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ADDITIONAL MATHEMATICS PROJECT WORK 2/2012 NAME : NUR AQILAH BINTI UDIN I/C NUMBER : 950322035230 FORM : 5 HAJAR TEACHER’S NAME : MR. WAN RAZALI

ADDMATH PW 2012

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Page 1: ADDMATH PW 2012

ADDITIONAL MATHEMATICS PROJECT WORK 2/2012

NAME : NUR AQILAH BINTI UDIN

I/C NUMBER : 950322035230

FORM : 5 HAJAR

TEACHER’S NAME : MR. WAN RAZALI

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CONTENT

TOPIC PAGE

ACKNOWLEDGEMENT………………………………………… 1

OBJECTIVES………………………………………………………… 2

INTRODUCTION…………………………………………………… 3-5

PART 1………………………………………………………………… 6-9

PART 2………………………………………………………………… 10-14

PART 3………………………………………………………………… 15-17

PART 4………………………………………………………………… 18-19

FURTHER EXPLORATION………………………………………. 20-23

CONCLUSION………………………………………………………… 24

REFLEXTION………………………………………………………… 25

REFERENCE………………………………………………………… 26

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ACKNOWLEDGEMENT

First of all, I wish to express gratitude to Allah SWT for His guidance and also giving me the strength and health to do this project work. Finally, the Additional Mathematics Project Work 2 was successfully completed with the inspiration, the gift and instructions were given by Him.

Peace and blessing be upon our Prophet Muhammad SAW and the family, next to his companions and the tabi’in , the gentlemen scholars until the servants to God who follow in their footsteps.

Not forgotten to my beloved parents who always make sure that I have been educating and nurturing of small through to this day in devotion to God Almighty. They also had providing everything such as money, to buy anything that are related to this project, their advice, which is the most needed and facilities such as Internet, books, computer and all that.

Then, infinity of appreciation goes to my teacher, Encik Wan Razali 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 always supported us to not procrastinate in doing it.

Besides that, my friends who were doing this project with me. Even, this project is individually but we were cooperated doing this project especially in discussion and sharing ideals to ensure our task finish completely.

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Last but not least, any part which involved directly or not in completing this project work. May Allah SWT give great rewards for His servants that always helpful in upholding His religion. Thank you every one.

OBJECTIVE

By finishing this task, there are a lot of benefits that were gained by myself. I hope by

this project work I will be more confident learn Additional Mathematics. A few of

objectives are :

To apply and adapt a variety of problem-solving strategies to solve problems. To improve thinking skills. To promote effective mathematical communications. To use the language of mathematics to express mathematical ideal precisely. To provide learning environment that stimulates and enhances effective learning. To adapt positive attitude towards mathematics.

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INTRODUCTION

Fire Water Tank Horizontal truck or trailer mounted water tank designed to deliver water to remote fires, where fire hydrant may not be available and a stationary tank provides standby water to fight the same type of remote fires. Throughout history, wood, ceramic and stone have been used as water tanks. These were all naturally occurring and manmade and some tanks are still in service. The Indus Valley Civilization (3000–1500 BC) made use of granaries and water tanks.[1] Medieval castles needed water tanks for the defenders to withstand a siege.[2] A wooden water tank found at the Año Nuevo State Reserve (California) was restored to functionality after being found completely overgrown with ivy. It had been built in 1884.[3]

Chemical contact tank of FDA and NSF polyethylene construction, allows for retention time for chemical treatment chemicals to "contact" ( chemically treat ) with product water. (black tank in foreground)Various materials are used for making a water

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tank: plastics (polyethylene, polypropylene), fiberglass, concrete, stone, steel (welded or bolted, carbon, or stainless), Earthen ponds function as water storage.

Ground water tank is made of lined carbon steel, it may receive water from a water well or from surface water allowing a large volume of water to be placed in inventory and used during peak demand cycles.

Elevated Water Tank is also known as a water tower, an elevated water tower will create pressure at the ground-level outlet of 1 psi per 2.31 feet of elevation, thus a tank elevated to 70 feet creates about 30 psi of discharge pressure. 30 psi is sufficient for most domestic and industrial requirements. (background legs shown)

Vertical cylindrical dome top tank may hold from fifty gallons to several million gallons. Horizontal cylindrical tank are typically used for transport; this low-profile transport storage creates a low center of gravity helping to maintain equilibrium for the transport vehicle, trailer or truck.

Hydro-pneumatic tank is typically a horizontal pressurized storage tank. Pressurizing this reservoir of water creates a surge free delivery of stored water into the distribution system.

Custom configurations include rectangular, cube shaped, cone bottom and special shapes for specific design requirements. By design a water tank/container should do no harm to the water. Water is susceptible to a number of ambient negative influences, including bacteria, viruses, algae, changes in pH, and accumulation of minerals, accumulated gas. A correctly designed water tank works to address and mitigate these negative effects.

Copper Poisoning: a falsely based news article, linked copper poisoning a plastic tank, the article indicated that rainwater was collected and stored in a plastic tank and that the tank did nothing to mitigate the low Ph. The water was then brought into homes with copper piping; the copper was released by the high acid rainwater and caused poisoning in humans. It is important to note that while the plastic tank is an inert container, it has no effect on the incoming water. Good practice would be to analyze any water source periodically and treat accordingly, in this case the collected acid rain should be analyzed, and ph adjusted before being brought into a domestic water supply system.

The release of copper due to acidic water is monitored may be accomplished with a variety of technology, beginning with Ph strips and going to more sophisticated Ph monitors, indicate Ph which when acidic or caustic, some with output communication capabilities. There is no "linkage" between the plastic tank and copper poisoning, a solution to the problem is easy, monitor 'stored rainwater' with 'swimming pool strips' cheap and available at, swimming pool supply outlets. If the water is too acidic, contact state/county/local health officials to obtain advice and precise solutions and ph limits

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and guidelines as to what should be used to treat rainwater to be used as domestic drinking water...

This a good point to discuss contamination of water supplies from a variety of origins, piping, tank materials of construction, animal and bird feces, mineral and gas intrusion, all and others to be considered and integrated into design.

Tank Volume in US Gallons Volumes of simple tank geometry may be calculated as follows. Beginning with the fact that a cubic foot contains 7.48 gallons. A cube or rectangle is calculated at (length) times (width) times (height) == (cubic feet) times (7.48)== gallons.

For a cylinder volume is calculated at Pi (3.14) times (radius squared) times (height) == (cubic feet) times(7.48)== gallons.

Articles and specifications for Water Tank applications and design considerations, these AWWA details are required in many states to complete a certification process to insure the quality of water being consumed.

American Water Works Association The AWWA is a reservoir of water tank knowledge; the association provides specifications for a variety of water storage tank applications as well as design. The AWWA's site provides scientific resources with which the reader will be able to develop an informed perspective on which to make decisions regarding their water tank requirements

The various type of water tanks in other country is shown below :

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Part one

TASK 1 :

The problem of sufficient water supply has become a main issue among the countries around the world. Proper planning is very important to make sure the water supply is sufficient. Carry out a simple study to solve the problem. You are suggested to use

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various resources such as Internet, printed materials, ground study and others. Discuss on how additional mathematics can be used to solve the problem.

SOLUTION :

For this project work I had conduct an investigation to study the water supply problem in Bachok. The amounts of the respondents are 1000 people. By doing this experiment, I had found a various problems had faced by the villagers. Their problems had been tabulated in the table below.

Type of problem Percentage (%)

Small size of water tank 45

Slow rate of water to transfer

23

Cloudy water colour 32

I had used the knowledge of basic additional mathematics information to solve one of the problems, which is small size of water tank.

Aim : To investigate the minimum surface area required to build 50m3.

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Method : Differentiation.

Assuming that the shape of water tank to be built is a cuboid with a base dimension of ( e × e ) m2 and the height, h as shown in the diagram below and the volume of the tank is 50m3. Find the minimum surface area needed to build the given tank.

h

e

ee× e× h=50

e2 h=50

Area=4 eh+2 e2

¿4 e50

e2+2 e2

¿ 200e

+2e2

¿200 e−1+2 e2

dAde

=0

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dAde

=−200 e−2+4 e

−200 e−2+4 e=0

200 e−2=4e

200

e2=4 e

50=e3

e=3√50

e=3.68403m

So that,

Area= 2003.684

+2(3.684)2

¿81.4325 m2

The height of water tank can be calculated by using the formula of volume.

volume=area× height

height= volumearea

¿ 5081.4325

¿0.614 m

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TASK 2 :

You are assigned as an engineer of a construction firm. You are responsible to build an enclosed water tank for housing estate which consists of 60 houses. The rate of water entering every house is different and the rates are 1000 cm3min-1 for the first house, 990 cm3min-1 for the second house, 980 cm3min-1 for the third house and so on.

By using at least 3 different methods, calculate the total volume of water used by all the houses in 1 minute, if all the houses in the housing estate are using the water at the same time.

SOLUTION :

METHOD 1

By using Arithmetic Progression,

1000, 990, 980, ………

n=60 , a=1000 , d=10

T n=a+ (n−1 ) d

T 60=1000+(60−1)(−10)

¿410 cm3 min−1

Sn=n2

(2 a+(n−1 ) d )

Sn=n2(a+(a+ (n−1 ) d ))

S60=602

(1000+410)

¿42300 cm3 min−1

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METHOD 2 By using Microsoft Excell.

a d Tn n Sn1000 -10 1000 1 10001000 -10 990 2 19901000 -10 980 3 29701000 -10 970 4 39401000 -10 960 5 49001000 -10 950 6 58501000 -10 940 7 67901000 -10 930 8 77201000 -10 920 9 86401000 -10 910 10 95501000 -10 900 11 104501000 -10 890 12 113401000 -10 880 13 122201000 -10 870 14 130901000 -10 860 15 139501000 -10 850 16 148001000 -10 840 17 156401000 -10 830 18 164701000 -10 820 19 172901000 -10 810 20 181001000 -10 800 21 189001000 -10 790 22 196901000 -10 780 23 204701000 -10 770 24 212401000 -10 760 25 220001000 -10 750 26 227501000 -10 740 27 234901000 -10 730 28 242201000 -10 720 29 249401000 -10 710 30 256501000 -10 700 31 263501000 -10 690 32 270401000 -10 680 33 277201000 -10 670 34 283901000 -10 660 35 29050

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1000 -10 650 36 297001000 -10 640 37 303401000 -10 630 38 309701000 -10 620 39 315901000 -10 610 40 322001000 -10 600 41 328001000 -10 590 42 333901000 -10 580 43 339701000 -10 570 44 345401000 -10 560 45 351001000 -10 550 46 356501000 -10 540 47 361901000 -10 530 48 367201000 -10 520 49 372401000 -10 510 50 377501000 -10 500 51 382501000 -10 490 52 387401000 -10 480 53 392201000 -10 470 54 396901000 -10 460 55 401501000 -10 450 56 406001000 -10 440 57 410401000 -10 430 58 414701000 -10 420 59 418901000 -10 410 60 42300

METHOD 3

By using the graph in computer application.

First, enter the detail in table by using Microsoft Excel.

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Then, convert the information in table to the graph.

Find the value ofSn, when n=60

6

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TASK 3 :

h

p

p

DIAGRAM 1

Assuming that the shape of the tank to be built is a cuboid with a base dimension of ( p × p ) m2 and height, h m as shown in the diagram 1 and the volume of the tank is 50m3, find the minimum surface area needed to build the given tank.

SOLUTION :

Because of the minimum construction cost, the surface area of tank should be minimum.

p × p ×h=50

p2 h=50

Method used is differentiation.

Area=4 ph+2 p2

¿4 p50

p2+2 p2

¿ 200p

+2 p2

¿200 p−1+2 p2

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dAdp

=0

dAdp

=−200 p−2+4 p

−200 p−2+4 p=0

200 p−2=4 p

200

p2=4 p

50=p3

p= 3√50

p=3.68403 m

So that,

Area= 2003.684

+2(3.684)2

¿81.4325

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TASK 4 :

If the number of houses in the housing estate increases in the future, what is the maximum number of houses that can be build so that the supply of water from thank can fulfils the demand of the residents.

SOLUTION :

Sn=n2

(2a+(n−1 ) d )

a=1000 , d=−10

Sn=n2(2 (1000 )+(n−1 ) (−10 ))

Sn=1000 n−5 n2+5n

Sn=1005 n−5 n2

dSn

dn=1005−10 n=0

Then,

n=100.5 , n=100

Or

Sn=5000 cm3

Sn=n2

(2 a+(n−1 ) d )

a=1000 , d=−10

5000=n2(2 (1000 )+(n−1 ) (−10 ))

10000=2000 n+10 n2−10 n

10 n2−1990 n−10000=0

n=203.90 , n=−4.904( ignore)

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So that,

The maximum number of houses that can be built = 203 houses.

FURTHER EXPLORATION

Advanced NASA Technology Supports Water Purification Efforts Worldwide

Whether in the confines of the International Space Station or a tiny hut village in sub-Saharan Africa, drinkable water is vital for human survival. Unfortunately, many people around the world lack access to clean water. Using technology developed for the space station, at-risk areas can now gain access to advanced water filtration and purification systems, making a life-saving difference in these communities.

The nonprofit organization Concern for Kids, or CFK, in Nye, Mont., has provided aid and disaster relief to countries such as Malaysia, Iraq and Indonesia since 1992. Among other services, the group raises funds to install water delivery systems and water storage tanks in at-risk regions.

Years later, CFK representatives learned about a deep-water well failure in the tiny Kurdish village of Kendala, Iraq, which left its residents without access to drinkable water. The population quickly dwindled from 1,000 residents to a mere 150. Those remaining were forced to use a nearby creek that contained water contaminated by livestock, which they sifted through fabric to remove dirt and debris.

Todd Harrison was president of CFK's board of directors at the time and strongly empathized with the people of Kendala. He set out on a mission to revive this ailing community by improving the deplorable conditions. The solution came in the form of a familial connection that put Harrison in touch with NASA engineers who developed technology to provide clean water aboard the space station.

Harrison's sister, Robyn Carrasquillo, was the engineering manager for the Environmental Control and Life Support System, or ECLSS, project at NASA's Marshall Space Flight Center. She and her team of engineers were responsible for developing the cutting-edge water purification system that recycles air and water aboard the station.

By efficiently recycling wastewater aboard the space station, there is a reduced need to provide the resource via resupply -- which would not be an option for long-duration

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space travel. Without this capability, the station’s current logistics resupply capacity would not be able to support the standard population of six crew members. "In a year, the water saved by recycling exceeded the initial launch weight and weight of replacement parts due to some initial issues," commented Carrasquillo. Two principal components make up the International Space Station Regenerative ECLSS: The Water Recovery System, or WRS, and the Oxygen Generation System, or OGS. The WRS conducts the water purification and filtration process in the ECLSS. Commercial companies took an interest in this part of the ECLSS project, as they sought to adapt it to an Earth-based water treatment system.

Harrison discovered an interesting relationship between CFK's water filtration system and NASA because of his familiarity with his sister's work. NASA’s previous research and application provided the Microbial Check Valve, or MCV, an integral component of the purification and filtration process.

Originally developed for the Space Shuttle Program by Umpqua Research Corporation, the MCV was later sold to WSC. The MCV is an iodinated-resin that provides a simple way to control microbial growth in water without the use of power. By dispensing iodine into the water, it performs an important secondary nutritional function for the populace. This chemical, when added to the diet, promotes proper brain functions and maintains bodily hormone levels -- which regulate cell development and growth. Children who lack iodine in their diets exhibit growth mental retardation.

With the help of U.S. Army Civil Affairs and Psychological Operations Command (Airborne) personnel, a 2,000-liter water tank and fresh water were brought to the Kurdish village. Workers ensured that the water was clean and iodinated to prevent bacteria and virus contamination. Carrasquillo recalls the installation efforts and associated challenges. "[CFK] encountered some technical issues that our group helped with by phone. The MCV had dried out during transit and we were able to do an assessment and reassure them it should be okay. In addition, the pumps that were available in the local village were oversized for the filtration system."

Carrasquillo's team strategized and implemented a bypass that allowed workers to use the available pump and start the system immediately. This workaround enabled the successful processing of Kendala's water supply.

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The International Space Station water recovery component of the Environmental Control and Life Support System. (NASA)

Volunteers help install and test a water purification system in Kendala, Iraq. (Concern for Kids)

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NASA Tank Station

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CONCLUSION

Water tank is the most important element in reticulation system. It play the important

role in making sure that the enough water supply for the residents in every moment. By

doing this beneficial project work, I can use the basic information in Additional

Mathematics like Arithmetic Progression and Differentiation to solve the problems that

faced by the residents at my country. I’m feel that useful to the residents in making the

problem solving.

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REFLEXTION

For this section, I want to DECLAIRE my own FEELING:)

1st time I got the task I don’t know how to make it. But after my teacher taught me all these, I know how to solve it. For me NEVER GIVE UP to find the SOLUTION.

Next day, I ponder myself and thinks the way.....a lot of action I take; REFER TO THE BOOK, SEARCH IN INTERNET, ASK TEACHER and so on.

Finally, i got the solution....

A big THANK I give to all people which are helping me during completing the task.

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s

REFERENCE

1. Web sites :

a. http://www.efka.utm.my/thesis/images/3PSM/2005/1JSB/Part4/

MAZLIANACA020024D05TTP.pdf

b. http://www.nasa.gov/station

2. Education Book

a. Matematik Tambahan Tingkatan 4 & 5

Khoo Cheng, Moy Wah Goon, Tey Kim Soon, Wong Teck Sing

Terbitan Pelangi Sdn. Bhd. 1996 Edisi ke-2

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Part two

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Part three

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Part four