Kerja Projek 2014 Add Maths Answer

8/11/2019 Kerja Projek 2014 Add Maths Answer

1/15

Title : Determine the area of the flower plot such that the cost of

constructing the garden is minimum.

Part 1 (Bahagian 1)

(a) Collection of pictures of things that related to circles or parts of circle. Pengumpulan 5 objek ang berlkaitan dengan buatan atau sebahagian daripada

bulatan.

!


2/15

(b) (i) Definition of Pi ()

The number P"# denoted b the $reek letter % & pronounced 'pie'# is one of themost common constants in all of mathematics. "t is the circumference of an circle#di ided b its diameter. obod knows its e*act alue# because no matter how mandigits ou calculate it to# the number ne er ends. +or most practical uses# ou can assumeit is ,.!- ."n /uclidean plane geometr # % is defined as the ratio of a circle's circumference to itsdiameter:The ratio C0d is constant# regardless of a circle's si1e. +or e*ample# if a circle has twice

the diameter d of another circle it will also ha e twice the circumference C# preser ingthe ratio C0d.2rea of the circle 3 % 4 area of the shaded s uare2lternati el % can be also defined as the ratio of a circle's area to the area of a s uarewhose side is e ual to the radius:These definitions depend on results of /uclidean geometr # such as the fact that all circlesare similar. This can be considered a problem when % occurs in areas of mathematics thatotherwise do not in ol e geometr . +or this reason# mathematicians often prefer to define% without reference to geometr # instead selecting one of its anal tic properties as adefinition. 2 common choice is to define % as twice the smallest positi e * for whichcos(*) 3 6.


3/15

b(ii) Brief History of Pi ()

The ancient 7ab lonians calculated the area of a circle b taking , times the s uare of itsradius# which ga e a alue of pi 3 ,. 8ne 7ab lonian tablet (ca. !966 !;


4/15


5/15

(b)

(a)

d ! d . d , Length of arc PQR

(cm) Panjang

lengkok PQR (cm)

Length of arc PAB

(cm) Panjang

lengkok PAB (cm)

Length of arc BCD

(cm) Panjang

lengkok BCD (cm)

Length of arc D&R

(cm) Panjang

lengkok D R (cm)! 9 ; % 6.5 % ! % -.5 %

, ? ; % ! % !.5 % ,.5 %, - 5 ; % !.5 % % .5 %- 5 , ; % % .5 % !.5 %5 ; ! ; % .5 % , % 6.5 %

"he length of arc PQR is e#$al to the s$m of length of arc PAB' BCD an! D&R% Panjang lengkok PQR adalah sama dengan jumlah panjang lengkok PAB! BCD dan

D R.

(b) eneralisation from "able (a) an! (b) " #es$mpulan da%$pada &adual (a) dan (')

Get (2ndaikan) : $ *nne% sem$c$%cle (+em$ 'ula,an lua%an)o -u,e% sem$c$%cle (+em$ 'ula,an dalaman)

,n$$$ . . . . . .........

,!6 +++= #n 3 #,# -#HH..

5


6/15

(c)

(i) Diameter semicircle PQR is 2 cm% Diameter semibulatan PI= ialah 6cm.


(cm) Panjang lengkok

PQR (cm)

Length of arc PAB


PAB (cm)

Length of arc BCD


BCD (cm)

Length of arc D&R


D R (cm)

! !? 1/ % 6.5 % 1 % 0.5 %, !5 !6 % ! % !.5 % ?.5 %, - !, !6 % !.5 % % ;.5 %- 5 !! !6 % % .5 % 5.5 %5 ; 9 !6 % .5 % , % -.5 %

"he length of arc PQR is e#$al to the s$m of length of arc PAB' BCD an! D&R% Panjang lengkok PQR adalah sama dengan jumlah panjang lengkok PAB! BCD dan D R.

,n$$$ . . . . . .........

,!6 +++= #n 3 #,# -#HH..

("r$e for !ifferent *al$es of !iameters )(7enar bagi nilai diameter ang berbe1a)

;


7/15

(c)

(ii) Diameter semicircle PQR is + cm% Diameter semibulatan PI= ialah ,6cm.



PQR (cm)

Length of arc PAB


PAB (cm)

Length of arc BCD


BCD (cm)

Length of arc D&R


D R (cm)! ? 15 % 6.5 % 1 % 13.5 %

, 5 !5 % ! % !.5 % ! .5 %

, - , !5 % !.5 % % !!.5 %- 5 ! !5 % % .5 % !6.5 %5 ; !9 !5 % .5 % , % 9.5 %; ? !? !5 % , % ,.5 %


8/15

Part +


9/15

9


10/15

!6


11/15

!!


12/15

!


13/15


14/15

=/+G/CT"8

2s a result of doing this project# " ha e learnt and practised a few alues such ascooperation. " ha e worked together with m classmates and also se eral friends fromother schools in m district.

8ther than that# " ha e also learnt the meaning of perse erance and patience when " wasworking on this assignment. The assignment was uite difficult but " still managed tocomplete it with the help of teachers and friends.

!-


15/15

oreo er# hardwork and punctualit was er important in this assignment to ensure thatwe properl and consistentl worked on this project and submitted it to our teachers ontime.

This project ha e taught me ne er to gi e up and to alwa s push m self harder to achi egreat results.

!5

Kerja Projek 2014 Add Maths Answer

Documents