kerja projek matematik tambahan 2011 (adib nyaer!!!)

8/6/2019 Kerja Projek Matematik Tambahan 2011 (Adib Nyaer!!!)

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ADDITIONAL MATHEMATIC 2011

PROJECT WORK

3

~CARTESIAN COORDINATE~

NAME : MUHAMMAD ADIB IDZAM BIN MOHD ZAMRI

IC NO.: 940122-07-5597

SCHOOL: SMK SULTAN AZLAN SHAH

CLASS: 5ST

TEACHER: MOHD ZULKHAIRI B MAT RIPIN

TABLE OF CONTENTS

Num.

Contents PAGE


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1 ACKNOLEDGEMENT2 OBJECTIVE3 Part 1

4 Part 2-Question (a)-Question (b)-Question (c)-Question (d)

5 Part 3-Question (a)-Question (b)-Question (c)

6 Further Exploration-Question (a)-Question (b)

ACKNOLEDGEMENT

First of all, I would like to say thank you to my parents for providing me

with the outstanding supports. Im very thankful with their helps in providing

a lot of money to buy materials in finishing the project and also their advices.

They also provided me with facilities such as internet access, books,

computers and etc.

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Next I would love to thank my beloved teacher, En. Zulkhairi for

guiding me throughout the project. His guide was helpful as I can finish the

project easily. He never give up guiding me. He did gave me few tips in

finishing the project given.

Besides that, Im also want to thank my friends who always lending

helpful hands to me. Even though the project is individually, but we did

cooperate doing this given project especially in brain storming and sharing

ideas to ensure we finished the project magnificently.

Last but not the least, any party which involved either directly or

indirect in completing this project work.. THANK YOU.

OBJECTIVESTHE AIM CARRYING OUT THE PROJECT WORK ARE:

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 increase students interest and confidence.


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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 mathematic.

PART 1


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QUESTION:

Rene Descartes, a renowned French Mathematician in the 16 th century, discovered

the beauty of Cartesian coordinates system while lying on his back and gazing at a

spider on the ceiling. Do some research and write about his discoveries.

ANSWER:

The Cartesian plane is named after the mathematician Rene Descartes. When 2

perpendicular number lines intersect, a Cartesian Plane is formed. Points on the

Cartesian plane are called 'ordered pairs'.

Descartes was able to work with algebra in geometric figures because of his

'discovery' that position could be plotted on a coordinate grid made from two

perpendicularly intersecting number lines, where any point could be located using a

unique ordered pair (x , y). This grid is named in his honour.

Descartes invented the system of using the first letters of the alphabet to represent

known quantities, and the last letters to represent unknowns. For example, in the

quadratic equation ax2 + bx + c = 0, the letters a, b, and c represent known values

(coefficients), while x represents the unknown solution to the equation.

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PART 2

Malaysia with its tropical climate is rich in flora and fauna. Beautiful gardens

are found all over Malaysia. SMK Permata decided to beautify the school

compound by getting the students involved in the planting and maintenance

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of the greenery in the school compound as shown in diagram 1. Each society

is allocated a plot of land in various shapes and sizes to nurture throughout

the year. The Mathematics Society, English Language Society and Malay

Language Society are allocated the region P, Q and R respectively as shown

in diagram 1.

Question:

(a)Determine the area of region P, Q and R by using at least three

different methods including the use of calculus. Verify the answers

obtained by using computer software. (Suggestions: GeoGebra, GSP,

graphing calculator etc)

Answer:

(a) to determine area

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METHOD 1: Using calculus, integration method

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METHOD 2: TO DETERMINE THE AREA FOR

DIFFERENT GEROMETRICAL SHAPES


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Area P: Using the formula for area of triangle , trapezium and rectangle.

Area Q: Using the formula for area of trapezium.

Area R: Using formula for area of trapezium and rectangle.

METHOD 3: USING FORMULA BASED ON

COORDINATES. 1


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QUESTION:

(b) Suppose there is a hedge along AB. The Mathematics Society wishes to

fence up the remaining sides of the region P. Determine the length of fence

required.

ANSWER:

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QUESTION:

(c) If a meter offence costs RM25.00, what is the total cost required by the

Mathematics Society to fence up region P? is it possible for the society to

carry out the fencing with an allocation of RM250.00? Explain your answer.

ANSWER:

The society does not have enough funds to fence up its plot of land.

QUESTION:

(d) During the Mathematics Week, the society was given a single flag chain of

length 9.20 meters to be used completely. The President of the society

wishes to tie the flag chain continuously from A to E and then to another

point along the hedge AB to crate a triangular-shaped area.

(1) Make a conjecture about the number of points that the flag chain can be

tied to along AB.

Support your conjecture with suitable calculations. Explain your answer.

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(2) Calculate the maximum area of the triangle obtained.Discuss.

ANSWER:

(1) 2 points.

(2)For maximum area, point k is chosen.

Maximum area enclosed =

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PART 3


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The Mathematic society decided to build a pond in region P as shown in

Diagram 2. The pond is in shape of a sector with center E, radius ED and a

depth of 1 meter.

QUESTION:


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(a) Calculate the angle AED, in radians, by using at least two

different methods.

ANSWER:

METHOD 1: Using Cosine Rule

METHOD 2: Using simple trigonometric ratio.

QUESTION:

(b) Determine the volume of water that has to be pumped in to fill

up 80% of the pond.

ANSWER:


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Volume of water to be pumped in =

QUESTION:(c) If the water is pumped into the pond at a constant rate of

0.001m3s-1, calculate

(1)- the rate of change of depth of water

(2)- the depth of water after 10 minutes

(3) the minimum time taken, in minutes, before the water

overflows, and

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(4)- the minimum time taken, in minutes, before the water

overflows, if the pond is triangular-shaped AED and has a depth of

2 meters.

ANSWER:

(1)

(2)Depth of water after 10 minutes =

(3) Time taken =

(4)


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Area of

Total volume of the water =

Minimum time taken =

FURTHEREXPLORATION

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Maps has been used for thousands of years to aid travelers during their

journey from one place to another. Maps can also be used to estimate

distance between places. In the year 2014, a recreation park will be

constructed in town marked X on the map of Malaysia in as shown Diagram

3. This town has the latitude of 50 41 N and has the same longitude as the

city of Malacca.

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QUESTION:

(a) Explore and find the distance between these two places in kilometer by

using,

(1) the map in Diagram 3

(2)the formula given below:

Where = difference in latitudes in degrees.

Is there a different between the answers obtained? Explain.

Distance= x60nauticallines

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ANSWER:

(1) Shortest distance measured = 360km

(2) Surface distance using formula =387km

QUESTION: 2


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Surf the Internet and use Google map to locate the position of your school

and two nearby hospitals/clinics. Print a copy of this Google map and mark

the position of these three places.

(1) solve the triangle obtained

(2) calculate the shortest distance from your school to the line joining the two

hospitals/clinics.

If internet service is not available, u can perform this task by using a

detailed map of your town.

ANSWER:

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2


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REFLECTION


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In the process of conducting the project, I have learnt that perseverance pays

off, especially when you obtained a just reward for all your hard works. For

me, succeeding in completing this project work has been reward enough. I

have also learnt that mathematics is used everywhere in daily life, from the

simple thing like beautify school compound, to determining distance between

places. Besides that, I have learned a large number of moral values that I

practice. This project work taught me to be more confidence when doing

something especially the homework given by the teacher. I also learned to be

more disciplined student who is punctual and independent.

kerja projek matematik tambahan 2011 (adib nyaer!!!)

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