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Additional Mathematics Project Work 1 2AL3SELANGOR EDUCATION DEPARTMENT

ADDITIONALMATHEMATICSPR0JECTwoRKIIzoLSIntroduction rone of the mathematical concepts which we must be familiar with is logarithms'Before the days of scientific calculators, logarithms were used to multiply or divideextreme numbers using mathematical tables. For these calculations, ten was the mostcommon base to usel Logarithm to the base of ten is also called the commontogarithm" other bases su-ch as fi,vo, five and eight can also be used' The ancientBabylonians had used bases up to 60.Logarithms have many applications in various fields of studies. In the eafly 17th..rr"tury it was rapidly uOopi.O by navigators, scientists, engineers and astronomers toperform computations more easily.

PART 1a) Write a history on logarithm.b) Find and explain the applications of logarithrn inJwo different fields of study"Explanation bf each application should include the following :

i) The field of studY chosen.iii Examples of proLlem solving related to the flreld of sfudy.

ii)iii)

PART 2The volume , V" incm3, of a solid sphere and its diameter, D, in cm, are related by theequation V -- mDn, where m and n are constants'You can find the value of m and of n by conducting the activities below'

a i) Choose six different spheres with diameters between 1 cm to 8 cm'Measure the diameters of the six spheres using a pair ofvernier callipers.Find the volume of each sphere without using the formula of volume.(You can use the apparatus in the science lab to help you)Tabulate the values of the diameter, D, in cm, and its correspondingvolume, V, incm3.

b Find the value of m andof n using logarithms with any two sets of valuesobtained in the table above.Selangor Education DePartment

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(A)PART 3In our daily life, the relation between two variables is not always in a linear form. Forexample, the relation between the volume, V, and the diameter, D, inPattZ above"Plot i/against D using suitable scales.When the graph V against D is drawn, the value of tn and Of n arc not easilydetermined from the graph. If the non-linear relation is changed to a linear form, aline of best fit can be drawn and the values of the constants and other information eanbe obtained easily.a) Reduce the equation V : mD'to a linear form.b) Using the data from Part 2, plotthe graph and draw the line of best fit.c) Fromthe graph, find

i) the value of m and of n, thus express Zin terms of D,ii) the volume of the sphere when the diameter is 5 cm, andiii) the radius of the sphere when the volume is 180 cm3.

FIIRTHER EXPLORATIONa) Compare the equation obtained in Part 3 (B) c (i) with the formuia of volume

of sphere. Hence, find the value of zc.b) Suggest another method to find the value of zu.

REFLECTIONWhat have you learnt while conducting the project? What moral values did youpractise? Express your feelings and opinions creatively through the usage ofsymbols, drawings, lyrics of a song or a poem.

(B)

Selangor Education DePartment

END OF PROJECT PAPER

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Additional Mathematics Project Work 2SELANGOR EDUCATION DEPARTMENT

PAR.T 1(a) Describe in brief(i) price index,(ii) weightage,(iii) composite index.(&) State four ways of weightage representations" Find the examples of the representatidns'

using internet or any printed materials"

PART 2We often hear oompiaints from the public about inflation. It causes an increasern the househoid expenditure in a family.The household expenditure for every family is different.a) Complete Table 1 for your family's monthly expenditure for the year 2013.

ItemAverage Monthly

Expenditure for the year20r3(to the nearest RM)Percentage ofmonthly expenses(to the nearest %)

FoodAccomodation(Rental / Loan)Transportation(Petrol/ Loan lBus fare etc)

ClothineEducationR-ecreationUtilities(Water / Electricity / Telephone)Medication

MiscellaneousTOTAL Table 1

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Additional Mathematics Project Work 2 20L3(b) Xf we want to compare the cost of living from one year to another, we have to

calculate the price index that involves some of the items mentioned above.(i) In order to calculate the price index of all the items above, we have to consider the

average monthly expenses of any previous year as the base year.Select the appropriate year as the base year. \

(ii) Hence, complete Table 2 below:

ItemAverage monthly

expenses for the year ... asthe base year(RM)

Average monthlyexpenses for the year20t3(RM)

FoodAccomodationCRental / Loan)Transportation(Petrol lLoan/ Bus fare etc)Ciothing

EducationRecreationUtilities(V/ater / Electricitv / Telephone)Medication

MiscellaneousTOTAL Table2

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Item Price indices for the year 2013based on the Year ...

WeightageFood

Accomodation(Rental / Loan) \Transportation(Petrol l'[-oanl Bus fare etc)

ClothineEducationRecreationUtiiities(Water / Electricitv / Teleohone)Ivledication

MiscellaneousTOTALTable 3

(c) ( i) Complete Table 3 based on the above information.

( ii) Hence, calculate the composite index for the average monthly expenditurein the year 2013 based on the selected base year.@ Ivlake a conclusion about your family's expenditure based on your findings.

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(a) You have conducted a survey on the price of the television for two different brandsfrom three different shops. You would like to make a comparison between two modesofpayment,namely,outhpuy*entandpaymentbyinstailment'tTable 4 (a) shows the prices of televisions by cash payment-in three different shopswhereas Table 4(b) shows the prices of televisions by installment'CompleteTable4.(a)and4(b)usingthedatayouobtained.

Additional Mathematics Project Work 2 2013

Price (RM) MeanPrice(RM)StandardDeviationaM)rand

Size ofTelevision(inches) Shop A Shop B Shop C243240243240 Table 4(a)

BrandSize of

Television(inches)Price (RM) Mean

Price(RM)StandardDeviation

(RM)hop A Shop B Shop C24JZ40243240 Table 4(b)

(b) Determine the brand and size of the television that you have decided to buy' Give yourreasons based on the furdings from part (a) above'

(c) The Ministry of Domestic Trade and consumer Affairs wishes to present the Fair PriceShop Award for one of the above shops. If you afe one of the panels forlhis awatd'determine ttre strof that deserve the award. bo yo,, consider the value of the mean andthe value of standard deviation in making your decision? Give your justifications"

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Additional Mathematics Project Work 2 20L3PART 4(a) Your family has a fixed monthly income. In order to buy the television, your

(b)

family needs to make some adjustment on the various types of expenditure.lYou can choose to pay by cash or by installmentfShow the average monthly expenditure that you have modified ig a table.

Assuming you have just started working with a monthly salary of RX{2 500"You intendto save 10% of your salary every month.Plan your monthly expenditure as in Table 1 above and add other items such assavings and contributions to your parents.

REFI,ECTIONWhat have you learnt while conducting the project? What moral values did you practise?Represent your feelings or opinions creatively through the usage of symbols, drawings or lyricsin a song or a poem.

END OF PROJECT PAPER

ffi

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RIIBRIC FOR ADDITIONAL MATIIBMATICS PROJECT WORK 2013Name: Form 5:...

Range ofmarks MarksAwarded Subtotal

Al" General Aspeet(6%)

Aooropriate title. IContent page. ISvstematic nresentation. t-2Creativitv. t-2

A2. Introduction(10%) Comprehensive introduction - may include history valuesand other information relevant to the task includingoictures and cantions. 5-7S atisfactory intro duction. 1-4Relatins siven task to real-life situations. I -3\

81. Specify the task(s%) Identiff and state all given information and required resultsin effective mathematical statements. 4-5identiff and state given information and required resultsincompletelv.

I -3C1. Procedure(3s %) In-depth understanding of the

questions.Use very efficient problem-solving strate gie s.Answer all questions correctly.

31-35Understand the questions.Use strategies that lead to solutions of the problems.Answer all ouestions correctlv.

15-30Partially understand the question. Use strategies that arepartiallv useful. Do not answer all questions correctly. s-14

C2. Communication& Reasoning(ts%)Communicate precisely and efficiently using mathematicalrepresentations such as symbolslgraphs/tables/diagrams.Refined and complex reasoning.

13-15Communicate effectively using mathernaticalrepresentations such as symbols/graphs/tables/diagrams.Use effective mathematical reasoning.

l0-12Communicate ineffectively. Limited use of mathematicalrepresentations such as symbols/graphs/tables/diagrams.Some evidence of mathematical reasoning.