1. Which of the following is a prime number? C. 2 and 3 A. 18 D.

10 liters
A. 91 D. 2 and -3 B. 20 24. 4 Ibs of nuts and raisins is 2/3 nuts. How much
B. 119 10. If the polynomial x^3 + 4x^2 - 3x + 8 is divided C. 30 in lbs is raisins?
C. 97 by x - 5. Determine the remainder D. 24 A. 2.6
D. 133 A. 218 18. Maria is 36 years old. Maria was twice as old B. 1.3
2. Which of the following pairs of numbers are B. 45 as Anna was when Anna is as old as Maria was. C. 3.9
prime twins? C. 42 How old is Anna now? D. 0.66
A. (7, 9) D. 210 A. 12 yrs 25. The gasoline tank of a car contains 50 liters of
B. (17, 19) 11. Find the value of k so that x + 2 is a factor of B. 24 yrs gasoline and alcohol. the mixture containing
C. (2, 4) 3x^3 – kx^2 + 2x – 4 C. 18 yrs 25% alcohol. How much of the mixture must
D. (1, 3) A. 8 D. 36 yrs be drawn off and replaced by pure alcohol so
3. If x + y = 1 and x^2 + y^2 = 2, find x^4 + y^4 B. -2 19. Melissa is 4 times as old as Jim. Pat is 5 years that the tank will contain a mixture of which
A. 4 C. -8 older than Melissa. If Jim is y. how old is Pat? 50% is alcohol?
B. ‘-1/2 D. 2 A. 4y + 5 A. 16 2/3 liters
C. ‘7/2 12. Expand (2x - y)^6 and simplify B. y + 5 B. 15 2/3 liters
D. ‘1/2 A. 64x^6 + 192x^5y + 240x^4y^2 + C. 5y + 4 C. 18 1/3 liters
4. Determine the positive values of the unknown 160x^3y^3 + 60x^2y^4 + 12xy^5 + D. 4 + 5y D. 22 3/4 liters
in the following simultaneous equations and y^6 20. In a certain family, the sum of the parents ages 26. Two planes leave New York at 10 AM. one
give their product. x(x + y) = 700, y(x + y) = 525 B. 64x^6 + 192x^5y - 240x^4y^2 + is twice the sum of their children's ages now. heading for Europe at 600 kph and one
A. 350 160x^3y^3 + 60x^2y^4 + 12xy^5 + Five years ago, the sum of the parents age was heading on the opposite direction at 150 kph.
B. 200 y^6 four times the sum of the children's ages At what time will they be 900 kms apart?
C. 250 C. 64x^6 - 192x^5y + 240x^4y^2 - during that time. In fifteen years, the sum of A. 11:30 A.M.
D. 300 160x^3y^3 + 60x^2y^4 - 12xy^5 + the parents age will be equal to the sum of B. 12: 15 P.M.
5. What are the values of n if (2n - 6) is greater y^6 their children's ages. How many children are C. 12 00 P.M
than 1 but less than 14? D. none of these there in the family? D. 11: 12 A.M
A. 4, 5, 6, 7, 8, 9, 10 13. Find the 13 term of (x + 2 / √y)^15 A. 8 27. Mr. Manuel makes a business trip from his
B. 4, 5, 6, 7, 8, 9 A. 1,863,680x^3y^-6 B. 7 house to Laguna in 2 hours. One hour later he
C. 3, 4, 5, 6, 7, 8 B. x^3y^6 C. 5 returns home in traffic at a rate 20 kph less
D. 2, 3, 4, 5, 6, 7 C. 1.000x^2y^6 D. 6 than his rate going. If Mr. Manuel is gone in a
6. Simplify i( raised to 29) + i( raised to 21) + i D. 2000x^2y^5 21. The sum of two numbers is 41. The larger total of 6 hours, how fast in kph did he travel
A. i 14. Find the 9th term in the expansion of (x^2 + number is 1 less than twice the smaller going to Laguna?
B. -2i x^-1)^-2 number Find the larger number. A. 64 kph
C. 3i A. 9x^28 A. 26 B. 65 kph
D. 2 B. 9x^-28 B. 30 C. 55 kph
7. What is the value of (sq.rt. of -10) x (sq rt of- C. x^28 C. 27 D. 60 kph
7)? D. -9x^-28 D. 28 28. Kevin flies (in his private jet) from Los Angeles
A. (sq.rt. of 70)i 15. The term free of x in the expansion of (x^3 + 22. The difference of the squares of the digits of a (LA) to San Francisco (SF). a distance of 450
B. -(sqrt. of 70) 3x^-2)^15 two digit positive number is 27. If the digits are miles, in 3 hours. He flies back in 2-7/19 hours.
C. -(sq.rt. of 70)i A. 990 reversed in order and the resulting number is If the wind is blowing from the north at a
D. sq.rt. of 70 B. 190 subtracted from the original number, the steady rate during both flights, find the
8. Express sq.rt. of- 9 as the product of a real C. 385 difference is also 27. Find the original number. airspeed of the plane in mph.
number and i D. 98,513,415 A. 96 A. 170
A. 81i 16. Find the tem involving x squared in the B. 85 B. 120
B. -9i expansion of (x^3 + k/x)^10 C. 74 C. 150
C. 9i A. 210 k sq. x sq. D. 63 D. 160
D. 3i B. 32 k sq x sq 23. How many liters of water must be added to 1 29. Kevin flies (in his private jet) from Los Angeles
9. Determine the value of k so that the sum of C. 92 k sq x sq liter of 35% boric acid solution in order to (LA) to San Francisco (SF). a distance of 450
the roots of 3kx^2 + 3k^2 - 4kx = 5 - 3x exceeds D. 120 k^7 x sq produce 20% boric acid solution? miles, in 3 hours. He flies back in 2-7/19 hours
the product of the roots by 3. 17. Alex is 8 years older than Cynthia. Twenty A. 0.75 liter If the wind is blowing from the north at a
A. -2 and 1/3 years ago, Alex was three times as old as B. 0.5 liter steady rate during both flights, find the
B. 2 and -1/3 Cynthia. How old is Cynthia now? C. 1.5 liters velocity of the wind.
 A. 24 mph C. 2-1/3 hrs A. Php 24.00 50. Three geometric means are to be inserted
B. 18 mph D. 3 hrs B. Php 48.00 between 6 and 14,405. Determine their
C. 25 mph 36. A contractor has 50 men of the same capacity C. Php 96.00 product.
D. 20 mph at work on a job in 30 days, the working day D. Php 60.00 A. 74,088
30. In his motorboat, a man can go downstream in being 8 hours, but the contract expires in 20 42. Find the fourth proportional to 7, 9 and 28. B. 1,452,729,852
1 hour less time than he can go upstream the days, how many workers should he add? A. 36 C. 10,374,481
same distance. If the current is 5 mph, how A. 15 B. 35 D. 25,412,184
fast can he travel downstream if it takes him 2 B. 20 C. 22 51. The first term of a geometric series is 256 and
hours to travel upstream the given distance? C. 25 D. 32 the last term is 81. Its sum is 781, what is the
A. 18 D. 30 43. Find the third proportional to 4 and 16. geometric ratio?
B. 20 37. A swimming pool can be filled by an inlet pipe A. 4 A. ‘2/3
C. 23 in 10 hours and emptied by an outlet pipe in B. 16 B. ‘3/4
D. 25 12 hours. One day the pool is empty and the C. 32 C. ‘3/5
31. What time after one o'clock will the hands of owner opens the inlet pipe to fill the pool but D. 64 D. ‘5/6
the clock coincide for the first time? he forgets to close the outlet. With both pipes 44. Find the mean proportional of 9 and 36 52. Find the 12th term of the harmonic
A. 1:7-5/11min open, how long will it take to fill the pool? A. 36 progression 1, 1/3, 1/5,...
B. 1:5-5/11min A. 27 B. 20 A. ‘1/9
C. 1:6-5/11min B. 5-5/11 C. 5 B. ‘1/23
D. 1:4-5/11min C. 60 D. 18 C. ‘1/17
32. What is the time between 3 and 4 o'clock D. 80 45. Find the nth tem of 6, 2, -2, D. ‘1/21
where the hands of the clock form an angle of 38. Tom inherited two different stocks whose A. -4n + 6 53. Find the 10th term of the given H.P. 6/5, 4/3,
96 degrees? yearly income was Php 2100. The total B. -2n + 6 3/2,....
A. 3:32 appraised value of the stocks was Php 40,000, C. 2n + 8 A. 12
B. 3:31 9/11 one was paying 4% and one 6% per year, what D. -4n + 10 B. -12
C. 3:33 9/11 was the value of the stock paying 6%? 46. Find the sum of all integers between 300 and C. ‘1/12
D. 3:30 A. 27,0000 800 that are exactly divisible by 14 D. ‘-1/12
33. lan remodel a kitchen in 20 hours and Jack in B. 23,000 A. 11,908
15 hours. If they work together, how many C. 25,000 B. 19,908
hours to remodel the kitchen? D. 24,000 C. 21,200
A. 8.6 39. A men's store bought 500 shirts, some at Php D. 18,205
B. 7.5 125 each, the rest at Php 200 each 1f the total 47. An arithmetic progression starts with 1, has 9
C. 5.6 cost of the shirts was Php 77,500, how many terms, and the middle term is 21. Determine
D. 12 shirts were purchased at Php 125 each? the sum of the first 9 terms.
34. John and Charles are linemen. John can string A. 350 A. 235
10 miles of line in 3 days, while together they B. 400 B. 148
can string it in 1 day. How long would it take C. 250 C. 112
Charles alone to string the same line D. 300 D. 189
A. 1-2/3 days 40. A collection of coins has a value of 64 cents. 48. The arithmetic mean of 80 numbers is 55. If 2
B. 1-1/2 days There are two more nickels than dimes and numbers, namely 150 and 350 are removed,
C. 1-3/4 days three times as many pennies as dimes. How what is the arithmetic mean of the remaining
D. 1-1/4 days many dimes are there? numbers?
35. Binoy, Boboy, and Bata are hired to paint signs A. 6 A. 50
in 8 hours Binoy can paint 1 sign, Boboy can B. 4 B. 51
paint 2 signs, and Bata can paint 1 1/3 signs. C. 3 C. 52
They all come to work the first day, but Bata D. 5 D. 53
doesn't like the job and quits after 3 hours. 41. There are 8 fruits in all in a basket which 49. Evaluate 1 -2/3 + 4/9 - 8/27 + 16/81 - 32/243 +
Boboy works half an hour longer than Bata and contains mangoes, papayas and watermelons. ...
quits. How long will it take Binoy to finish the The cost of each kind of fruits are Php 12.00, A. 1.333
two signs they were supposed to paint? Php 25 00 and Php 50.00, respectively Find the B. divergent
A. 2 hrs total cost of the mangoes if all the fruits has a C. 0.666
B. 1-1/2 hrs total cost of Php 198.00 D. 0.6