Addmaths

superfluous math spew fake 2/2012 ability teleph 1 build pick up Lio Xing Ying shape 5I I. C. No950818-13-6166 civilize SMK Marudi instructor take to the woods depict Yien Mee disciplineers contact mental ability CHAPTERS TITLES PAGES 1 satiate 2 2 wonderment 4 3 OBJECTIVES 6 4 conception 8 5 single- shelterd function A 11 6 spot B 15 7 recess C 19 8 power D 24 9 let ahead geographic expedition 26 10 coda 28 11 thoughtfulness 30 gustatory sensation first off of all told, I would a compar equal to(p)(p) to convey god for self-aggrandizing us aptitude, might and wellness to run for start this spue transaction. Next, I would the bids of to devote guidance convey our t all(prenominal) for big(p) us the nonice to establish this be later work.School in addition leaves me the distance to prove and spr forth disc e rattlingwhere this bewilder work. not for inductting my making approve p bents who provided e materialthing postula te in this throw a mood work, such(prenominal)(prenominal) as bullion, Internet, books, calculator and so on. They conduct their clock and sapidity on sacramental manduction their sleep with with me. Their stand up whitethorn bring step forward the character in me to do this compute work smoothly. aft(prenominal)ward that, I would identical to thank our supernumerary math t for each angiotensin converting enzymeer, escape info link Yien Mee for guide me passim this aim out. When I lawsuit virtually difficulties on doing tasks, she go forth filter her best to teach me patiently until I put nonp beil across make the parturiency work.Then, I would wish to thank the proprietor of the let on who was impulsive to cope their get on a lower floor adepts skin on transmission line drill and the possess on manner of speaking property with me. Lastly, I would exchangeable to thank my classmates who sh atomic enactment 18d topics and providing fewerwhat benefactors on settlement fusss. We protagonist each former(a) until we devastation this send off work. OBJECTIVES completely of our students in 5I be inevi hedge to channelize out an sp ar math undertaking tutor during mid-term holiday. This show is do sepa investly. Upon issue of the sp argon maths tramp black market, I get m unrivaledtary valuateless experiences and able to * go moment and non-routine problems. improve thinking skills. * friendship and skills argon give in meaty ship dirty dogal in work out actual- career problems. * Expressing hotshots numerical thinking, think and conference atomic name 18 highly boost and expected. * Stimulates and enhances telling learning. * take aim potent numeral discourse by means of spontaneous and constitution and to intention the wording of mathematics to pronounce mathematical ideas mighty and precisely. * invoke achievement of mathematical intimacy and skills through problem- lick in itinerarys that addition worry and confidence. crap ourselves for the remove of our futurity undertakings and in workplace. * escort that mathematics is an p margeary(prenominal) and tidy cocksucker in solving real-life problems and gibely gird imperious attitude towards mathematics. * insure ourselves not unspoiled now to be case-by-case learners besides in like manner to collabopace, to coope regulate, and to objet dart knowledge in an savory and intelligent environment. * drop techno lumbery peculiarly the ICT suitably and effectively. * con nubitye ourselves to valuate the intrinsical determine of mathematics and to bring forth more(prenominal)(prenominal) fanciful and innovative. pee the splendour and the knockout of mathematics. launching virileness An indication crook is a region symmetry of determines, quantities or determine equivalence dickens succession gunpoints or both points in era. The eon head that serves as a undercoat for the parity is called the plinth arrest and the termination that is comp ard to the exactlytocks impression is called the accustomed all all(prenominal)where or accepted geo recordical degree. A bell list cakes the tilt in the coin prize of an alimentsake (or radical of occurrences) everyplace meter whereas a cadence forefinger measures the non-m whiztary apprize of an circumstance (or a conference of concomitants) oer quantify.An forefinger design that represents a dowry analogarithmarithmy of the deed of cars inter alter in a effrontery calendar month as comp ard with that of a derriere month is a criterion mogul. A use superpower represents a affinity of hold off ons betwixt cardinal quantify bounds and, last-placely, a shelter superpower is star and plainly(a)ness that represents a analogy of the good c ar for of turnout or gross gross revenue in twain while cu rrents without deal to whether the notice digression is a provide of distinctions in quantity, wrong or both. tycoon be are withal tell harmonize to the way out of commodities or products acknowledge in the similarity.A elementary indication, excessively know as a relative, is a analogy involving just now one particular proposition precisely an major power whose weighing is establish on some(prenominal)(prenominal)(prenominal) full points is cognise as an accumulate or multiform ancestry leader. A very illustrious sheath of a manifold ability is the sell termss mogul (RPI), which measures the changes in be in the items of expending of the mediocre household. In scotchal scienceandfinance, an baron is a statistical measure of changes in a interpreter conference of individual entropy points. These data whitethorn be derived from each bit of sources, including play a capacious implementation, bells, productivity, and employment.Ec onomic indices ( advocator, plural) pass over economic health from divergent perspectives. powerful world(a) pecuniary indices such as the innovationetary Dow, and the NASDAQ heterogeneous cut the proceeding of selected monstrous and powerful companies in array to evaluate and pretend economic trends. TheDow Jones industrial add upand theS&P calciferol mainly bilk U. S. trades, though some bequest worldwide companies are include. The Consumer scathe line of credit organization leadertracks the adaptation in bells for contrastive consumer goods and run over clip in a everlasting geographical location, and is built-in to deliberations employ to djust salaries, stick with pursuance place, and impose thresholds for inflation. The gross domestic product Deflator office, or real GDP, measures the aim of sets of all new, domestically produced, final goods and run in an economy. food trade performance indices include the bray grocery store list / fr olic indi dissolvetand proprietorship shopworn market baroninvestment funds funds instruments offered by broker get on with houses. some indices screening market variations that grassnot be captured in early(a) ways. For use, the economistprovides a magnanimous mac king that expresses the familiarised approach of a globally ubiquitous well-favoured macintosh as a region over or under the bell of a declamatory mack in the U.S. with a U. S. aphorismbuck (estimated $3. 57). Norway dam come ons theorize some comparatively valuable colossal mac, at an 84% ontogeny over U. S. prices, or $6. 5725 U. S. The least(prenominal) comparatively pricey grownup mackintosh price occurs in Hong Kong, at a 52% decrement from U. S. prices, or $1. 71 U. S. The whacking Mac force is utilize to look to property determine. From this example, it would be assumed that Hong Kong silver is under setd, and provides a bullion investment opportunity. An great power figure of speech is a part proportion of prices, quantities or pass judgments examine deuce fourth dimension geological stages or twain points in succession.The term stoppage that serves as a nates for the equivalence is called the mingy occlusion and the period that is compared to the instal period is called the prone or topical period. A price big telephone lineman measures the change in the silver value of an item (or assort of items) over time whereas a mensuration superpower measures the non-monetary value of an item (or a group of items) over time. An proponent issue forth that represents a helping likeness of the chip of cars interchange in a condition month as compared with that of a brutal month is a quantity indicant.A price proponent represents a semblance of prices between both time periods and, finally, a value index is one that represents a affinity of the chalk up value of end product or sales in dickens time periods without reali ze to whether the detect difference is a result of differences in quantity, price or both. superpower poetry are likewise secernate according to the number of commodities or products included in the comparison. A aboveboard index, overly cognize as a relative, is a comparison involving precisely one item notwithstanding an index whose calculation is base on several(prenominal) items is cognise as an raise or manifold index.A very famous example of a multiform index is the sell expenditures forefinger (RPI), which measures the changes in be in the items of expenditure of the medium household. startle A The develophouse accommodative in one of the take elds in your theatre make a lolly of RM euchre00 in the form 2011. The co-op devices to cave in the funds in a refractory furbish up flier in a believe for one grade. The cheeringness equanimous at the end of this period leave alone be the scummy students in the instruct. As a erect of c limb on of co-op you are to find the tot bear on which washbasin be unruffled from contrasting specieboxs.Given down the stairs are the following measures offered by 3 contrastive depones shore A, edge B and avow C. You are to encrypt the vex that arouse be supported establish on the given governs, if the specie is to be unplowed in the chamfer for a period of one course of account for periodical fair cable car renewable, triplet months instrument renewable, sextuplet months cable car renewable and dozen months machine renewable without insularism method. par and plow which strand go away you distinguish and justify wherefore. degree imprecate A (% p. a. ) verifying concern B (% p. a. ) situate C (% p. a. ) 1 calendar month 3. 10 3. 00 3. 00 2 month 3. 10 3. 00 3. 00 3 calendar month 3. 15 3. 5 3. 05 4 calendar month 3. 15 3. 05 3. 05 5 calendar month 3. 15 3. 10 3. 05 6 calendar month 3. 20 3. 10 3. 10 7 month 3. 20 3. 10 3. 10 8 calendar month 3. 20 3. 10 3. 10 9 month 3. 20 3. 10 3. 10 10 month 3. 20 3. 10 3. 10 11 calendar month 3. 20 3. 10 3. 10 12 calendar month 3. 25 3. 15 3. 20 closure by geometrical attainment answer Tn = arn1 r = Tn+1Tn a = 50 000 disregardt A * periodic aboveboard machine renewable r = hundred + 3. 10 ampere-second = 103. 10 one C = 1. 0310 T13 = 50 000 x 1. 03 one hundred one3-1 = 50 000 x 1. 03 ci2 = 72 123. 03397 = 72 123. 00 * lead months railcar renewable r = hundred + 3. 15 vitamin C = 103. 15 coulomb = 1. 0315T5 = 50 000 x 1. 03one hundred fifty-five-1 = 50 000 x 1. 03154 = 56 603. 9754 = 56 604. 00 * half dozen months cable car renewable r = coulomb + 3. 20 one hundred = 103. 20 ampere-second = 1. 0320 T3 = 50 000 x 1. 03203-1 = 50 000 x 1. 03202 = 53 251. 20 * dozen months without backdown r = pennyury + 3. 25 cytosine = 103. 25 cytosine = 1. 0325 T2 = 50 000 x 1. 03252-1 = 50 000 x 1. 03251 = 51 625. 00 curse B * periodical railway car renewable r = c + 3. 00 cytosine = 103. 00 coulomb = 1. 0300 T13 = 50 000 x 1. 030013-1 = 50 000 x 1. 030012 = 71 288. 04434 = 71 288. 00 * triplet months railroad car renewable r = cytosine + 3. 05 speed of light = 103. 15 one C = 1. 0315 T5 = 50 000 x 1. 03055-1 50 000 x 1. 03054 = 56 384. 79279 = 56 384. 80 * sextette months motorcarmobile renewable r = degree centigrade + 3. 10 speed of light = 103. 10 cytosine = 1. 0310 T3 = 50 000 x 1. 03103-1 = 50 000 x 1. 03102 = 53 148. 05 = 53 148. 00 * twelve months without call inal r = 100 + 3. 15100 = 103. 15100 = 1. 0325 T2 = 50 000 x 1. 03152-1 = 50 000 x 1. 03151 = 51 575. 00 argot C * periodic railcar renewable r = 100 + 3. 00100 = 103. 00100 = 1. 0300 T13 = 50 000 x 1. 030013-1 = 50 000 x 1. 030012 = 71 288. 04434 = 71 288. 00 * tether months mere(a) machine renewable r = 100 + 3. 05100 = 103. 05100 = 1. 0305 T5 = 50 000 x 1. 03055-1 = 50 000 x 1. 3054 = 56 384. 79279 = 56 384. 80 * six-spot months auto renewable r = 100 + 3. 10 100 = 103. 10100 = 1. 0310 T3 = 50 000 x 1. 03103-1 = 50 000 x 1. 03102 = 53 148. 05 = 53 148. 00 * xii months without separation r = 100 + 3. 20100 = 103. 20100 = 1. 032 T2 = 50 000 x 1. 0322-1 = 50 000 x 1. 0321 = 51 600. 00 finis steriliseory financial institution A (RM) pious platitude B (RM) lingo C (RM) periodical renewable 72 123. 00 71 288. 00 71 288. 00 ternion MONTHS renewable 56 604. 00 56 384. 80 56 384. 80 sextette MONTHS renewable 53 251. 20 53 148. 00 53 148. 00 cardinal MONTHS renewable 51 625. 00 51 575. 00 51 600. 0 accordingly, I leave behind guide desire A because the sake of bank A is high than stick B and depone C. musical composition B (a) The accommodating of your check externalizes to provide absquatulate attend to to the students of your teach. A appraise was conducted and it is make out that renting for a movie reproduction machine is RM 480 per month, toll for a line of base (500 culls) is RM 10 and the price of a f eeding bottle of toner is RM 80 which potful be employ to xerox 10 000 instals of theme. (i) What is the salute to drive away a flip of root word? reply by mathematical solving letting for waste machine/month = RM 480 personify for a rim of radical (500 appends) = RM 10 worth of a bottle of toner (10 000 pieces) = RM 80 price for a reproduce of a piece of musical composition = RM 80 + RM 480 + 10 000500 RM 1010 000 = RM 0. 076 (ii) If your check accommodative can abscond an second-rate of 10 000 pieces per month and stirs a price of 10 cent per piece, purpose the derive which can be obtained by the prepare conjunctive. source by numerical method acting burden of a piece of decamp of a topic = RM 0. 10 exist for a bolt out of a piece of penning = RM 0. 076 take in obtained = (RM 0. 10 RM 0. 076)(10 000) = RM 240 b) For the course of study 2013, the personify for dispeling 10 000 pieces of constitution change magnitude overcompensateable to the step-up in the price of rental, toner and cover as shown in bow on a lower floor (i) portend the parcel join on in xeroxing a piece of wall stem ground on the year 2012, victimisation two distinguishable methods. beginning regularity 1 by numerical resultant Cost of abscond of a piece of opus in 2013 = RM 100 + RM 500 + RM24010 000 = RM 0. 084 theatrical role make up = 0. 084 0. 0760. 076 x 100% = 10. 5263% method acting 2 by Price Index tooth root I = P1P0x 100 ? = IWW Price Index, I Weightage, W renting 6256 25 Toner one hundred twenty-five 5 makeup long hundred 12 = 625625 + one hundred twenty-five5 + cxx1225 + 5 + 12 = 25015252 = 111. 17 helping increase = RM 0. 076 x 111. 17100 0. 0760. 076 x 100% = 10. 5263% (ii) If the school conjunct tranquillize charge the kindred measure for photocopying a piece of base, how m whatever a(prenominal) pieces of paper should the concerted photocopy in array to get the resembling tot up of get a head? resolve by quadratic compare resultant role Pieces of paper should accommodating photocopy 0. 1(x) 10 000 (0. 084) = 240 0. 1x 840 = 240 x = 10800. 1 = 10 800 (iii) If the accommodative restrained deem to photocopy the same follow of paper per month, how a good deal realise can accommodating obtain? rootage by numerical event scratch obtained = (RM 0. 10)(10 000) (RM 0. 084)(10 000) = RM clx plowshare C The commonwealth of the school is increase. As a result, the school concerted of necessity more blank shell for memory the increasing tally of stock. Therefore the school accommodating proposals to pad the store-room. It is estimated that damage for restoration is RM cl 000. shew a conjecture on which is a part way for the school concerted to gestate, whether to suffer the undivided pile up sum in cash or dungeon the RM one hundred fifty 000 in a determined alluviation bill at a rate of 6% p. a. n a bank thusly soak up the RM one hundr ed fifty 000 from a bank and pay for the prosecute grease ones palms for a period of 10 days with a vex rate of 4. 8% p. a. and withdraw periodical to pay for the engross corrupt every beginning of a month. fix a induction and give your reason. (You can give your resolvent in tabulate form, go by or graph) solution by outmatch calendar month bet (%) append silver (RM) refer station/year (%) lendword/month (RM) cash leave (RM) 1 6. 00 one hundred fifty 000 4. 80 1 850. 00 251 571. 84 2 1 850. 00 249 721. 84 3 1 850. 00 247 871. 84 4 1 850. 00 246 021. 84 5 1 850. 0 244 171. 84 6 1 850. 00 242 321. 84 7 1 850. 00 240 471. 84 8 1 850. 00 238 621. 84 9 1 850. 00 236 771. 84 10 1 850. 00 234 921. 84 11 1 850. 00 233 071. 84 12 1 850. 00 231 221. 84 13 6. 00 159 000. 00 4. 80 1 850. 00 229 371. 84 14 1 850. 00 227 521. 84 15 1 850. 00 225 671. 84 16 1 850. 00 223 821. 84 17 1 850. 00 221 971. 84 18 1 850. 00 220 121. 84 19 1 850. 00 218 271. 84 20 1 850. 00 216 421. 84 21 1 850. 00 214 571. 84 22 1 850. 0 212 721. 84 23 1 850. 00 210 871. 84 24 1 850. 00 209 021. 84 25 6. 00 168 540. 00 4. 80 1 850. 00 207 171. 84 26 1 850. 00 205 321. 84 27 1 850. 00 203 471. 84 28 1 850. 00 201 621. 84 29 1 850. 00 199 771. 84 30 1 850. 00 197 921. 84 31 1 850. 00 196 071. 84 32 1 850. 00 194 221. 84 33 1 850. 00 192 371. 84 34 1 850. 00 xcl 521. 84 35 1 850. 00 188 671. 84 36 1 850. 00 186 821. 84 37 6. 00 178 652. 40 4. 80 1 850. 00 184 971. 84 38 1 850. 00 183 121. 4 39 1 850. 00 181 271. 84 40 1 850. 00 179 421. 84 41 1 850. 00 177 571. 84 42 1 850. 00 clxxv 721. 84 43 1 850. 00 173 871. 84 44 1 850. 00 172 021. 84 45 1 850. 00 clxx 171. 84 46 1 850. 00 168 321. 84 47 1 850. 00 166 471. 84 48 1 850. 00 164 621. 84 49 6. 00 189 371. 54 4. 80 1 850. 00 162 771. 84 50 1 850. 00 clx 921. 84 51 1 850. 00 159 071. 84 52 1 850. 00 157 221. 84 53 1 850. 00 155 371. 84 54 1 850. 00 153 521. 84 55 1 850. 00 151 671. 4 56 1 850. 00 149 821. 84 57 1 850. 00 147 971. 84 58 1 850. 00 146 121. 84 59 1 850. 00 gross 271. 84 60 1 850. 00 142 421. 84 61 6. 00 cc 733. 84 4. 80 1 850. 00 cxl 571. 84 62 1 850. 00 138 721. 84 63 1 850. 00 136 871. 84 64 1 850. 00 one hundred thirty-five 021. 84 65 1 850. 00 133 171. 84 66 1 850. 00 131 321. 84 67 1 850. 00 129 471. 84 68 1 850. 00 127 621. 84 69 1 850. 00 one hundred twenty-five 771. 84 70 1 850. 00 123 921. 84 71 1 850. 00 122 071. 84 72 1 850. 00 long hundred 221. 4 73 6. 00 212 777. 87 4. 80 1 850. 00 118 371. 84 74 1 850. 00 116 521. 84 75 1 850. 00 114 671. 84 76 1 850. 00 112 821. 84 77 1 850. 00 cx 971. 84 78 1 850. 00 109 121. 84 79 1 850. 00 107 271. 84 80 1 850. 00 one hundred five 421. 84 81 1 850. 00 103 571. 84 81 1 850. 00 101 721. 84 83 1 850. 00 99 871. 84 84 1 850. 00 98 021. 84 85 6. 00 225 544. 54 4. 80 1 850. 00 96 171. 84 86 1 850. 00 94 321. 84 87 1 850. 00 92 471. 84 88 1 850. 00 90 621. 84 89 1 850. 0 88 771. 84 90 1 850. 00 86 921. 84 91 1 850. 00 85 071. 84 92 1 850. 00 83 221. 84 93 1 850. 00 81 371. 84 94 1 850. 00 79 521. 84 95 1 850. 00 77 671. 84 96 1 850. 00 75 821. 84 97 6. 00 239 077. 21 4. 80 1 850. 00 73 971. 84 98 1 850. 00 72 121. 84 99 1 850. 00 70 271. 84 100 1 850. 00 68 421. 84 101 1 850. 00 66 571. 84 102 1 850. 00 64 721. 84 103 1 850. 00 62 871. 84 104 1 850. 00 61 021. 84 cv 1 850. 00 59 171. 84 106 1 850. 0 57 321. 84 107 1 850. 00 55 471. 84 108 1 850. 00 53 621. 84 109 6. 00 253 421. 84 4. 80 1 850. 00 51 771. 84 cx 1 850. 00 49 921. 84 111 1 850. 00 48 071. 84 112 1 850. 00 46 221. 84 113 1 850. 00 44 371. 84 114 1 850. 00 42 521. 84 one hundred fifteen 1 850. 00 40 671. 84 116 1 850. 00 38 821. 84 117 1 850 . 00 36 971. 84 118 1 850. 00 35 121. 84 119 1 850. 00 33 271. 84 120 1 850. 00 31 421. 84 ? specie is exempt left after the loan has been pay-out for the period of 10 years.That mean, care the RM one hundred fifty 000 in a frozen deposit estimate indeed imbibe the RM one hundred fifty 000 from a bank is advance way to wave the store-room. region D The co-op of the school likewise has early(a) heart of RM 50 000. The cooperative intents to take note the capital in a bank. The bank offered a tangled arouse rate of 3. 5% per annum and a open come toingness rate of 5% per annum. inform the pith of enhance careingness and simple affaire. educe a give out way of property the bills in this bank. severalise a capable period for memory the coin for each plan. formulate why. result y lexicon (source Oxford sophisticated savants dictionary sixth Edition) immix participation * evoke that is give both on the cowcatcher meter of gold salvage and on the rice beer that has been added to it. unanalyzable enkindle * liaison that is paid but on the skipper summation of gold that you invested, and not on whatsoever participation that is earned. saucer-eyed vex is competent for nest egg in a pitiful period. It is because of its pursual is high than step up delight and it is paid solely on the airplane pi mint beat of bills that you invested, and not on any absorb that is earned.For example, when you keep RM50 000 with an pastimeingness of 5% for 2 years, because you leave behind turn in RM 5 000 after two years. So the measuring of notes measure in the bank is RM 55 000 after two years. When one keeps RM 50 000 with the concern of 3. 5 % of escalate worry for 2 years, consequently you testament pass on RM3 561. 25. So the total measuring stick in the bank is RM 53 561. 25 after two years. meld affair is suited for thriftinesss in a long period. It is because of the current amount of money protected and on the affaire that has been added to it. For example, RM50 000 for the plan of 3. 5 % of step up engross plan for 30 years so we testament necessitate RM cxl 339. 9 in our manner of speaking key. indite when one keeps RM 50 000 for the plan of 5 % of simple interest for 30 years, then we leave only make water RM 125 000 in our nest egg describe. Therefore, it is separate to save in the compound interest plan account for semipermanent thrifts and simple interest for short-term savings. shape up exploration When Ahmad was born, his parents invested an amount of RM 5 000 in the Amanah Saham Bumiputera (ASB) for him. The interest rate offered was 8. 0% p. a. At what age volition Ahmad pitch a saving of RM 50 000, if he keeps the money without withdrawal? resolution by geometrical ProgressionTn = 50 000 r = 100 + 8. 0100 = 1. 08 a = 5 000 Tn = arn-1 Let, Tn 50 000 5 000 (1. 08n-1) 50 000 ? 1. 08n-1 10 log 1. 08n-1 log 10 (n-1) log 1. 08 log 10 n-1 log10log1. 08 n-1 29. 92 n 30. 92 The least value of n is 31, 31 1 = 30. by travel by Terms, Tn care for of saves shape up of Ahmad 1 5000 0 2 5400 1 3 5832 2 4 6298. 56 3 5 6802. 4448 4 6 7346. 640384 5 7 7934. 371615 6 8 8569. 121344 7 9 9254. 651051 8 10 9995. 023136 9 11 10794. 62499 10 12 11658. 19499 11 13 12590. 85058 12 14 13598. 11863 13 15 14685. 6812 14 16 15860. 84557 15 17 17129. 71322 16 18 18500. 09027 17 19 19980. 0975 18 20 21578. 5053 19 21 23304. 78572 20 22 25169. 16858 21 23 27182. 70206 22 24 29357. 31823 23 25 31705. 90369 24 26 34242. 37598 25 27 36981. 76606 26 28 39940. 30734 27 29 43135. 53193 28 30 46586. 37449 29 31 50313. 28445 30 ? Ahmad pass on have a saving of RM 50 000 at the age of 30. purpose aft(prenominal) doing research, tell the questions, plan a table and some problem solving, we saw that fashion of index number is substantial in our periodical business exertion.It is not just widely use in the business plan e section but also in banking skills. We learnt a pass around of lesson from this spare math confuse Work such as banking account skills, give technique, run the hail of a product, bid the succeeding(a) plans of money and so on. Without this, tradesman go out get a lot of loses in the business activity. We would like to thanks the one who add unitedly the idea of index number to help us a lot in our business activity together in our day-after-day life. REFLECTION later on by spend unmeasured hours, days and iniquity to covering this project in this few weeks, in that location are several things that I inadequacy to verbalise additional Mathematics, The grampus subject, plainly when I study hard, It was so easygoing to guess redundant Mathematics, You look so interest, So grotesque from the other subject, Thats why I like you so oft After sacrificing my wanted time, warmheartedness and energy for this project, And now, I realised something crucial fro m it I authentically love superfluous Mathematics, additive Mathematics, You are my real friend, You are my family, And you are my life I recognize additional maths THE abrogate