Algebra Flashcards
If y varies directly with x and y = 4 when x = 5, what is the value of y when x = 8?
a) 43/3
b) 32/5
c) 54/7
d) 5/8
b) 32/5
A military camp has 300 men. The required meal budget for six months of training is 1 million pesos. At the end of training period, 128 men were laid off and the remaining is to undergo the next stage of training for 2 months. What is the required budget at this point?
a) 201,000.11 pesos
b) 190,111.11 pesos
c) 180,000.11 pesos
d) 191,111.11 pesos
d) 191,111.11 pesos
Find a number such that three-eights of the number minus one-half of it is 14 less than three-fourths of the number.
a) 16
b) 17
c) 18
d) 19
a) 16
Find three consecutive integers such that the sum of the first plus one-third of the second plus three-eights of the third is 25.
a) 12, 13, and 14
b) 13, 14, and 15
c) 14, 15, and 16
d) 15, 16, and 17
c) 14, 15, and 16
The sum of the digits of a three-digit number is 14. The hundreds digit being 4 times the units digit. If 594 is subtracted from the number, the order of the digits will be reversed. What is the number?
842
Dominic’s present age is 10 years more than Michele’s present age. In 5 years, Michele’s age will be three-fifths of Dominic’s age. What are their present ages?
a) Dominic is 15 yrs. old; Michele is 5 yrs. old
b) Dominic is 25 yrs. old; Michele is 15 yrs. old
c) Dominic is 35 yrs. old; Michele is 25 yrs. old
d) Dominic is 20 yrs. old; Michele is 10 yrs. old
d) Dominic is 20 yrs. old; Michele is 10 yrs. old
A mother is now three times as old as her daughter. In 4 years, the mother will be four times as old as the daughter was, two years ago. How old is the daughter?
a) 12 yrs. old
b) 13 yrs. old
c) 14 yrs. old
d) 15 yrs. old
12 yrs. old
Two trains leave a city at the same time, one traveling east and the other traveling west. At the end of 9.5 hours, they are 1292 miles apart. If the rate of the train traveling east is 8 miles per hour faster than the rate of the other train, find their rates.
a) Traveling east = 82 mph; Traveling west = 54mph
b) Traveling east = 72 mph; Traveling west = 64mph
c) Traveling east = 62 mph; Traveling west = 94mph
d) Traveling east = 72 mph; Traveling west = 54mph
b) Traveling east = 72 mph; Traveling west = 64 mph
On a 130-mile trip from Orlando to Sarasota, Roberto encountered a heavy thunderstorm for the last 40 miles of the trip. During the thunderstorm, he drove an average of 20 miles per hour slower than before the storm. The entire trip took 2.5 hours. How fast did he drive before the storm?
a) 55 mph
b) 60 mph
c) 70 mph
d) 65 mph
b) 60 mph
John Paul always runs his pontoon boat at full throttle, which results in the boat traveling at a constant speed. Going up the river against the current, the boat traveled 72 miles in 4.5 hours. The return trip down the river, with the help of the current, only took three hours. Find the speed of the boat and the speed of the current.
a) Speed of boat = 10 mph; Speed of current = 5 mph
b) Speed of boat = 30 mph; Speed of current = 6 mph
c) Speed of boat = 20 mph; Speed of current = 7 mph
d) Speed of boat = 20 mph; Speed of current = 4 mph
d) Speed of boat = 20 mph; Speed of current = 4 mph
Bryan’s Pest Control stocks a 7% solution of insecticide for lawns and also a 15% solution. How many gallons of each should be mixed to produce 40 gallons that is 12% insecticide?
a) 15 gallons 7% insecticide; 25 gallons 15% insecticide
b) 25 gallons 7% insecticide; 15 gallons 15% insecticide
c) 20 gallons 7% insecticide; 20 gallons 15% insecticide
d) 10 gallons 7% insecticide; 30 gallons 15% insecticide
a) 15 gallons 7% insecticide; 25 gallons 15% insecticide
How many liters of pure alcohol must we add to 20 liters of a 40% solution to obtain a 60% solution?
a) 5 liters
b) 10 liters
c) 20 liters
d) 30 liters
b) 10 liters
If Jim can mow a lawn in 50 minutes, and his son, Todd, can mow the same lawn in 40 minutes, how long will it take them to mow the lawn if they work together?
a) 11.11 minutes
b) 22.22 minutes
c) 33.33 minutes
d) 44.44 minutes
b) 22.22 minutes
It takes Pat 12 hours to detail a boat. After he had been working for 3 hours, he was joined by his brother Mike, and together they finished the detailing in 5 hours. How long would it take Mike to detail the boat by himself?
a) 14 hours
b) 15 hours
c) 16 hours
d) 17 hours
b) 15 hours
The organizer for a church picnic ordered coleslaw, potato salad, and beans amounting to 50 pounds. There was to be three times as much potato salad as coleslaw. The number of pounds of beans was to be 6 less than the number of pounds of potato salad. Find the number of pounds of each.
a) 8 lbs coleslaw; 24 lbs potato salad; 18 lbs beans
b) 9 lbs coleslaw; 23 lbs potato salad; 18 lbs beans
c) 10 lbs coleslaw; 24 lbs potato salad; 16 lbs beans
d) 9 lbs coleslaw; 20 lbs potato salad; 21 lbs beans
a) 8 lbs coleslaw; 24 lbs potato salad; 18 lbs beans
Sari had scores of 94, 84, 86, and 88 on her first four exams of the semester. What score must she obtain on the fifth exam to have an average of 90 or better for the five exams?
a) x ≤ 98
b) x ≥ 98
c) x ≤ 90
d) x ≥ 90
b) x ≥ 98
Suppose that in a certain culture, the equation Q(t) = 15,000e^(0.3t) expresses the number of bacteria present as a function of the time t, where t is expressed in hours. Find the initial number of bacteria.
a) 14,000
b) 15,000
c) 16,000
d) 17,000
b) 15,000
Suppose that in a certain culture, the equation Q(t) = 15,000e^(0.3t) expresses the number of bacteria present as a function of the time t, where t is expressed in hours. Find the number of bacteria after 3 hours.
a) 32,894.05
b) 34,894.05
c) 36,894.05
d) 38,894.05
c) 36 894.05
Suppose that in a certain culture, the equation Q(t) = 15,000e^(0.3t) expresses the number of bacteria present as a function of the time t, where t is expressed in hours. Find the number of hours it will take for the bacteria count to double.
a) 2.31 hours
b) 2.32 hours
c) 2.33 hours
d) 2.34 hours
a) 2.31 hours
Find the first term of the arithmetic sequence if the fourth term is 26 and the ninth term is 61.
a) 5
b) 6
c) 7
d) 8
a) 5
Find the sum of the first 30 terms of the arithmetic sequence 3, 7, 11, 15, …
a) 1,827
b) 1,828
c) 1,829
d) 1,830
d) 1,830
State University had an enrollment of 15,600 students in 1994. Each year, the enrollment increased by 1050 students. What was the enrollment in 2009?
a) 21,350 students
b) 21,530 students
c) 31,530 students
d) 31,350 students
d) 31,350 students
Find the ninth term of the geometric sequence 27, 9, 3, 1, …
a) 1/9
b) 1/27
c) 1/81
d) 1/243
d) 1/243
Find the sum of 1, 3, 9, 27, …, 6561
a) 9841
b) 9481
c) 8941
d) 8491
a) 9841
Find the sum of the infinite geometric sequence 1, 1/2, 1/4, 1/8, …
a) 0.25
b) 0.5
c) 0.75
d) 2
d) 2
Suppose an element has a half-life of 3 hours. If at a particular moment we have 768 grams of the element, how many grams of it will remain 24 hours later?
a) 2 g
b) 1 g
c) 3 g
d) 4 g
c) 3 g
A rubber ball is dropped from a height of 27 m. Each time that it hits the ground, it bounces to a height of 2/3 of that from which it fell. Find the total distance travelled by the ball until it comes to rest.
a) 125 m
b) 130 m
c) 135 m
d) 140 m
c) 135 m
Determine the 5th term of the expansion (2x + 3y)^12.
a) 10,264,320 x5 y6
b) 10,264,320 x7 y8
c) 10,264,320 x2 y3
d) 10,264,320 x3 y4
d) 10,264,320 x3 y4
Determine the middle term of the expansion (3a - b)^8.
a) 5,670 a2 b2
b) 5,670 a4 b4
c) 5,670 a3 b3
d) 5,670 a5 b5
b) 5,670a4b4
What is the coefficient of the term containing x^4 in the expansion of (x - 2y)^10?
a) 10,440
b) 11,440
c) 12,440
d) 13,440
d) 13,440
