assignment for additional mathematics

 CONTENT

Acknowledgement

Objectives

Introduction

Part 1

Part 2

Part 3

Further Exploration

Conclusion

Reflection

ACKNOWLEDGEMENT

First 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 as money, to buy anything that are related to this project work and their 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 not procrastinate in doing it.

Then I would like to thank my teacher  forguiding me and my friends throughout this project. We had some difficulties 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 but not least, my friends who were doing this project with me and sharing our ideas. They were helpful that when we combined and discussed together, we had this task done.

OBJECTIVES

-          The 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 solving in 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

INTRODUCTION

We as additional mathematic learner has been asked to do project about solving problem using additional mathematic.This year we have been given a choice of choosing between two topic.The topics are sketching track field and assorted muffin.We must choose one of the topic and finish the assignment according to our priority in answering the question.This project can be done individual or group,and with pleasant i choose to do individualy.When this project is done

- Experienced a challenging classroom environment, interesting and meaningful, then the improve thinking skills

- Experience a classroom environment where knowledge and skills used in a meaningful way in solving real-life problems

- Experience completing projects to stimulate and enhance effective learning

- Acquire mathematical skills effectively through oral and written, and using the language of mathematics to express mathematical ideas and accurate

- Mathematical knowledge and skills through problem solving in ways that increase their interest and confidence

- Prepare ourselves to meet our future in the field of endeavor

- Realize that mathematics is an important and powerful tool in solving problems in life and to develop positive attitudes towards mathematics

- Train ourselves to appreciate the intrinsic value of mathematics and be more creative and innovative

- Realize the importance and beauty of mathematics

Part 1

i)Show  that an athlete running in the first lane will cover 400 metres in one lap of the track.

                                                                    

r = 38.2

θ

 = 180° X π/180°

   = π

                                                             

s=r θ

s = 38.2 X π

s = 120 M

   s=r θ

s = 38.2 X π

s = 120 M

                     Total Perimeter = 120 M + 120 M + 80 M + 80 M = 400 M

Part 2

(i)                  Calculate the distance of running in the second lane until the eight lane.

Complete the table 1.

Lane	Diameter (m)	Perimeter / Running Distance (m)
1	76.4	400
2	78.4	406.3
3	80.4	412.58
4	82.4	418.87
5	84.4	425.15
6	86.4	431.43
7	88.4	437.72
8	90.4	444

Table 1

(i)Used another method to find the running distance / perimeter.

a=400

d=6.3

Tn=a+(n-1)d

Lane	Diameter  (m)	Calculation	Perimeter (m)
1	76.4	400+(1-1)6.3	400
2	78.4	400+(2-1)6.3	406.3
3	80.4	400+(3-1)6.3	421.6
4	82.4	400+(4-1)6.3	418.9
5	84.4	400+(5-1)6.3	425.2
6	86.4	400+(6-1)6.3	431.5
7	88.4	400+(7-1)6.3	437.8
8	90.4	400+(8-1)6.3	444.1

Table 2

Part 3

(a)    (i)Calculate the difference distance from the starting position for each lane . The  running distance of each athlete should 400 metre for a lap.

Complete Table 2.

Comparision between  lanes	Calculation	Difference distance  (m)
Lane 1 & Lane 2	406.3 – 400	6.3
Lane 2 & Lane 3	412.58 – 406.30	6.3
Lane 3 & Lane 4	418.86 – 412.58	6.3
Lana 4 & Lane 5	425.15 – 418.86	6.3
Lane 5 & Lane 6	431.43 – 425.15	6.3
Lane 6 & Lane 7	437.71 – 431.43	6.3
Lane 7 & Lane 8	443 – 437.71	6.3

Table 3

(ii)Used another method to find the difference distance between the lane

a=406.3-400

a=6.3

Lane	Diameter Difference (m)	Calculation	Arc Difference (m)
Lane 1 & Lane 2	2	2 X 3.141	6.282
Lane 2 & Lane 3	2	2 X 3.141	6.282
Lane 3 & Lane 4	2	2 X 3.141	6.282
Lana 4 & Lane 5	2	2 X 3.141	6.282
Lane 5 & Lane 6	2	2 X 3.141	6.282
Lane 6 & Lane 7	2	2 X 3.141	6.282
Lane 7 & Lane 8	2	2 X 3.141	6.282

Table 4

(b)Sketch the athletic track plan with eight lanes, showing the starting position each lane.

  

Further Question

1)      To construct a 400 (m) track in your school field,it is suggested to have at least four lanes. Suggest the minimum area for track. Give your reasons.

diameter 4 lanes-83.4 M

Area = Length x Witdh

Length=75.4+4+4

               =83.4                       

Witdh= 80+4+4+ (75.4/2)+(75.4/2)

           =163.4

83.4 x 163.4 =13627.56m²

2)      Calculate the area of the school field.How many maximum lanes can be constructed based on your findings ?

Hence ,if your school wish to construct the eight lanes track,find  the approximate minimum area needed. Give your reasons.

Area field

Length x Witdh

=200m x 500m

=50000m²

Minimum area for 8 lanes= length x Witdh

Length= 75.4 + 8 + 8 =91.4

Witdh=80 + (75.4/2) + (75.4/2) + 8 +8 =171.4

          =171.4 X 91.4= 15665.96 m²

Field for  can build 3 track 8 lanes because 15665.96 m² x 3 =46997.88 m²

3)      For the standard sport even, a site for discus throw with a sector shape will be built in the field of the athletic track. You can find the information  from internet , sport magazines and sport teachers.

a)      Find the approximate area for the site.

           Area = Length x Witdh

          Length= 50 + 2.5/2 = 51.25 m

          Witdh=  2.5+ 0.75 + 0.75= 4

          Area= 51.25 x 4 = 205

                                                                                                                                      

b)    Using the suitable scale, draw and label the diagram of the site.Determine the standard  angle of the center of the sector.

                                        

c)       Suggest the range of the distance for the score obtained ( score1, score2, score3 )

         50 / 3 = 16.66666667

d)      Calculate the area covered representing each point / score.

       Area sector 1= 1/2 (16.667)² x  ( 34.92 x (22/7 /180)

                                           =84.65185469

   

       Area sector 2 = 1/2 (16.667 + 16.667)² x (34.92 x (22/7 /180)

                                       = 338.7437081 – 84.65185649

                                       = 254.0918534

    

       Area sector 3 = 1/2 (16.667 + 16.667 +16.667)² x (34.92 x (22/7 /180)

                                        =762.1733432 – 254.0918534 – 84.65185469

                                        = 423.4296351


CONCLUSION


After doing research, answering the questions, plan a table and some problem solving,we saw that usage of circular measure  is important in our daily  activity. It is not justwidely use in the sport but also in certain job like the engineer used this method to solve the problem. We learnt a lot of lesson from this Additional Mathematics Project Work such as measure skill using different method. Without this,the athletes cannot used the track effectively because of the measure is not accurate.We would like to thanks the one who contribute the idea of circular measure and progression  to help us a lot in our  activity everyday.