93639430 additional mathematics project work 2012

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ADDITIONAL MATHEMATICS

PROJECT WORK 1/2012

Name : Aiman Nurrasyid

I/C No : 950812-14-5047

Class : 5K4

Teacher s Name : Puan Nadia

School : Permatapintar High School


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CONTENTAcknowledgement

Objectives

Introduction

Part 1

Part 2

Part 3

Further Exploration

Conclusion

Reflection


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ACKNOWLEDGEMENTFirst of all, I would like to say thank you, for giving me the

strength to do this project work.

Not forgotten my parents for providing everything, such asmoney, to buy anything that are related to this project work andtheir advise, support which are the most needed for this project.Internet, books, computers and all that. They also supported meand encouraged me to complete this task so that I will notprocrastinate in doing it.

Then I would like to thank my teacher, Puan Nadia forguiding me and my friends throughout this project. We had somedifficulties in doing this task, but she taught us patiently until weknew what to do. She tried and tried to teach us until weunderstand what we supposed to do with the project work. Last butnot least, my friends who were doing this project with me and

sharing our ideas. They were helpful that when we combined anddiscussed together, we had this task done.


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OBJECTIVESThe aims of carrying out this project work are:

to apply and adapt a variety of problem-solving strategies tosolve problems.

to improve thinking skills.

to promote effective mathematical communication.

to develop mathematical knowledge through problem solvingin a way that increases students interest and confidence.

to use the language of mathematics to express mathematicalideas precisely.

to provide learning environment that stimulates and enhanceseffective learning.

to develop positive attitude towards mathematics.


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INTRODUCTIONIn geometry a polygon ( /p l n/) is a flat shape consisting of straight lines

that are joined to form a closed chain or circuit .A polygon is traditionally a plane figure that is bounded by a closed path,composed of a finite sequence of straight line segments (i.e., by a closedpolygonal chain) . These segments are called its edges or sides , and thepoints where two edges meet are the polygon's vertices (singular: vertex) orcorners . An n -gon is a polygon with n sides. The interior of the polygon issometimes called its body . A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.

The word "polygon" derives from the Greek ( pols ) "much","many" and ( gna ) "corner" or "angle". (The word gnu ,with a short o, is unrelated and means "knee".) Today a polygon ismore usually understood in terms of sides.

The basic geometrical notion has been adapted in various ways to suitparticular purposes. Mathematicians are often concerned only with theclosed polygonal chain and with simple polygons which do not self-

intersect, and may define a polygon accordingly. Geometrically two edgesmeeting at a corner are required to form an angle that is not straight (180);otherwise, the line segments will be considered parts of a single edge however mathematically, such corners may sometimes be allowed. In fieldsrelating to computation, the term polygon has taken on a slightly alteredmeaning derived from the way the shape is stored and manipulated incomputer graphics (image generation). Some other generalizations of polygons are described below.

History

Polygons have been known since ancient times. The regular polygons wereknown to the ancient Greeks, and the pentagram, a non-convex regularpolygon (star polygon ), appears on the vase of Aristophonus, Caere, dated to

Historical image of polygons (1699)
http://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Polygonal_chainhttp://en.wikipedia.org/wiki/Plane_%28mathematics%29http://en.wikipedia.org/wiki/Shapehttp://en.wikipedia.org/wiki/Closed_curvehttp://en.wikipedia.org/wiki/Line_segmenthttp://en.wikipedia.org/wiki/Closed_polygonal_chainhttp://en.wikipedia.org/wiki/Closed_polygonal_chainhttp://en.wikipedia.org/wiki/Polytopehttp://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Simple_polygonhttp://en.wikipedia.org/wiki/Simple_polygonhttp://en.wikipedia.org/wiki/Simple_polygonhttp://en.wikipedia.org/wiki/Polygon#Polygons_in_computer_graphicshttp://en.wikipedia.org/wiki/Polygon#Generalizations_of_polygonshttp://en.wikipedia.org/wiki/Polygon#Generalizations_of_polygonshttp://en.wikipedia.org/wiki/Regular_polygonhttp://en.wikipedia.org/wiki/Pentagramhttp://en.wikipedia.org/wiki/Star_polygonhttp://en.wikipedia.org/wiki/File:Fotothek_df_tg_0003352_Geometrie_%5E_Dreieck_%5E_Viereck_%5E_Vieleck_%5E_Winkel.jpghttp://en.wikipedia.org/wiki/Star_polygonhttp://en.wikipedia.org/wiki/Pentagramhttp://en.wikipedia.org/wiki/Regular_polygonhttp://en.wikipedia.org/wiki/Polygon#Generalizations_of_polygonshttp://en.wikipedia.org/wiki/Polygon#Generalizations_of_polygonshttp://en.wikipedia.org/wiki/Polygon#Polygons_in_computer_graphicshttp://en.wikipedia.org/wiki/Simple_polygonhttp://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Polytopehttp://en.wikipedia.org/wiki/Closed_polygonal_chainhttp://en.wikipedia.org/wiki/Closed_polygonal_chainhttp://en.wikipedia.org/wiki/Line_segmenthttp://en.wikipedia.org/wiki/Closed_curvehttp://en.wikipedia.org/wiki/Shapehttp://en.wikipedia.org/wiki/Plane_%28mathematics%29http://en.wikipedia.org/wiki/Polygonal_chainhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Wikipedia:IPA_for_English#Keyhttp://en.wikipedia.org/wiki/Geometry


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the 7th century B.C. Non-convex polygons in general were notsystematically studied until the 14th century by Thomas Bredwardine.

In 1952, Shephard generalized the idea of polygons to the complex plane,

where each real dimension is accompanied by an imaginary one, to createcomplex polygons.

Polygons in nature

Numerous regular polygons may be seen in nature. In theworld of geology, crystals have flat faces, or facets, which arepolygons. Quasicrystals can even have regular pentagons asfaces. Another fascinating example of regular polygonsoccurs when the cooling of lava forms areas of tightlypacked hexagonal columns of basalt, which may be seen atthe Giant's Causeway in Ireland, or at the Devil's Postpile inCalifornia.

The most famous hexagons in nature are found in theanimal kingdom. The wax honeycomb made by beesis an array of hexagons used to store honey andpollen, and as a secure place for the larvae to grow.

There also exist animals that themselves take theapproximate form of regular polygons, or at leasthave the same symmetry. For example, sea starsdisplay the symmetry of a pentagon or, lessfrequently, the heptagon or other polygons. Other

echinoderms, such as sea urchins, sometimes display similar symmetries.Though echinoderms do not exhibit exact radial symmetry, jellyfish andcomb jellies do, usually fourfold or eightfold.

Radial symmetry (and other symmetry) is also widely observed in the plantkingdom, particularly amongst flowers, and (to a lesser extent) seeds andfruit, the most common form of such symmetry being pentagonal. Aparticularly striking example is the starfruit, a slightly tangy fruit popular inSoutheast Asia, whose cross-section is shaped like a pentagonal star.

The Giant's Causeway, inNorthern Ireland

Starfruit, a popular fruit inSoutheast Asia
http://en.wikipedia.org/wiki/Complex_polytopehttp://en.wikipedia.org/wiki/Geologyhttp://en.wikipedia.org/wiki/Quasicrystalhttp://en.wikipedia.org/wiki/Lavahttp://en.wikipedia.org/wiki/Hexagonhttp://en.wikipedia.org/wiki/Basalthttp://en.wikipedia.org/wiki/Giant%27s_Causewayhttp://en.wikipedia.org/wiki/Irelandhttp://en.wikipedia.org/wiki/Devil%27s_Postpilehttp://en.wikipedia.org/wiki/Californiahttp://en.wikipedia.org/wiki/Honeycombhttp://en.wikipedia.org/wiki/Beehttp://en.wikipedia.org/wiki/Hexagonhttp://en.wikipedia.org/wiki/Sea_starhttp://en.wikipedia.org/wiki/Pentagonhttp://en.wikipedia.org/wiki/Heptagonhttp://en.wikipedia.org/wiki/Echinodermhttp://en.wikipedia.org/wiki/Sea_urchinhttp://en.wikipedia.org/wiki/Symmetry_%28biology%29#Radial_symmetryhttp://en.wikipedia.org/wiki/Jellyfishhttp://en.wikipedia.org/wiki/Ctenophorehttp://en.wikipedia.org/wiki/Carambolahttp://en.wikipedia.org/wiki/Giant%27s_Causewayhttp://en.wikipedia.org/wiki/Northern_Irelandhttp://en.wikipedia.org/wiki/Carambolahttp://en.wikipedia.org/wiki/File:Carambolas.jpghttp://en.wikipedia.org/wiki/Southeast_Asiahttp://en.wikipedia.org/wiki/Southeast_Asiahttp://en.wikipedia.org/wiki/Carambolahttp://en.wikipedia.org/wiki/File:Carambolas.jpghttp://en.wikipedia.org/wiki/File:Giants_causeway_closeup.jpghttp://en.wikipedia.org/wiki/Northern_Irelandhttp://en.wikipedia.org/wiki/Giant%27s_Causewayhttp://en.wikipedia.org/wiki/File:Carambolas.jpghttp://en.wikipedia.org/wiki/File:Giants_causeway_closeup.jpghttp://en.wikipedia.org/wiki/Carambolahttp://en.wikipedia.org/wiki/Ctenophorehttp://en.wikipedia.org/wiki/Jellyfishhttp://en.wikipedia.org/wiki/Symmetry_%28biology%29#Radial_symmetryhttp://en.wikipedia.org/wiki/Sea_urchinhttp://en.wikipedia.org/wiki/Echinodermhttp://en.wikipedia.org/wiki/Heptagonhttp://en.wikipedia.org/wiki/Pentagonhttp://en.wikipedia.org/wiki/Sea_starhttp://en.wikipedia.org/wiki/Hexagonhttp://en.wikipedia.org/wiki/Beehttp://en.wikipedia.org/wiki/Honeycombhttp://en.wikipedia.org/wiki/Californiahttp://en.wikipedia.org/wiki/Devil%27s_Postpilehttp://en.wikipedia.org/wiki/Irelandhttp://en.wikipedia.org/wiki/Giant%27s_Causewayhttp://en.wikipedia.org/wiki/Basalthttp://en.wikipedia.org/wiki/Hexagonhttp://en.wikipedia.org/wiki/Lavahttp://en.wikipedia.org/wiki/Quasicrystalhttp://en.wikipedia.org/wiki/Geologyhttp://en.wikipedia.org/wiki/Complex_polytope


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Moving off the earth into space, early mathematicians doing calculationsusing Newton's law of gravitation discovered that if two bodies (such as thesun and the earth) are orbiting one another, there exist certain points in space,called Lagrangian points, where a smaller body (such as an asteroid or a

space station) will remain in a stable orbit. The sun-earth system has fiveLagrangian points. The two most stable are exactly 60 degrees ahead andbehind the earth in its orbit; that is, joining the center of the sun and the earthand one of these stable Lagrangian points forms an equilateral triangle.Astronomers have already found asteroids at these points. It is still debatedwhether it is practical to keep a space station at the Lagrangian point although it would never need course corrections, it would have to frequentlydodge the asteroids that are already present there. There are already satellites

and space observatories at the less stable Lagrangian points.

Polygons are fun in Math Many shapes they haveThey are geometrical.
http://en.wikipedia.org/wiki/Isaac_Newtonhttp://en.wikipedia.org/wiki/Lagrangian_pointhttp://en.wikipedia.org/wiki/Trojan_asteroidhttp://en.wikipedia.org/wiki/Trojan_asteroidhttp://en.wikipedia.org/wiki/Lagrangian_pointhttp://en.wikipedia.org/wiki/Isaac_Newton


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PART 1Question (a)


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Question (b)

A closed shape consisting of line segments that has at least three sides.Triangles, quadrilaterals, rectangles, and squares are all types of polygons.

The word "polygon" comes from Late Latin polygnum (a noun),from Greek (polygnon/polugnon ), noun use of neuter of (polygnos/polugnos , the masculine adjective), meaning"many-angled". Individual polygons are named (and sometimes classified)according to the number of sides, combining a Greek -derived numericalprefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral or quadrangle, and nonagon are exceptions. For large numbers,mathematicians usually write the numeral itself, e.g. 17-gon. A variable can

even be used, usually n-gon. This is useful if the number of sides is used in aformula. Some special polygons also have their own names; for example theregular star pentagon is also known as the pentagram.

Polygons have been known since ancient times. The regularpolygons were known to the ancient Greeks, and the pentagram, a non-convex regular polygon (star polygon ), appears on the vase of Aristophonus,Caere, dated to the 7th century B.C. Non-convex polygons in general werenot systematically studied until the 14th century by Thomas Bredwardine. In1952, Shephard generalized the idea of polygons to the complex plane,where each real dimension is accompanied by an imaginary one, to createcomplex polygons.

Question (c)

1. 2.

3. ( )( )( ) ( )

4. | |
http://en.wikipedia.org/wiki/Late_Latinhttp://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Numerical_prefixhttp://en.wikipedia.org/wiki/Numerical_prefixhttp://en.wikipedia.org/wiki/Pentagonhttp://en.wikipedia.org/wiki/Dodecagonhttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Quadrilateralhttp://en.wikipedia.org/wiki/Nonagonhttp://en.wikipedia.org/wiki/Mathematicianhttp://en.wikipedia.org/wiki/Numeral_systemhttp://en.wikipedia.org/wiki/Formulahttp://en.wikipedia.org/wiki/Regular_polygonhttp://en.wikipedia.org/wiki/Star_polygonhttp://en.wikipedia.org/wiki/Pentagonhttp://en.wikipedia.org/wiki/Pentagramhttp://en.wikipedia.org/wiki/Regular_polygonhttp://en.wikipedia.org/wiki/Regular_polygonhttp://en.wikipedia.org/wiki/Pentagramhttp://en.wikipedia.org/wiki/Star_polygonhttp://en.wikipedia.org/wiki/Complex_polytopehttp://en.wikipedia.org/wiki/Complex_polytopehttp://en.wikipedia.org/wiki/Star_polygonhttp://en.wikipedia.org/wiki/Pentagramhttp://en.wikipedia.org/wiki/Regular_polygonhttp://en.wikipedia.org/wiki/Regular_polygonhttp://en.wikipedia.org/wiki/Pentagramhttp://en.wikipedia.org/wiki/Pentagonhttp://en.wikipedia.org/wiki/Star_polygonhttp://en.wikipedia.org/wiki/Regular_polygonhttp://en.wikipedia.org/wiki/Formulahttp://en.wikipedia.org/wiki/Numeral_systemhttp://en.wikipedia.org/wiki/Mathematicianhttp://en.wikipedia.org/wiki/Nonagonhttp://en.wikipedia.org/wiki/Quadrilateralhttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Dodecagonhttp://en.wikipedia.org/wiki/Pentagonhttp://en.wikipedia.org/wiki/Numerical_prefixhttp://en.wikipedia.org/wiki/Numerical_prefixhttp://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Late_Latin


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PART 2Question (a)

Cost = RM 20 300 = RM 6000

Question (b)

Question (c)

The herb garden is an equilateral triangle of sides 100m with a maximumarea of 4330.13m.

CONJECTURE Regular polygon will give maximum area.Eg:

Square

p(m) q(m) (degree) Area(m)60 140 38.21 2597.8970 130 49.58 3463.9780 120 55.77 3968.57

90 110 58.99 4242.53100 100 60.00 4330.13110 90 58.99 4242.53120 80 55.77 3968.57130 70 49.58 3463.97140 60 38.21 2597.89


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Rectangle

Question (d)

i. 60 < p < 140,60 < q < 140

ii. When p increases, q decreases,When q increases, p decreases

iii. The sum of the lengths of any two sides of a triangle is greater thanthe length of the third side. Triangle Inequality Theorem.


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PART 3Question (a)

i. Quadrilateral

2 + 2 = 300 m

+ = 150 m

Area =

The maximum area is 5625 m.

ii. Regular Pentagon

tan ( )

Area = 10 140 140020 130 260030 120 360040 110 440050 100 500060 90 540070 80 560075 75 5625

m

m


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iii. Regular Hexagon

tan ( )

iv. Regular Octagon

tan 67.5

tan

( )

v. Regular Decagon

tan

tan ( )


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Question (b)(i)LOCAL HERBS

1. Misai Kucing (Orthosiphon stamineus) Orthosiphon is a medicinal plant native to South East Asia andsome parts of tropical Australia. It is an herbaceous shrub whichgrows to a height of 1.5 meters. Orthosiphon is a popular gardenplant because of its unique flower, which is white and bluish withfilaments resembling a cat's whiskers. In the wild, the plant can beseen growing in the forests and along roadsides.

Common names in Southeast Asia are Misai Kucing (Malaysia),Kumis Kucing and Remujung (Indonesia), and Yaa Nuat Maeo (Thailand). The scientific names are Orthosiphon stamineus Benth,Ocimum aristatum BI and Orthosiphon aristatus (Blume).

Medicinal UsesOrthosiphon is used for treating the ailments of the kidney, since ithas a mild diuretic effect. It is also claimed to have anti-allergenic,anti-hypertensive and anti-inflammatory properties, and is commonly used for kidneystones and nephritis. Orthosiphon is sometimes used to treat gout, diabetes, hypertensionand rheumatism. It is reportedly effective for anti-fungal and anti-bacterial purposes.

How To CureIn Malaysia, people eat the leaves raw. They take a few leaves, heat them with water to

make the water bitter, and then mix it with tea bags.

ResearchOrthosiphon began to interest researchers early in the 20th century, when it wasintroduced to Europe as a popular herbal health tea.

Commercial productsOrthosiphon is available in many products treating for detoxification, water retention,hypertension, obesity or kidney stones. It comes in tablets, capsules, tea sachets, bottleddrinks, raw herbs, dried leaves or extracts.
http://en.wikipedia.org/wiki/Nephritishttp://en.wikipedia.org/wiki/Gouthttp://en.wikipedia.org/wiki/Diabeteshttp://en.wikipedia.org/wiki/Hypertensionhttp://en.wikipedia.org/wiki/Rheumatismhttp://en.wikipedia.org/wiki/Rheumatismhttp://en.wikipedia.org/wiki/Hypertensionhttp://en.wikipedia.org/wiki/Diabeteshttp://en.wikipedia.org/wiki/Gouthttp://en.wikipedia.org/wiki/Nephritis


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2. Kacip Fatimah (Labisia Pumila)

Kacip fatimah ( Labisa pumila ) is the female version of Tongkat Ali. Kacip Fatimah is asmall woody and leafy plant that grows and can be found widely in the shade of forest

floors. The leaves are about 20 centimetres long, andthey are traditionally used as a kind of tea by womenwho experience a loss of libido. Despite its longhistory of traditional use, the active components andmode of action have not been well studied, thoughsome preliminary research has been published.

UsesExtract from these herbs is usually ground intopowder substances and are made into capsules andpills. A concoction made from boiling the plant in

water is given to women in labour to hasten delivery of their babies. After childbirth, itmay still be consumed by mothers to regain their strength. In other medicinalpreparations, it can treat gonorrhoea, dysentery and eliminate excessive gas in the body.

Traditionally, it is used in Borneo for enhancing vitality, overcome tiredness and help totone vaginal muscles for women.

The claimed uses of Kacip Fatimah include:

Helps establish a regular menstrual cycle when periods fail to appear for reasonslike stress, illness or when the pill is discontinued

Prevents cramping, water retention and irritability for those with painful periods. Balances, builds and harmonizes the female reproductive system to encouragehealthy conception

Supports healthy vaginal flora to prevent irritation and infections. Alleviates fatigue, smooths menopausal symptoms and promote emotional well

being. Prolong energy during Playtime. Helps to solve the problems related to constipation Tightens vaginal skin and walls. Anti -dysmenorrhoea; cleansing and avoiding painful or difficult menstruation Anti-flatulence, drive away and prevent the formation of gas.

Firming and toning of abdominal muscles.

As the plant contains phytoestrogen , it is not to be taken by pregnant women and periodsof menstruation.
http://en.wikipedia.org/wiki/Tongkat_Alihttp://en.wikipedia.org/wiki/Vaginal_florahttp://en.wikipedia.org/wiki/Dysmenorrhoeahttp://en.wikipedia.org/wiki/Phytoestrogenhttp://en.wikipedia.org/wiki/Phytoestrogenhttp://en.wikipedia.org/wiki/Phytoestrogenhttp://en.wikipedia.org/wiki/Phytoestrogenhttp://en.wikipedia.org/wiki/Dysmenorrhoeahttp://en.wikipedia.org/wiki/Vaginal_florahttp://en.wikipedia.org/wiki/Tongkat_Ali


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3. Tongkat Ali (Eurycoma Longifolia)

Eurycoma longifolia (commonly called tongkat ali or pasak bumi) is a flowering plant inthe family Simaroubaceae, native to Indonesia, Malaysia, and, to a lesser extent, Thailand,

Vietnam, and Laos. It is also known under the names penawar

pahit, penawar bias, bedara merah, bedara putih, lempedu pahit,payong ali, tongkat baginda, muntah bumi, petala bumi (all theabove Malay); bidara laut (Indonesian); babi kurus (Javanese);cay ba binh (Vietnamese) and tho nan (Laotian). Many of thecommon names refer to the plant's medicinal use and extremebitterness. "Penawar pahit" translates simply as "bitter charm"or "bitter medicine". Older literature, such as a 1953 article inthe Journal of Ecology , may cite only "penawar pahit" as theplant's common Malay name.

GrowthEurycoma longifolia is a small, evergreen tree growing to 15 m (49 ft) tall with spirallyarranged, pinnate leaves 20 40 cm (8 16 inches) long with 13 41 leaflets. The flowersare dioecious, with male and female flowers on different trees; they are produced in largepanicles, each flower with 5 6 very small petals. The fruit is green ripening dark red, 1 2 cm long and 0.5 1 cm broad.

ProductsFake Eurycoma longifolia products have been pulled off the shelves in several countriesbut are still sold over the Internet, mostly shipped from the UK. In a medical journalarticle, published March 2010, it was noted that "estimates place the proportion of counterfeit medications sold over the Internet from 44% to 90%"with remedies for sexual dysfunction accounting for the greatestshare. It is therefore recommended that buyers of Eurycomalongifolia request from Internet vendors conclusive information,and proof, on the facilities where a product has beenmanufactured.

In Malaysia, the common use of Eurycoma longifolia as a foodand drink additive, coupled with a wide distribution of productsusing cheaper synthetic drugs in lieu of Eurycoma longifolia quassinoids, has led to theinvention of an electronic tongue to determine the presence and concentration of genuineEurycoma longifolia in products claiming to contain it.

On the other hand, consumers who lack the sophisticated electronic tongue equipmentinvented in Malaysia for testing the presence of Eurycoma longifolia, but want moreclarity on whether the product they obtained is indeed Eurycoma longifolia or a fake, canuse their own tongue to taste the content of capsules for the bitterness of the material.Quassinoids, the biologically active components of Eurycoma longifolia root, areextremely bitter. They are named after quassin, the long-isolated bitter principle of thequassia tree. Quassin is regarded the bitterest substance in nature, 50 times more bitter
http://en.wikipedia.org/wiki/Flowering_planthttp://en.wikipedia.org/wiki/Simaroubaceaehttp://en.wikipedia.org/wiki/Indonesiahttp://en.wikipedia.org/wiki/Malaysiahttp://en.wikipedia.org/wiki/Thailandhttp://en.wikipedia.org/wiki/Vietnamhttp://en.wikipedia.org/wiki/Laoshttp://en.wikipedia.org/wiki/Journal_of_Ecologyhttp://en.wikipedia.org/wiki/Journal_of_Ecologyhttp://en.wikipedia.org/wiki/Journal_of_Ecologyhttp://en.wikipedia.org/wiki/Evergreenhttp://en.wikipedia.org/wiki/Treehttp://en.wikipedia.org/wiki/Pinnatehttp://en.wikipedia.org/wiki/Leafhttp://en.wikipedia.org/wiki/Flowerhttp://en.wikipedia.org/wiki/Plant_sexualityhttp://en.wikipedia.org/wiki/Paniclehttp://en.wikipedia.org/wiki/Petalhttp://en.wikipedia.org/wiki/Fruithttp://en.wikipedia.org/w/index.php?title=Quassinoids&action=edit&redlink=1http://en.wikipedia.org/wiki/Quassinhttp://en.wikipedia.org/wiki/Quassiahttp://en.wikipedia.org/wiki/Quassiahttp://en.wikipedia.org/wiki/Quassinhttp://en.wikipedia.org/w/index.php?title=Quassinoids&action=edit&redlink=1http://en.wikipedia.org/wiki/Fruithttp://en.wikipedia.org/wiki/Petalhttp://en.wikipedia.org/wiki/Paniclehttp://en.wikipedia.org/wiki/Plant_sexualityhttp://en.wikipedia.org/wiki/Flowerhttp://en.wikipedia.org/wiki/Leafhttp://en.wikipedia.org/wiki/Pinnatehttp://en.wikipedia.org/wiki/Treehttp://en.wikipedia.org/wiki/Evergreenhttp://en.wikipedia.org/wiki/Journal_of_Ecologyhttp://en.wikipedia.org/wiki/Laoshttp://en.wikipedia.org/wiki/Vietnamhttp://en.wikipedia.org/wiki/Thailandhttp://en.wikipedia.org/wiki/Malaysiahttp://en.wikipedia.org/wiki/Indonesiahttp://en.wikipedia.org/wiki/Simaroubaceaehttp://en.wikipedia.org/wiki/Flowering_plant


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than quinine. Anything that isn't bitter, and strongly so, cannot contain quassinoids fromEurycoma longifolia .

In the US, the FDA has banned numerous products such as Libidus, claiming to useEurycoma longifolia as principal ingredient, but which instead are concoctions designed

around illegal prescription drugs, or even worse, analogues of prescription drugs thathave not even been tested for safety in humans, such as acetildenafil. In February 2009,the FDA warned against almost 30 illegal sexual enhancement supplements, but thenames of these products change quicker than the FDA can investigate them. Libidus, forexample, is now sold as Maxidus, still claiming Eurycoma longifolia (tongkat ali) asprincipal ingredient. The government of Malaysia has banned numerous fake productswhich use drugs like sildenafil citrate instead of tongkat ali in their capsules. To avoidbeing hurt by bad publicity on one product name, those who sell fake tongkat ali fromMalaysia have resorted to using many different names for their wares. Products claimingvarious Eurycoma longifolia extract ratios of 1:20, 1:50, 1:100, and 1:200 are sold.Traditionally Eurycoma longifolia is extracted with water and not ethanol. However, the

use of selling Eurycoma longifolia extract based on extraction ratio may be confusing andis not easily verifiable.

In expectation of a competitive edge, some manufacturers are claiming standardization of their extract based on specific ingredients. Alleged standards / markers are theglycosaponin content (35 45%) and eurycomanone (>2%). While eurycomanone is oneof many quassinoids in Eurycoma longifolia, saponins, known in ethnobotany primarilyas fish poison played no role in the academic research on the plant.

A large number of Malaysian Eurycoma longifolia products (36 out of 100) have beenshown to be contaminated with mercury beyond legally permitted limits.

Herbal Nutrition Increase strength of the body. Help to stimulate the production of testosterone that is one of the important

hormones for male. Help to increase the blood rate and body metabolism.
http://en.wikipedia.org/wiki/Quininehttp://en.wikipedia.org/wiki/Acetildenafilhttp://en.wikipedia.org/wiki/Sildenafilhttp://en.wikipedia.org/wiki/Citratehttp://en.wikipedia.org/wiki/Ethanolhttp://en.wikipedia.org/wiki/Glycosaponinhttp://en.wikipedia.org/w/index.php?title=Eurycomanone&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Quassinoids&action=edit&redlink=1http://en.wikipedia.org/wiki/Mercury_%28element%29http://en.wikipedia.org/wiki/Mercury_%28element%29http://en.wikipedia.org/w/index.php?title=Quassinoids&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Eurycomanone&action=edit&redlink=1http://en.wikipedia.org/wiki/Glycosaponinhttp://en.wikipedia.org/wiki/Ethanolhttp://en.wikipedia.org/wiki/Citratehttp://en.wikipedia.org/wiki/Sildenafilhttp://en.wikipedia.org/wiki/Acetildenafilhttp://en.wikipedia.org/wiki/Quinine


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Question (b)(ii)


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FURTHER EXPLORATION

POLYGONAL BUILDINGS

University of Economics and Business, Vienna

The new Library & Learning Center rises as a polygonal block from the centre of the newUniversity campus. The LLC s design takes the form of a cube with both inclined andstraight edges. The straight lines of the building s exterior separate as they move inward,becoming curvilinear and fluid to generate a free-formed interior canyon that serves asthe central public plaza of the centre. All the other facilities of the LLC are housed withina single volume that also divides, becoming two separate ribbons that wind around eachother to enclose this glazed gathering space.

The Center comprises a Learning Center with workplaces, lounges and cloakrooms,library, a language laboratory, training classrooms, administration offices, study servicesand central supporting services, copy shop, book shop, data center, cafeteria, event area,clubroom and auditorium.

Vienna, Austria 2008 2012 28000 m 2 Gross Area: 42000 m Length: 136m Width: 76m Height: 30m (5 Floors) Zaha Hadid with Patrik Schumacher


20/23

Pittman Dowell Residence, Los Angeles

The project is a residence for two artists. Located 15 miles north of Los Angeles at theedge of Angeles forest, the site encompasses 6 acres of land originally planned as ahillside subdivision of houses designed by Richard Neutra. Three level pads were createdbut only one house was built, the 1952 Serulnic Residence. The current owners have over

the years developed an extensive desert garden and outdoor pavilion on one of the unbuiltpads. The new residence, to be constructed on the last level area, is circumscribed by thesole winding road which ends at the Serulnic house.

Five decades after the original house was constructed in this remote area, the city hasgrown around it and with it the visual and physical context has changed. In a similar way,the evolving contemporary needs of the artists required a new relationship betweenbuilding and landscape that is more urban and contained. Inspired by geometricarrangements of interlocking polygons, the new residence takes the form of a heptagonalfigure whose purity is confounded by a series of intersecting diagonal slices though space.Bounded by an introverted exterior, living spaces unfold in a moir of shifting

perspectival frames from within and throughout the house. An irregularly shaped voidcaught within these intersections creates an outdoor room at the center whose edges blurinto the adjoining living spaces. In this way, movement and visual relationships expandand contract to respond to centrifugal nature of the site and context.

Los Angeles, USA Residential - Houses Micheal Maltzan Architecture 3200 SF
http://architecturelab.net/keyword/los-angeles/http://architecturelab.net/keyword/usa/http://architecturelab.net/keyword/residential/http://architecturelab.net/keyword/houses/http://architecturelab.net/keyword/michael-maltzan-architecture/http://architecturelab.net/keyword/michael-maltzan-architecture/http://architecturelab.net/keyword/houses/http://architecturelab.net/keyword/residential/http://architecturelab.net/keyword/usa/http://architecturelab.net/keyword/los-angeles/


21/23

Casa da Musica, Porto

The Casa da Musica is situated on a travertine plaza, between the city's historic quarterand a working-class neighborhood, adjacent to the Rotunda da Boavista. The square is nolonger a mere hinge between the old and the new Porto, but becomes a positive encounterof two different models of the city.

The chiseled sculptural form of the white concrete shell houses the main 1,300 seatconcert hall, a small 350 seat hall, rehearsal rooms, and recording studios for the OportoNational Orchestra.

A terrace carved out of the sloping roofline and huge cut-out in the concrete skinconnects the building to city. Stairs lead from the ground level plaza to the foyer where asecond staircase continues to the Main Hall and the different levels above. Heavyconcrete beams criss-cross the huge light well above. The main auditorium, shaped like asimple shoebox, is enclosed at both ends by two layers of corrugated glass walls. Theglass, corrugated for optimal acoustics and sheer beauty, brings diffused daylight into theauditorium. The structural heart of the building is formed by four massive walls thatextend from the base to the roof and connect the tilted external walls with the core of thestructure. The two one meter thick walls of the main auditorium act as internaldiaphragms tying the shell together in the longitudinal direction. The principal materialsare white concrete, corrugated glass, travertine, plywood, and aluminum.

Porto, Portugal 22.000 square meters 2005 Concert Hall

Rem Koolhaas and Ellen van Loon


22/23


23/23

REFLECTIONWhile I conducting this project, a lot of information that I

found. I have learnt how polygons appear in our daily life.

Apart from that, this project encourages the student to work together and share their knowledge. It is also encourage student togather information from the internet, improve thinking skills andpromote effective mathematical communication.

Not only that, I had learned some moral values that I practice.This project had taught me to responsible on the works that aregiven to me to be completed. This project also had made me feltmore confidence to do works and not to give easily when we couldnot find the solution for the question. I also learned to be morediscipline on time, which I was given about a month to completethis project and pass up to my teacher just in time. I also enjoydoing this project I spend my time with friends to completethis project and it had tighten our friendship.

Last but not least, I proposed this project should be continuebecause it brings a lot of moral value to the student and also testthe students understanding in Additional Mathematics.

93639430 additional mathematics project work 2012

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