Ai Ling Ong

Free Mobile Software To Draw Quadratic, Algebraic & Trigonometry Graphs

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.

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

See below for the screenshots:

screen-shot-mobile-graphs1

screen-shot-mobile-graphs2

screen-shot-mobile-graphs3

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.

O Level Additional Math - How To Prove Trigonometry Identity

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.
[pmath]a^2-b^2=(a+b)(a-b)[/pmath] 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 [pmath](sec A - tan A)^2 = {1- sin A}/{1+ sin A}[/pmath]

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

= [pmath]( {1 - sin A}/{cos A})^2[/pmath]

= [pmath]{(1-sin A)^2}/{(cos A)^2} [/pmath]

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

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

= [pmath]{1 - sin A}/{1 + sin A} [/pmath] (Proven)

Total number of steps = 6

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

I created a 'do your best for exams' video for you

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.

How Do You "Study" For Math?

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.

Dessert: Be Thankful For What You Have

A blind boy sat on the steps of a building with a hat by his feet. He held up a sign which said: 'I am blind, please help.' There were only a few coins in the hat.

A man was walking by. He took a few coins from his pocket and dropped them into the hat. He then took the sign, turned it around, and wrote some words. He put the sign back so that everyone who walked by would see the new words.

Soon the hat began to fill up. A lot more people were giving money to the blind boy. That afternoon the man who had changed the sign came to see how things were. The boy recognized his footsteps and asked, 'Were you the one who changed my sign this morning? What did you write?'

The man said, 'I only wrote the truth. I said what you said but in a different way.'
What he had written was: 'Today is a beautiful day and I cannot see it.'

Do you think the first sign and the second sign were saying the same thing?

Of course both signs told people the boy was blind. But the first sign simply said the boy was blind. The second sign told people they were so lucky that they were not blind. Should we be surprised that the second sign was more effective?

Moral of the Story: Be thankful for what you have . Be creative . Be innovative . Think differently and positively .

Invite others towards good with wisdom . Live life with no excuse and love with no regrets . When life gives you a 100 reasons to cry, show life that you have 1000 reasons to smile . Face your past without regret . Handle your present with confidence . Prepare for the future without fear . Keep the faith and drop the fear .

Great men say, 'Life has to be an incessant process of repair and reconstruction, of discarding evil and developing goodness . In the journey of life, if you want to travel without fear, you must have the ticket of a good conscience . '

The most beautiful thing is to see a person smiling!!
And even more beautiful is, knowing that you are the reason behind it!

Do you like this story? Drop me a comment at the box below.

After 'O' levels: Single Intake For JCs (Junior Colleges)

It was reported in Strait Times on the reasons for single intake, the start of Junior Colleges for 2009.

It was mentioned that the GCE 'O' level results will be out in early January so that all year 1 students can report for their respective JCs on 2 Feb 09. No more 1st 3 months of JC!

This also means the following:

Entry to JCs is now solely based on your 'O' level results
Preliminary exams results are perhaps not viewed as important since they would not be used for admission
Every student is admitted at the same time based on a common examinations, fairer ground compared to old system of entry by prelim results.
Attitude towards prelims might change since they are not used, hence the outcome is not important. (It was my first time in my life that some students have time to play sports after a prelim paper; well I don't mean to say that this is totally wrong, in fact it is perhaps a good form of break after a stressful paper. Never during my time did we have the courage to play in the midst of prelims, games come only after the completion of the papers)

So how did you fare for your prelims? Do you like this new policy of JC admission?

Leave me a comment at the box below.