Algebra 2
1. Which of the following is a prime number?
A. 91
B. 119
C. 97
D. 133
2. Which of the following pairs of numbers are prime twins?
A. 7, 9
B. 17, 19
C. 2, 4
D. 1, 3
3. If x + y = 1 and x^2 + y^2 = 2, find x^4 + y^4
A. 4
B. -1/2
C. 7/2
D. ½
4. Determine the positive values of the unknown in the following simultaneous equations and give
their product.
x(x + y) = 700
y(x + y) = 525
A. 350
B. 200
C. 250
D. 300
5. What are the values of n if (2n – 6) is greater than 1 but less than 14?
A. 4, 5, 6, 7, 8, 9, 10
B. 4, 5, 6, 7, 8, 9
C. 3, 4, 5, 6, 7, 8
D. 2, 3, 4, 5, 6, 7
6. Simplify i(raised to 29) + i(raised to 21) + i.
A. I
B. -2i
C. 3i
D. 2i
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7. What is the value of (sq. rt of -10) x (sq. rt of -7)?
A. (sq. rt of 70)i
B. –(sq. rt of 70)i
C. –(sq. rt of 70)i
D. sq. rt of 70
8. Express sq. rt of -9 as the product of a real number and i.
A. 81i
B. -9i
C. 9i
D. 3i
9. Determine the value of k so that the sum of the roots of 3kx 2 + 3k2 – 4kx = 5 – 3x exceeds the
product of the roots by 3.
A. -2 and 1/3
B. 2 and -1/3
C. 2 and 3
D. 2 and -3
10. If the polynomial x3 + 4x2 – 3x + 8 is divided by x – 5, determine the remainder.
A. 218
B. 45
C. 42
D. 210
11. Find the value of k so that x + 2 is a factor of 3x3 – kx2 + 2x – 4.
A. 8
B. -2
C. -8
D. 2
12. Find the tenth term of the given H.P. 6/5, 4/3, 3/2,….
A. 12
B. -12
C. 1/12
D. -1/12
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13. Find the 13th term of (x + 2 / sq. rt of y)15
A. 1,863,680x3y-6
B. x3y6
C. 1,000x2y6
D. 2,000x2y5
14. Find the 9th term in the expansion of (x2 + x-1)-2
A. 9x28
B. 9x-28
C. x28
D. -9x-28
15. The term free of x in the expansion of (x3 + 3x-2)15
A. 990
B. 190
C. 385
D. 98,513,415
16. Find the term involving x squared in the expansion of (x^3 + k/x)^10
A. 210 k sq. x sq
B. 32 k sq. x sq.
C. 92 k sq. x sq.
D. 120 k^7 x sq.
17. Alex is 8 years older than Cynthia. Twenty years ago Alex was three times as old as Cynthia.
How old is Cynthia now?
A. 18
B. 20
C. 30
D. 24
18. Maria is 36 yrs. Old. Maria was twice as old as Anna was when Anna is as old as Maria was.
How old is Anna now?
A. 12 yrs
B. 24 yrs
C. 18 yrs
D. 36 yrs
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19. Melissa is 4 times as old as Jim. Pat is 5 years older than Melissa. If Jim is y, how old is Pat?
A. 4y + 5
B. y + 5
C. 5y + 4
D. 4 + 5y
20. In a certain family, the sum of the parent’s ages is twice the sum of their children’s ages now.
Five years ago, the sum of the parents’ ages was four times the sum of the children’s ages during
that time. In fifteen years, the sum of the parents’ age will be equal to the sum of their
children’s ages. How many children are there in the family?
A. 8
B. 7
C. 5
D. 6
21. The sum of two numbers is 41. The larger number is 1 less than twice the smaller number. Find
the larger number.
A. 26
B. 30
C. 27
D. 28
22. The difference of the squares of the digits of a two digit positive number is 27. If the digits are
reversed in order and the resulting number subtracted from the original number, the difference
is also 27. Find the original number.
A. 96
B. 85
C. 74
D. 63
23. How many liters of water must be added to 1 liter of 35% boric acid solution in order to produce
20% boric acid solution?
A. 0.75 liter
B. 0.5 liter
C. 1.5 liters
D. 1.0 liter
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24. 4 lbs of nuts and raisins is 2/3 nuts. How much in lbs are raisins?
A. 2.6
B. 1.3
C. 3.9
D. 0.65
25. The gasoline tank of a car contains 50 liters of gasoline and alcohol, the mixture containing 25%
alcohol. How much of the mixture must be drawn off and replaced by pure alcohol so that the
tank will contain a mixture of which 50% is alcohol?
A. 16 2/3 liters
B. 15 2/3 liters
C. 18 1/3 liters
D. 22 3/4 liters
26. Two planes leave New York at 10 A.M. one heading for Europe at 600 kph and one heading on
the opposite direction at 150 kph. At what time will they be 900 kms apart?
A. 11 : 30 A.M.
B. 12 : 15 A.M.
C. 12 : 00 P.M.
D. 11 : 12 A.M.
27. Mr. Manuel makes a business trip from his house to Laguna in 2 hours. One hour later he
returns home in traffic at a rate 20 kph less than his rate going. If Mr. Manuel is gone in a total
of 6 hours, how fast in kph did he travel going to Laguna?
A. 64 kph
B. 65 kph
C. 55 kph
D. 60 kph
28. Kevin flies from Los Angeles to San Francisco, a distance of 450 miles, in 3 hours. He flies back in
2-7/19 hours. If the wind is blowing from the north at a steady rate during both flights, find the
airspeed of the plane in mph.
A. 170
B. 120
C. 150
D. 160
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29. Kevin flies from Los Angeles to San Francisco, a distance of 450 miles, in 3 hours. He flies back in
2-7/19 hours. If the wind is blowing from the north at a steady rate during both flights, find the
velocity of the wind.
A. 24 mph
B. 18 mph
C. 25 mph
D. 20 mph
30. In his motorboat, a man can go downstream in 1 hour less time than hen can go upstream the
same distance. If the current is 5 mph, how fast can he travel downstream if it takes him 2
hours to travel upstream the given distance?
A. 18
B. 20
C. 23
D. 25
31. What time after one o’clock will the hands of the clock coincide fir the first time?
A. 1:7-5/11 min
B. 1:5-5/11 min
C. 1:6-5/11 min
D. 1:4-5/11 min
32. What is the time between 3 and 4 o’clock where the hands of the clock form an angle of 96
degrees?
A. 3:32
B. 3:31 9/11
C. 3:33 9/11
D. 3:30
33. Ian remodel a kitchen in 20 hours and Jack in 15 hours. If they work together, how many hours
to remodel the kitchen?
A. 8.6
B. 7.5
C. 5.6
D. 12
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34. John and Charles are linemen. John can string 10 miles of line in 3 days, while together they can
string it in 1 day. How long would it take Charles alone to string the same line?
A. 1-2/3 days
B. 1-1/2 days
C. 1-3/4 days
D. 1-1/4 days
35. Binoy, Boboy, and Bata are hired to paint signs. In 8 hours Binoy can paint 1 sign. Boboy can
paint 2 signs, and Bata can paint 1 1/3 signs. They all come to work the first day, but Bata
doesn’t like the job and quits after 3 hours. Boboy works half an hour longer than Bata and
quits. How long will it take Binoy to finish the two signs they were supposed to paint?
A. 2 hrs
B. 1-1/2 hrs
C. 2-1/3 hrs
D. 3 hrs
36. A contractor has 50 men of the same capacity at work on a job in 30 days, the working day being
8 hrs, but the contract expires in 20 days, how many workers should he add?
A. 15
B. 20
C. 25
D. 30
37. A swimming pool can be filled by an inlet pipe in 10 hours and emptied by an outlet pipe in 12
hours. One day the pool is empty and the owner opens the inlet pipe to fill the pool. But he
forgets to close the outlet. With both pipes open, how long will it take to fill the pool?
A. 27
B. 5-5/11
C. 60
D. 80
38. Tom inherited two different stocks whose yearly income was 2100 Php. The total appraised
value of the stocks was 40,000 Php; one was paying 4% and one 6% per year. What was the
value of the stock paying 6%?
A. 27,000
B. 23,000
C. 25,000
D. 24,000
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39. A men’s store bought 500 shirts, some at 125 Php each, the rest at 200 Php each. If the total
cost of the shirts was 77,500 Php, how many shirts were purchased at 125 Php each?
A. 350
B. 400
C. 250
D. 300
40. A collection of coins has a value of 64 cents. There are two more nickels than dimes and three
times as many pennies as dimes. How many dimes are there?
A. 6
B. 4
C. 3
D. 5
41. There are 8 fruits in all in a basket which contains mangoes, papayas and watermelons. The
costs of each kind of fruits are 12.00 Php, 25.00 Php and 50.00 Php, respectively. Find the total
cost of the mangoes if all the fruits has a total cost of 198.00 Php.
A. 24.00 Php
B. 48.00 Php
C. 96.00 Php
D. 60.00 Php
42. Find the fourth proportional to 7, 9, and 28.
A. 36
B. 35
C. 22
D. 32
43. Find the third proportional to 4 and 16.
A. 4
B. 16
C. 32
D. 64
44. Find the mean proportional of 9 and 36.
A. 36
B. 20
C. 5
D. 18
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45. Find the nth term of 6,2,-2,…..
A. -4n + 6
B. -2n + 6
C. 2n + 8
D. -4n + 10
46. Find the sum of all integers between 300 and 800 that are exactly divisible by 14.
A. 11,908
B. 19,908
C. 21,200
D. 18,205
47. An arithmetic progression starts with 1, has 9 terms, and the middle term is 21. Determine the
sum of the first 9 terms.
A. 235
B. 148
C. 112
D. 189
48. The arithmetic mean of 80 numbers is 55. If 2 numbers, namely 150 and 350 are removed, what
is the arithmetic mean of the remaining numbers?
A. 50
B. 51
C. 52
D. 53
49. Evaluate 1 – 2/3 + 4/9 – 8/27 + 16/81 – 32/243 + …..
A. 1.333
B. Divergent
C. 0.666
D. 0.6
50. Three geometric means are to be inserted between 6 and 14,406. Determine their product.
A. 74,088
B. 1,452,729,852
C. 10,374,481
D. 25,412,184
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