form 4 add maths project - copy

8/7/2019 Form 4 Add Maths Project - Copy

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PROJECT WORK FOR

ADDITIONAL MATHEMATHICS

-2010-

PROJECT WORK 1

Name Lim Looi Ling

Class 4C

I/C 941122-14-6724

Teacher Mdm Sarah

School Wesley Methodist School


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Content

CONTENTS PAGES

OBJECTIVE 2

INTRODUCTION 3-4

PART 1 (QUESTION) 5-8

PART 2 (FURTHER EXPLORATION) 9-16

REFLECTION 17

RUBRIC 18-19


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Objective

i. To apply and adapt a variety of problem-solving strategies to solve

problems;

ii. To improve thinking skills;

iii. To promote effective mathematical communication;

iv. To develop mathematical knowledge through problem solving in a way

that increases students interest and confidence;

v. To use the language of mathematics to express mathematical ideas

precisely;

vi. To provide learning environment that stimulates and enhances effective

learning;

vii. To develop positive attitude towards mathematics.


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Introduction

The diagram below shows the gate of an art gallery. A concrete structure

is built at the upper part of the gate and the words ART GALLERY is written on

it. The top of the concrete structure is flat whereas at the bottom is parabolic in

shape. The concrete structure is supported by two vertical pillars at both ends.

The distance between the two pillars is 4 metres and the height of the

pillar is 5 metres. The height of the concrete structure is 1 metre. The shortest

distance from point A of the concrete structure to point B, that is the highest

point on the parabolic shape, is 0.5 metres.


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Question:

(a) The parabolic shape of the concrete structure can be represented byvarious functions depending on the point of reference. Based ondifferent points of reference, obtain at least three different functions

which can be used to represent the curve of this concrete structure.

(b) The front surface of this concrete structure will be painted before thewords ART GALLERY is written on it. Find the area to be painted.

Solution:

(a)Function 1


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Function 2


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Function 3


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(b)


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Further Exploration

(a) You are given four different shapes of concrete structures as shown inthe diagrams below. All the structures have the same thickness of

40cm and are symmetrical

(i) Given that the cost to construct 1 cubic metre of concrete isRM840.00, determine which structure will cost the minimum to

construct.

(ii) As the president of Arts Club, you are given the opportunity todecide on the shape of the gate to be constructed. Which shape

would you choose? Explain and elaborate on your reasons forchoosing the shape.


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Solution:

(i) Structure 1


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Structure 2


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Structure 3


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Structure 4

(ii) As the president of the Arts Club, I will decide Structure 4 as the shape of

the gate to be constructed. It is because Structure 4 will cost the minimum and

it is easier to be constructed compared to Structure 1 which is a curve.


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(b) The following questions refer to the concrete structure in the diagram

below.

If the value ofkincreases with a common difference of 0.25 m;

(i) Complete Table 1 by finding the values ofkand the corresponding areasof the concrete structure to be painted.

(ii) Observe the values of the area to be painted from Table 1. Do you seeany pattern? Discuss.

k(m) Area to be painted()0.00 0.25

0.50 0.75 1.00 1.25 1.50

1.75 2.00


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(ii) There is a pattern in the area to be painted.

The area to be painted decreases as the kincreases 0.25m and form a series of

numbers:

3, 2.9375, 2.875, 2.8125, 2.75, 2.6875, 2.625, 2.5625, 2.5

We can see that the difference between each term and the next term is the

same.

We can deduce that this series of numbers is an Arithmetic Progression (AP),with a common difference,

In conclusion, when kincreases 0.25m, the area to be painted decreases by

-0.0625


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(c) Express the area of the concrete structure to be painted in terms ofk. Find

the area when kapproaches the value of 4 and predict the shape of the

concrete structure.

The shape of the concrete structure will be a rectangle with length 4m and

breadth 0.5m, which may look like this:


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Reflection

While I conducting the project, I had learned some moralvalues that I practice. This project had taught me toresponsible on the works that are given to me to be

completed. This project also had make me felt moreconfident to do works and not to give up easily when wecould not find the solution for the question. I also learned to

be more discipline on time, which I was given about amonth to complete this project and pass up to my teacher

just in time. I also enjoy doing this project during my school

holiday as I spend my time with friends to complete thisproject and it had tightened our friendship.


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RUBRIC FOR ADDITIONAL MATHEMATICS PROJECT WORK 1/2010Name: Narendar a/l Samuthiram Form: 5 Elit

A. Report Presentation

1. General

Aspect (6%)

Appropriate title. 1

Contents page. 1

Systematic presentation. 1 2

Creativity. 1 2

2. Introduction

(7%)

Comprehensive introduction may include

history/moral/aesthetical values and others.5 7

Satisfactory introduction. 3 4

Incomplete introduction. 1 2

B. Task Specification

1. Specify the

Task (5%)

Identify and state all given information and required

results in proper mathematical statements.4 5

Identify and state given information and required

results incompletely. 1 3

C. Problem-Solving

1. Procedure

(42 %)

Evidence of making and proving conjectures. 3 5

In-depth understanding of the problem.

Use very efficient problem solving strategies.

Answer all questions correctly.

20 25

Understand the problem.

Use strategies that lead to solutions of the problems.

Answer all questions correctly.

10 19


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Partially understand the problem.

Use strategies that are partially useful.

Do not answer all questions correctly.

1 9

Concise and efficient communication using

symbol/tables/diagrams when necessary. 8 12

Not concise and inefficient communication. 1 7

2. Findings

(20%)

Answer all questions correctly. 8 12

Partially answer questions correctly. 1 7

Detail discussion of findings. 5 8

Satisfactory discussion of findings. 1 4

3. Exploration

(10%)

Explore the task concisely and efficiently. 6 10

Explore the task. 1 5

D. Conclusion

1. Conclusion

(5 %)

Draw relevant conclusions/generalisation. 2 5

E. Reflection

1. Reflection

(5 %)

Comprehensive reflection. 1 5

Total score (A1 + A2 + B1 + C1 + C2 + C3 + D1 + E1) 100

form 4 add maths project - copy

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