99093402 Additional Mathematics Project Work 2012 Sabah

7/28/2019 99093402 Additional Mathematics Project Work 2012 Sabah

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Additional Mathematics Project Work 2012 1 | P a g e

CONTENT PAGE

No. Content Page

1. Content Page 1

2. Objectives 2

3. Acknowledgement 3

4. Part 1

Part 1 (a) 4 Part 1 (b) 5

5. Part 2

Part 2 (a) 6-7 Part 2 (b)(i) 8 Part 2 (b)(ii) 8 Part 2 (b)(iii) 9 Part 2 (c)(i) 9 Part 2 (c)(ii) 9 Part 2 (c)(iii) 9-10

6. Part 3

Part 3 (a)(i) 11 Part 3 (a)(ii) 11 Part 3 (b)(i) 12 Part 3 (b)(ii) 12 Part 3 (b)(iii) 12-13 Part 3 (b)(iv) 14 Part 3 (c) 15-16

7. Further Exploration 17-18

8. Reflection 19


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OBJECTIVES

The aims of carrying out this project work are:

i. To apply and adapt a variety of problem-solving strategies to solve problems.ii. To improve thinking skills.

iii. To promote effective mathematical communication.iv. To develop mathematical knowledge through problem-solving in a way that increases

students interest and confidence.

v. To develop positive attitude towards mathematics.


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ACKNOWLEDGEMENT

First and foremost, I would like to thank Allah that I have finally succeeded in finishingthis project work. I would like to thank my beloved Additional Mathematics teacher, Pn. Suriati

Bohari, for all the guidance she had provided me during the process in finishing this project

work. I also appreciate her patience in guiding me completing this project work. I would like to

give a thousand thanks to my parents for giving me their full support, financially and mentally.

They gave me moral support when I needed it. Who am I without their love and support? I would

also like to give my thanks to my fellow friends who had helped me in finding the information

that I am clueless, and the time we spent together in study group on finishing this project work.

Last but not least, I would like to express my highest gratitude to all those who gave me the

possibility to complete this coursework. I really appreciate all the help I got.

Again, thank you very much.


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Part 1

a)

Types of Drinks Manufacture by

NESTLE Milo NCM FoodMARIGOLD Grape Drinks Fabriqu

Ribena Ms Foods

Dutch Lady Hydrox Innovation SDN.BHD

Susu Segar Desa Cattle SDN.BHD

b)

Price: RM 1.20

Location: Giant Supermarket

Price: RM 1.00

Location: Giant Supermarket

Price: RM 0.90

Location: Servey Supermarket
http://4.bp.blogspot.com/-8w4s16BFgZI/T93NmZ4JaAI/AAAAAAAAAM0/x3g-Ue1HIEI/s1600/images+(8).jpghttp://4.bp.blogspot.com/-8w4s16BFgZI/T93NmZ4JaAI/AAAAAAAAAM0/x3g-Ue1HIEI/s1600/images+(8).jpghttp://4.bp.blogspot.com/-8w4s16BFgZI/T93NmZ4JaAI/AAAAAAAAAM0/x3g-Ue1HIEI/s1600/images+(8).jpg


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Price: RM 1.50

Location: Tai Yang Supermarket

Price: RM 2.50

Location: Asia Super Store
http://1.bp.blogspot.com/-5SQJix2ZTUs/T93I8X82fKI/AAAAAAAAAMY/0a302MGwO44/s1600/images+(11).jpghttp://1.bp.blogspot.com/-5SQJix2ZTUs/T93I8X82fKI/AAAAAAAAAMY/0a302MGwO44/s1600/images+(11).jpg


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Part 2 (a)

No. Types of drinks

StudentsName

NESTLEMilo

MARIGOLDGrape

Drinks

Ribena DutchLady

Susu Segar

1 Faizal Mustafa 2 Farmizi Abd Muluk 3 Mohd Arief Salim 4 Mohd Najhan Rani 5 Firdaus 6 Ryan Izzairy 7 Erfan Sudirman 8 Mohd Nur Alif Arman 9 Ihsan Ismail

10 Perima Pawawoi 11 Frederick Romzy 12 Bensan Alex 13 Mohd Razeef

Muhammad

14 Sahrudin Saul 15 Safar Moktar 16 Ihsyam

17 Rogan Awing 18 Surianti Abd Wahab 19 Nurazila John

20 Nurul FadilawatyAziah

21 Nurul Asikin Amirul 22 Nur Zulaika Sidek 23 Nur Fazirah Karim 24 Nurul Hanisah

Halbani

25 Asnita Mapasisi 26 Sharmiza Adlina

Junaidi

27 Nohazirah Basri 28 Pazilawaty Putara 29 Noor Salina Mustapa 30 Santi 31 Nur Shafina 32 Nurul Ammarah 33 Noor Majidah 34 Dorfiana John


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35 Cecilia Regina Matius 36 Nurul Asyira Harezam 37 Haslina 38 Norasafasina Chuli 39 Nur Faezah

40 Flisilin Martin 41 Munirah Musli 42 Jumaini Jamal 43 Nadeera Nasir 44 Siti Zainab Seman 45 Rossahira Natasya 46 Zaniah Alwani 47 Siti Aisyah Eindrad

48 Nurul Hikmah Syakira

M. Abu

49 Armawaty Saing 50 Kamarul Ruslan


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b)

i. Frequency Table

Types of Drinks Number of Students

NESTLE Milo 18MARIGOLD Grape Drinks 9

Ribena 10

Dutch Lady 10

Susu Segar 3

ii. Charts and Graphs

0

2

4

6

8

10

12

14

16

18

20

NESTLE

Milo

MARIGOLD

Grape

Drinks

Ribena Dutch Lady susu segar

Number of Students

Number of Students

0

2

46

8

10

12

14

16

18

20

NESTLE Milo MARIGOLD

Grape

Drinks

Ribena Dutch Lady susu segar

Number of Students

Number of Students


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iii. Based on the following chart, we know that NESTLE Milo has the highest frequency.

Meanwhile, Ribena has the lowest frequency compared five types of drinks that have been

listed.

c) i.

Types of Drinks Sugar Content (g)

NESTLE Milo 7 g

MARIGOLD Grape Drinks 11.0 g

Dutch Lady 18.5 g

Ribena 6 g

Susu Segar 23 g

ii. Mean: 23+19+7+11+6 = 66

= 66/5= 13.2

Standard Deviation: = - (174.24)=12.20

iii) Tooth Decay: All soft drinks are acidic which corrodes the teeth by eroding its enamel.

The high amount of sugar consumed through soft drinks lead to the development of

bacteria that attack the teeth thus aggravating dental problems. People who drink three or

more glasses of aerated drinks (gaseous drinks) daily have much higher chances of dentaldecay, fillings and teeth loss. Therefore, soft drinks contain acid and sugar that corrode and

destroy the teeth in one shot.

Obesity: Soft drinks are mainly composed of filtered H2O, artificial additives and refinedsugar. Thus, they lack nutritional value and only add up calories through their refined

sugar; therefore, they make you gain weight. But is shifting to "Diet Soft Drink" the

solution? The fact is that diet soft drinks contain aspartame (an artificial low-caloriesweetener). Although aspartame does not add up the calories it makes you feel hungrier

and crave for food. The Food and Drug Administration (FDA) no longer allows foods

containing aspartame to be labeled as "weight reduction product ". Now it insists to labelthese products simply as "Diet Drink" or "Diet Food ". Research also shows that aspartame

causes migraines, dizziness and more over it reduces your memory. It has been

experimentally proved that soft drinks are one of the prominent reasons for obesity. Theweight gain is directly related to the amount of soft drink that a person takes in. With everysingle can, people unknowingly add many extra calories to their body weight.

* Another very common effect of soft drinks is diabetes. With every can of soft drink, people

add large amount of sugar in their body. Long habitual intake of soft drinks can lead toineffective insulin production from pancreases which consequently affect the sugar level in the

body. This further leads to diabetes.


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Additional Mathematics Project Work 2012 10 |

P a g e

* It has been proved that frequent consumption of soft drink can lead to weakening of the bones

and osteoporosis. Soft drinks impair the calcification of the growing bones in children.

* Studies also say that soft drinks increase the risk of tooth decay. The acidic content of soft

drinks can dissolve the tooth enamel and make them weaker. It is recommended that people

should avoid taking soft drinks between meals to prevent dental erosion and tooth decay.

* This fact may shock you, but is quite true. Researchers have proved that constant and habitual

intake of soft drink can lead to kidney stones formation. This happens because of the acidic and

mineral radical balance. The body tries to buffer the acidity caused by the soft drinks with thecalcium from the bones. This leads to calcium erosion, which ultimately gets settled in the

kidney in the form of stones.

* Soft drink also leads to impaired digestive system. Soft drink contains phosphoric acid whichcompetes with the hydrochloric acid present in stomach and affects its functioning. The

ineffectiveness of stomach leads to undigested food which further causes indigestion and

gassiness.

* Soft drinks cause dehydration in the body. Both the sugar and caffeine components of soft

drinks are dehydrating agents. They both lead to excess urination, which makes you thirstier than

before.

* Soft drinks have strong caffeine content. Caffeine causes irritability, restlessness, tension, high

blood pressure, excessive urination and other side effects. It is also believed that soft drinksincrease blood pressure. Some studies also claim that soft drink has harmful effects on liver.

* The sweetener used in soft drinks is Aspartame. It is 200 times sweeter than normal sugar and

is far more harmful with many side effects.

Next time, when head towards the refrigerator or a store to satiate your thirst with a can of soft

drink, make sure you remind yourself of all the side effects that gulping down the beverage will

bring forth.


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P a g e

Part 3

a) i.

Length (cm) Width(cm) Height(cm)

Amount Packaging

Material Used (cm)

4 6 10.399980 255.999600

4 6 10.399990 255.999800

4 6 10.399995 255.999900

4 6 10.399911 255.998220

4 6 10.416667 256.333340

4 6 10.416669 256.333380

4 6 10.416711 256.334220

4 6 10.417100 256.342000

4 6 10.418967 256.3793444 6 10.418950 256.379000

ii.

Length, L (cm) Width, W (cm) Height, H (cm)

Total Surface

Area (or

Amount of

Packaging

Material Used),

A (cm2)

Volume of

Cuboid, V (cm3)

4 6 10.416667 256.333340 250.000008

4 6 10 256 250


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P a g e

b) i. In mathematics and the arts, two quantities are in the golden ratio () if the ratio of thesum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the

smaller one. The figure on the right illustrates the geometric relationship. Expressedalgebraically:

where the Greek letterphi( ) represents the golden ratio. Its value is:

ii.

iii.

Width, x

(cm)Length, 1.6x (cm) Height, h (cm)

Total Surface Area ,

A (cm2)

Volume of Cuboid, V

(cm3)

5 8 6.250000 242.500000 250.000000

Width,x (cm) Length, 1.6x (cm) Height,h (cm) Total surface area,A

(cm2)

1 1.6 156.250000 815.700000

2 3.2 39.062500 419.050000

3 4.8 17.361111 299.633332

4 6.4 9.765625 254.325000

5 8 6.250000 242.500000

6 9.6 4.340278 250.616674

7 11.2 3.188776 272.871446

8 12.8 2.441406 306.362490

9 14.4 1.929012 349.477762

10 16 1.562500 401.250000
http://en.wikipedia.org/wiki/Phi_(letter)http://en.wikipedia.org/wiki/Phi_(letter)http://en.wikipedia.org/wiki/Phi_(letter)http://en.wikipedia.org/wiki/Phi_(letter)


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P a g e

Calculation using differentiation, V = 250 cm3

1.6xh = 250

h = 250/1.6xA = 2[1.6x + 1.6xh+xh]

= 2[1.6x + 2.6xh]

= 2[1.6x + 2.6x (250/1.6x)]= 3.2x + 812.5/x

Dy/dx = 6.4x812.5x0 = 6.4x812.5/x0 = 6.4x - 812.5

x = 812.5/6.4

x = 5.03 cm (from tabulation table above, x = 5 cm)

1.6x = 8.0 cmH=250/1.6(5.)

= 6.25 cm

Length = 8.0cm; Width = 5.0cm; and Height = 6.25cm


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P a g e


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P a g e

c)

h = 6.25 cm=1/3 x 6.25x

= 250

x = 10.954 cm

= 6.25+(10.954/2)= 8.3102

Total surface area

= (10.954 x 8.3102) x 4 + 10.954

= 301.99cm

h = 6.25 cm

= 1/3 r x 6.25= 250r =6.18 cm

= 6.25 + (6.18/2) = 6.972

Total surface area

= rl +r= (6.18)(6.972) + (6.18)= 255.3466cm
http://2.bp.blogspot.com/-AhIX508_jzg/T93NvIxhqQI/AAAAAAAAANM/dn1WlWoqU_E/s1600/j.jpghttp://3.bp.blogspot.com/-9lCt9QRT0UY/T93Ns3OCCYI/AAAAAAAAANE/MPMsnftCAWY/s1600/kk.jpghttp://2.bp.blogspot.com/-AhIX508_jzg/T93NvIxhqQI/AAAAAAAAANM/dn1WlWoqU_E/s1600/j.jpghttp://3.bp.blogspot.com/-9lCt9QRT0UY/T93Ns3OCCYI/AAAAAAAAANE/MPMsnftCAWY/s1600/kk.jpg


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P a g e

h = 6.25 cm= r x 6.25= 250

r = 3.568

Total surface area

= 2(3.568) + 2(3.568)(6.25)= 220.1cm
https://encrypted-tbn1.google.com/images?q=tbn:ANd9GcR4ZM6As1ihaJpPv889yQRZpvfvW-UvEZyZBtwiSc3vSpz5EVgzqpbX2mdY


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P a g e

FURTHER EXPLORATION

a)

Shape s of packaging Pro(s) Con(s)

Pyramid

-the stability of the drinkpackaging will be more stable

because the base area larger

-the shape of the drinkpackaging become more

unique because its rarelyfound in the market.

-the cost of packagingmaterial will be higher

because more total surface

area required.

Cone

-the stability of the drinkpackaging will be more stable

because the base area larger

-the shape of the drink

packaging become moreunique because its rarelyfound in the market.

-hard to put the straw into it

-the cost of packaging

material will be higher

because more total surfacearea required.

Cylinder-easy to bring it anywhere

-the quantity of water is morethan usual-can be recycle

-the cost is more expensive

-are not stable


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P a g e

PACKAGING MATERIAL

One of the packaging material uses is plastic. Plastic is easily to use but hard to dispose. It is

light, strong, easy to produce and cheaper. It mostly uses in big bottles drinks.


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P a g e

REFLECTION

In the making of this project, I have spent countless hour doing this project. I

realized that is subject is a compulsory to me. Without it, I cant fulfill my bigdreams and wishes

I used to hateAdditional MathematicsIt always makes me wonder why this subject is so difficultI always tried to love every part ofitIt always an absolute obstacle for meThroughout day and nightI sacrificedmy precious time to have funFrom

Monday, Tuesday, Wednesday, Thursday, FridayAnd even the weekend that I always looking forward to

Additional Mathematics.

From now on, I will do my best on every second that I will learn Additional

Mathematics.

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99093402 Additional Mathematics Project Work 2012 Sabah

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