A

5 (p.66)

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33
Q

Set 4 Problem 46: Find the solution set: |3-2x|≥7

A

(-∞,-2)U(5,∞) (p. 66)

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34
Q

Set 4 Problem 61: To stimulate his lazy student in the pursuit of integral calculus, a math professor offered to pay him P12 for every problem correctly solved and to fine him P6 for every incorrect solution. After the student has solved 36 problems, neither of them owed any money to the other. How many did the student solve incorrectly?

A

12 (p. 69)

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35
Q

Set 5 Problem 13: Find the third proportional to 4 and 10.

A

25 (p.79)

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36
Q

Set 5 Problem 15: A car’s stopping distance varies directly with the speed it travels and inversely with the friction value of the road surface. If a car takes 60 ft to stop at 32 mph on a road whose friction value is 4, what would be the stopping distance of a car traveling at 60 mph on a road with a friction value of 2?

A

225 ft (p.80)

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37
Q

Set 5 Problem 16: Evaluate Equation 5.1.

A

0 (p.80)

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38
Q

Set 5 Problem 17: By how much will the product of the roots exceed the sum of the roots from the equation x^2-6x+10=0?

A

4 (p.80)

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39
Q

Set 5 Problem 20: Find the sum of the cubes of two numbers such that their sum multiplied by the sum of their squares is 65, and their difference multiplied by the difference of their squares is 5.

A

35 (p.80)

40
Q

Set 5 Problem 25: The log of the product AB is equal to 1.819543936 and the log of the quotient A/B is equal to -0.2632414348. Find the value of B.

A

11 (p.81)

41
Q

Set 5 Problem 34: The sum of the first “n” terms of the series is 2^(n-3)-8. Find the seventh term.

A

512 (p.83)

42
Q

Set 5 Problem 35: Find the sum of all integers between 84 and 714 which are divisible by 5.

A

50,085 (p.83)

43
Q

Set 5 Problem 43: Find the 6th term in the expansion of Equation 5.2.

A

Equation 5.3 (p.84)

44
Q

Set 5 Problem 48: How many minutes after 2 o’clock when the hands of the clock are perpendicular to each other for the first time?

A

27.27 min (p.84)

45
Q

Set 5 Problem 53: Simplify:

A

1/(y+4) (p.85)

46
Q

Set 5 Problem 60: What is the value of x in the equation|x+2|=11-2x?

A

{3} (p.86)

47
Q

Set 5 Problem 66: A busy manager leaves his office at one afternoon. At that time, the hands of a clock in the course of normal operation describe a time somewhere between 4:00 and 5:00 on a standard clock face. Within one hour or less, he returns and noticed the hands have exactly exchanged positions. What time did the manager leave his office?

A

4:26.853 PM (p.87)

48
Q

Set 6 Problem 2: Admission tickets to a theatre were P60 for adults and P25 for children. The total amount collected was P14,000 and the total attendance was 280 persons. How many children attended that day?

A

80 (p.94)

49
Q

Set 6 Problem 11: There are three consecutive odd integers. Three times the largest is seven times the smallest. What is the largest integer?

A

7 (p.96)

50
Q

Set 6 Problem 12: Three numbers are in direct proportion in the following manner: A is to B as 24.5 is to 20.2 while B is to C as 36 is to 15. If C is 52.8 , what is the value of A?

A

153.7 (p.96)

51
Q

Set 6 Problem 13: An elevated concrete tank is filled through its inlet pipe and then is emptied through the outlet pipe, in a total time of 9 hours. If the water enters through the inlet pipe and simultaneously allowed to leave through the outlet, the tank is filled in 20 hours. How long will it take to fill the tank if the outlet is closed?

A

4 hrs (p.96)

52
Q

Set 6 Problem 14: Find the 15th term of the harmonic progression 1, 1/3, 1/5, 1/7,…

A

1/29 (p.96)

53
Q

Set 6 Problem 18: A man 42 years old has a son 8 years old. In how many years will the father be three times as old as his son?

A

9 (p.96)

54
Q

An arithmetic progression has its 4th term 25 and 11th term 102.
Set 6 Problem 22: Find the common difference.

A

11 (p.97)

55
Q

An arithmetic progression has its 4th term 25 and 11th term 102.
Set 6 Problem 23: Find the first term.

A

-8 (p.97)

56
Q

An arithmetic progression has its 4th term 25 and 11th term 102.
Set 6 Problem 24: Find the sum of the first 10 terms of the AP.

A

415 (p.97)

57
Q

Set 6 Problem 36 Solve for x in the following matrix equation:

A

1 (p.173)

58
Q

Set 6 Problem 65: In the year 2000, approximately 40 million tourists visited South America and the Caribbean. The number of tourists to that area had been increasing at an average rate of 0.80 million tourists per year. In the same year, 17 million tourists visited the Middle East. The number of tourists to the Middle East had been increasing at an average rate of 1.8 million tourists per year. If the trend continues, when would you expect the number of tourists of the two places be equal?

A

2023 (p.104)

59
Q

Set 6 Problem 73: An expensive chain necklace consists of 18K gold chain whose weight increases uniformly from a weight of 1 carat for the end chain to 89 carats for the middle chain where a pendant is attached. The clasp weigh as much (in carats) as the total number of chains. If the necklace altogether weighs 1,198 carats, how many chains are there in the necklace?

A

27 (p.106)

60
Q

Set 7 Problem 2: The ratio of 9th term to the 4th term of a geometric progression is 1024. Find the common ratio.

A

4 (p.111)

61
Q

Set 7 Problem 8: A company produces and sells a certain product that costs P250 per unit, and the company’s fixed charges amount to P408,000 per year. The selling price for the product is P420. How many units must be produced and sold annually in order for the company to break even?

A

2,400 (p.112)

62
Q

Set 7 Problem 22: A chemistry experiment calls for a 30% solution of copper sulfate. Karla has 40 ml of 25% solution. How many ml of 50% solution should she add to obtain the required 30% solution?

A

10 ml (p.114)

63
Q

Set 7 Problem 24: Under normal conditions, a siren can be heard from only 125 feet. A car and an emergency vehicle are heading toward each other. The car is traveling at a speed of 44 fps while the emergency vehicle is traveling at 74 fps. If the vehicles are 1000 feet apart and under normal conditions, in how many seconds will the driver of the car first hear the siren?

A

7.42 sec (p. 115)

64
Q

Set 7 Problem 37: A man has two investments, one paying 5% annual interest and the other 8%. The total annual income from the two investments is P4,650. If the interest rates were interchanged, the total annual income would be P5,100. How much is invested at 5% interest rate originally?

A

P45,000 (p. 117)

65
Q

Set 7 Problem 43: Find the mean proportional 4 and 9.

A

6 (p. 117)

66
Q

Set 7 Problem 46: The denominator of a fraction is 5 more than the numerator. If half the numerator plus one is added to both terms of the fraction, the resulting fraction will be 5/6. What is the original fraction?

A

16/21 (p.118)

67
Q

Set 7 Problem 48: Solve the inequality: 5/3(x+1) greater than or equal to (2-x).

A

[1/8,+∞) (p. 118)

68
Q

Set 7 Problem 54: Compute the smaller angle between the hands of the clock at 8:25 AM.

A

102.5 deg (p.119)

69
Q

Set 8 Problem 9: How many terms of the progression 3, 5, 7, 9 …. will be taken so that their sum will 2,600?

A

50 (p.129)

70
Q

Set 8 Problem 12: The average of 11 numbers is 10. One of the numbers is eliminated leaving only 10 numbers. If the average of the remaining numbers is 9.3, what number is eliminated?

A

17 (p.130)

71
Q

Set 8 Problem 19: Fred is three times as old as his sister Mary. Four years ago he was five times as old as his sister. How old is Fred now?

A

8 (p.131)

72
Q

Set 8 Problem 28: The fifth term of an arithmetic progression is 5 and the tenth term is ten times the fourth term. What is the first term?

A

-7 (p.133)

73
Q

Set 8 Problem 55: A pile of log contains 20 logs on the topmost layer and each lower layer contains one more log than the layer above. If there are 25 layers in the pile, how many logs are there in all?

A

800 (p.137)

74
Q

Set 8 Problem 66: In a certain college of 500 students 65% are honors. 75% of the male students are honors and 55% of the female students are honors. How many male students are there in the college?

A

250 (p.139)

75
Q

Set 8 Problem 73: If two marbles are removed at random from a bag containing black and white marbles, the chance that they are both black is 1/3. If 3 are removed at random, the chance that they are all black is 1/6. How many marbles are there in all in the box?

A

10 (p.140)

76
Q

Set 9 Problem 1: The formula for the area of the circle with its diameter is A=(πD²)/4. Express the diameter D in terms of the area A in rationalized denominator form.

A

(2√(πA))/π (p.145)

77
Q

Set 9 Problem 4: Factor the expression x^2-6xy-x+3y+9y^2 as completely as possible.

A

(x-3y)(x-3y-1) (p.145)

78
Q

Set 9 Problem 7: Use the remainder theorem to solve for k, if the polynomial f(x)=x^3+kx^2-6x+4 when divided by x-3 has a remainder of 40.

A

3 (p.146)

79
Q

Set 9 Problem 27: The arithmetic mean of two numbers is 20 and their geometric mean is 16. What is the difference of the 2 numbers?

A

24 (p.149)

80
Q

Set 9 Problem 35: Find the value of k so that 2x^2+(k+2)x-3=0 has sum of the roots equal to the product of the roots.

A

1 (p.150)

81
Q

Set 9 Problem 57: Find the 6th term in the expansion of (a-3b)^8.

A

-13,608a^3b^5 (p.154)

82
Q

Set 9 Problem 75: What time after 1 o’clock PM, when the angle formed by the hour hand and the minute hand of the clock is bisected by the line connecting the center of the 3 o’clock mark?

A

1:23.08 PM (p.157)

83
Q

Set 10 Problem 4: Find the term involving z^4 in the expansion of Equation 10.1.

A

126,720x^4z^4 (p.161)

84
Q

Set 10 Problem 8: A student can answer a certain test in 5 hours. A second student, who takes 3 minutes longer to answer each question, can answer the test in 6 1/2 hours. How many questions are there in the test?

A

30 (p.162)

85
Q

Set 10 Problem 11: There are 6 geometric means between 3 and 384. Find the common ratio.

A

2 (p.163)

86
Q

Set 10 Problem 17: The fourth term of a geometric progression is 189 and the eight terms is 15,309. Find the 6th term.

A

1,701 (p.165)

87
Q

Set 10 Problem 22: A set out to walk and covers 1.5 ft in the 1st second, 1.75 ft in the 2nd second, 2.0 ft in the 3rd second and so on. How long would it take A to round a 211.5 ft circular track?

A

36 s (p.165)

88
Q

Set 10 Problem 24: Factor x^4 -24x^2+44 completely.

A

(x^2-24x-4) (x^2-2x-4) (p.166)

89
Q

Set 10 Problem 42: The population of a certain community is 150,000 and in ten years it is estimated to be 183,000. If the population grows at a proportional to the amount present, what was the population 10 years ago?

A

122,945 (p.169)

90
Q

A shirt factory has a production capacity of 8,000 units per month. Material and labor cost is P180 per shirt and fixed monthly operating cost is P675,000. Each shirt can be sold for P450.
Set 10 Problem 51: What is the break-even number of units of shirts?

A

2,500 shirts (p.171)

91
Q

A shirt factory has a production capacity of 8,000 units per month. Material and labor cost is P180 per shirt and fixed monthly operating cost is P675,000. Each shirt can be sold for P450.
Set 10 Problem 52: What is the profit or loss if the factory produced only 3,000 shirts per month?

A

P135,000 (p.171)

92
Q

A shirt factory has a production capacity of 8,000 units per month. Material and labor cost is P180 per shirt and fixed monthly operating cost is P675,000. Each shirt can be sold for P450.
Set 10 Problem 53: What is the profit per month if at present it has able to produce and sell 75% of its full capacity?

A

P945,000 (p.171)

93
Q

When A and Z Company charges P 6,000 for a seminar on construction management techniques, it attracts 100 people. For each P 200 decrease in the fee, an additional 10 people will attend the seminar. The managers are wondering how much to charge for the seminar to maximize their revenue.
Set 10 Problem 61: How many people should attend to maximize revenue?

A

200 (p.172)

94
Q

When A and Z Company charges P 6,000 for a seminar on construction management techniques, it attracts 100 people. For each P 200 decrease in the fee, an additional 10 people will attend the seminar. The managers are wondering how much to charge for the seminar to maximize their revenue.
Set 10 Problem 62: How much is the charge for the seminar to maximize revenue?

A

P4,000 (p.172)

95
Q

When A and Z Company charges P 6,000 for a seminar on construction management techniques, it attracts 100 people. For each P 200 decrease in the fee, an additional 10 people will attend the seminar. The managers are wondering how much to charge for the seminar to maximize their revenue.
Set 10 Problem 63: How much is the maximum revenue?

A

P800,000 (p.172)

96
Q

Set 10 Problem 67: One secretary can type a certain large report in 10 hrs. A second secretary can type the same report in 8 hours. How long will it take to type the same report if the two secretaries work together?

A

4.44 hrs (p.173)

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