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Question: what would be the shortcuts solutions for each item thank...

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What would be the shortcuts /solutions for each item thank, its for a review. I will star answer

D. ECE Board March 1996 For a particular expeninent you need 5 liters of 1 0% solution43 You find 7% answer, 12% solution on the shelf. How much of the 7% solution you mix with solutio to get 5 liters of 10%solubot17- ECE Board November 1999 November 2000 The tme required for two examinees to solve the same Problem differ by two minutes. Together they can solve 32 Problems in one hour. Haw long will it take for the slower Problem solver to salve tha same Problem? A A. 5 minules / B. 2 minutes С 3 minutes D. 4 minutss ECE Board Apr 1998 The denominator of a certain fraction is three more than twice the numerator, I is added to both terms of the fraction, tha resuitirg fraction is 315. Find the original fraction.cs A. E5 В 13 R. 5:13 D. 3/5 ECE Board April 2001 Ana is 5 years oider than Beth. In 5 years the product af their ages will be 1.5 times the product of their present ages. How od is Beth naw? B ECE Boardf April 1998 In tha expansion of (x +4y)2 the numerical cpefficient of the 5th term is 12. ECE Board A Fin A. -3360 C.-950 D.3360 -A. 63330 d the coefficient of the term invowing b in the expansion of В 126720 C. 500880 D. 253440 4 ECE Board Novembor 1998 Find the ralio of an infinile geometric series if the sum is 2 and the frst term is C 13, ECE Board April 2001 The seating section in a Coliseum has 30 seals in the f 32 seats in the second row, 34 seats in the third row, and so on. until the tenth row is reached, aftor wrich thare are ten rows, each containing 50 seats. Find the total number of saats in the ECE Bbard April $999 If 16 is 4 mare than y, find 5x-1. A 900 C 890 D. 1000 4. ECE Board Novernber 2001 A piece of papar is o.05 inches thick, Each tme the paper is folded into haif, the thickness is doubled. If the paper was tolded 12 timas, how thick in feet the folded paper be? o A. 10.24 ECE Board Aprid 1999 Mixe. Lauic and Joy can mow the lawnin 4 6 and 7 hoursg raspectively What fraclion e ihe yard can they maw in 1 hour hf lhey work tcgether?AAS B. 12.34 0 11.25 84 ECE BOard November 2001/A If one third of the air in a tank is removed by each strcke nf an air pump. What fractional part of the total air is removed in 6 strokes? D A. 0.7122 8. 0.6122 C 0.8122 O C9122 54 1 ECE Board November 200 takes an airplane one hour ECE Board November 1999 r and forty-five minutes to travel 500 e same distance in ore The sum ot the digits of a two-digit number is 11 lf the digits are reversed, the resulting numbor is seven more than twice the original number What is tha original number?sC A 44 hour and fifteen minutes wth the wind. What is the aiplane? A. 342.85 mph B, 375.50 mph C. 450.50 mph 0 285.75 mph C. 83 ECE Board November 2002 004/ November 2006 ECE Board November 1999 At exacily what time after 2 olock will the hour hand and the minute hand extend in opposite directions for the first time? A. 2:43 and 0.83 sac 8. 2:43 and 6.30 sec C, 2:43 and 40.5 sec D. 2:43 and 37.8 sec Find the sum of the roots ot 5x2+10x+2-0 e

18. ECE Board November 2002 he sum of the ages of Peter and Paul is 21: Peter will be twice as old as Paul 3 years from now. What is the present age of ECE B0ard April 2005 Solve for x if 82 and 1 Pete? B. 6 C. 14 9. ECE Board Apnil 2003 Smplity the expression; the square root ef the cube rcot.of 64 ECE Board April 2005 How many terms of the progression 3,5,7,should there that their sum will be 2600. 8 A. 60 B, 50 C. 52 D. 55 be so A. 4x B. 8x D. 2x ECE Board Aprii 2005 20. ECE Board April 2003 A company sels 80 units and makes P8O profit. sells 110 units and makes P140 proft. If the profit is a inear function of the number of unis suld; what is the average profit per unit If the comgany sels 250 units? A. P1.76 B P1.68 C. P1.66 D. P1.88 If the 1 term of the geometric progression is 27 and the 4tht term is -1, the third term isA . ECE Board November 2003 Harry ia cne third as old as Ron and 8 years younger thar Hernione. If Harry is 8 years old, what is the sum of their-agesrc ECE Bbard Noverhber 2012 Selve for x 8x-2y+2 and 1 A. 40 D. 50 22 ECE Board Navember 2003 e sum of the three consecutive even integers is 78. What is the largest integer? ECE Board April 2010 Transform the fraction by rationalizing the 4x denominator 24 B. 28 C. 32 ECE Board A Solve for x in the folowing equationas B. A. 4 ECE Board Apri 2006 Sove forxin sha following equation. x3x 5xt7x+ 24 ECE Board April 2004 625 x- 4. and the remaindoris 157.Than the vaue of k is D. 1 34, ECE Board April 2015 25. ECE Board Aprit 2004 Given that w varles directhy as the pcoduct of x and y and inversely as the square ofz and that w when2ye and z3. What is the value of w,whenyes and 27 B. .307 3ab2- C. a3 -3a2b+3a2b+b3 D. a3 -3a2b+3ab-b2 ECE Board November 2007 2, Board A It 16 is four more than3x, then x A. 16 B 21 C. 3 D. 4 Give the factors of a2x28 A. 2a-2x D. 2x -2a ECE Board Aphu 2004/November 2002 36, ECE Board April 1998 our prsitive integers form an arnthmetc progressibn. If the product of the 1Band the last term Is 70 and the 2 and the third lerm is 88, find the 1 term. Arc tan 2cos arcsinis equal to: C. 14

ECE Board November 1991 The captain of a ship views the top of a lighthouse at an angle of 60° with the hornzontal, at an elevation of 6 meters above sea level Five minutes later the same captain of the ship views the top of the same lighthouse at an angle 30 with he horizontal Assume that the ship is moving directly away from the lighthouse determne the speed of the ship. The lighthouse is known to be 50 meters above sea level, Solve the problems by trigonometry.C ECE Board November 1998 B. 22.16 mi min C. 10.16 my min D 12.16 m min Solve the equation cos A 1 COSA 46 ECE Board Apnt 1992 ECE Board November 1998 C&e 520 degrees is equal to ta QA cost-B sin t From the gven equation, derive another equation showing the relationship beween P Q and A and B not invoving any of tha trigonometric funcion of angle C. tan 45 degrees D, sin 20 degrees B. P2+Q2 A+82 CE Board Apni 2000 hree times the sina of a certain angle is bwice of the square of the cosine of the csame angle. Find the angle: A From the top of the building 1C0m high, the angle of depression of a point A due East of it is 30,From a point B due south of the building, the angla of elevation of the top is 60 . Find the Salve angl A of an oblique tiangle ABC, if a 25.b 16 and C A. 52 degrees and 40 minutes D. 54 degrnes and 30 minutes C. 50 degroes and 40 minutes D. 54 degrees and 20 minutes A1003,choths C 100-3 30 A pole caat a snadow of 15 m. How long when the angie of elevation af the sun s 61 degr tho polo has iea degrae from the ventical directy toward the sun? An cbserve found the angle of elavation at the top of the tree to 27. After moving 10m closer (on the same vertical and 64. Find the height or the treo, Solve for x in the equalion: arctan (2x)arctan A From point A at the foot of the mountain, the angic of elevation of the top B is 80. AMe an indlination of 30 to the horizon, and reaching a point C, an abservor finds that tho angle ABC s 135. Th mcuntain intA r ascending the mountaln one (1 mile at e hypoteruse of a right tiangle is 3 m Fnd tha lengths et the two legs if oie leg is 14 m longer,nan he otherAM e haight of the B. 13 cm, 27 cm ir sin A Am auadrant llein B %.Bin cuadrant i.fr Poirts A and B 1000m apurt aro plotted on a straight highw running Eest nd West. From A. the boanng of a tower C is 32 degrees N ofW from B the beanirg of C is 26 degrecs N or E approximato the shortest distance of tower C to the highway B

Problem The Roman Numeral for,2018 is A, MMXVi B. MMXI C. WMMXVIll DMMXVx 56 Problem log of 2 to the base 2 plus log of x to the base 2 is equal to 2, find the value ofx A A. 2 B. 4 52 Problelns In the spherical triangle shown. fol D. 5 57 Problem parts are given: A С 75°00 c 1C010 A Meralco tower and a monument stand on a level plane The angles of deprassion of the top and bottom of the monument viewed from the top of the Meraloo tower at 13 degrees and 35 degrees respectively. The height of the tower is 50 m. Find the height of the monument. A A. 33.541 m B. 64.12 m C. 32.10 D. 36 44 m 8. Problem A:40°18 b-6625 B. x2xyy2 A. 41 14 48, 83 10 48 B. 45 23 43, 6312 45 C. 40 13 35, 66 12 45 D. 22 243, 601245 D. 0 59. Problem Find the angle B of a triangle if a And C 287 degrees. A. 53 0325 8. 49 0325 C. 39 0325 D. 19 0325 132 m., b 224 m. 53 Problem Given the parts of the spherical triangle: A 60 30 b 3615 60. Problem A car travels nerthward from a point B for one hour, then eastward for 30 one hour, then eastward for 30 min then sh ted N 30 E. Afterexactly 2 hours, the car will be 64.7 kmdirectly away from B. What is the speed of the car in -4030 A. 45 B. 40 C. 50 D. 55 A, 45 35 В 44°30 С 47043 D. 45 40 blent If log af 2 to the base 2 plus ogol to he base 2 equal to 2,find the,value ofx A. 2 B. 4 C. 3 D. 5 Problem A. 2X C. 3x

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