Contoh Folio Addmath 2010 (Project Work 1)

 Additional Mathematics Project Work 1  

Additional mathematics project work 1

Nama kt sini 480123-3912-1329 5sc1 Pn. Cikgu Sekolah Menengah Kebangsaan

……….

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 Additional Mathematics Project Work 1  

Contents Appreciation Objectives Introduction

6-9

Procedure and Findings

10-14

 Further Exploration

Conclusion Reflection References

18

Appendix

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 Additional Mathematics Project Work 1  

Appreciation Firstly, I would like to give a big thanks to my parents for providing everything, such as money, to buy anything that are related to this project work, their advice and support. Then, I want to thank my teacher; Pn. Cikgu for teaching me Additional Mathematics form 5 and guiding me throughout this project.

Last but not least, my friends who were doing this project with me and sharing our ideas and knowledge. They were helping each other so we can complete our project without any problems.

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 Additional Mathematics Project Work 1  

Objectives The objectives of this project work are:

 Apply and adapt a variety of problem-solving strategies to solve problems.

knowledge through problem solving in a way that  Develop mathematical knowledge

increases students’ interest and confidence.

 Develop positive attitude towards mathematics.

 Improve thinking skills and creativity.

communication.  Promote efficiency of mathematical communication.

 Provide learning environment that stimulates and enhances effective

learning.

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 Additional Mathematics Project Work 1  

Introduction Around AD 1000, the Islamic mathematician Ibn al-Haytham (Alhacen) was the first to derive the formula for the sum of the fourth powers of an arithmetic progression, using a method that is readily generalizable to finding the formula

for the sum of any higher integral powers, which he used to perform integration. In the 11th century, the Chinese polymath Shen Kuo developed 'packing' equations that dealt with integration. In the 12th century, the Indian In dian mathematician, Bhāskara II, developed an early derivative representing infinitesimal change, change, and he described an early form of Rolle's Theorem. Also in the 12th century, the Persian mathematician Sharaf alDīn al-Tūsī  discovered the derivative of  cubic

polynomials , an important result in

differential calculus .

In the 14th century, Indian mathematician Madhava of Sangamagrama, along with other mathematician-astronomers mathematician-astronomers of the Kerala School of astronomy and mathematics, described special cases of Taylor series, which are treated in the text Yuktibhasa. In the 19th century, calculus was put on a much more rigorous footing by mathematicians such as Cauchy, Riemann, and Weierstrass. It was also during this period that the ideas of calculus were generalized to Euclidean space and the complex plane. Lebesgue generalized the notion of the integral so that virtually any function has an integral, while Laurent Schwartz extended differentiation in much the same way. Calculus is a ubiquitous topic in most modern high schools and universities

around the world.

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 Additional Mathematics Project Work 1  

Procedure and Findings (A) Function I

Maximum point (0,4.5) and pass through point (2,4)

  −     −  =

2

+

2

+ 4.5

b=0, c=4.5 = =

2

+ 4.5 ---------- (1)

Substitute (2,4) into (1)

    −  −   

4=

2

2

+ 4.5

4

+ 4.5 = 4

4

=

=

0.5 .

+

.

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 Additional Mathematics Project Work 1   Function II

Maximum point (0,0.5) and pass through point (2,0)

  −     −      −−  −    =

2

+

2

+ 0.5

b=0, c=0.5 =

0

=

2

0=

2

4

=

=

=

+ 0.5 ---------- (2) 2

+ 0.5

0.5

0.125 .

+

.

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 Additional Mathematics Project Work 1   Function III

Maximum point (2,4.5) and pass through point (0,4)

  −     −  =

2

+

2

+ 4.5 ---------- (3)

b=2, c=4.5 =

2

Substitute (0,4) into (3)

 −   −−  −   −    4=

0

2

4= 4

+ 4.5

4

0.5

=

=

=

2

+ 4.5

0.125 .

+

.

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 Additional Mathematics Project Work 1   (b)

2

− −   ⅆ − −    −− −   

= 4×1

2

0.125

2

+ 0.5

0

0.125

=4

2

3

2

3

+ 0.5

0

2

=4 =

2

3

4

0

=4

3

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 Additional Mathematics Project Work 1  

Further Exploration (a) (1) Structure

Area

=2

2 3



2

2

Volume = 2 × 0.4 = Cost

=

3 16 15 16 15



3

× 840

= RM896.00

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 Additional Mathematics Project Work 1   Structure 2

Area

=4×1

 

= 3

2

−

1 2

× 4 × 0.5

Volume = 3 × 0.4 = 1.2 3 Cost

= 1.2 1.2 × 840 840 = RM1008.00

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 Additional Mathematics Project Work 1   Structure 3

Area

−     1

=4×1 = 2.75

2

× 1 + 4 × 0.5

2

Volume = 2.75 × 0.4 = 1.1 3 Cost

= 1.1 1.1 × 840 840 = RM924.00

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 Additional Mathematics Project Work 1   Structure 4

Area

=4×1

 

= 2.5

−   1 2

× 2 + 4 × 0.5

2

Volume = 2.5 2.5 × 0.4 0.4 =1 3 Cost

= 1 × 840 = RM840

Conclusion The minimum cost to construct is Structure 4.

(2) As the president of the Arts Club, I would like to choose structure 4 because it is the cheapest and I can minimize the construction cost.

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 Additional Mathematics Project Work 1   (B) (1) 2

k (m) 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Area to be painted (m ) 3 2.9375 2.875 2.8125 2.75 2.6875 2.625 2.5625 2.5

Area to be painted was calculated using this formula: 4

−    1 2

4+

0.5

(B) (2)

Areas to be painted are: 3, 2.9375, 2.875, 2.8125, 2.75, 2.6875, 2.625, 2.5625, and 2.5 This is an Arithmetic Progression (AP) with Common difference, d = 2.9375 - 3 = -0.0625 or d = 2.875 - 2.9375 = -0.0625 When k increases by 0.25m, the area to be painted decreases by 0.0625 m (C)

−    −   − −   − 

Area of concrete structure = 4 × 1 =4 =4

= 3 When

→ →

1

1

4+

4

1

1 4

2

4

4

1 4

1

∴ Area →  2

4+

2

2

14

0.5

 Additional Mathematics Project Work 1  

CONCLUSION I notice that quadratic function and integration so close in our daily life. Solving problems will be easy by using calculus as well as quadratic function. As the result, we can calculate and identify problems involving integration (calculus) and quadratic function.

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 Additional Mathematics Project Work 1  

Reflection I found a lot of information while conducting this project. Moreover, this project encourages the student to think critically to identify and solve problems. It is also encourage student to gather information using the technologies such as the internet, improve thinking skills and promote effective mathematical communication. Lastly, I proposed this project should be continue because it brings a lot of advantages to the student and also test the student’s understanding in Additional Mathematics.

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 Additional Mathematics Project Work 1  

Reference   

Additional Mathematics Textbooks http://en.wikipedia.org/wiki/Calculus http://en.wikipedia.org/wiki/Integration_( http://en.wikipedia.org/ wiki/Integration_(mathematics) mathematics)

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 Additional Mathematics Project Work 1  

Appendix

18