Project Work 1~Add Math!!

8/9/2019 Project Work 1~Add Math!!

1/23

Additional

mathematics projectwork 1

[2010]

calculus in Our Life

NAME :

TEACHER :

I/C :

SCHOOL :


2/23

Question task 1

CURRICULUM DEVELOPMENT DIVISION

MINISTRY OF EDUCATION MALAYSIA

ADDITIONAL MATHEMATICS PROJECT WORK 1/2010

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 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 pointB, that is the highest point on the parabolic shape, is 0.5 metres.

(a) The parabolic shape of the concrete structure can be represented by various functions

depending on the point of reference. Based on different points of reference, obtain at

least three different functions which can be used to represent the curve of this concrete

structure.

5 m

4 m

1 m B

A

0.5 m


3/23

(b) The front surface of this concrete structure will be painted before the words ART

GALLERY is written on it. Find the area to be painted.

FURTHER EXPLORATION

(a) You are given four different shapes of concrete structures as shown in the diagrams

below. All the structures have the same thickness of 40 cm and are symmetrical.

Structure 1 Structure 2

Structure 3 Structure 4

(i) Given that the cost to construct 1 cubic metre of concrete is RM840.00,

determine which structure will cost the minimum to construct.

5 m

1 m

0.5 m

4 m

5 m

1 m

1 m

0.5 m

5 m

4 m

1 m

2 m

0.5 m

4 m4 m

5 m

1 m

0.5 m


4/23

(ii) As the president of the Arts Club, you are given the opportunity to decide on the

shape of the gate to be constructed. Which shape would you choose? Explain

and elaborate on your reasons for choosing the shape.

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

If the value ofkincreases with a common difference of0.25m;

(i) complete Table 1 by finding the values ofkand the corresponding areas of the

concrete structure to be painted.

(ii) observe the values of the area to be painted from Table 1. Do you see any

pattern? Discuss.

k(m) Area to be painted (m2)(correct to4 decimal places)

0

0.25

Table 1

k

0.5 m

1 m

4 m


5/23

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

approaches the value of4 and predict the shape of the concrete structure.

REFLECTION

While you were conducting the project, what have you learnt? What moral values did you

practise? Represent your opinions or feelings creatively through usage of symbols, illustrations,

drawings or even in a song.


6/23

CONTENT

No Contents Page

1 Introduction2 Procedure and Findings3 Further Exploration

4 Conclusion5 Reflection


7/23

INTRODUCTION

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


8/23

Objectives

The aims of carrying out this project work are:-

to apply and adapt a variety of problem-solving strategies to solve problems;

to improve thinking skills;

to prom

ote effectivem

athem

atical comm

unication;

to develop mathematical knowledge through problem solving in a way that increases

students interest and confidence;

to use the language ofmathematics to express mathematical ideas precisely;

to provide learning environment that stimulates and enhances effective learning;

to develop positive attitude towards mathematics.


9/23

Procedure and Findings

Question:

(a) The parabolic shape of the concrete structure can be represented by various

functions depending on the point of reference. Based on different 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 the words

ART GALLERY is written on it. Find the area to be painted.

Answer : (a)

Function 1


10/23

Function 2


11/23

Function 3


12/23

Answer : (b)


13/23

Further Exploration

Question :

(a) You are given four different shapes of concrete structures as shown in the

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 is RM840.00,

determine which structure will cost the minimum to construct.

(ii) As the president of Arts Club, you are given the opportunity to decide on

the shape of the gate to be constructed. Which shape would you choose?

Explain and elaborate on your reasons for choosing the shape.


14/23

(a)~(i) Structure 1


15/23

Structure 2


16/23

Structure 3


17/23

Structure 4


18/23

Answer (a) ~(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.


19/23

Question :

(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 areas of the

concrete structure to be painted.

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

Discuss.

Answer : b ~(i)

k(m) Area to be painted()

0.00 0.25 0.50 0.75 1.00 1.25

1.50 1.75 2.00


20/23

Answer : b ~(ii)

There is a pattern in the area to be painted.

The area to be painted decreases as thek

increases 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 acommon difference,

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

-0.0625


21/23

Question :

(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.

Answer :

(c)

The shape of the concrete structure will be a rectangle with length 4m and breadth 0.5m,

which may look like this:


22/23

Conclusion

After doing research, answering questions, drawing graphs and some

problem solving, I saw that the usage of calculus is important in daily life.It is not

just widely used in science, economics but also in engineering. In conclusion,

calculus is a daily life nessecities. Without it, marvelous buildings cant be built,

human beings will not lead a luxurious life and many more. So, we should be

thankful of the people who contribute in the idea of calculus.


23/23

Reflection

Documents

Project Work 1~Add Math!!