Logarithm in our daily lifeProject Work For Additional Mathematic 2013Name: Kajeshwaran DanarajanTeacher Name: Pn Roiamah BasriClass:5SC3School:SMK Taman TasikI/C :960907145637

IntroductionI am a student taking Additional Mathematics for SPM are required to do project work while I

am in Form 5. This year Curriculum Development Division, Ministry of Education has prepare 2 task forSPM students 2013. We are SPM student need to choose and complete a task based on our interest.We need to submit a report individually. I also gain some knowledge about Additional Mathematicswhen I complete the project. I also apply the knowledge I gain when I am doing the project use in mydaily life and solve my problem in my Additional Mathematics. I also adapt in varieties of problem whenI am doing this project but I am use many variety to solve those problems.

I also gathering some info and experience in classroom those challenging , interesting andmeaningful and hence improve my thinking skills.Experience classroom environments where expressingones mathematical thinking, reasoning and communication are highly encouraged and expectedExperience classroom environments that stimulates and enhances effective learning.Acquire effectivemathematical communication through oral and writing, and to use the language of mathematics toexpress mathematical ideas correctly and precisely .Enhance acquisition of mathematical knowledge andskills through problem­solving in ways that increase interest and confidence .Prepare ourselves for thedemand of our future undertakings and in workplace .Realise that mathematics is an important andpowerful tool in solving real­life problems and hence develop positive attitude towards mathematics.Train ourselves not only to be independent learners but also to collaborate, to cooperate, and to shareknowledge in an engaging and healthy environment

Use technology especially the ICT appropriately and effectively.Train ourselves to appreciatethe intrinsic values of mathematics and to become more creative and innovative.Realize the importanceand the beauty of mathematics.

We are expected to submit the project work within two weeks from the first day the task isbeing administered to us. Failure to submit the written report will result in us not receiving certificate.

Appreciation

First of all I need to wish thanks to honourable god are keep me healthy till the AdditionalMathematics project end. Secondly I would wish thank the principal of SMK Taman Tasik, Pn Maimonbinti Haron to giving the permission to doing the Additional Mathematics project. I would like to wishthanks to my Additional Mathematics teacher Pn Roiamah because she help me to conduct this project.I also wish my brother Uthaya Kumar because he help me to do the equation of logarithm.

ObjectiveWe are the students who taking Additional Mathematics and are required to carry out a project

work while we are in Form 5. This year the Curriculum Development Division, Ministry of

Education has prepared two tasks for us. We have to choose and complete only ONE task based onour area of interest. This project can be done in groups or individually, but each of us are expected tosubmit an individually written report.

The aims of carrying out project work are:• To apply and adapt a variety of problem­solving strategies to solve problems;• To improve thinking skills;• To promote effective mathematical communication;• To develop mathematical knowledge through problem solving in a way that

increases student's interest and confidence;• To use the language of mathematics to express mathematical ideas precisely;• To provide learning environment that stimulates and enhances effective learning;• To develop positive attitude towards mathematics.

Part 1(A) History of logarithm

Logarithms were invented independently by John Napier, a Scotsman, and by Joost Burgi, aSwiss. Napier's logarithms were published in 1614; Burgi's logarithms were published in 1620.

The objective of both men was to simplify mathematical calculations. This approach originallyarose out of a desire to simplify multiplication and division to the level of addition and subtraction. Ofcourse, in this era of the cheap hand calculator, this is not necessary anymore but it still serves as auseful way to introduce logarithms.

(B) The First Field of Logarithms : Chemistry

In a chemistry logarithms are use to define the solution of pH value.p(h) = – log10 (h)Where h is the hydronium ion concentration in mole per liter. We usually round pH value to

nearest tenth.

Example:Find the pH of a solution with hydronium ion concentration 4.5 × 10­5p(h) = – log10 (4.5 × 10­5)

= – ( log10 4.5 + log10 10­5 )= – [ log10 4.5 + (–5)(log10 10) ]= – [ 0.6532 + (–5) ]= – ( 0.6532 – 5 )= – (–4.3468)= 4.3468

The Second Field of Logarithms: Physics

The loudness of sound is measured in units called decibels. These units are measured by first assigningan intensity I0 to a very soft sound (which is called the threshold sound). The sound we wish to measureis assigned an intensity I, and we measure the decibel rating d of this sound with the equation.

Example:

Find the decibel rating of a sound with intensity 5000I୦.

dB= 10log10 (5000Io/Io)dB= 10log10 5000

36.99 decibels

Part 2

(a) i) By using a pair of vernier calipers, the diameter of six (6) different spheres is taken.

ii) The volume of spheres is obtained by using water displacement method.

iii) The value of diameter, D,in cm and its corresponding volume V in cm3 are tabulated below

Diameter (cm) Volume (cm3)

2 4.19

3 14.14

4 33.52

5 65.48

6 113.14

7 179.67

When diameter d=4 cm , volume v=33.52cm3

33.52 = m × 4nlog 1033.52 = log 10 (m × 4n)log1033.52 = log10 m + n log 10 41.525 = log 10 m + 0.602n

When diameter d=7 cm, volume v=179.67cm3

179.67 = m × 7nlog10179.67 = log10 (m × 7n)log10179.67 = log10 m + log10 7nlog10179.67 = log10 m + n log10 72.254 = log10 m + 0.845n

By forming the simultaneous equation,

1.525 = log10 m + 0.602n2.254 = log10 m + 0.845n0.729 = 0.243nn = 0.729/0.243n = 3

By substituting n= 3 into one of the equation,1.525 = log10 m + 0.602 x 3log10m = 1.525 – 1.806log10m = – 0.281m = 0.524

Part 3PART 3

(A) Based on the table in PART 2 (a) (ii), graph V against D is drawn.

Diameter (cm) Volume (cm3)

2 4.19

3 14.14

4 33.52

5 65.48

6 113.14

7 179.67

(B) a) To reduce the equation V = mDn to a linear form,V =m×Dnlog 10V = log 10 (m × Dn)log10V = log 10 m + n log 10 Dlog10V = n log 10 D + log 10 m

where , log10V=Y , n=m, log 10 D=X, log 10 m=c

log10D 0.301 0.477 0.602 0.699 0.778 0.845

log10V 0.622 1.151 1.525 1.816 2.053 2.255(b)

(c) i) Based on the graph in (B) (b),

Gradient, m =

= 3n = m n = 3

y­intercept, c = –0.28log10 m = clog10 m = –0.28m = 0.525

ii) When the diameter, D = 5 cm, log10 5 = 0.699Based on the graph in (B) (b),log10 V = 1.816V = 65.48 cm3

iii) When the volume, V = 180 cm3, log10 180 = 2.255Based on the graph in (B) (b),log10 D = 0.85D = 7.08 cm

Part 4

Reflection

I had learned how to conduct a project work successfully. Second, I learn howimportant is the cooperation among team mate.I also learned how to use logarithm in a daily life.

References

Websitehttp://eng.wikipedia.com