Addmath Project Work HANIF

7/31/2019 Addmath Project Work HANIF

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NAME : MOHD SHAFIQ BIN ABDUL

RAHMAN

FORM : 5 IHSAN

TEACHER : MISS NUR BAITI AKMAL BINTINANI


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INTRODUCTIONWe students taking Additional Mathematics are required to carry out a project work

while we are in Form 5. This year the Curriculum Development Division, Ministry of

Education has prepared four tasks for us. We are to choose and complete only one task based

on our area of interest. This project can be done in individually. Upon completion of the

Additional Mathematics Project Work, we are to gain valuable experiences and able to:

Apply and adapt a variety of problem solving strategies to solve routine and non-routine

problems

Experience classroom environments which are challenging, interesting and meaningful

and hence improve their thinking skills.

Experience classroom environments where knowledge and skills are applied in

meaningful ways in solving real-life problems

Experience classroom environments where expressing ones mathematical thinking,

reasoning and communication are highly encouraged and expected

Experience classroom environments that stimulates and enhances effective learning.

Acquire effective mathematical communication through oral and writing, and to use the

language of mathematics to express mathematical ideas correctly and precisely

Enhance acquisition of mathematical knowledge and skills through problem-solving inways that increase interest and confidence

Prepare ourselves for the demand of our future undertakings and in workplace

Realize that mathematics is an important and powerful tool in solving real-life problems

and hence develop positive attitude towards mathematics.

Train ourselves not only to be independent learners but also to collaborate, to cooperate,

and to share knowledge in an engaging and healthy environment

Use technology especially the ICT appropriately and effectively

Train ourselves to appreciate the intrinsic values of mathematics and to become more

creative and innovative

Realize the importance and the beauty of mathematics.

We are expected to submit the project work within three weeks from the first day the

task is being administered to us. Failure to submit the written report will result in us not

receiving certificate.


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APPRECIATIONFirst and foremost, I would like to thank my Additional Mathematics teacher, Miss. Nur

Baiti Akmal Binti Nani as she gives us important guidance and commitment during this project

work. She has been a very supportive figure throughout the whole project.

I also would like to give thanks to all my friends especially 5 Ihsan members for

helping me and always supporting me to help complete this project work. They have done a

great job at collecting form 4 end of year result for additional mathematics and sharing

information with other people including me. Without them this project would never have had

its conclusion.

For their strong support, I would like to express my gratitude to my beloved parents.

Also for helping me to find the mark to complete this project. They have always been by my

side and i hope they will still be there in the future.

Last but not least, i would also like to thank all the teacher and my friend for helping

me collect the much needed data and statistics for this. Not forgetting too all the other people

who were involved directly or indirectly towards making this project a reality.


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HISTORY OF CIRCULAR

MEASURE

HISTORY OF CIRCULAR MEASURE

The concept of radian measure, as opposed to the degree of an angle, is normally credited toRoger Cotes in 1714. He had the radian in everything but name, and he recognized its

naturalness as a unit of angular measure. The idea of measuring angles by the length of the arc

was used already by other mathematicians. For example al-Kashi (c. 1400) used so-called

diameter parts as units where one diameter part was 1/60 radian and they also used sexagesimal

subunits of the diameter part.

The term radian first appeared in print on 5 June 1873, in examination questions set by

James Thomson (brother of Lord Kelvin) at Queen's College, Belfast. He used the term as early

as 1871, while in 1869, Thomas Muir, then of the University of St Andrews, vacillated between

rad, radial and radian. In 1874, Muir adopted radian after a consultation with James Thomson.

DEFINITION OF CIRCULAR MEASURE

What is Circular Measure?

Circular Measure is a measuring system used in measuring circles. It is also used in measuring

angle in radian.

Example :-

1 circle = 360 degrees (4 quadrants)

1 quadrant = 90 degrees

1 degree = 60 minutes

1 minute = 60 seconds.


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How to use units of Circular Measurement?

Many methods have been used throughout history to measure the arc of a circle,

although only two remain in common use, the degree and the radian. The degree probably

originated with the ancient Babylonians at least 3,000 years ago. The radian, as a unit of

circular measure, is usually credited to Roger Cotes in 1714.

Instructions :

1) Use degrees for most practical applications. The Babylonians probably divided a circle

into 360 parts because the number 360 has so many factors and because the year was

composed of a little more than 360 days. This is still the most widely-used unit of

circular measure today.

2) Express arcs in radians for mathematical purposes. This is a more natural unit of

measure and is used almost exclusively in mathematics. It measures the circumference c

of a circle in terms of its radius r. From geometry we know that c = 2 pi r. c/r = 2 pi, so

a radian divides a circle into 2 pi, or about 6.28 parts

3) Convert degrees d into radians by multiplying the number of degrees by pi/180. 360

degrees is equal to 2 pi radians so d degrees = 2 pi d/360 radians = pi d/180 radians.

4) Calculate the radians r by multiplying the degrees by 180/pi. 2 pi radians = 360 degrees

so r radians = 360/2 pi degrees = 180/pi degrees.

5) Work with grads under very limited circumstances. This unit is 1/400 of a circle and

was introduced as part of the metric system, but it was only adopted in specific areas

such as surveying. Today, the grad is only used in the French artillery.


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QUESTION 2

a) Estimation Method 1 : (AREA)

Area of pavement = ( 300 - 100 )

Area of tile = 25 10

Number of tiles = ( 300 - 100 ) (25 10 )

= 1005

Estimation Method 2 : ( Using concept of Arithmetic progression )

Starting from the interior.

The number of tiles for the first layer =

The number of tiles for the second layer =

The number of tiles for the third layer =


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This is an arithmetic progression with a = , d =

Number of tiles

i. Comparison between the two methods. Choose the best.

Method 2 is has a more accurate estimation compared to Method 1. Method 2 takes

into consideration the spaces between tiles whereas Method 1 does not. Method 1

is quick and simple therefore easier to understand. This is a major reason why it is

being practiced by most masons with some modification. These masons, with theirexperience, will deduct or add a certain number of tiles from the estimation of the

total number of tiles required by the are calculated to compensate for the space used

between tiles, and the calculations are quite accurate.

ii. Which method is most used?

Method 2 since it is more accurate than Method 1.


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b)

1) Tiles needed for octagon shape

Method 1 (AREA)

Area of one trapezium =

Area of octagonal pavement =

Number of tiles =

= 905

Method 2 (ARITHMETIC PROGRESSION)

Referring to the diagram below,


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PQ = 2OP sin 22.5

P1Q1 = PQ + 2P1R1

P2Q2 = P1Q 1+ 2P2R2

P1R1 = P2R2 = 10 tan 22.5

Thus, this is an arithmetic progression.

The number of layers required.

PP1 = P1R2 =

=

= 18.4776 18

a = PQ = 200 sin 22.5

and d = 2P1R1 = 20 tan 22.5

Number of tiles required =

Total number of tiles for the octagon pavement = 8 106

= 848

2) Comparison between circle shape and octagonal shape pavement

Comparing the circle and octagonal shape, the octagonal shape is easier to construct

because it is made of straight line layers and we only need to feel a few spaces between the

tiles. If it is in a circle shape, it will be a task to arrange the tiles and fill in the spaces between

the tiles.


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FURTHER EXPLORATION

a) The estimated amount of tiles needed for two circular plots pavement.

Based on the diagram below.


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METHOD 1 (AREA)

67.11

= 1.172 radian

Area of segment KLMN

= (300)(1.172 sin 67.11)

11283.60 cm

Number of tiles required

= 45

Number of tiles required for the pavement

=2(1005 45)

= 1920


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METHOD 2

Calculating the number of tiles required for the arcs passing through points K1, K2, K3, and K4

i. Arc passing through point K1

Arc length =

Number of tiles required

ii. Arc passing through point K2

Arc length =

Number of tiles required 10.47

iii. Arc passing through point K3

Arc length =


iv. Arc passing through point K4


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Arc length = )


v. Total number of tiles required for the pavement

1887

b) Estimate the number of tiles needed for two octagon shaped pavement.

Refer to the diagram below.


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Total area of pavement

Number of tiles required 1762


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c) Choose an alternative shape that is easiest to build the pavement.

I would suggest a rectangular shape since itll be easier to construct and determine the

amount of tiles needed. Besides, the work of filling the spaces in between the tiles can

be reduced because the tiles are rectangular in shape and we can estimate its distance

from each tile.

d) Is it reasonable to use aluminium tins and sand to build the pavement?

No, since the pavement is where people will walk on, and if they use aluminium tins,

itll absorb heat and make the pavement hot. Besides, using aluminium to make

pavements is not very environmental friendly since its much more costly.


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REFLECTIONAdditional Mathematics...From The Day I Born...

From The Day I Was Able To Holding Pencil...

From The Day I Start Learning...

And..

From The Day I Heard Your Name...

I Always Thought That You Will Be My Greatest Obstacle

And

Rival In Excelling In My Life...

But After Countless Of Hours...

Countless Of Days...

Countless Of Nights...

After Sacrificing My Precious Time Just For You...

Sacrificing My Computer Games...

Sacrificing My Video Games...

Sacrificing My Facebook...

Sacrificing My Internet...

Sacrificing My Anime...

I Realized Something Really Important In You...

I Really Love You...

You Are My Real Friend...

You My Partner...

You Are My Soul Mate...

I LOVE YOU ADDITIONAL MATHEMATICS.


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CONCLUSION

After doing research, answering questions, drawing graphs and some problem

solving, I saw that the usage of statistics is important in daily life. It is not just widely used

in markets but also in interpreting the condition of the surrounding like the air or the

water. Especially in conducting an air-pollution survey. In conclusion, statistics is a daily

life necessity. Without it, surveys cannot be conducted, the stock market cannot be

interpret and many more. Therefore, we should be thankful of the people who contribute

in the idea of statistics.


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CONTENT

NO

PAGE

1 Table of content 1

2 Introduction 2

3 Appreciation 3

4 History of Circular Measure 4

5 Part (a) 6

6 Part (b) 8

7 Further exploration 10

8 Reflection 15

9 Conclusion 16

10 References 17


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References

www.worldteacherspress.com

www.heartscan.com.my

www.tips.com.my/article.php

http://nutriweb.org.my

http://www.mediafire.com/view/?baqm4eov5v79hzn

http://mistermukabuku.blogspot.com/2012/06/10-trial-spm-matematik-tambahan.html

Blog A Form 4 Sasbadi by Pua Kim Teck

Preston Additional Mathematics Form 4 & 5 reference book by Tan Li Lan

Fokus Ungu Matematik Tambahan Form 4 & 5 by Wong Teck Sing

Additional Mathematics Form 4 Text Book.
http://www.mediafire.com/view/?baqm4eov5v79hznhttp://mistermukabuku.blogspot.com/2012/06/10-trial-spm-matematik-tambahan.htmlhttp://www.mediafire.com/view/?baqm4eov5v79hznhttp://mistermukabuku.blogspot.com/2012/06/10-trial-spm-matematik-tambahan.html

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Addmath Project Work HANIF