Additional Mathematics Project Work 3/2011

Additional Mathematics Project Work 3 2011

Curriculum Development Division, Ministry of Education Malaysia

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CURRICULUM DEVELOPMENT DIVISION

MINISTRY OF EDUCATION MALAYSIA

ADDITIONAL MATHEMATICS PROJECT WORK 3/2011

Part 1

Rene Descartes, a renowned French Mathematician in the 16th

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.

Part 2

Malaysia with its warm 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 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.

Diagram 1

F G H

E

C

A B

Q R

P

7 m

6 m

2 m

4 m

3 m

3 m

D



2

(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)

(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.

(c) If a meter of fence 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.

(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 create a

triangular-shaped area.

(i) 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.

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

Part 3

The Mathematics society decided to build a pond in region P as shown in Diagram 2. The pond

is in the shape of a sector with centre E, radius ED and a depth of 1 meter.



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

(b) Determine the volume of water that has to be pumped in to fill up 80% of the pond.

(c) If the water is pumped into the pond at a constant rate of 0.001 m3

s-1

, calculate

(i) the rate of change of depth of the water,

(ii) the depth of water after 10 minutes,

(iii) the minimum time taken, in minutes, before the water overflows, and

(iv) the minimum time taken, in minutes, before the water overflows, if the pond is

triangular-shaped AED and has a depth of 2 meters.

FURTHER EXPLORATION

Maps have 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 5 41’ N and has the same

longitude as the city of Malacca.

Diagram 2

Pond

F G H

E

C

A B

Q R

P

7 m

6 m

2 m

4 m

3 m

3 m

D



4

Explore and find the distance between these two places in kilometer by using,

(i) the map in Diagram 3

(ii) the formula given below:

where = difference in latitudes in degrees.

Is there a difference between the answers obtained? Explain.

Distance = × 60 nautical miles

Diagram 3

X



5

(a) Surf the Internet and use the 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.

(i) Solve the triangle obtained.

(ii) Calculate the shortest distance from your school to the line joining the two

hospitals/clinics.

If Internet service is not available, you can perform this task by using a detailed map of

your town.

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,

drawing or even in a song.

END OF PROJECT PAPER

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Additional Mathematics Project Work 3/2011