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Archive for September 2008

I was searching for some convenient learning tools for plotting of graphs when I came across this mobile software for plotting of graphs.

In one of my post on Drawing of Quadratic Graphs, I introduced a very popular free software Graphmatica.

I have tested out this mobile software on my hp. It works!

It is good for sketching cubic, quadratic and trigo graphs. Very simple to use by inputting the coefficients of each terms.

How to download from computer to your handphone.

  1. Download the required file from here ( I downloaded the TVH-72g Graphing Calculator JAR )
  2. When the file is on your desktop, bluetooth it to your handphone
  3. Go to your handphone Received Files, click on it and it is available for use immediately!

See below for the screenshots:

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This software is beneficial for knowing the general shape of the graphs.

For more information, click here

I would love to hear your experience in using this cool mobile software. Leave me your comments in the section below.

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Dear Ms Ong,
i had just taken my class test on simple trigonometric identities and well as further trignonometric identities yesterday.
sadly to say, i left all the proving of trigonometric identities blank which is worth a total of 9 marks.
Im starting to get panic about trigonometric identities for my coming common test,end of year exams as well as the big O Level.
so im actually here to ask you if you may guide me on how to do them in a faster way, because i realised ive no time to tackle those proving questions.
Best Wishes,
Priscilla Fong

I received this email among the many others in my mailbox. I think this is a common problem face in proving Trigo Identity question. I shall provide a few strategies to handle this sort of question.

  • Usually start with the left hand side or whichever side which is more complicated.
  • When given trigo functions in the form of sec, cosec or cot x , it is advisable to change it to basic trigo functions like sin, cos, tan
  • When question involves power (especially square power), formulas should be considered.
  • Have the END in mind before you begin i.e if the end result involves only sin, your working should eventually eliminate the other trigo functions and stick on to sin.
  • It should take less than 8 steps for a 3-4 marks proving question.
  • a^2-b^2=(a+b)(a-b) is sometimes used in proving Trigo Identity. (Algebra rule)

I am going to use an example to illustrate how to use the above strategies

Q: Prove the identity (sec A - tan A)^2 = {1- sin A}/{1+ sin A}

(sec A - tan A)^2 =( {1}/{ cos A}-{sin A}/{cos A})^2 (Change sec and tan into sin & cos)

=  ( {1 - sin A}/{cos A})^2

= {(1-sin A)^2}/{(cos A)^2} 

=  {(1 - sin A)(1 - sin A)}/{(1 - sin^2 A)} (applying formula)

= {(1 - sin A)(1 - sin A)}/{(1 - sin A)(1 + sin A)}  (applying algebraic rule)

= {1 - sin A}/{1 + sin A}  (Proven)

Total number of steps = 6

Additional resource: You may want to read on A-Math Trigo Graphs here.

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Here is the video which takes me about 45 minutes to create:

http://www.youtube.com/watch?v=ZyJL2z6xO2w

Click here to download of the slides in pdf format & send it to at least one other friends who is taking exams.

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With ‘O’ level just right in the face, I just received an email asking me how to study for Math.

In fact, when you do a search on this site, you would have noticed I have written a few posts on “studying” for Math. Here are some of the posts I have done:

This time, instead of providing an answer to this question, I will be interested to know how you study for Math. Go ahead and leave your studying skills in the comment section.

I look forward to your reply.

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About Ai Ling

Hi, my name is Ai Ling Ong and I'm a professional Math Trainer specializing in GCE 'O' level Mathematics (Additional & Elementary). More than 10 years of teaching experience, I have coached hundreds of students more than 80 schools in Singapore. Read more about me here
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