This year's assignment theme is linear law which is picked from Form 5 Chapter 2.
I will go according to the order of the marking scheme:
All pages need to be blank A4 papers, and handwritten. I will be providing the answers only the questions can be referred from the handout that your teachers gave you.
ALL GRAPHS MUST BE PLOTTED ACCORDING TO THE QUESTIONS.
For the cover page,
Projek Matematik Tambahan SPM 2017
Nama:______________
Kelas:_______________
Angka Giliran:_____________
Next, the index page, d.i.y
Part 1
1. Linear Equation:
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and the first power of a single variable. A linear equation is an equation for a straight line.
Example:
Nonlinear Equation:
A nonlinear equation is an equation whose graph does not form a straight line. Equations with exponents greater than one are nonlinear. The sum of the exponents of the variables in the equation is more than one.
Example:
No.

Equation

Sketch
of Graph

State
linear equation of nonlinear equation

1


linear


2



Nonlinear

3



linear

4



Nonlinear

5



Nonlinear

6



linear

7



Nonlinear

8



Nonlinear

9



linear

10



Nonlinear

3.
PART 2
Task 1
a)
bi)
bii)
c)
Task 2
a)
bi)
bii)
c)
d)
e)
Conclusion:
Task 3
a)
*** For this graph follow my scale, the scale given is rigged.
bii)
c)
d)
e)
Conclusion:
Part 3
Task 1
Task 2
Task 4
Task 5
Task 6
Task 7
Task 8
Task 9
Task 11
Task 12
Task 13
Conclusion:
For the conversion of nonlinear equation to linear equation, identify the variables and the constants. Identify the Y, m, X, c to form the linear equation of Y=mX+c. Y is the value of the yaxis, X is the
value of the xaxis, Y and X are the variable whereas m and c are the constants. m is the gradient, and c is the yintercept of the straight line, Y=mX+c. There are many possible linear forms, it is best to apply the linear law according to the question. The constant values will change the value of the gradient and the yintercept of the straight line, Y=mX+c, the straight line plotted may have a positive gradient (the straight line will go up), have a negative gradient (the straight line will go down), or have a negative or a positive yintercept.
By multiplying, dividing or by applying the logarithmic rules the variables, you can manipulate the nonlinear equation into a linear equation.
Further Exploration:
Task 1
a)
b)
Task 2
The engineering applications that are useful to graph can be represented in different ways. Especially of interest is direct variation, which is the form many engineering application take, including Hooke's law and Ohm's law.
Electrical engineers use Ohm's law frequently for it states the most basic relationship between voltage, resistance and current. It is used in almost all calculations to analyse and test circuits in any electrical piece or equipment or device.
Linear law can be used to verify formula, especially in Physics. For example, if we convert and plot the graph of the formula of an oscillating pendulum using linear law, we must get a straight line graph, if not the experimental results are not accurate.
Say that you wish to evaluate an experimental value for g, the acceleration due to gravity, at an unknown location by measuring the time an object takes to strike the ground when dropped from various heights.
The Physics relationship is,
Graphing the data as
on a set of coordinate axes yields data that follows a linear relationship and the slope determined by a linear regression yields the experimental value of g/2.
Lanchester's linear law.
In ancient combat between phalanxes of armies with spears. For instance, one solder could only ever fight exactly one other soldier at a time. If each soldier kills, and is killed by, exactly one other, then the number of soldiers remaining at the end of the battle is simply the difference between the larger army and the smaller army, assuming same weapons.
The linear law also applies to unaimed fire into enemyfilled area. The rate of attrition depends on the density of the available targets in the target area as well as the number of weapons shooting. If two forces, occupying the identical land area, they will both suffer the same rate and the number of casualties, until the smaller force is eliminated eventually: the greater probability of any one shot hitting the larger force is balanced by the greater number of shots directed at the smaller force.
Reflection
Version 1.0
While I was carrying out this project, I have learnt how to appreciate the beauty of Mathematics. I have learnt how to apply my linear law skills more efficaciously. I also learnt that linear law is very important in our lives, it can help us to solve and confirm the correctness of a law, or an equation.
The moral values that I have put into practice is compassion in executing this project. I have poured my heart, mind and soul into completing this project with the best result. I also put in a lot of hard work in order to complete this project. I also did not give up in doing my project, I have completed it to the end.
In the making of this project, I have spent countless nights researching and completing this project. I realised this subject is compulsory for me. Without it, I could not fulfill my abjured hopes and dreams. These are the benefits of the project.
This skill of linear law has helped me improve drastically in proving the validity of a certain formula in Physics or in any field. I simply just used linear law, applying all the knowledge that I have gained from this, I managed to prove that the existing laws are true.
Version 2.0
In the making of this project, I have spent countless nights researching and completing this project. I realised this subject is compulsory for me. Without it, I could not fulfill my abjured hopes and dreams. These are the benefits of the project.
While I was carrying out this project, I have learnt how to appreciate the beauty of Mathematics. I have learnt how to apply my linear law skills more efficaciously. I also learnt that linear law is very important in our lives, it can help us to solve and confirm the correctness of a law, or an equation.
The moral values that I have put into practice is compassion in executing this project. I have poured my heart, mind and soul into completing this project with the best result. I also put in a lot of hard work in order to complete this project. I also did not give up in doing my project, I have completed it to the end.
This skill of linear law has helped me improve drastically in proving the validity of a certain formula in Physics or in any field. I simply just used linear law, applying all the knowledge that I have gained from this, I managed to prove that the existing laws are true.
***Basically you can swap around with the sequence.
For the most ridiculous part in the project of "represent your opinion or feelings creatively by using symbols, illustrations, painting or songs" do it yourselves, just kidding.
From a curve to a line,
Complexity to simplicity,
Equations of nonlinear to linear,
I have the savvy on the application of linear law.
I can't picture the complicated,
convoluted, complex equations.
Using linear law,
finally,
it is as simple as counting from one to ten.
What I can't see or picture,
it doesn't mean I can't simplify them
into my frame of reference.
Maths is beautiful and complex.
It can be simplified
into crystal clear,
speckless wonders.
Cheers! Everyone. This is the end of the post, the index you need to do it according to your pagination. Be mindful about plotting your graph, please use pencils instead of pens, I use them from illustration purposes.
Good luck. May the odds be in your favour.
Blogger.
*****All of the above are for students' reference.
*****All of the above are for students' reference.
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Answer : Circle produced maximum area among the others shape .
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Area =πr^2
=π(〖150/π)〗^2
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(ii) Suggest at least three examples how you would utilize this concept in your daily life . Give your reason .
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