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 student’s 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 finishing this 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 Food

MARIGOLD Grape Drinks Fabriqué

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

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Location: Servey Supermarket

Price: RM 1.50

Location: Tai Yang Supermarket

Price: RM 2.50

Location: Asia Super Store

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Part 2 (a)

No. Types of drinks

Student’sName

NESTLE Milo

MARIGOLD Grape Drinks

Ribena Dutch Lady

Susu Segar

1 Faizal Mustafa C̸2 Farmizi Abd Muluk C̸3 Mohd Arief Salim C̸4 Mohd Najhan Rani C̸5 Firdaus C̸6 Ryan Izzairy C̸7 Erfan Sudirman C̸8 Mohd Nur Alif Arman C̸9 Ihsan Ismail C̸10 Perima Pawawoi C̸11 Frederick Romzy C̸12 Bensan Alex C̸13 Mohd Razeef

MuhammadC̸

14 Sahrudin Saul C̸ C̸15 Safar Moktar C̸16 Ihsyam17 Rogan Awing C̸18 Surianti Abd Wahab C̸19 Nurazila John C̸20 Nurul Fadilawaty

AziahC̸

21 Nurul Asikin Amirul C̸22 Nur Zulaika Sidek C̸23 Nur Fazirah Karim C̸24 Nurul Hanisah

HalbaniC̸

25 Asnita Mapasisi C̸26 Sharmiza Adlina

JunaidiC̸

27 Nohazirah Basri C̸28 Pazilawaty Putara C̸29 Noor Salina Mustapa C̸30 Santi C̸31 Nur Shafina C̸32 Nurul Ammarah C̸33 Noor Majidah C̸34 Dorfiana John C̸

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35 Cecilia Regina Matius C̸36 Nurul Asyira Harezam C̸37 Haslina C̸38 Norasafasina Chuli C̸39 Nur Faezah C̸40 Flisilin Martin C̸41 Munirah Musli C̸42 Jumaini Jamal C̸43 Nadeera Nasir C̸44 Siti Zainab Seman C̸45 Rossahira Natasya C̸46 Zaniah Alwani C̸47 Siti Aisyah Eindrad48 Nurul Hikmah Syakira

M. AbuC̸

49 Armawaty Saing C̸50 Kamarul Ruslan C̸

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b)i. Frequency Table

Types of Drinks Number of Students

NESTLE Milo 18MARIGOLD Grape Drinks 9

Ribena 10Dutch Lady 10Susu Segar 3

ii. Charts and Graphs

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NESTLE Milo

MARIGOLD Grape Drinks

Ribena Dutch Lady susu segar02468

101214161820

Number of Students

Number of Students

NESTLE Milo MARIGOLD Grape Drinks

Ribena Dutch Lady susu segar02468

101214161820

Number of Students

Number of Students

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: σ = - (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 dental decay, 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 refined sugar. 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-calorie sweetener). 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 label these 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. The weight gain is directly related to the amount of soft drink that a person takes in. With every single can, people unknowingly add many extra calories to their body weight.

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* 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 to ineffective insulin production from pancreases which consequently affect the sugar level in the body. This further leads to diabetes.* 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 the calcium 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 which competes 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 drinks increase 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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Part 3

a) i.

Length (cm) Width(cm) Height(cm)Amount Packaging Material Used (cm)

4 6 10.399980 255.9996004 6 10.399990 255.9998004 6 10.399995 255.9999004 6 10.399911 255.9982204 6 10.416667 256.3333404 6 10.416669 256.3333804 6 10.416711 256.3342204 6 10.417100 256.3420004 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 250.0000084 6 10 256 250

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b) i. In mathematics and the arts, two quantities are in the golden ratio (φ) if the ratio of the sum 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. Expressed algebraically:

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

Width,x (cm) Length, 1.6x

(cm)

Height,h (cm) Total surface

area,A (cm2)1 1.6 156.250000 815.7000002 3.2 39.062500 419.0500003 4.8 17.361111 299.6333324 6.4 9.765625 254.3250005 8 6.250000 242.5000006 9.6 4.340278 250.6166747 11.2 3.188776 272.8714468 12.8 2.441406 306.3624909 14.4 1.929012 349.47776210 16 1.562500 401.250000

ii.

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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

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Calculation using differentiation, V = 250 cm31.6x²h = 250 h = 250/1.6x² A = 2[1.6x² + 1.6xh+xh]  = 2[1.6x² + 2.6xh]  = 2[1.6x² + 2.6x (250/1.6x²)]  = 3.2x² + 812.5/x

Dy/dx = 6.4x – 812.5xˉ² 0 = 6.4x – 812.5/x² 0 = 6.4x³ - 812.5 x³ = 812.5/6.4 x = 5.03 cm (from tabulation table above, x = 5 cm) 1.6x = 8.0 cm H=250/1.6(5.)²  = 6.25 cmLength = 8.0cm; Width = 5.0cm; and Height = 6.25cm

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c)

h = 6.25 cm =1/3 x 6.25x² = 250x = 10.954 cm

= √6.25²+(10.954/2)² = 8.3102

Total surface area = ½(10.954 x 8.3102) x 4 + 10.954²= 301.99cm²

h = 6.25 cm = 1/3 Π r² x 6.25= 250r =6.18 cm = √6.25² + (6.18/2) ² = 6.972

Total surface area= Πrl + Πr²= Π(6.18)(6.972) + Π(6.18)²= 255.3466cm²

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h = 6.25 cm = Πr² x 6.25 = 250 r = 3.568

Total surface area= 2Π(3.568)² + 2Π(3.568)(6.25)= 220.1cm²

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FURTHER EXPLORATION

a)

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

Pyramid-the stability of the drink packaging will be more stable because the base area larger

-the shape of the drink packaging become more unique because it’s rarely found in the market.

-the cost of packaging material will be higher because more total surface area required.

Cone-the stability of the drink packaging will be more stable because the base area larger-the shape of the drink packaging become more unique because it’s rarely found in the market.

-hard to put the straw into it

-the cost of packaging material will be higher because more total surface area required.

Cylinder-easy to bring it anywhere-the quantity of water is more than usual-can be recycle

-the cost is more expensive-are not stable

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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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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 can’t fulfill my big dreams and wishes…

I used to hate Additional Mathematics…It always makes me wonder why this subject is so difficult…I always tried to love every part of it…It always an absolute obstacle for me…Throughout day and night…I sacrificed my precious time to have fun…From…Monday, Tuesday, Wednesday, Thursday, Friday…And 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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