add math project work 2009

8/3/2019 Add Math Project Work 2009

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NO. TITLE PAGE

1. Acknowledgement 2

2. Introduction 3

3. Conjecture 9

4. Discussion 9

5. Identifying Information 11

6. Strategy 12

7. Conclusion 37

8. Attachment 44

9. Appendix 46


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ACKNOWLEDGEMENT

Firstly, I would like to thank our Additional Mathematics teacher,

Madam Cheah Siew Ling for guiding us throughout this project. She

explained and showed us every content of this project clearly.

Next, I would like to thank my friends for giving assistance and

advice about this project. Moreover they also gave me mental support in

doing this project.

Last but not least, I appreciate that my parents fully believed and

supported me throughout this project. They sacrificed their time to send me

to my friends house in order to complete this project. Furthermore they had

contributed money for me to carry out this assignment so that I couldcomplete the assignment in time.


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INTRODUCTION

Our group would like to complete the task given by solving the question related tocircles.

A circle is a simple shape ofEuclidean geometry consisting of those points in aplane which are the same distance from a given point called thecentre. The commondistance of the points of a circle from its center is called itsradius.

Circles are simple closed curves which divide the plane into two regions, an

interior and an exterior. In everyday use, the term "circle" may be used interchangeably

to refer to either the boundary of the figure (known as theperimeter) or to the wholefigure including its interior. However, in strict technical usage, "circle" refers to the

perimeter while the interior of the circle is called adisk. Thecircumferenceof a circle is

the perimeter of the circle (especially when referring to its length).

A circle is a special ellipse in which the two foci are coincident. Circles are conicsections attained when a right circular cone is intersected with a plane perpendicular to

the axis of the cone.In short, a circle is defined as the locus of all points equidistant from a central

point.

Definitions Related to Circles

arc: a curved line that is part of the circumference of a circle

chord: a line segment within a circle that touches 2 points on the circle.

circumference: the distance around the circle.

diameter: the longest distance from one end of a circle to the other.

origin: the center of the circle

pi ( ): A number, 3.141592..., equal to (the circumference) / (the diameter) of any circle.

radius: distance from center of circle to any point on it.sector: is like a slice of pie (a circle wedge).

tangent of circle: a line perpendicular to the radius that touches ONLY one point on thecircle.

Chord, secant, tangent, and diameter Arc, sector, and segment
http://en.wikipedia.org/wiki/Shapehttp://en.wikipedia.org/wiki/Euclidean_geometryhttp://en.wikipedia.org/wiki/Point_%28geometry%29http://en.wikipedia.org/wiki/Plane_%28mathematics%29http://en.wikipedia.org/wiki/Distancehttp://en.wikipedia.org/wiki/Centre_%28geometry%29http://en.wikipedia.org/wiki/Centre_%28geometry%29http://en.wikipedia.org/wiki/Centre_%28geometry%29http://en.wikipedia.org/wiki/Radiushttp://en.wikipedia.org/wiki/Radiushttp://en.wikipedia.org/wiki/Curvehttp://en.wikipedia.org/wiki/Plane_%28mathematics%29http://en.wikipedia.org/wiki/Interior_%28topology%29http://en.wikipedia.org/wiki/Perimeterhttp://en.wikipedia.org/wiki/Perimeterhttp://en.wikipedia.org/wiki/Perimeterhttp://en.wikipedia.org/wiki/Disk_%28mathematics%29http://en.wikipedia.org/wiki/Disk_%28mathematics%29http://en.wikipedia.org/wiki/Disk_%28mathematics%29http://en.wikipedia.org/wiki/Circumferencehttp://en.wikipedia.org/wiki/Circumferencehttp://en.wikipedia.org/wiki/Circumferencehttp://en.wikipedia.org/wiki/Ellipsehttp://en.wikipedia.org/wiki/Focus_%28geometry%29http://en.wikipedia.org/wiki/Conic_sectionhttp://en.wikipedia.org/wiki/Conic_sectionhttp://en.wikipedia.org/wiki/Conical_surfacehttp://en.wikipedia.org/wiki/File:Circle_slices.svghttp://en.wikipedia.org/wiki/File:CIRCLE_LINES.svghttp://en.wikipedia.org/wiki/File:Circle_slices.svghttp://en.wikipedia.org/wiki/File:CIRCLE_LINES.svghttp://en.wikipedia.org/wiki/File:Circle_slices.svghttp://en.wikipedia.org/wiki/File:CIRCLE_LINES.svghttp://en.wikipedia.org/wiki/Conical_surfacehttp://en.wikipedia.org/wiki/Conic_sectionhttp://en.wikipedia.org/wiki/Conic_sectionhttp://en.wikipedia.org/wiki/Focus_%28geometry%29http://en.wikipedia.org/wiki/Ellipsehttp://en.wikipedia.org/wiki/Circumferencehttp://en.wikipedia.org/wiki/Disk_%28mathematics%29http://en.wikipedia.org/wiki/Perimeterhttp://en.wikipedia.org/wiki/Interior_%28topology%29http://en.wikipedia.org/wiki/Plane_%28mathematics%29http://en.wikipedia.org/wiki/Curvehttp://en.wikipedia.org/wiki/Radiushttp://en.wikipedia.org/wiki/Centre_%28geometry%29http://en.wikipedia.org/wiki/Distancehttp://en.wikipedia.org/wiki/Plane_%28mathematics%29http://en.wikipedia.org/wiki/Point_%28geometry%29http://en.wikipedia.org/wiki/Euclidean_geometryhttp://en.wikipedia.org/wiki/Shape


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History of Circles

The compass in this 13th century manuscript is a symbol of God's act ofCreation. Notice also the circular shape of the halo

The circle has been known since before the beginning of recorded history. It is the basisfor the wheel, which, with related inventions such as gears, makes much of modern

civilization possible. In mathematics, the study of the circle has helped inspire the

development of geometry and calculus.

Early science, particularly geometry and Astrology and astronomy, was connected to the

divine for most medieval scholars, and many believed that there was something

intrinsically "divine" or "perfect" that could be found in circles.

Some highlights in the history of the circle are:

1700 BCThe Rhind papyrus gives a method to find the area of a circular field.The result corresponds to 256/81 as an approximate value of.

300 BCBook 3 ofEuclid's Elements deals with the properties of circles. 1880Lindemannproves that is transcendental, effectively settling the

millennia-old problem ofsquaring the circle.

________________________________________________________________________

The task given lets us to understand the relations of circles well and hence learn toapply problem-solving strategies and mathematical skills in our daily life. The learning of

circles would play an important role in building a circular building such as Petronas Twin

Tower. For example the task in part 1(a) is aimed to create awareness among students

that mathematics is applicable in our daily lives.Throughout the project, we know that circle is important because without it, we

would not learn shapes math geometry and other stuff. It helps us concentrate with work

sometimes.
http://en.wikipedia.org/wiki/Wheelhttp://en.wikipedia.org/wiki/Gearhttp://en.wikipedia.org/wiki/Sciencehttp://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Astrology_and_astronomyhttp://en.wikipedia.org/wiki/History_of_science_in_the_Middle_Ageshttp://en.wikipedia.org/wiki/Rhind_papyrushttp://en.wikipedia.org/wiki/Euclid%27s_Elementshttp://en.wikipedia.org/wiki/Ferdinand_von_Lindemannhttp://en.wikipedia.org/wiki/Squaring_the_circlehttp://en.wikipedia.org/wiki/File:God_the_Geometer.jpghttp://en.wikipedia.org/wiki/Squaring_the_circlehttp://en.wikipedia.org/wiki/Ferdinand_von_Lindemannhttp://en.wikipedia.org/wiki/Euclid%27s_Elementshttp://en.wikipedia.org/wiki/Rhind_papyrushttp://en.wikipedia.org/wiki/History_of_science_in_the_Middle_Ageshttp://en.wikipedia.org/wiki/Astrology_and_astronomyhttp://en.wikipedia.org/wiki/Geometryhttp://en.wikipedia.org/wiki/Sciencehttp://en.wikipedia.org/wiki/Gearhttp://en.wikipedia.org/wiki/Wheel


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TASK SPECIFICATION

PART 1

a) The task is carried out by collecting pictures of 5 such objects related to circles orparts of a circle. Some of the examples are clock, wheel, donut, CD-ROM and plate. The

aim is to create awareness among students that mathematics is applicable in our daily

lives.

b) For this part, I used the internet resources as a reference to get the definition of pi

and brief history of pi ().

PART 2

a) Semicircle PAB andBCR of diameter d1 and d2 respectively are inscribed in thesemicircle PQR such that the sum ofd1 and d2 is equal to 10 cm. Table 1 can be

completed by using various values ofd1, and the corresponding value ofd2. For this part,

the formulae I had used to find the length of arcs PQR,PAB andBCR is s =(2r).

The relation between the lengths of arcsPQR,PAB andBCR is determined. Thus, d1+ d2= 10.

b) (i) Semicircle PAB,BCD andDER of diameter d1, d2 and d3 are inscribed in the

semicircle PQR such that the sum ofd1, d2 and d3 is equal to 10 cm. The task is carriedout by using the various values ofd1 and d2 and the corresponding values ofd3. The

relation between the lengths of arcsPQR,PAB,BCD andDER is determined and thefindings are tabulated. Thus,d1 +d2 +d3 = 10.

(ii) Based on the findings in (a) and (b), generalisations are made about the length

of the arc of the outer semicircle and the lengths of arcs of the inner semicircles for

n inner semicircles wheren= 2, 3, 4.

c) For different values of diameters of the outer semicircle, generalizations stated in b (ii)

is still true that the length of arc of the outer semicircle is equal to the sum of the lengthsof arc of the inner semicircles for n semicircles where n = 1,2,3,4...

PART 3

a) The Mathematics Society is given a task to design a garden to beautify the school. The

shaded region in Diagram 3 will be planted with flowers and the two inner semicirclesare fish ponds. The area of the flower plot isy m

2 and the diameter of one of the fish

ponds isx m. To find the area of semicircles, the formula, r2

is applied. Thus, y is

expressed in terms of andx.


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b) The diameters of the two fish ponds are calculated when the area of the area of theflower plot is 16.5 m2. Quadratic equation is used to get the diameters of the two fish

ponds.

c) The non-linear equation obtained in (a) is reduced to simpler linear form that is valuesfor the vertical axis and x values for the horizontal axis. A straight line graph is plottedusing Microsoft Excel. Using the straight line graph, the area of the flower plot is

determined when the diameter of one of the fish ponds is 4.5 m.

d) The cost of the fish ponds is higher than that of the flower plot. Thus, differentiation

and completing the square methods are used to determine the area of the flower plotsuch that the cost of constructing the garden is minimum.

e) The principal suggested an additional of 12 semicircular flower beds to the design

submitted by the Mathematics Society. The sum of the diameters of the semicircular

flower beds is 10 m. The diameter of the smallest flower bed is 30 cm and the diameter ofthe flower beds are increased by a constant value successively. Arithmetic progression

is used to determine the common difference in order to determine the diameters of

the remaining flower beds.

The formulas used are and .Note: All answers in this folio are in at least 1 significant figure.


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PROBLEM SOLVING

PART 1

(a)There are a lot of things around us related to circles or parts of a circle. Forinstance, pictures of 5 such objects are collected from internet resources.

Round Table World Globe Coins

Car wheel Football


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(b)Pi or is a mathematical constant whose value is the ratio of any circle'scircumference to its diameter in Euclidean space; this is the same value as theratio of a circle's area to the square of its radius. It is approximately equal to

3.14159 in the usual decimal notation (see the table for its representation in some

other bases). is one of the most important mathematical and physical constants:

many formulae from mathematics, science, and engineering involve .

Definition of

In Euclidean plane geometry, is defined as theratio ofa circle's circumference to its diameter:

The ratio C/dis constant, regardless of a circle's size.

For example, if a circle has twice the diameter dof

another circle it will also have twice the circumference C,

preserving the ratioC

/d.Alternatively can be also defined as the ratio of a

circle's area (A) to the area of a square whose side is

equal to the radius:

These definitions depend on results of Euclideangeometry, such as the fact that all circles are similar.

This can be considered a problem when occurs in areasof mathematics that otherwise do not involve geometry.

For this reason, mathematicians often prefer to define

without reference to geometry, instead selecting one of its analytic properties as adefinition. A common choice is to define as twice the smallest positive x for

which cos(x) = 0. The formulas below illustrate other (equivalent) definitions.

The numerical value of truncated to 50 decimal places is:

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510

History ofThe ancient Babylonians calculated the area of a circle by taking 3 times the

square of its radius, which gave a value ofpi = 3. One Babylonian tablet (ca.19001680 BC) indicates a value of 3.125 forpi, which is a closer approximation.

In the EgyptianRhind Papyrus(ca.1650 BC), there is evidence that the Egyptians

calculated the area of a circle by a formula that gave the approximate value of3.1605 forpi.

The ancient cultures mentioned above found their approximations by
http://en.wikipedia.org/wiki/Mathematical_constanthttp://en.wikipedia.org/wiki/Ratiohttp://en.wikipedia.org/wiki/Circlehttp://en.wikipedia.org/wiki/Euclidean_geometryhttp://en.wikipedia.org/wiki/Sciencehttp://en.wikipedia.org/wiki/Engineeringhttp://en.wikipedia.org/wiki/Euclidean_geometryhttp://en.wikipedia.org/wiki/Euclidean_geometryhttp://en.wikipedia.org/wiki/Ratiohttp://en.wikipedia.org/wiki/Ratiohttp://en.wikipedia.org/wiki/Circlehttp://en.wikipedia.org/wiki/Circumferencehttp://en.wikipedia.org/wiki/Diameterhttp://en.wikipedia.org/wiki/Areahttp://en.wikipedia.org/wiki/Radiushttp://en.wikipedia.org/wiki/Similarity_%28geometry%29http://en.wikipedia.org/wiki/Mathematical_analysishttp://en.wikipedia.org/wiki/Trigonometric_functionhttp://en.wikipedia.org/wiki/Truncationhttp://en.wikipedia.org/wiki/Truncationhttp://en.wikipedia.org/wiki/Decimalhttp://www-history.mcs.st-and.ac.uk/~history/Diagrams/Rhind_papyrus.jpeghttp://www-history.mcs.st-and.ac.uk/~history/Diagrams/Rhind_papyrus.jpeghttp://www-history.mcs.st-and.ac.uk/~history/Diagrams/Rhind_papyrus.jpeghttp://www-history.mcs.st-and.ac.uk/~history/Diagrams/Rhind_papyrus.jpeghttp://en.wikipedia.org/wiki/Decimalhttp://en.wikipedia.org/wiki/Truncationhttp://en.wikipedia.org/wiki/Trigonometric_functionhttp://en.wikipedia.org/wiki/Mathematical_analysishttp://en.wikipedia.org/wiki/Similarity_%28geometry%29http://en.wikipedia.org/wiki/Radiushttp://en.wikipedia.org/wiki/Areahttp://en.wikipedia.org/wiki/Diameterhttp://en.wikipedia.org/wiki/Circumferencehttp://en.wikipedia.org/wiki/Circlehttp://en.wikipedia.org/wiki/Ratiohttp://en.wikipedia.org/wiki/Euclidean_geometryhttp://en.wikipedia.org/wiki/Engineeringhttp://en.wikipedia.org/wiki/Sciencehttp://en.wikipedia.org/wiki/Euclidean_geometryhttp://en.wikipedia.org/wiki/Circlehttp://en.wikipedia.org/wiki/Ratiohttp://en.wikipedia.org/wiki/Mathematical_constant


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measurement. The first calculation ofpi was done by Archimedes of Syracuse

(287212 BC), one of the greatest mathematicians of the ancient world.Archimedes approximated the area of a circle by using the Pythagorean Theorem

to find the areas of two regular polygons: the polygon inscribed within the circle

and the polygon within which the circle was circumscribed. Since the actual area

of the circle lies between the areas of the inscribed and circumscribed polygons,the areas of the polygons gave upper and lower bounds for the area of the circle.

Archimedes knew that he had not found the value ofpi but only an approximation

within those limits. In this way, Archimedes showed thatpi is between 3 1/7 and 3 10/71.

A similar approach was used by Zu Chongzhi (429501),a brilliant Chinese mathematician and astronomer. Zu

Chongzhi would not have been familiar with Archimedesmethodbut because his book has been lost, little is

known of his work. He calculated the value of the ratio of

the circumference of a circle to its diameter to be 355/113.To compute this accuracy forpi, he must have started

with an inscribed regular

24,576-gon and performed

lengthy calculations

involving hundreds of square roots carried out to 9

decimal places.

Mathematicians began using the Greek letter

in the 1700s. Introduced by William Jones in 1706,

use of the symbol was popularized by Euler, who

adopted it in 1737.

Figure: Zu Chongzhi

Figure: William Jones
http://en.wikipedia.org/wiki/File:William_Jones,_the_Mathematician.jpghttp://en.wikipedia.org/wiki/File:Zu_Chongzhi.jpghttp://en.wikipedia.org/wiki/File:William_Jones,_the_Mathematician.jpghttp://en.wikipedia.org/wiki/File:Zu_Chongzhi.jpg


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PART 2

(a)

Diagram 1 shows a semicircle PQR of diameter 10cm. Semicircles PAB andBCR ofdiameter d1 and d2 respectively are inscribed in PQR such that the sum of d1 and d2 is

equal to 10cm. By using various values of d1and corresponding values of d2, the relationbetween the lengths of arc PQR, PAB, andBCR is determined.

The length of arc (s) of a circle can be found by using the formula

, where r is the radius.The result is as below. Note thatd1 +d2= 10cm.

d1 (cm) d2(cm)Length of arc PQR in

terms of (cm)

Length of arc PAB in

terms of (cm)

Length of arcBCR in

terms of (cm)

1 9 5 0.5 4.5

2 8 5 1.0 4.0

3 7 5 1.5 3.5

4 6 5 2.0 3.0

5 5 5 2.5 2.5

6 4 5 3.0 2.0

7 3 5 3.5 1.5

8 2 5 4.0 1.0

9 1 5 4.5 0.5

10 0 5 5.0 0.0Table 1


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From Table 1 we can see that the length of arc PQR is a constant and is not affected bythe changes in d1 and d2. Apart of that, we can also realize the relation between the

lengths of arcs PQR, PAB, andBCR whereby the length of arc PQRin terms of is equal

to the sum of the length of arc PABin terms of and the length of arcBCRin terms of .

Hence, we can conclude thatLength of arc PQR = Length of arc PAB + Length of arc BCR

SPQR = SPAB+ SBCR

To check the answer,

Let d1= 4, and d2= 6, thus r1=2, and r2= 3

SPQR= SPAB + SBCR

5 = r1+ r2

5 = 2 + 3

5 = 5 #

(b)

Diagram 2 shows a semicircle PQR of diameter 10 cm. Semicircles PAB, BCD and DER

of diameter d1, d2 and d3 respectively are inscribed in the semicircle PQR such that the

sum of d1, d2 and d3 is equal to 10 cm.

(i) Using various values of d1, d2 and corresponding values of d3, a table is drawnagain. The relation between the lengths of arcs PQR, PAB, BCD andDER isdetermined. Note that d1 + d2 + d3 = 10 cm

Again, we use the same formula to find the length of arc ofPQR, PAB, BCDandDER.

, where r is the radius.


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d1 (cm) d2 (cm) d3 (cm)

Length of arc

PQRin terms of

(cm)

Length of arc

PABin terms of

(cm)

Length of arcBCD

in terms of (cm)

Length of arcDER

in terms of (cm)1 1 8 5 0.5 0.5 4.0

1 2 7 5 0.5 1.0 3.5

1 3 6 5 0.5 1.5 3.0

1 4 5 5 0.5 2.0 2.5

1 5 4 5 0.5 2.5 2.0

1 6 3 5 0.5 3.0 1.5

1 7 2 5 0.5 3.5 1.0

1 8 1 5 0.5 4.0 0.5

2 1 7 5 1.0 0.5 3.5

2 2 6 5 1.0 1.0 3.02 3 5 5 1.0 1.5 2.5

2 4 4 5 1.0 2.0 2.02 5 3 5 1.0 2.5 1.5

2 6 2 5 1.0 3.0 1.0

2 7 1 5 1.0 3.5 0.5

3 1 6 5 1.5 0.5 3.0

3 2 5 5 1.5 1.0 2.5

3 3 4 5 1.5 1.5 2.0

3 4 3 5 1.5 2.0 1.5

3 5 2 5 1.5 2.5 1.03 6 1 5 1.5 3.0 0.5

4 1 5 5 2.0 0.5 2.5

4 2 4 5 2.0 1.0 2.0

4 3 3 5 2.0 1.5 1.5

4 4 2 5 2.0 2.0 1.0

4 5 1 5 2.0 2.5 0.5

5 1 4 5 2.5 0.5 2.0

5 2 3 5 2.5 1.0 1.5

5 3 2 5 2.5 1.5 1.0

5 4 1 5 2.5 2.0 0.56 1 3 5 3.0 0.5 1.56 2 2 5 3.0 1.0 1.0

6 3 1 5 3.0 1.5 0.5

7 1 2 5 3.5 0.5 1.0

7 2 1 5 3.5 1.0 0.5

8 1 1 5 4.0 0.5 0.5

Table 2


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Again, we can conclude that:

Length of arc PQR = Length of arc PAB + Length of arc BCD + Length of arc CDR

SPQR = SPAB + SBCD + SDER


Let d1 = 1, d2 = 4, d3 = 5, thus r1 = 0.5, r2 = 2.0, r3 = 2.5,

SPQR = SPAB + SBCD + SDER

5 = 0.5 + 2.0 + 2.5

5 = 5 #

(ii) Base on the findings in the table in(a) and (b) above, we can make ageneralisation that:

The length of the arc of the outer semicircle is equal to the sum of the

length of arcs of any number of the inner semicircles.

Sout = S1 + S2 + + Sn, n = 2, 3, 4, ...

where,

S1 + S2 + + Sn = length of arc of inner semicircleSout = length of arc of outer semicircle

(c)

Diagram above shows a big semicircle with n number of small inner circle. From the

diagram, we can see that


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The length of arc of the outer semicircle

The sum of the length of arcs of the inner semicircles

Factorise /2

Substitute

Thus we get,

where d is any positive real number.

Therefore we can see that

As a result, we can conclude that,

The length of the arc of the outer semicircle is equal to the sum of the length of arcs

of any number of the inner semicircles. This is true for any value of the diameter of

the semicircle.

To prove this, different values of diameters of the outer semicircle are taken.

(1)Assume the diameter of outer semicircleABCis 30 cm and 4 semicircles areinscribed in the outer semicircle with diameter d1, d2, d3, and d4 cm respectively.

dout

(cm)d1 (cm) d2 (cm) d3 (cm) d4 (cm)

S1(cm)

S2(cm)

S3(cm)

S4(cm)

Sout

(cm)

30 10 5 6 9 5.0 2.5 3.0 4.5 15.030 15 4 4 7 7.5 2.0 2.0 3.5 15.030 20 8 1 1 10.0 4.0 0.5 0.5 15.0

(2)Assume the diameter of outer semicircleABCis 40 cm and 4 semicircles areinscribed in the outer semicircle with diameter d1, d2, d3, and d4 cm respectively.

dout

(cm)d1 (cm) d2 (cm) d3 (cm) d4 (cm)

S1(cm)

S2(cm)

S3(cm)

S4(cm)

Sout

(cm)

40 15 9 9 7 7.5 4.5 4.5 3.5 20.040 20 8 8 4 10.0 4.0 4.0 2.0 20.0


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40 25 7 1 7 12.5 3.5 0.5 3.5 20.0


Sout = S1 + S2 + + Sn, where n = 4

Sout = S1 + S2 + S3 + S4

Let the diameter of outer semicircle ABC = 30cm, d1= 10, d2= 5, d3= 6, d4= 9

15.0 = 5.0 +2.5 +3.0 +4.515.0 = 15.0#

Let the diameter of outer semicircle ABC = 40cm, d1= 15, d2= 9, d3= 9, d4= 7

20.0 = 7.5 +4.5 +4.5 +3.520.0 = 20.0#

Thus, shown that the generalizations stated in b(ii) is still true for different values of

diameters of the outer semicircle, which is :

The length of the arc of the outer semicircle is equal to the sum of the

length of arcs of any number of the inner semicircles.

Sout = S1 + S2 + + Sn, n = 2, 3, 4, ...where,

S1 + S2 + + Sn = length of arc of inner semicircle

Sout = length of arc of outer semicircle


16/17

PART 3

(a)The area of the flower plot isy m2 and the diameter of one of the fish ponds isx m.Hence we can know that the diameter of another fish pond is (10-x) m2.

The formulae for area of a semicircle is .

Area of flower plot = Area ofADC- (Area ofAEB + Area ofBFC)

y =

[

]

=

[

5

]=

*

2 5 5

+

= *

+

= *

+

=

=

y = (b)Given the area of the flower plot is 16.5m2. (Use = )16.5

4 10

4


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1 0 4

16.5 1 0 4 (227 )

16.5( 722) 1 0 4 5.25 1 0 4

2 1 1 0 1 0 2 1 0Factorize the equation to get the value ofx.

7 3 0

7 3.

The diameters of the two fish ponds are 7cm and 3cm.

(c)Linear law is applied in this question.Equation obtained: y = Change it to linear form of Y = mX + C.

Y =

m =

C =

x (cm) 0 1 2 3 4 5 6 7

(cm) 7.8540 7.0686 6.2832 5.4978 4.7124 3.9270 3.1416 2.3562

A graph of againstx is plotted and the line of best fit is drawn.

add math project work 2009

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