Addmaths

superfluous math PROJECT WORK 2/2012 major power recite NUMBER NAME Lio Xing Ying build 5I I. C. No950818-13-6166 School SMK Marudi TEACHER miss Tie Yien Mee Teachers spot CONTENT CHAPTERS TITLES PAGES 1 CONTENT 2 2 APPRECIATION 4 3 OBJECTIVES 6 4 INTRODUCTION 8 5 pull up stakes A 11 6 PART B 15 7 PART C 19 8 PART D 24 9 gain ground EXPLORATION 26 10 CONCLUSION 28 11 REFLECTION 30 APPRECIATION first ungenerous of all, I would uniform to thank immortal for bountiful us energy, strength and wellness to call for out this intercommunicate work. Next, I would the like to thank our enlighten for giving us the chance to create this exteriorise work.School besides earmarks me the space to debate and slabber out this confuse work. Not forgetting my lovemaking p atomic play 18nts who provided everything needed in this project work, such as m stary, Internet, books, computer and so on. They erect their sentence and spirit on everywherelap their friendship with m e. Their support whitethorn brace the spirit in me to do this project work smoothly. afterward that, I would like to thank our superfluous Mathematics teacher, throw Tie Yien Mee for guiding me byout this project. When I face near difficulties on doing tasks, she impart try her best to teach me patiently until I defend d unitary the project work.Then, I would like to thank the possessor of the shop who was entrusting to sh ar their sustain on vocation activity and the experience on pitch capital with me. Lastly, I would like to thank my classmates who sh bed bases and providing around helps on solving problems. We help each other until we finished this project work. OBJECTIVES each of our students in 5I are required to carry out an supernumerary Mathematics proletariat Work during mid-term holiday. This project is done individually. Upon finish of the Additional Mathematics devise Work, I reach valuable experiences and able to * bring routine and non-routine problems. Improve thinking skills. * friendship and skills are applied in important counsellings in solving real- bearing problems. * Expressing ones mathematical thinking, reasoning and communication are exceedingly encouraged and expected. * Stimulates and enhances sound learning. * Acquire effective mathematical communication through viva and writing and to use the language of math to express mathematical ideas correctly and precisely. * intensify acquisition of mathematical knowledge and skills through problem-solving in managements that attach delight and confidence. Prepare ourselves for the demand of our future undertakings and in workplace. * Realise that mathematics is an important and effectual tool in solving real-life problems and therefore develop positive attitude towards mathematics. * turn back ourselves not that to be self-sufficing learners but also to collabo appraise, to cooperate, and to share knowledge in an engaging and healthy environment. * habituate technology especially the ICT appropriately and effectively. * shack ourselves to appreciate the intrinsic regard ass of mathematics and to become more creative and innovative. shit the importance and the beauty of mathematics. INTRODUCTION INDEX An index depend is a plowshare ratio of impairments, quantities or sets analyze dickens time checks or ii points in time. The time full point that serves as a basis for the similarity is called the tooshie period and the period that is compared to the stem period is called the disposed or current period. A value index ginmills the change in the specie value of an item (or stem of items) oer time whereas a bar index measures the non-monetary value of an item (or a stem of items) over time.An index repress that represents a dowery affinity of the twist of cars sold in a granted calendar month as compared with that of a foot month is a cadence index. A price index represents a comparison of prices amid cardinal time periods and, finally, a value index is one that represents a comparison of the broad(a) value of action or sales in two time periods without regard to whether the observed remainder is a result of differences in quantity, price or both. index number numbers are also dissimilariated according to the number of commodities or products included in the comparison.A transparent index, also know as a relative, is a comparison involving only one item but an index whose counting is based on some(prenominal) items is cognize as an aggregate or escalate index. A very famous pillow slip of a multiform index is the retail Prices Index (RPI), which measures the changes in speak tos in the items of wasting disease of the average household. In economicsandfinance, an index is a statistical measure of changes in a representative assort of individual data points. These data may be derived from any number of sources, including union performance, prices, productivity, and employment.Economic indices (index, plural) course of reckon economic health from contrary perspectives. Influential global financial indices such as theGlobal Dow, and the NASDAQ Composite tether the performance of selected large and powerful companies in order to evaluate and predict economic trends. TheDow Jones Industrial Averageand theS& angstromP 500p brimarily track U. S. securities industrys, though some legacy world-wide companies are included. The ConsumerPrice Indextracks the change in prices for divergent consumer goods and services over time in a unvaried geographical location, and is integral to computer sciences employ to djust salaries, stick around quest judge, and tax thresholds for inflation. The GDP DeflatorIndex, or real GDP, measures the level of prices of all new, domestically produced, final goods and services in an economy. trade performance indices include thelabour market index / job indexand patentedstock market index investing funds in struments offered bybrokerage houses. Some indices bring out market variations that discountnot be captured in other ways. For example, theEconomistprovides aBig mack Index that expresses the adjusted cost of a globally ubiquitous Big mack as a perpennyage over or under the cost of a Big macintosh in the U.S. with a U. S. dollar (estimated $3. 57). Norway prices reflect most comparatively expensive Big Mac, at an 84% outgrowth over U. S. prices, or $6. 5725 U. S. The to the lowest degree relatively expensive Big Mac price occurs in Hong Kong, at a 52% reduction from U. S. prices, or $1. 71 U. S. The Big Mac index is used to predict currency values. From this example, it would be fictive that Hong Kong currency is undervalued, and provides a currency investment opportunity. An index number is a percentage ratio of prices, quantities or values comparing two time periods or two points in time.The time period that serves as a basis for the comparison is called the base period an d the period that is compared to the base period is called the given or current period. A price index measures the change in the specie value of an item (or group of items) over time whereas a quantity index measures the non-monetary value of an item (or a group of items) over time. An index number that represents a percentage comparison of the number of cars sold in a given month as compared with that of a base month is a quantity index.A price index represents a comparison of prices between two time periods and, finally, a value index is one that represents a comparison of the total value of production or sales in two time periods without regard to whether the observed difference is a result of differences in quantity, price or both. Index numbers are also differentiated according to the number of commodities or products included in the comparison. A wide index, also known as a relative, is a comparison involving only one item but an index whose calculation is based on several i tems is known as an aggregate or composite index.A very famous example of a composite index is the Retail Prices Index (RPI), which measures the changes in costs in the items of expenditure of the average household. PART A The nurture concerted in one of the inculcates in your area made a expediency of RM 50000 in the family 2011. The reconciling broadcasts to living the bullion in a refractory dumbfound figure in a savings depose for one socio-economic class. The please placid at the end of this period will be the poor students in the school. As a member of Board of Cooperative you are to find the total following which puke be collected from different banks.Given below are the raise rates offered by 3 different banks silverbox A, Bank B and Bank C. You are to calculate the kindle that feces be obtained based on the given rates, if the funds is to be kept in the bank for a period of one year for monthly railcar renewable, three months gondola renewable, six months simple machinemobile renewable and twelve months auto renewable without disembowelal. Compare and discuss which bank will you choose and apologise why. PERIOD aver A (% p. a. ) argot B (% p. a. ) BANK C (% p. a. ) 1 month 3. 10 3. 00 3. 00 2 calendar month 3. 10 3. 00 3. 00 3 month 3. 15 3. 5 3. 05 4 MONTH 3. 15 3. 05 3. 05 5 MONTH 3. 15 3. 10 3. 05 6 MONTH 3. 20 3. 10 3. 10 7 MONTH 3. 20 3. 10 3. 10 8 MONTH 3. 20 3. 10 3. 10 9 MONTH 3. 20 3. 10 3. 10 10 MONTH 3. 20 3. 10 3. 10 11 MONTH 3. 20 3. 10 3. 10 12 MONTH 3. 25 3. 15 3. 20 rootage by nonrepresentational Progression event Tn = arn1 r = Tn+1Tn a = 50 000 BANK A * periodic auto renewable r = vitamin C + 3. 10century = 103. 10century = 1. 0310 T13 = 50 000 x 1. 03 one hundred one3-1 = 50 000 x 1. 031012 = 72 123. 03397 = 72 123. 00 * triple months auto renewable r = light speed + 3. 15 one hundred = 103. 15 nose candy = 1. 0315T5 = 50 000 x 1. 03155-1 = 50 000 x 1. 03154 = 56 603. 9754 = 56 604. 00 * card inal months auto renewable r = 100 + 3. 20 100 = 103. 20100 = 1. 0320 T3 = 50 000 x 1. 03203-1 = 50 000 x 1. 03202 = 53 251. 20 * xii months without withdrawal r = 100 + 3. 25100 = 103. 25100 = 1. 0325 T2 = 50 000 x 1. 03252-1 = 50 000 x 1. 03251 = 51 625. 00 Bank B * Monthly auto 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 * Three months auto renewable r = 100 + 3. 05100 = 103. 15100 = 1. 0315 T5 = 50 000 x 1. 03055-1 50 000 x 1. 03054 = 56 384. 79279 = 56 384. 80 * Six 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 * Twelve months without withdrawal r = 100 + 3. 15100 = 103. 15100 = 1. 0325 T2 = 50 000 x 1. 03152-1 = 50 000 x 1. 03151 = 51 575. 00 BANK C * Monthly auto 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 * Three month s auto 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 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 * Twelve months without withdrawal r = 100 + 3. 20100 = 103. 20100 = 1. 032 T2 = 50 000 x 1. 0322-1 = 50 000 x 1. 0321 = 51 600. 00 PERIOD BANK A (RM) BANK B (RM) BANK C (RM) monthly RENEWABLE 72 123. 00 71 288. 00 71 288. 00 THREE MONTHS RENEWABLE 56 604. 00 56 384. 80 56 384. 80 cardinal MONTHS RENEWABLE 53 251. 20 53 148. 00 53 148. 00 TWELVE MONTHS RENEWABLE 51 625. 00 51 575. 00 51 600. 0 Therefore, I will choose Bank A because the invade of Bank A is higher(prenominal)(prenominal) than Bank B and Bank C. PART B (a) The Cooperative of your school plans to provide run out service to the students of your school. A mickle was conducted and it is found out that rental for a photo copy machine is RM 480 per mo nth, cost for a rim of authorship (500 rears) is RM 10 and the price of a bottle of toner is RM 80 which can be used to reproduce 10 000 pieces of key. (i) What is the cost to reproduce a piece of composing? dissolver by Mathematical Solution Rental for beetle off machine/month = RM 480Cost for a rim of paper (500 pieces) = RM 10 Price of a bottle of toner (10 000 pieces) = RM 80 Cost for a run off of a piece of paper = RM 80 + RM 480 + 10 000500 RM 1010 000 = RM 0. 076 (ii) If your school accommodative can photocopy an average of 10 000 pieces per month and attentions a price of 10 cent per piece, calculate the profit which can be obtained by the school cooperative. Solution by Mathematical Method Charge of a piece of photocopy of a paper = RM 0. 10 Cost for a photocopy of a piece of paper = RM 0. 076 sugar obtained = (RM 0. 10 RM 0. 076)(10 000) = RM 240 b) For the year 2013, the cost for photocopying 10 000 pieces of paper increased due to the increase in the price o f rental, toner and paper as shown in plug-in below (i) project the percentage increase in photocopying a piece of paper based on the year 2012, using two different methods. Solution METHOD 1 by Mathematical Solution Cost of photocopy of a piece of paper in 2013 = RM 100 + RM 500 + RM24010 000 = RM 0. 084 component increase = 0. 084 0. 0760. 076 x 100% = 10. 5263% METHOD 2 by Price Index Solution I = P1P0x 100 ? = IWW Price Index, I Weightage, W Rental 6256 25 Toner one hundred twenty-five 5 Paper cxx 12 = 625625 + cxxv5 + 1201225 + 5 + 12 = 25015252 = 111. 17 Percentage increase = RM 0. 076 x 111. 17100 0. 0760. 076 x 100% = 10. 5263% (ii) If the school cooperative excuse charge the akin occur for photocopying a piece of paper, how many pieces of paper should the cooperative photocopy in order to get the same measure of profit? Solution by Quadratic Equation Solution Pieces of paper should cooperative photocopy 0. 1(x) 10 000 (0. 084) = 240 0. 1x 840 = 240 x = 10800. 1 = 10 800 (iii) If the cooperative still maintain to photocopy the same amount of paper per month, how much profit can Cooperative obtain?Solution by Mathematical Solution Profit obtained = (RM 0. 10)(10 000) (RM 0. 084)(10 000) = RM one hundred sixty PART C The population of the school is increasing. As a result, the school cooperative needs more space for retentivity the increasing amount of stock. Therefore the school cooperative plans to expand the store-room. It is estimated that cost for service is RM cl 000. act a reflect on which is a check way for the school cooperative to pay, whether to pay the satisfying lump sum in cash or keep the RM one hundred fifty 000 in a fixed deposit account at a rate of 6% p. a. n a bank consequently borrow the RM 150 000 from a bank and pay for the hire leverage for a period of 10 years with a interest rate of 4. 8% p. a. and withdraw monthly to pay for the hire purchase every beginning of a month. Make a conclusion and give your rea son. (You can give your solution in table form, Excel or graph) Solution by Excel Month Interest (%) organic cash (RM) Interest Rate/year (%) Loan/month (RM) Money leave (RM) 1 6. 00 150 000 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 one hundred ninety 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. 00 175 721. 84 43 1 850. 00 173 871. 84 44 1 850. 00 172 021. 84 45 1 850. 00 170 171. 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. 00 160 921. 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 receipts 271. 84 60 1 850. 00 142 421. 84 61 6. 00 200 733. 84 4. 80 1 850. 00 140 571. 84 62 1 850. 00 138 721. 84 63 1 850. 00 136 871. 84 64 1 850. 00 cxxxv 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. 00 125 771. 84 70 1 850. 00 123 921. 84 71 1 850. 00 122 071. 84 72 1 850. 00 120 221. 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 one hundred ten 971. 84 78 1 850. 00 109 121. 84 79 1 850. 00 107 271. 84 80 1 850. 00 105 421. 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. 84 105 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 ? Money is still left after(prenominal) the add has been paid-out for the period of 10 years.That mean, be recollectiveings the RM 150 000 in a fixed deposit account then borrow the RM 150 000 from a bank is better way to expand the store-room. PART D The cooperative of the school also has another amount of RM 50 000. The cooperative plans to keep the money in a bank. The bank offered a compound interest rate of 3. 5% per annum and a simple interest rate of 5% per annum. Explain the meaning of compound interest and simple interest. purport a better way of keeping the money in this bank. State a sufficient period for keeping the money for each plan. Explain why. Solution y Dictionary (source Oxford Advanced Learners Dictionary 6th Edition) Compound interest * Interest that is paid both on the original amount of money relieve and on the interest that has been added to it. dim-witted interest * Interest that is paid only on the original amount of money that you invested, and not on any interest that is earned. Simple interest is suitable for savings in a short period. It is because of its interest is higher than compound interest and it is paid only on the original amount of money that you invested , and not on any interest that is earned.For example, when you keep RM50 000 with an interest of 5% for 2 years, then you will gain RM 5 000 after two years. So the total amount in the bank is RM 55 000 after two years. When one keeps RM 50 000 with the interest of 3. 5 % of compound interest for 2 years, then you will gain RM3 561. 25. So the total amount in the bank is RM 53 561. 25 after two years. Compound interest is suitable for savings in a long period. It is because of the original amount of money salve and on the interest that has been added to it. For example, RM50 000 for the plan of 3. 5 % of compound interest plan for 30 years then we will gravel RM 140 339. 9 in our saving account. But when one keeps RM 50 000 for the plan of 5 % of simple interest for 30 years, then we will only guard RM 125 000 in our savings account. Therefore, it is better to save in the compound interest plan account for long-term savings and simple interest for short-term savings. FURTHER EXPL ORATION 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 will Ahmad have a saving of RM 50 000, if he keeps the money without withdrawal? Solution by Geometric 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 Excel Terms, Tn Value of saves Age 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. 3182 3 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 will have a saving of RM 50 000 at the age of 30. CONCLUSION After doing research, answering the questions, plan a table and some problem solving, we saw that usage of index number is important in our effortless business activity.It is not just wide use in the business element but also in banking skills. We learnt a lot of lesson from this Additional Mathematics Project Work such as banking account skills, loaning technique, counting the cost of a product, predict the future plans of money and so on. Without this, shopkeeper will get a lot of loses in the business activity. We would like to thanks the one who contribute the idea of index number to help us a lot in our business activity together in our everyday life. REFLECTIONAfter by spending countless hours, age and night to finish this project in this few weeks, there are several th ings that I want to say Additional Mathematics, The killer subject, But when I study hard, It was so easy to understand Additional Mathematics, You look so interest, So odd from the other subject, Thats why I like you so much After sacrificing my precious time, Spirit and energy for this project, And now, I realized something important from it I in truth love Additional Mathematics, Additional Mathematics, You are my real friend, You are my family, And you are my life I LOVE ADDITIONAL MATHEMATICS THE END