add math!!~

ntk sesape yg nk da t'hilang keje addmath..

The diagram below shows the gate of an art gallery. A concrete structure is built at the upper part of the gate and the words 'ART GALLERY' is written on it. The top of the concrete structure is flat whereas the bottom is parabolic in shape. The concrete structure is supported by two vertical pillars at both ends.

The distance between the two pillars is 4 metres and the height of the pillar is 5 metres. The height of the concrete structure is 1 metre. The shortest distance from point A of the concrete structure to point B, that is the highest point on the parabolic shape, is 0.5 metres.

(a) The parabolic shape of the concrete structure can be represented by various functions depending on the point of reference. Based on different points of reference, obtain at least three different functions which can be used to represent the curve of this concrete structure.

(b) The front surface of this concrete structure will be painted before the words 'ART GALLERY' is written on it. Find the area to be painted.

FURTHER EXPLORATION

(a) You are given four different shapes of concrete structures as shown in the diagrams below. All the structures have the same thickness of 40 cm and are symmetrical.

(i) Given that the cost to construct t cubic metre of concrete is RM840.00, determine which structure will cost the minimum to construct.

(ii) As the president of the Arts Club, you are given the opportunity to decide on the shape of the gate to be constructed. Which shape would you choose? Explain and elaborate on your reasons for choosing the shape.

(p) The following questions refer to the concrete structure in the diagram below. If the value of k increases with a common difference of 0.25 m;

(i) complete Table 1 by finding the values of k and the corresponding areas of the concrete structure to be painted.

(ii) observe the values of the area to be painted from Table 1. Do you see any pattern? Discuss.

(c) Express the area of the concrete structure to be painted in terms of k. Find the area a k approaches the value of 4 and predict the shape of the concrete structure.

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, drawings or even in song.

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PART 1
The prices of goods sold in shops vary from one shop to another. Shoppers tend to buy goods which are not only reasonably priced but also give value for their money. You are required to carry out a survey on four different items based on the following categories i.e. food, detergent and stationery. The survey should be done in three different shops.
(a) Collect pictures, newspaper cuttings or photos on items that you have chosen. Design a collage to illustrate the chosen items.
(b) Record the items and their prices systematically as in Table 1. Since items may be differently packed, be sure to use consistent measurements for each item selected so that comparison can be done easily and accurately.



(c) Create at least two suitable graphical representations (the use of ICT is encouraged) to compare and contrast the prices of the items chosen.
(d) Based on the graphical representations that you have constructed in Part 1(c), interpret, discuss and draw conclusions. Comments on your findings.

(e) Identify an item that has a large price difference among the shops. Calculate the mean and the standard deviation of that particular item. Hence, suggest and discuss possible reasons for the price difference.

PART 2
Every year SMK Indah organises a carnival to raise funds for the school. This year the school plans to install air conditioners in the school library. Last year, during the carnival, your class made and sold butter cakes. Because of the popularity of butter cakes, your class has decided to carry out the same project for this year's carnival.
(a) Suggest a shop from Part 1 from which you would go to purchase the ingredients for the butter cakes. State and discuss your reasons for purchasing from the shop you suggested.
(b) Complete Table 2 with the prices of the items found in the shop/supermarket that you have chosen.



(i) Calculate the price index for each of the ingredients in Table 2 for the year 2010 based on the year 2009.
(ii) Calculate the composite index for making a butter cake in the year 2010 based on the year 2009. Discuss how you obtained your answers.
(iii) In the year 2009, the butter cake was sold at RM15.00 each. Suggest a suitable selling price for the butter cake in the year 2010. Give reasons for your answer.

(c) (i) Find out from reliable sources how to determine suitable capacity of air-conditioner to be installed based on volume/size of a room.

(ii) Work in groups to estimate the volume of your school library. Explain how you arrive at your answer. Hence, determine the number of air conditioners with the appropriate capacity required for your library.

(iii) If your class intends to sponsor one air conditioner for the school library, how many butter cakes must your class sell in order to buy the air conditioner?

PART 3
As a committee member for the carnival, you are required to prepare an estimated budget to organise this year's carnival. The committee has to take into consideration the increase in expenditure from the previous year due to inflation. The price of food, transportation and tents has increased by 15%. The cost of games, prizes and decorations remains the same, whereas the cost of miscellaneous items has increased by 30%.

(a) Complete Table 3 based on the information given above.



(b) Calculate the composite index for the estimated budget of the carnival in the year 2010 based on the year 2009. Comment on your answer.
(c) The change in the composite index for the estimated budget for the carnival from the year 2009 to the year 2010 is the same as the change from the year 2010 to the year 2011. Determine the composite index of the budget for the year 2011 based on the year 2009.

FURTHER EXPLORATION

Index numbers are being used in many different daily situations, for example air pollution index, stock market index, gold index and property index.
Obtain information from the Internet or other reliable sources on the importance of two different types of index numbers of your choice. Elaborate the use and the importance of these index numbers in daily life situations.

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, drawings or even in a song.