First of all, I would like to say Alhamdulillah, for giving me the strength and health to do this project workand finish it on time. Not forgotten to my parents for providing everything, such as money, to buy anything that are related to this project work, their advice, which is the most needed for this project and facilities such as internet, books, computers and all that. They also supported me and encouraged me to complete this task so that I will not procrastinate in doing it. Then I would like to thank to my teacher, Sir Zaki for guiding me throughout this project. Even I had some difficulties in doing this task, but he taught me patiently until we knew what to do. He tried and tried to teach me until I understand what I’m supposed to do with the project work. Besides that, I would love to express my gratitude to my friends who always supporting me. Even this project is individually but we are cooperated doing this project especially in disscussion and sharing ideas to ensure our task will finish completely. Last but not least, any part which involved either directly or indirect in completing this project work. Thank you everyone. The aims of carrying out this project work are: i. To develop mathematical knowledge through problem solving in a way that increases student interest and confidence. . vii. vi. ii. To use the language of mathematics to express mathematical ideas precisely. To provide learning environment that stimulates and enhances effective learning. v. To apply and adapt a variety of problem-solving strategies to solve problems. To develop positive attitude towards mathematics. To promote effective mathematical communication. To improve thinking skills. iv. iii. 50 170 3816.86 5.73 3.69 11.50 JADUAL 1 PERATUS PERBELANJAAN BULANAN (KEPADA % TERDEKAT) 18.20 5.51 22.ITEM MAKANAN PERUMAHAN (SEWA/ANSURAN PINJAMAN) PENGANKUTAN (PETROL/ANSURAN KERETA/TAMBANG BAS DLL) PAKAIAN PENDIDIKAN REKREASI UTILITI (AIR/ELEKTRIK/TELEFON/INTERNET) PERUBATAN LAIN-LAIN JUMLAH MIN PERBELANJAAN BULANAN BAGI TAHUN 2013 (KEPADA RM TERDEKAT) 710 554 867.50 225. .50 141 430 300 198.27 7.45 100 NOTA: min perbelanjaan bulanan keluarga saya bagi tahun 2013.60 14.90 4. 50 225.50 170 3816.50 103 350 210 141.50 JADUAL 2 MIN PERBELANJAAN BULANAN BAGI TAHUN 2013 (RM) 930 554 867.50 .50 200.50 141 430 300 198.ITEM MAKANAN PERUMAHAN (SEWA/ANSURAN PINJAMAN) PENGANKUTAN (PETROL/ANSURAN KERETA/TAMBANG BAS DLL) PAKAIAN PENDIDIKAN REKREASI UTILITI (AIR/ELEKTRIK/TELEFON/INTERNET) PERUBATAN LAIN-LAIN JUMLAH MIN PERBELANJAAN BULANAN BAGI TAHUN 2008 SEBAGAI TAHUN ASAS (RM) 710 493 779.50 133 3120. ITEM MAKANAN PERUMAHAN (SEWA/ANSURAN PINJAMAN) PENGANKUTAN (PETROL/ANSURAN KERETA/TAMBANG BAS DLL) PAKAIAN PENDIDIKAN REKREASI UTILITI (AIR/ELEKTRIK/TELEFON/INTERNET) PERUBATAN LAIN-LAIN JUMLAH INDEKS HARGA PADA TAHUN 2013 BERASASKAN TAHUN 2008 131 112 111 137 123 143 140 112 128 PEMBERAT (DALAM % TERDEKAT) 12 10 10 12 11 13 12 10 11 JADUAL 3 . JENAMA SAIZ TELEVISYEN (INCH) HARGA (RM) KEDAI KEDAI KEDAI A B C TUNAI TUNAI TUNAI MIN SISIHAN PIAWAI LG SAMSUNG 24 32 40 24 32 40 JADUAL 4 (a) . 36 151.75 45.12 163.40 224.94 116.JENAMA SAIZ TELEVISYEN (INCH) HARGA (RM) KEDAI KEDAI KEDAI A B C ANSURAN ANSURAN ANSURAN 709 929 1599 779 929 1599 829 1117 1728 800 1089 1549 JADUAL 4 (b) 854 1329 1929 870 1300 1830 MIN SISIHAN PIAWAI 24 LG 32 40 24 32 40 797 1125 1679 816 1106 1659 62.30 SAMSUNG . Sugar.15 times while other sectors may have increased their production only marginally. The index number is obtained as a result of an average of all these items. geographic location or other characteristics such as income. 2. sales or changes exports or imports over a certain period of time. Characteristics of an Index Numbers 1. etc. On the other hand. There are expressed as percentage : Index number is calculated as a ratio of the current value to a base value and expressed as a percentage. 3. average is a single figure representing a group expressed in the same units. mean that the net increase in the index reflects an equivalent increase in industrial production in all sectors of the industry. . an index number is a statistical measure designed to show changes in a variable or a group or related variables with respect to time. An index number is used for purposes of comparison in cases where the series being compared could be expressed in different units i. a manufactured products index (a part of the whole sale price index) is constructed using items like Dairy Products. Generally used to indicate the state of the economy. Edible Oils. These items naturally are expressed in different units like sugar in kgs. index numbers are aptly called barometers of economic activity .15times compared to 1980-81. It is a very well known fact that the wage contracts of workers in our country are tied to the cost of living index numbers. Tea and Coffee. Index numbers are specialized averages: An index number is an average with a difference. But it does not.e. An index number is commonly referred to as an index. Some sectors might have increased their production more than2. profession. which are expressed in different units. milk in liters. Index number capture the changes in the group of related variables over a period of time. By definition. which are not capable of direct measurement. etc. For example. Index numbers are used in comparing production.Index Number Index numbers are today one of the most widely used statistical indicators. however. It must be clearly understood that the index number for the base year is always 100. The role-played by index numbers in Indian trade and industry is impossible to ignore.1 in 1992-93 (base year 1980-81) it means that the industrial production in that year was up by 2. etc. Index numbers measures changes that are not directly measurable: An index number is used for measuring the magnitude of changes in such phenomenon. Index numbers essentially. if the index of industrial production is 215. the increase may not be as a result of increase in the volume of production as one would have it but because of increase in the price.5 paise in 1992. which forms the basis of many a wages agreement between the employees union and the employer. Deflates time series data Index numbers play a vital role in adjusting the original data to reflect reality. the real purchasing power of the rupee can be found out as follows: 100/202=0. found out as follows: 100/202=0.5 paise in 1992. nominal income(income at current prices) can be transformed into real income(reflecting the actual purchasing power) by using income deflators.495 It indicates that if rupee was worth 100 paise in 1984 its purchasing power is 49. nominal income (income at current prices) can be transformed into real income(reflecting the actual purchasing power) by using income deflators. 3. 4.Uses of index numbers 1. assume that industrial production is represented in value terms as a product of volume of production and price. For example. generally the consumer price index. 4. Deflates time series data Index numbers play a vital role in adjusting the original data to reflect reality.495 It indicates that if rupee was worth 100paise in 1984 its purchasing power is 49. . Establishes trends Index numbers when analyzed reveal a general trend of the phenomenon under study. assume that industrial production is represented in value terms as a product of volume of production and price. Similarly. The inflation which has caused the increase in the series can be eliminated by the usage of an appropriate price index and thus making the series real. Helps in policy making It is widely known that the dearness allowances paid to the employees is linked to the cost of living index. If the subsequent years industrial production were to be higher by 20% in value. Suppose the consumers price index for urban non-manual employees increased from 100 in 1984 to 202 in 1992. Index numbers of unemployment of the country not only reflects the trends in the phenomenon but are useful in determining factors leading to unemployment. Similarly. Determines purchasing power of the rupee Usually index numbers are used to determine the purchasing power of the rupee. Thus index numbers guide policy making. 2. From time to time it is the cost of living index. For eg. For example. If an attempt is being made to compare the prices of edible oils this year to the prices of edible oils last year. The value index as such measures changes in net monetary worth. we are interested in the quantum of production of edible oils in those years. etc. 3. Its limited use is owing to the inability of the value index to distinguish the effects of price and quantity separately. It combines price and quantity changes to present a more spatial comparison. instead of the price of edible oils.Types of index numbers Three are three types of principal indices. Price Index The most frequently used form of index numbers is the price index. it involves. A price index compares charges in price of edible oils. Quantity Index A quantity index measures the changes in quantity from one period to another. By constructing a price index number. Usually value index is used in sales. Though the value index enables comparison of value of a commodity in a year to the value of that commodity in a base year. we are summarizing the price movements of each type of oil in this group of edible oils into a single number called the price index. a comparison of two price situations over time and secondly. Value Index The value index is a combination index. the heterogeneity of the edible oils given the various varieties of oils. They are: 1. Consumer Price Index (CPI) are some of the popularly used price indices. If in the above example. The index of industrial production measures the increase or decrease in the level of industrial production in a given period compared to some base period. . foreign trade. inventories. it has limited use. 2. It is the quantity index that needs to be constructed here. then we are comparing quantities in two different years or over a period of time. firstly. The popular quantity index used in this country and elsewhere is the index of industrial production (HP). The Whole Price Index (WPI). Additional Mathematics..“ After spending countless hours... Sacrificing my internet… Sacrificing my holiday... You are my soul mate ! I LOVE U ADDITIONAL MATHEMATICS ! . From the day I was able to hold pencil. I really love you. I realized something really important in you. You my partner.. Sacrificing my Facebook... Sacrificing my Movies.. From the day I start to learn and from the day I heard your name. You are my real friend......... Sacrificing my chatting. days and night to finish this project and also sacrificing my time for chatting and movies in this mid year holiday.. After sacrificing my precious time just for you… Sacrificing my play time. I always thought that you will be my greatest obstacle and rival in excelling in my life. there are several things that I can say.