A-Maths Tuition

Revisit: A-Math Logarithms Equations (Plus: Types of Equations & How To Identify Them Easily)

With the school holidays period at this moment, it is perhaps a good time to revisit some of the 'killer' topics in O Level Math. I will start off with revisiting A-Math Logarithm Equations (Why: Logarithm is a brand new concepts taught only in Sec 3 unlike some other topics which are taught fundamentally in lower Sec; being such a new concept, some students could be a little overwhelmed by what Logarithm is all about)

Previous posts include Solving Reader's Logarithm Equations, Top 7 Commonly Made Mistakes in Logarithms

Photo By zebtron

To solve logarithm equations, it is very important to be able to identify the main types of equations.

Types of Logarithm Equations

There are 4 main types which I have classified:

Only Log (singing to the tune of "Only you" lalalalala.....)
Same Log-Log
Different Log-Log
Clones!

Features of each type of Log Equations

Only Log: Log appears once
Log with same bases (bases are the subscript beside Log)
Log with different bases
Exact looking log appears more than once

Examples for each type as stated above:

[pmath]log_2 \{3x+1}/{2x-7} = 3[/pmath]
[pmath]log_3 (2x+1) - log_3 (x-7) = 2[/pmath]
[pmath]log_4 3y - 2log_2 x = 1[/pmath]
[pmath](log_5 x)^2 = 2log_5 x [/pmath]

In the next post, I will be showing step by step way to solve Clones! type of Logarithm Equations. Ensure you subscribe to our feed to be posted of updates.

Additional Math Holiday Programme : Key Concepts Revision (For Sec 4 - 2009)

Update (8Nov08): 'O' Level A-Math Essential Concepts Revision Workshop Early Bird Registration has started. More details here =>http://www.WinnersEducation.com/holidaya-math.html

I want to personally train you for O level. (But there are only limited seats!)

With the academic term ending, we have received many enquiries from
referral from previous participants and website subscribers
for our 2009 programmes.

To ensure that the best is brought to you, there are still some
minor details to be confirmed.

Being our faithful subscriber of singaporeolevelmaths.com, I want you
to be notified first and enjoy the exclusive bonuses before anyone else.

So if you are looking for coaching programmes or
workshops to improve your current results in Additional Math,
go to this website,

http://www.WinnersEducation.com

fill up the details and get to be the limited few who will be
notified exclusively of the latest events.

Act fast if you really want to make a difference to your current results.

Cheers to your success,
Ai Ling
http://www.WinnersEducation.com

PS: Please send this message to friends who want to improve their
Additional Math results today. (Click on Tell A Friend Icon)

PPS: This is currently open to only subscribers in Singapore.

Sec 2 to Sec 3: How To Prepare Yourself For Additional Math

Posting results of the subject combination would be released next week for many schools. It is a transitional period of the Secondary 2 to Secondary 3 (Grade 8 to Grade 9), from juniors, they become seniors of the schools.

Today, I'm going to talk about how you can prep yourself (mentally & physically) for an "additional" math subject, assuming you have selected to take up Additional Math as one of your 'O' level subject. If you are thinking of the consequences of not taking A-Math, you may want to read about it here.

Myths of A-Math (My seniors said A-Math ...)

A-Math is very tough, very difficult, very hard to understand, always fail, very different from Elementary Math (E-Math).., lots of formula to remember ... don't understand the concepts

Truths of A-Math

Just like E-Math, you just need to know the right strategies and constantly apply them.
It all boils down to linking up the basic concepts and sometimes cross topics (there are some topics which will require you to bring in the tools you have learnt previously)
There would be new topics which you will see it 1st time in your life, pay more attention to them. After all,just like when we meet someone new, we need more time to warm up to them compared to old friends ;-)
There are cross-over between E and A Math. So learning A-Math is advantageous to you as some of the basic concepts are already taught in E-Math

Topics You Must Prep Yourself (before school starts)

Simultaneous Equations
Similar Triangles
Algebraic Rules
Quadratic Graphs & Equations

By familiarizing yourself on these topics, you will have a smoother transition of having another Math subject.

I would love to hear from the Sec 4s (2009) on 'What advice would you give your seniors on preparing for A-Math?' Leave your comments in the section below. I'm sure your juniors would appreciate your opinions.

Update: Sec 2 to Sec 3: How To Prepare Yourself For Elementary Math

A-Math: This Plane Geometry Question Almost Drives Me To Insanity!

Plane geometry is one of the top killer questions in A-Math as there are many things to prove in addition to the many lines, circles, triangles, angles ...

Read about the post I wrote earlier What you need to know to do well in Plane Geometry Part 1

I must admit this question almost drives me to insanity ;-) but luckily I saw the light when I was on the verge of sane and insanity ...

Question: Prove that a circle can be drawn passing through the points T,P,X and Q. [3 marks]

planegeometry-circle

Let me know how you handle this question in the comments section. For those who wants the step by step solution, drop me a comment as well. I highly recommend that you think about this question first before asking for solution.

There are 2 strategies I have used to help me in this Plane Geometry question. Do you want to know? so that you can learn and use them in your own question.

Hint: You must use one of the properties of circles.

Update: Video solution Here

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.

Exam Question : Usage of Binomial Formula

Harry - a vivd reader of askalwayslovely.blogspot.com sent me an email asking about solving of the following question. He did it using trial and error. I believe it will take him some time. He felt that his approach was not the best so he emailed me asking for alternatives.

In fact for this question, there is a step by step way which will get us the answer in less than 8 minutes time.

Question: If the coefficient of [pmath]x^k[/pmath] and [pmath]x^(k+1)[/pmath] in the expansion of [pmath](2x+3)^19[/pmath] are equal, find [pmath]k[/pmath]

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