# Add Maths Project Form 5 SPM

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WORK 1/2014

NAME:

CLASS: 5S2

IC NUMBER:

ANGKA GILIRAN: PC016 A

SCHOOL: Sekolah Menengah Jenis KebangsaanHeng Ee

TEACHERS NAME: Mr Khaw Inn Seng

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CONTENT

No. Content Page Number

1. Acknowledgement 3

2. Objective 4

3. Introduction 5-6

4. Activity 1 7-9

5. Activity 2 Part (a) 10-11Part (b) 12

6. Activity 3 13

7. Activity 4Part (a) 14-15

Part (b) 15-16

8. Activity 5Part (a) 17-18

Part (b) 18-199. Reflection 20

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Acknowledgement

First of all , I would like to thank the principal of Sekolah Menengah Jenis

Kebangsaan Heng Ee, Mr. Low Lim Wah for giving me the permission to do this

Not forgotten my parents for providing everything , such as money to buy

anything that are related to this project work and their advise , which is the most needed

for this project . 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 , Mr Khaw Inn Seng for guiding me and

my friends throughout this project . We had some difficulties in doing this task , but he

taught me and my friends patiently on ways to accomplish this project work and the

ways to solve the question in this project work . He tried and tried to teach us until we

understand what we supposed to do with the project work .

Last but not least, I would like to thank my friends who were doing this projectwith me. They were helpful that when we combined and discussed together , sharing

information and ideas in order to get this project work done.

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Aim and Objective

Aim :

The aim for this project is to survey the suitable perimeter for track and field

event tournament.

Project Work Objective :

At the end of this project, I will be able to

Collect data of the circumference and radius of semicircle.

Calculate the distance in each lane.

Solve problems by using various strategies.

Relate my knowledge with data obtained.

State the cause of injury during the running and ways to avoid accidents.

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Introduction

A Brief History Of Running Track

Thesport of track and field has its roots in humanprehistory.Track andfield-style events are among the oldest of all sportingcompetitions,as

running, jumping and throwing are natural and universal forms of human

physical expression. The first recorded examples of organized track and field

events at asports festival are theAncient Olympic Games.At the first

Games in 776 BC inOlympia, Greece,only one event was contested:

thestadion footrace.The scope of the Games expanded in later years to

include further running competitions, but the introduction of theAncient

Olympic pentathlon marked a step towards track and field as it is recognized

todayit comprised a five-event competition of thelong jump,javelinthrow,discus throw,stadion footrace andwrestling.

Track and field events were also present at thePanhellenic Games in Greece

around this period, and they spread to Rome in Italy around 200 BC. After

the period ofClassical antiquity (in which the sport was largely Greco-

Roman influenced) new track and field events began developing in parts

ofNorthern Europe in theMiddle Ages.Thestone put andweight

throw competitions popular amongCeltic societies

inIreland andScotland were precursors to the modernshot put andhammer

throw events. One of the last track and field events to develop was thepole

vault,which stemmed from competitions such as theFierljeppen contests in

theNorthern European Lowlands in the 18th century.

An early model ofhurdling at theDetroit Athletic Club in 1888.

Discrete modern track and field competitions, separate from general sporting

festivals, were first recorded in the 19th century. These were typically

organised byeducational institutions,military organisations andsports

clubs as competitions between rival establishments. Competitions in the

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Englishpublic schools were conceived as human equivalents ofhorse

racing,fox hunting andhare coursing,influenced by aClassics-rich

curriculum. The RoyalShrewsbury School Hunt is the oldest running club in

the world, with written records going back to 1831 and evidence that it was

established by 1819. The school organisedPaper Chase races in whichrunners followed a trail of paper shreds left by two "foxes" even today

RSSH runners are called "hounds" and a race victory is a "kill". The first

definite record of Shrewsbury's (cross-country) AnnualSteeplechase is in

1834, making it the oldest running race of the modern era. The school also

lays claim to the oldest track and field meeting still in existence, originating

in the Second Spring Meeting first documented in 1840. This featured a

series of throwing and jumping events with mock horse races including the

Derby Stakes, the Hurdle Race and the Trial Stakes. Runners were entered

by "owners" and named as though they were horses. 13 miles (21 km) awayand a decade later, the firstWenlock Olympian Games were held atMuch

Wenlock racecourse. Events at the 1851 Wenlock Games included a "half-

mile foot race" (805 m) and a "leaping in distance" competition.

In 1865, DrWilliam Penny Brookes of Wenlock helped set up theNational

Olympian Association,which held their first Olympian Games in 1866

atThe Crystal Palacein London. This national event was a great success,

attracting a crowd of over ten thousand people. In response, that same year

the Amateur Athletic Club was formed and held a championship for

"gentlemen amateurs" in an attempt to reclaim the sport for the educatedelite. Ultimately the "allcomers" ethos of the NOA won through and the

AAC was reconstituted as theAmateur Athletic Association in 1880, the

first national body for the sport ofathletics.TheAAA Championships,

the de factoBritish national championships despite being for England only,

have been held annually since 3 July 1880 with breaks only during two

world wars and 20062008. The AAA was effectively a global governing

body in the early years of the sport, codifying its rules for the first time.

The establishment of the modernOlympic Games at the end of the 19th

century marked a new high for track and field. TheOlympic athleticsprogramme,comprising track and field events plus amarathon race,

contained many of the foremost sporting competitions of the1896 Summer

Olympics.The Olympics also consolidated the use ofmetric

measurements in international track and field events, both for race distances

and for measuring jumps and throws. The Olympic athletics programme

http://en.wikipedia.org/wiki/Public_school_(United_Kingdom)http://en.wikipedia.org/wiki/Horse_racinghttp://en.wikipedia.org/wiki/Horse_racinghttp://en.wikipedia.org/wiki/Fox_huntinghttp://en.wikipedia.org/wiki/Hare_coursinghttp://en.wikipedia.org/wiki/Classicshttp://en.wikipedia.org/wiki/Shrewsbury_Schoolhttp://en.wikipedia.org/wiki/Paper_Chase_(game)http://en.wikipedia.org/wiki/Steeplechase_(athletics)http://en.wikipedia.org/wiki/Wenlock_Olympian_Gameshttp://en.wikipedia.org/wiki/Much_Wenlockhttp://en.wikipedia.org/wiki/Much_Wenlockhttp://en.wikipedia.org/wiki/William_Penny_Brookeshttp://en.wikipedia.org/wiki/National_Olympian_Associationhttp://en.wikipedia.org/wiki/National_Olympian_Associationhttp://en.wikipedia.org/wiki/The_Crystal_Palacehttp://en.wikipedia.org/wiki/Amateur_Athletic_Associationhttp://en.wikipedia.org/wiki/Athletics_(sport)http://en.wikipedia.org/wiki/AAA_Championshipshttp://en.wikipedia.org/wiki/Olympic_Gameshttp://en.wikipedia.org/wiki/Athletics_at_the_Summer_Olympicshttp://en.wikipedia.org/wiki/Athletics_at_the_Summer_Olympicshttp://en.wikipedia.org/wiki/Marathonhttp://en.wikipedia.org/wiki/1896_Summer_Olympicshttp://en.wikipedia.org/wiki/1896_Summer_Olympicshttp://en.wikipedia.org/wiki/Metric_systemhttp://en.wikipedia.org/wiki/Metric_systemhttp://en.wikipedia.org/wiki/Metric_systemhttp://en.wikipedia.org/wiki/Metric_systemhttp://en.wikipedia.org/wiki/1896_Summer_Olympicshttp://en.wikipedia.org/wiki/1896_Summer_Olympicshttp://en.wikipedia.org/wiki/Marathonhttp://en.wikipedia.org/wiki/Athletics_at_the_Summer_Olympicshttp://en.wikipedia.org/wiki/Athletics_at_the_Summer_Olympicshttp://en.wikipedia.org/wiki/Olympic_Gameshttp://en.wikipedia.org/wiki/AAA_Championshipshttp://en.wikipedia.org/wiki/Athletics_(sport)http://en.wikipedia.org/wiki/Amateur_Athletic_Associationhttp://en.wikipedia.org/wiki/The_Crystal_Palacehttp://en.wikipedia.org/wiki/National_Olympian_Associationhttp://en.wikipedia.org/wiki/National_Olympian_Associationhttp://en.wikipedia.org/wiki/William_Penny_Brookeshttp://en.wikipedia.org/wiki/Much_Wenlockhttp://en.wikipedia.org/wiki/Much_Wenlockhttp://en.wikipedia.org/wiki/Wenlock_Olympian_Gameshttp://en.wikipedia.org/wiki/Steeplechase_(athletics)http://en.wikipedia.org/wiki/Paper_Chase_(game)http://en.wikipedia.org/wiki/Shrewsbury_Schoolhttp://en.wikipedia.org/wiki/Classicshttp://en.wikipedia.org/wiki/Hare_coursinghttp://en.wikipedia.org/wiki/Fox_huntinghttp://en.wikipedia.org/wiki/Horse_racinghttp://en.wikipedia.org/wiki/Horse_racinghttp://en.wikipedia.org/wiki/Public_school_(United_Kingdom)
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greatly expanded over the next decades, and track and field contests

remained among the Games' most prominent. The Olympics was the elite

competition for track and field, and onlyamateur sportsmen could compete.

Track and field continued to be a largely amateur sport, as this rule was

strictly enforced:Jim Thorpe was stripped of his track and field medals fromthe1912 Olympics after it was revealed that he had

playedbaseballprofessionally.

With the rise of numerous regional championships, as well as the growth in

Olympic-stylemulti-sport events (such as theCommonwealth Games and

thePan-American Games), competitions between international track and

field athletes became widespread. From the 1960s onwards, the sport gained

more exposure and commercial appeal throughtelevision coverage and the

increasing wealth of nations. After over half a century of amateurism, the

amateur status of the sport began to be displaced bygrowingprofessionalism in the late 1970s. As a result, the Amateur Athletic

Union was dissolved in the United States and it was replaced with a non-

amateur body solely focused on the sport of athletics: The Athletics

Congress (laterUSA Track and Field). The IAAF soon followed suit in 1982,

abandoning amateurism, and later removing all references to it from its

name by rebranding itself as the International Association of Athletics

Federations. The following year saw the establishment of theIAAF World

Championships in Athleticsthe first ever global competition just for

athleticswhich, with the Olympics, became one of track and field's mostprestigious competitions.

From the 1990s onwards, track and field became increasingly more

professional and international, as the IAAF gained over two hundred

member nations. The IAAF World Championships in Athletics became a

fully professional competition with the introduction ofprize money in 1997,

and in 1998 theIAAF Golden Leaguean annual series of major track and

field meetings in Europeprovided a higher level of economic incentive in

the form of a US\$1 million jackpot. In 2010, the series was replaced by the

more lucrativeIAAF Diamond League,a fourteen-meeting series held inEurope, Asia, North America and the Middle Eastthe first ever worldwide

annual series of track and field meetings.

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100 m

100mField

1.2mLane 1

Lane 2

Lane 3

Lane 4

Lane 5

Lane 6

Lane 7

Lane 8

Activity 1 : Collecting Information

http://en.wikipedia.org/wiki/File:DETROIT_ATHLETIC_CLUB-1988.jpghttp://en.wikipedia.org/wiki/File:DETROIT_ATHLETIC_CLUB-1988.jpghttp://en.wikipedia.org/wiki/File:DETROIT_ATHLETIC_CLUB-1988.jpghttp://en.wikipedia.org/wiki/File:DETROIT_ATHLETIC_CLUB-1988.jpghttp://en.wikipedia.org/wiki/File:DETROIT_ATHLETIC_CLUB-1988.jpghttp://en.wikipedia.org/wiki/File:DETROIT_ATHLETIC_CLUB-1988.jpghttp://en.wikipedia.org/wiki/File:DETROIT_ATHLETIC_CLUB-1988.jpghttp://en.wikipedia.org/wiki/File:DETROIT_ATHLETIC_CLUB-1988.jpg
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Given that the smallest circumference of semicircle is 100 meter. The length

of straight line of the field track is also 100 meter. The width of each lane is

1.2 meter.

Show your working to determine the distance of each lane and complete

Table 1.(Use = 3.142)

Solution :

Let S be the circumference of the semicircles, R is the radius of the first

semicircle

S = R

Therefore, R =

By using the formula of arithmetic progression,

Radius of each semicircle = a + (n-1)d, where a= radius of the first

semicircle, n=number of term, d=difference between any two consecutive

terms

But, a =

, d = 1.2 m

Therefore, radius of each semicircle, r =

(n-1)1.2

Distance of each lane, d = 100 + 100 + 2S

= 200 + 2S

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Lane

Circumference ofSemicircle (S) , inmeter(3 decimal places)

places)

Distance of EachLane (d) , inmeter(3 decimal

places)

1 100.000

(1-

1)1.2=31.827

100 + 100 +2(100.000)=

400.000

233.027 =

103.771

(2-

1)1.2=33.027

100 + 100 +2(103.771)=

407.542

334.227 =

107.541

(3-

1)1.2=34.227

100 + 100 +2(107.541)=

415.082

435.427 =

111.312

(4-

1)1.2=35.427

100 + 100 +2(111.312)=

422.624

5

36.627 =

115.082

(5-

1)1.2=36.627

100 + 100 +2(115.082)=

430.164

637.827 =

118.852

(6-

1)1.2=37.827

100 + 100 +2(118.852)=

437.704

739.027 =

122.623

(7-

1)1.2=39.027

100 + 100 +2(122.623)=

445.246

840.227 =

126.393

(8-

1)1.2=40.227

100 + 100 +2(126.393)=

452.786

Table 1

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100 m

100mStarting line of

Lane 1

Finishing line

Activity 2 : Data Analysis

Diagram 2 shows the starting line of Lane 1 and finishing line of all lanes.

Diagram 2

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(a)Based on Diagram 2, the starting line of Lane 1 has been given. You areasked to determine the distance of starting line of Lane 2, Lane 3, Lane 4,Lane 5, Lane 6, Lane 7 and Lane 8 from the finishing line for a 400 meterevent. Hence, complete Table 2. Use at least twosuitable problemsolving strategies.

Solution :

Method 1:

Shortest distance between starting line and finishing line

= - 400m

Method 2:

Distance between two starting line

= - , where L = Distance of lane , n = number of term of lane

nth lane

Shortest distance

between starting line

and finishing line, in

meter

(2 decimal places)

-

1 400.00400.00 =0.00 0.00

2 407.54400.00 = 7.54 407.54400.00 = 7.54

3 415.08400.00 = 15.08 415.08407.54 =7.54

4 422.62400.00 = 22.62 422.62415.08 = 7.54

5 430.16400.00 = 30.16 430.16422.62 = 7.54

6 437.70400.00 = 37.70 437.70430.16 = 7.547 445.24400.00 = 45.24 445.24437.70 = 7.54

8 452.78400.00 = 52.78 452.78445.24 = 7.54

Table 2

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(b)Make a conclusion from the data obtained in Table 2.

The shortest distance between starting line and finishing line increases

down the lane. This is because of the distance of the track increases. As the

lanes keep increasing, the shortest distance between starting line and

finishing line will be increased also. But the distance of starting line

between two consecutive lanes is the same. This explains why the starting

line of each lane is different because distance of starting line and finishing

line of each lane will be 400 meter. Fair game will be played.

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Activity 3: Data Interpretation

Oil paint is to be used to draw all the tracks. The price of a tin of 5 liter oilpaint is RM10. Given that 2 liter of oil paint is needed to draw a 100 meter

track. Calculate the number of tin of oil paint needed and the cost (in RM)

to draw all the eight tracks.

Solution :

Price of 1 liter oil paint =

= RM 2

Length of track that 1 liter of oil paint can draw = = 50 m

Total length of tracks= 400 + 407.542 + 415.082 +422.624+ 430.164 + 437.704 + 445.246 +

452.786= 3411.15m (2 d.p.)

Volume of oil paint needed =

= 68.22 l

Number of tins of oil paint needed

=

=13.644= approximately 14 tins of oil paint needed

Cost to draw all the eight tracks = 14 10 = RM 140

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1.2m

Finishing line

Starting line of

Lane 1

Activity 4: Further Exploration

The design of tracks shown in Diagram 1 is the track that is usually used in

the tracks tournament.

(a)Using your own creativity, create twodesigns of tracks which has ameasurement of 400m in Lane 1 and width of each lane is the same.

Design 1

400m

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Finishing line

Starting line of

Lane 1

1.2m

Design 2

(b)Based on your track designed in question (a) and Diagram 1, Whichdesign would you choose for your school tournament?State your justification.

I will choose the design of Diagram 1 for my school tournament. This

design of track is recognized by the International Association of Athletics

Federations .If a track is to allow for such a curb (it can be removed when

not in use), the track's inner lane line must be specified at 30 centimeters

inside the aforementioned runner's 400-meter path. If no curb is needed, as is

the case at the high school level, the track can be built with an inner line 20

centimeters removed from the runner's circuit. Says Fisher, "Somebody

400m

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decided however many years ago that if you're running against a white stripe,

you can run 20 centimeters from that stripe and not step on the stripe. You

can safely compete at that distance. And if you step on the stripe, you may

get disqualified, but you're not going to get hurt. At the high-end levels, you

run against a rail, and because of the psychological fear of hitting that rail

and breaking an ankle, you're afraid to run that close to it. It's determined

that the path of travel is 30 centimeters from a rail. So there are tracks built

for a rail. There are tracks built to not have a rail. One track cannot be built

for both."

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Activity 5: Conclusions

Based on a study by American Academy of Physical Medicine andRehabilitation, 70% of athletes were injured during the track events.According to runnersworld.com, about 40% of athletes were knee injuries.For women, backbone and ankle injuries always happened while running.Headache can also be occurred especially during hot weather.

(a)What are the causes of track and field injuries?

Examples of track and field injuries are shin splints, high ankle sprain,

groin strain and back muscle pain.

Shin splints are caused by overstraining of your muscles where they

attach to your shin. The most common cause is overuse or overtraining

associated with poor foot and leg biomechanics. Shin splints can be caused

by a number of factors which are mainly biomechanical (abnormal

movement patterns) and errors in training . In appropriate footwear,

increasing your training too quickly and running on hard or angled surfaces

will also cause shin splints.

A groin strain is a muscular tear or rupture to any one of your groin

muscles; usually one of the hip adductor muscle group. Your body has five

Any of these groin muscles can be strained but the most common is adductor

longus. A groin strain usually occurs with high speed activities such as

kicking, change of direction or sprinting.

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Most causes of low back pain are muscle, ligament or joint related. Most

commonly, these back injuries are caused by muscular strains, ligament

sprains and joint dysfunction, particularly when pain arises suddenly during

high speeds or poor lifting postures are the most common causes.

High ankle sprains most commonly occur when your foot is planted on

the ground and then an excessive outwards twisting of your foot occurs.

High ankle ligaments can also sprain when your ankle is loaded severely and

pushed into excessive dorsiflexion. This often occurs in football tackles.

(b)What are the ways to avoid track and field injuries?

Start slow and gradually, never increase training by more than 10% per

workout AND 10% per week. Good warm up and cool down, maintain good

strength to get this, try hitting the gym. Stay well hydrated and dont diet

while training because this will affect your workouts.

The amount of training you carry out plays a key role in determining

your real injury risk. Studies have shown that your best direct injury

predictor may be the amount of training you completed last month. Fatigued

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muscles do a poor job of protecting their associated connective tissues,

increasing the risk of damage to bone, cartilage, tendons and ligaments. If

you are a runner, the link between training quantity and injury means that

the total mileage is an excellent indicator of your injury risk. The more miles

you accrue per week, the higher the chances of injury. One recent

investigation found a marked upswing in injury risk above 40 miles of

running per week.

If you have been injured before then you are much more likely to get

hurt than an athlete who has been injury free. Regular exercises have a way

of uncovering the weak areas of the body. If you have knees that are put

under heavy stress, because of your unique biomechanics during exercises,

your knees are likely to hurt when you engage in your sport for a prolonged

modification to your biomechanics then your knees are likely to be injured

again.

The second predictor of injury is probably the number of consecutive

days of training you carry out each week. Scientific studies strongly suggest

that reducing the number of consecutive days of training can lower the risk

of injury. Recovery time reduces injury rates by giving muscles and

connective tissues an opportunity to restore and repair themselves between

work-outs.

http://www.brianmac.co.uk/physiol.htmhttp://www.brianmac.co.uk/physiol.htm
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Reflection

1. What have you learned during the implementation of this project work?

Throughout the project while I was conducting it, I have learned many

things. I have realized the importance of mathematics in daily life apart from

the regular calculations of simple numbers. Moreover, I have learnt to be

more patient and not to give up easily when doing my work. These are the

positive attitudes one should have to be able to do something successfully.

Besides, I learned how to cooperate with friends. My friends and I discussed

about the project and we shared ideas amongst ourselves. This discussionhas made me more confident when doing something. I also learned the ways

to communicate with the people around us when I try to ask information

from the workers, designer, architect and engineer.

2. List the good values that you have practiced during this project.

I have practiced several good values while carrying out this project work

such as self-discipline. I have tried my very best to complete this project

work without procrastinating and hence, managed to hand it in on time. This

project had taught me to be responsible on the works that are given to me

and to be completed. Nevertheless, I have to be hardworking when doing the

tasks given and have to be patient when solving problems that occurred.

Besides, I have also practiced teamwork with my fellow friends by sharing

ideas and information throughout the process of doing this project work. I

have also learnt to be polite when talking or asking information from other

people. By practicing all these good values, I have succeeded in completing

this project work of Additional Mathematics.