Ok..This is just a question for Add Math Project for year 2009..Just look it first ok..the solution will be given later..ho ho ho..Just wait and wait…Add Math Project 2009 or Additional Mathematics Project 2009 this year i think it is soo easy then the last2 year..Hahha..However its still can make our brain headache to manage it..Add Math oh Add Math..hahha..This year is more question add math about circle..Add math project for circle..Ceh why i’m talking add math and add math again and again.. [^-^]

Orait..ini hanya soalan untuk Add Math project 2009 ataupun Additional Mathematics 2009 SPM..jawapan len kali akan di postkan..Har Har Har..Sebenarnya post ini hanya bermain2 dengan perkataan2 Add Math Project tu..LEbih2 lagi Answer for Add Math Project..Ahh..korang diam aje kalau post kali ni merepek..Hi hi hi..Oklah tgk la soalan di dulu..Solution dia nnt2 aku bg..ho ho ho

First of all, let’s include the question of the project for the convenient of discussion.

PART 1

There are a lot of things around us related to circles or parts of a circle.

(a) Collect pictures of 5 such objects. You may use camera to take pictures around your school compound or get pictures from magazines, newspapers, the internet or any other resources.

(b) Pi or ? is a mathematical constant related to circles. Define ? and write a brief history of ?.

PART 2

(a) Diagram 1 shows a semicircle PQR of diameter 10 cm. Semicircles PAB and BCR of diameter d₁ and d₂ respectively are inscribed in the semicircle PQR such that the sum of d₁ and d₂ is equal to 10 cm.

Complete Table 1 by using various values of d₁ and the corresponding values of d₂. Hence, determine the relation between the lengths of arcs PQR, PAB and BCR.

(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 and d₂ and the corresponding values of d3, determine the relation between the lengths of arcs PQR, PAB, BCD and DER. Tabulate your findings.

(ii) Based on your findings in (a) and (b), make generalisations about the length of the arc of the outer semicircle and the lengths of arcs of the inner semicircles for n inner semicircles where n = 2, 3, 4….

(c) For different values of diameters of the outer semicircle, show that the generalisations stated in b (ii) is still true.

PART 3
The Mathematics Society is given a task to design a garden to beautify the school by using the design as shown in Diagram 3. The shaded region will be planted with flowers and the two inner semicircles are fish ponds.

(a) The area of the flower plot is y m² and the diameter of one of the fish ponds is x m. Express y in terms of it and x.

(b) Find the diameters of the two fish ponds if the area of the flower plot is 16.5 m². (Use ?=22/7 )

(c) Reduce the non-linear equation obtained in (a) to simple linear form and hence, plot a straight line graph. Using the straight line graph, determine the area of the flower plot if the diameter of one of the fish ponds is 4.5 m.

(d) The cost of constructing the fish ponds is higher than that of the flower plot. Use two methods to determine the area of the flower plot such 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 as shown in Diagram 4. 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 of the flower beds are increased by a constant value successively. Determine the diameter of the remaining flower beds.