Contoh Kerja Projek Matematik Tambahan 2013 Negeri Pahang

FOREWARD

First of all, I would like to say Alhamdulillah, for giving me the strength and health to do this project work. Not forgotten my parents for providing everything, such as money, to buy any thing that are related to this project work and their advice, which is the most needed for this project. Internet, books, computers, and etc. 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 my teacher, Encik Mohd Rozali bin Senik for guiding me and my friends throughout this project. We had some difficulties in doing this task, but he taught us patiently until we knew what to do. He tried and tried to teach us until we understand what we supposed to do with the project work. Last but not least, my friends who were doing this project with me and sharing our ideas. They were helpful that when we combined and discussed together, we had this task done.

 OBJECTIVE

 OBJECTIVE

We students taking Additional Mathematics are required to carry out a project work while we are in Form 5. This year the Curriculum Development Division, Ministry of Education has prepared four tasks for us. We are to choose and complete only ONE task based on our area of interest. This project can be done in groups or individually, but each of us are expected to submit an individually written report. Upon completion of the Additional Mathematics Project Work, we are to gain valuable experiences and able to:

·         Apply and adapt a variety of problem solving strategies to solve routine and non-routine problems;

·         Experience classroom environments which are challenging, interesting and meaningful and hence improve their thinking skills.

·         Experience classroom environments where knowledge and skills are applied in meaningful ways in solving real-life problems

·         Experience classroom environments where expressing ones mathematical thinking ,reasoning and communication are highly encouraged and expected

·         Experience classroom environments that stimulates and enhances effective learning.

·         Acquire effective mathematical communication through oral and writing, and to use the language of mathematics to express mathematical ideas correctly and precisely

·         Enhance acquisition of mathematical knowledge and skills through problem-solving in ways that increase interest and confidence

·         Prepare ourselves for the demand of our future undertakings and in workplace

·         Realise that mathematics is an important and powerful tool in solving real-life problems and hence develop positive attitude towards mathematics.

·         Train ourselves not only to be independent learners but also to collaborate, to cooperate, and to share knowledge in an engaging and healthy environment

·         Use technology especially the ICT appropriately and effectively

·         Train ourselves to appreciate the intrinsic values of mathematics and to become more creative and innovative

·         Realize the importance and the beauty of mathematics

HISTORY OF INDEX NUMBER

Index numbers are meant to study the change in the effects of such factors which cannot be measured directly. According to Bowley, “Index numbers are used to measure the changes in some quantity which we cannot observe directly”. For example, changes in business activity in a country are not capable of direct measurement but it is possible to study relative changes in business activity by studying the variations in the values of some such factors which affect business activity, and which are capable of direct measurement. Index numbers are commonly used statistical device for measuring the combined fluctuations in a group related variables. If we wish to compare the price level of consumer items today with that prevalent ten years ago, we are not interested in comparing the prices of only one item, but in comparing some sort of average price levels. We may wish to compare the present agricultural production or industrial production with that at the time of independence. Here again, we have to consider all items of production and each item may have undergone a different fractional increase (or even a decrease). How do we obtain a composite measure? This composite measure is provided by index numbers which may be defined as a device for combining the variations that have come in group of related variables over a period of time, with a view to obtain a figure that represents the ‘net’ result of  the change in the constitute variables.

Index numbers may be classified in terms of the variables that they are intended to measure. In business, different groups of variables in the measurement of which index number techniques are commonly used are (i) price, (ii) quantity, (iii) value and (iv) business activity. Thus, we have index of wholesale prices, index of consumer prices, index of industrial output, index of value of exports and index of business activity, etc. Here we shall be mainly interested in index numbers of prices showing changes with respect to time, although methods described can be applied to other cases. In general, the present level of prices is compared with the level of prices in the past. The present period is called the current period and some period in the past is called the base period.

Index Numbers:

Index numbers are statistical measures designed to show changes in a variable or group of related variables with respect to time, geographic location or other characteristics such as income, profession, etc. A collection of index numbers for different years, locations, etc., is sometimes called an index series.

Simple Index Number:

A simple index number is a number that measures a relative change in a single variable with respect to a base.

Composite Index Number:

A composite index number is a number that measures an average relative changes in a group of relative variables with respect to a base.

PART 1

The price of goods sold in shop vary from one shop to  another. Shoppers tend to buy goods which are not only reasonably price but also give value for their money.

You are required to carry out a survey on four different items based on the following categories: food, detergent and stationery. The survey should be done in three different shop.

Part 1(a)

Collect picture, newspaper cuttings or photos on item that you have chosen. Design a collage to illustrate the chosen item.

FOOD

             

STATIONERY

       

DETERGENT

Part 1(b)

Record the item and their prices systematically as such in Table 1. Since item may be differently packed, be sure to use consistent measurements for each item selected so that comparison can be done easily and accurately.

The data in the table below is only serve as a REFERENCE to you:

Category	Item	Mydin	Eng Hong	Nirwana
	Nasi Lemak	1.00	1.50	2.00
Food	Curry puff	0.50	0.50	0.50
	Teh tarik	1.00	1.20	1.30
	Total Price	2.50	3.20	3.80
	Glue	0.90	0.80	0.80
Stationery	Pen	1.90	1.20	1.30
	Eraser	0.70	0.50	0.40
	Total Price	3.50	2.50	2.50
	Dynamo	4.00	4.30	4.50
Detergent	Kuat Harimau	5.20	5.50	5.80
	Soflan	4.20	4.50	4.70
	Grand Total	19.40	20.00	21.30

Part 1(c)

Create at least two suitable graphical representations (the use of ICT is encouraged) to compare contrast the price of the item chosen.

Part 1 (d):

Based on the graphical representations that you have constructed in part 1(c), interpret,discuss and draw consclusion. Comment on your findings.

Based on the graphical representations that I have constructed in Part 1(c), it is shown that there are large and small differences among the prices of items in each category between the shops. In the food category, the smallest price difference are of those of curry puffs, while the highest is the price of Nasi Lemak. Besides food, stationery also shows a smallest price. On the other hand,

detergent shows a highest price difference between its items. The graph also show that most of the items that are high priced comes from the Nirwana Supermarket, while the lowest price items come from the Mydin Supermarket. The graph 1(d) will show the conclusion of the difference among the shops based upon the shops grand total.

 

Graph 1(d)

Part 1(e)

Identify an item that has large price difference among the shops. Suggest anddiscuss possible reasons for the price difference.

 Kuat Harimau : Mydin – 5.20

                           Eng Hong – 5.50

                           Nirwana – 5.80

Mean = (5.20 + 5.50 + 5.80) ÷ 3

          =  5.50

Standard deviation :

σ =

   = TOLONG KIRAKAN

Reason of difference in price :

·       Bulk buying from the retailer gives the lower cost :

resulted in lower relling price.

·       Hypermarket own brands are much cheaper than the expansive brand-don’t involve in advertiving :

resulted in lower –selling price

·       Sales and discount offer by the supermarket.

FUTHER EXPLORATION

Index numbers are being used in many different daily situations, for example, air pollution index, stock market index, gold index and property index.

Obtain information from the internet or other reliable sources on the importance of two different types of index numbers of your choice. Elaborate the use and the importance of these index numbers in daily life situations.

1. AIR QUALITY INDEX

An air quality index (AQI) is a number used by government  agencies to communicate to the public how polluted the air is currently or how polluted it is forecast to become. As the AQI increases, an increasingly large percentage of the population is likely to experience increasingly severe adverse health effects. Different countries have their own air quality indices which are not all consistent. Different countries also use different names for their indices such as Air Quality Health Index, Air Pollution Index and Pollutant Standards Index.

Definition and Usage :

Air quality is defined as a measure of the condition of air relative to the requirements of one or more biotic species or to any human need or purpose. To compute the AQI requires an air pollutant concentration from a monitor or model. The function used to convert from air pollutant concentration to AQI varies by pollutant, and is different in different countries.  Air quality index values are divided into ranges, and each range is assigned a descriptor and a colour code. Standardized public health advisories are associated with each AQI range.

The AQI can go up (meaning worse air quality) due to a lack of dilution of air  pollutants. Stagnant air, often caused by an anticyclone, temperature inversion ,or  low wind speeds lets air pollution remain in a local area, leading to high concentrations of  pollutants and hazy conditions.  An agency might encourage members of the public to take public transportation or work from home when AQI levels are high.

Most air contaminants do not have an associated AQI. Many countries monitor ground-level ozone ,particulates ,sulphur dioxide, carbon monoxide and nitrogen dioxide and calculate air quality indices for these pollutants.

Indices by Location :

Hong Kong

The Air Pollution Index (API) levels for Hong Kong are related to the measured concentrations of ambient respirable suspended particulate (RSP), sulphur dioxide (SO2),carbon monoxide (C2), ozone (O3) and nitrogen dioxide (NO2) over a 24-hour period based on the potential health effects of air pollutants.

An API level at or below 100 means that the pollutant levels are in the satisfactory range over 24 hour period and pose no acute or immediate health effects. However, air  pollution consistently at "High" levels (API of 51 to 100) in a year may mean that the annual Hong Kong "Air Quality Objectives" for protecting long-term health effects could be violated. Therefore, chronic health effects may be observed if one is persistently exposed to an API of 51 to 100 for a long time.

"Very High" levels (API in excess of 100) means that levels of one or more pollutant(s)is/are in the unhealthy range. The Hong Kong Environmental Protection Department provides advice to the public regarding precautionary actions to take for such levels.

API	Air Pollution Index	Health Implications
0-25	Low	None expected
26-50	Medium	None expected for the general population.
51-100	High	Acute health effects are not expected but chronic effects may be observed if one is persistently exposed to such levels.
101-200	Very High	People with existing heart or respiratory illnesses may notice mild aggravation of their health conditions. Generally healthy individuals may also notice some discomfort.
201-500	Severe	People with existing heart or respiratory illnesses may experience significant aggravation of their symptoms. There may also be widespread symptoms in the healthy population(e.g. eye irritation, wheezing, coughing, phlegm and sore throats).

Canada

Air quality in Canada has been reported for many years with provincial Air Quality Indices (AQIs). Significantly, AQI values reflect air quality management objectives, which are based on the lowest achievable emissions rate, and not exclusively concern for human health. The Air Quality Health Index or (AQHI) is a scale designed to help understand the impact of air quality on health. It is a health protection tool used to make decisions to reduce short-term exposure to air pollution by adjusting activity levels during increased levels of air pollution. The Air Quality Health Index also provides advice on how to improve air quality by proposing behavioural change to reduce the environmental footprint. This index pays particular attention to people who are sensitive to air pollution. It provides them with advice on how to protect their health during air quality levels associated with low, moderate, high and very high health risks.

The Air Quality Health Index provides a number from 1 to 10+ to indicate the level of health risk associated with local air quality. On occasion, when the amount of air  pollution is abnormally high, the number may exceed 10. The AQHI provides a local air quality current value as well as a local air quality maximums forecast for today, tonight, and tomorrow, and provides associated health advice.

Health Risk	Air Quality Health Index	Health Messages
		At Risk Population	*General Population
Low	1-3	Enjoy your usual outdoor activities	Ideal air quality for outdoor activities
Moderate	4-6	Consider reducing or rescheduling strenuous activities outdoors if you are experiencing symptoms.	No need to modify your usual outdoor activities unless you experience symptoms such as coughing and throat irritation.
High	7-10	Reduce or reschedule strenuous activities outdoors. Children and the elderly should also take it easy.	Consider reducing or rescheduling strenuous activities outdoors if you experience symptoms such as coughing and throat irritation.
Very High	Above 10	Avoid strenuous activities outdoors. Children and the elderly should also avoid outdoor physical exertion.	Reduce or reschedule strenuous activities outdoors,  especially if you experience symptoms such as coughing and throat irritation.

Singapore

Singapore uses the Pollutant Standards Index to report on its air quality, with details of the calculation similar but not identical to that used in Malaysia and Hong Kong. The PSI chart below is grouped by index values and descriptors, according to the National Environment Agency.

PSI	Descriptor	General Health Effects
0-50		None
51-100	Moderate	Few or none for the general population
101-200	Unhealthy	Mild aggravation of symptoms among susceptible persons i.e. those with underlying conditions such as chronic heart or lung ailments; transient symptoms of irritation e.g. eye irritation,  sneezing or coughing in some of the healthy population.
201-300	Very Unhealthy	Moderate aggravation of symptoms and decreased tolerance in persons with heart or lung disease; more widespread symptoms of transient irritation in the healthy population.
301-400	Hazardous	Early onset of certain diseases in addition to significant aggravation of symptoms in susceptible persons; and decreased exercise tolerance in healthy persons.
Above 400	Hazardous	PSI levels above 400 may be life-threatening to ill and elderly persons. Healthy people may experience adverse symptoms that affect normal activity.

2.BODY MASS INDEX

The body mass index(BMI), or Quetelet index, is a measure for human body shape based on an individual's weight and height. It was devised between 1830 and 1850 by the Belgian polymath Adolphe Quetelet during the course of developing "social physics". Body mass index is defined as the individual's body mass divided by the square of their height. The formulae universally used in medicine produce a unit of measure of kg/m². BMI can also be determined using a BMI chart, which displays BMI as a function of weight (horizontal axis) and height (vertical axis) using contour lines for different values of BMI or colours for different BMI categories.

The factor for UK/US units is more precisely 703.06957964, but that level of precision is not meaningful for this calculation. To work from stone and pounds first multiply the stone by 14 then add the pounds to give the whole mass in pounds; to work from feet and inches first multiply the feet by 12 then add the inches to give the whole height in inches.

Usage :

While the formula previously called the Quetelet Index for BMI dates to the 19thcentury, the new term "body mass index" for the ratio and its popularity date to a paper  published in the July edition of 1972 in the Journal of Chronic Diseases by Ancel Keys, which found the BMI to be the best proxy for body fat percentage among ratios of weight and height; the interest in measuring body fat being due to obesity becoming a discernible issue in prosperous Western societies. BMI was explicitly cited by Keys as being appropriate for population studies, and inappropriate for individual diagnosis. Nevertheless, due to its simplicity, it came to be widely used for individual diagnosis, despite its inappropriateness.

BMI provided a simple numeric measure of a person's thickness or thinness, allowing health professionals to discuss overweight and underweight problems more objectively with their patients. However, BMI has become controversial because many people, including physicians, have come to rely on its apparent numerical authority for medical diagnosis, but that was never the BMI's purpose; it is meant to be used as a simple means of classifying sedentary (physically inactive) individuals, or rather, populations, with an average body composition. For these individuals, the current value settings are as follows: a BMI of 18.5 to 25 may indicate optimal weight; a BMI lower than 18.5 suggests the person is underweight while a number above 25 may indicate the person is overweight; a person may have a BMI below 18.5 due to disease; a number above 30 suggests the person is obese(over 40, morbidly obese).

For a given height, BMI is proportional to mass. However, for a given mass, BMI is inversely proportional to the square of the height. So, if all body dimensions double and mass scales naturally with the cube of the height, then BMI doubles instead of remaining the same. These results in taller people having a reported BMI that is uncharacteristically high compared to their actual body fat levels. In comparison, the Ponderal index is based on this natural scaling of mass with the third power of the height. However, many taller  people are not just "scaled up" short people, but tend to have narrower frames in proportion to their height.

BMI Prime :

BMI Prime, a simple modification of the BMI system, is the ratio of actual BMI to upper limit BMI (currently defined at BMI 25). As defined, BMI Prime is also the ratio of  body weight to upper body weight limit, calculated at BMI 25. Since it is the ratio of two separate BMI values, BMI Prime is a dimensionless number, without associated units. Individuals with BMI Prime less than 0.74 are underweight; those between 0.74 and 1.00have optimal weight; and those at 1.00 or greater are overweight. BMI Prime is useful clinically because individuals can tell, at a glance, by what percentage they deviate from their upper weight limits. For instance, a person with BMI 34 has a BMI Prime of 34/25 =1.36, and is 36% over his or her upper mass limit. In South East Asian populations (see international variation section below) BMI Prime should be calculated using an upper limit BMI of 23 in the denominator instead of 25. Nonetheless, BMI Prime allows easy comparison between populations whose upper limit BMI values differ.