Algebra “THE ESTABLISHED LEADER IN EE REVIEW” LEGIT MULTIVECTOR Review and Training Center Ground Floor, Cuevasville Tower F. Cayco corner Earnshaw St. Sampaloc, Manila Tel. No. (02) 8731-7423 LEGIT MULTIVECTOR REVIEW AND TRAINING CENTER ALGEBRA LAWS OF EXPONENTS : ( () ) √ ( ( ) ) LAWS OF RADICALS : √ √ √ √ √ √ √ √ √ (√) QUADRATIC EQUATION : Quadratic Equation Formula : √ √ √ Nature of the Roots : ( ) ( Sum of the roots : ) Product of the roots : Test of Factoring : ) ) Algebra Page | 1 LEGIT MULTIVECTOR REVIEW AND TRAINING CENTER ALGEBRA REMAINDER THEOREM : - () () FACTOR THEOREM : () - ( ) BINOMIAL THEOREM : Pascal’s Triangle Binomial Expansion ( ) ( ) ( ) ( ) ( ) 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 BINOMIAL THEOREM FORMULA : ( ( ) ) ( ( )( ) ( )() ( ) ) rth term of (a + b)n : ( ) ( )( ( ) ) Alternate Formula : Note: ( ) Middle term of (a + b)n : Sum of Exponents : ( ) Sum of Coefficients : Note: for n is negative or a fraction, e.g., (a + b)−2, (a + b)1/3, … Algebra Page | 2 LEGIT MULTIVECTOR REVIEW AND TRAINING CENTER ALGEBRA RATIO : PROPORTION : . VARIATION : Direct Variation Attention : a. Inverse Variation b. Joint Variation ARITHMETIC PROGRESSION (A.P.) - Formulas : ( ( ( ( ) ) ) ) [ ( ( )] ) Algebra Page | 3 LEGIT MULTIVECTOR REVIEW AND TRAINING CENTER ALGEBRA GEOMETRIC PROGRESSION (G.P.) - Formulas : ( [ √ ] ( ) ( ) ) √ HARMONIC PROGRESSION (H.P.) - Formulas : Algebra Page | 4 LEGIT MULTIVECTOR REVIEW AND TRAINING CENTER ALGEBRA REE – Apr. 2012 / Sept. 2016 1. If f(x) = 10^x + 1, then f(x + 1) – f(x) is equal to A. 10(10^x) B. 9(10^x) C. 1 D. 9(10^x + 1) 2. Which of the following pairs of numbers are prime twins? A. (7, 9) B. (17, 19) C. (2, 4) D. (1, 3) REE – Apr. 2003 / Apr. 2004 3. 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 REE – Apr. 2003 4. 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) C. –(sq.rt. of 70)i D. sq.rt. of 70 REE – Feb. 2014 / Sept. 2015 / Apr. 2019 / Aug. 2019 5. A group consists of n engineers and n nurses. If two of the engineers are replaced by two other nurses, then 51% of the group members will be nurses. Find the value of n. A. 100 B. 110 C. 80 D. 55 2 6. Determine the value of k so that the sum of the roots of 3kx exceeds the product of the roots by 3. A. –2 and 1/3 B. 2 and –1/3 C. 2 and 3 + 3k2 – 4kx = 5 – 3x D. 2 and –3 REE – Mar. 1998 7. If the polynomial x3 + 4x2 – 3x + 8 is divided by x – 5, determine the remainder. A. 218 B. 45 C. 42 D. 210 3 2 8. Find the value of k so that x + 2 is a factor of 3x – kx + 2x – 4. A. 8 B. –2 C. –8 D. 2 REE – May 2010 / Apr. 2019 / Aug. 2019 9. How many possible positive real roots are there in x^4 – 4x^3 + 7x2 – 6x – 18 = 0? A. 1 or 2 B. 3 or 1 C. 3 or 0 D. 1 or 0 10. Find the 13th term of (x + 2 / y A. 1,863,680x3y-6 B. x3y6 )15 C. 1,000x2y6 D. 2,000x2y5 11. Find the 9th term in the expansion of (x2 + x–1)–2 A. 9x28 B. 9x–28 C. x28 D. –9x–28 REE – May 2010 12. 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. 13. 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 REE – Apr. 2013 14. Marsha is 10 years older than John, who is 16 years old. How old is Marsha? A. 24 yrs. B. 26 yrs. C. 6 yrs. D. 12 yrs. Algebra Page | 5 LEGIT MULTIVECTOR REVIEW AND TRAINING CENTER ALGEBRA 15. 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 REE – May 2010 / Sept. 2017 16. 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 REE – Apr. 2011 17. A four-pound mixture of raisins and nuts is 2/3 raisins. How many pounds of nuts are there? A. 1.3 pounds B. 1.6 pounds C. 2.4 pounds D. 2.6 pounds REE – Apr. 2011 18. A bus leaves Manila at 12 NN for Baguio 250 km away, traveling an average of 55 kph. At the same time, another bus leaves Baguio for Manila traveling 65 kph. At what time will they meet? A. 3:25 PM B. 4:25 PM C. 2:05 PM D. 3:05 PM REE– May 2009 19. Kevin flies (in his private jet) from Los Angeles (LA) to San Francisco (SF), 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 REE– Sept. 2009 20. Kevin flies (in his private jet) from Los Angeles (LA) to San Francisco (SF), 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 REE – Sept. 2011 21. A boat can travel 10 miles downstream and at the same time can travel 6 miles upstream. If the current of water is 3 mph, find the speed of a boat in still water. A. 8 mph B. 9 mph C. 7 mph D. 12 mph REE – Oct. 2000 22. What time after one o’clock will the hands of the clock coincide for the first time? A. 1:7-5/11min B. 1:5-5/11min C. 1:6-5/11min D. 1:4-5/11min 23. 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 REE – April 2017 / Apr. 2019 / Aug. 2019 24. A and B can do a piece of work in 3 days, B and C in 4 days, while A and C in 2.5 days. In how many days can all of them do the work together? A. 3.17 B. 1.02 C. 3.83 D. 2.03 Algebra Page | 6 LEGIT MULTIVECTOR REVIEW AND TRAINING CENTER ALGEBRA REE – Sept. 2003 / Apr. 2004 / Sept. 2004 25. 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 REE – Sept. 2002 26. A contractor has 50 men of the same capacity at work on a job in 30 days, the working day being 8 hours, but the contract expires in 20 days, how many workers should he add? A. 15 B. 20 C. 25 D. 30 27. 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 REE – Sept. 2007 28. 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 REE – Apr. 2000 29. There are 8 fruits in all in a basket which contains mangoes, papayas and watermelons. The cost of each kind of fruits are Php 12.00, Php 25.00 and Php 50.00, respectively. Find the total cost of the mangoes if all the fruits has a total cost of Php 198.00 A. Php 24.00 B. Php 48.00 C. Php 96.00 D. Php 60.00 REE – Sept. 2015 / Apr. 2018 30. An equation of the form is A. an inequality B. an equality C. a proportion D. a ratio 31. Find the fourth proportional to 7, 9 and 28. A. 36 B. 35 C. 22 D. 32 32. Find the third proportional to 4 and 16. A. 4 B. 16 C. 32 D. 64 33. Find the mean proportional of 9 and 36. A. 36 B. 20 C. 5 D. 18 REE – Apr. 2013 34. A student already finished 70% of his homework in 42 minutes. How many minutes does he still have to work? A. 18 B. 16 C. 20 D. 24 REE – Sept. 2011 / Sept. 2018 35. Find the sum of all odd integers between 100 and 1000. A. 247500 B. 374200 C. 148500 D. 454500 Algebra Page | 7 LEGIT MULTIVECTOR REVIEW AND TRAINING CENTER ALGEBRA REE – Apr. 2012 / Apr. 2019 36. In a pile of logs, each layer contains one more log than the layer above and the top contains just one log if there are 105 logs in the pile, how many layers are there? A. 11 B. 12 C. 13 D. 14 REE – Apr. 1999 37. 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 38. 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 REE – Feb. 2014 / Apr. 2017 / Sept. 2017 / Sept. 2018 39. What is the next term in the geometric sequence 16, −4, 1, −1/4, …? A. 1/16 B. 1/8 C. −1/8 D. 0 REE – Apr. 2001 40. Evaluate 1 – 2/3 + 4/9 – 8/27 + 16/81 – 32/243 + …. A. 1.333 B. divergent C. 0.666 D. 0.6 REE – Sept. 2017 / Apr. 2019 41. Find the sum of a geometric progression if there are 4 geometric means between 3 and 729. A. 1092 B. 1222 C. 582 D. 980 REE – Sept. 2011 / Apr. 2015 42. A ball is dropped from a height of 18 m. On each rebound it rises 2/3 of the height from which it last fell. What distance has it traveled at the instant it strikes the ground for the 5th time? A. 37.89 m B. 73.89 m C. 75.78 m D. 57.78 m REE – Apr. 2016 43. A ball is dropped from a height of 18 m. On each rebound it rises 2/3 of the height from which it last fell. What is the total distance it travels in coming to rest? A. 80 m B. 90 m C. 72 m D. 86 m 44. Find the 10th term of the given H.P. 6/5, 4/3, 3/2,…. A. 12 B. –12 C. 1/12 D. –1/12 REE – April 2017 / Apr. 2019 45. The geometric mean and the arithmetic mean of two numbers are 8 and 10 respectively. What is the harmonic mean? A. 7.5 B. 5.7 C. 6.4 D. 4.6 Algebra Page | 8
