Weekly Question

O level A-Math Essential Concepts Workshop Student's Feedback [Including Parent's Comment]

Dear Ms. Ling,
Thank you so much for the photos and looking forward to the work she has done for the past 4 days.
I'm very contented that she has learnt alot from this workshop and my money is worth it. Appreciate you help in motivating and making A-Maths a joyful and interesting workshop for my kid.
Tks, Shoba (Parent of Devyaah)

“I have benefitted a lot from this workshop. Ai Ling has put across alot of different and creative ways to make us understand the complex concepts in A-Maths and make it easier to remember the various formulas. I haven't been getting good results in my school exams but through this workshop, I had learnt the common mistakes I always make and had understood the concepts better. I will really recommend the workshop to my classmates as I think it has been really beneficial for me. Thank You (=”

Nurul Arinie, Regent Sec Sch

“Very good, I understand the concepts better and know how to apply the formulae. I have improved and am happy about it. This programme focuses on the key concepts.”
Bryanesh Balu, Yuan Ching Sec Sch

“I like this workshop very much, I really learnt alot!! I like the way you teach I can understand easily, the story makes us remember the most and all the different types of methods you used to teach us I love them. I will remember it forever. The music make me feel like the environment is good for learning and it prevented me from getting too stressed up. I like the way you help me to recap yesterday's things and your method of teaching us is so special. Thank you!!"

Jonas Tan, Regent Sec Sch

“I came into this course thinking that I wouldn't learn much but I was wrong. I've learnt alot more than I imagined I could in four days. I would definitely recommend this to others. I have learnt a great deal and it definitely has helped me a lot. I've not been for other programmes so I wouldn't know how to compare but this definitely is one to remember. Thank you for the assistance you have given me for the past 4 days. I'll continue to look at A-Math in a new perspective. Thank you for your 100% attention towards us to improve our A-Math”

Devyaah, Whitley Sec Sch

Photos of workshop here

O level A-Math: Fatal Mistake In Logarithm Equation You Must Aviod

This is a common mistake I notice in my O level A-Math essential concepts revision workshop.

Solve the following equation:

First, you must identify the type of question since different types of question require different strategies.
It's a different log-log question.
Strategy required: Change base.

Change base formula used.
Reason for changing to base 2: Between changing to base 2 or x, we choose base 2 as x is an unknown, we choose not to work with THE unknown most of the time, don't we?

Since we observe that there is a common term (log2 x),

Did you observe the fatal mistake (It's #7 Common mistake in Logarithm?

The correct way to do the substitution would be:

Solve the quadratic equation for y. Substitute the value back to find x.

Remember to check for validity of answers.

O Level A-Math: Fatal Mistake In Quadratic Equations You Must Avoid [Includes the 'trap' & How to avoid it]

This was one of the tricky questions included in quadratic questions pre review (I begin every A-Math lesson with pre review so that students can 'show off' their level of understanding in the concepts we're going to discuss. And as I guess it, everyone falls into the 'trap'

Reasons for students falling into the 'trap'

" .... is always positive, oh b^2 - 4ac >0"
" for all real values of x, so it further supports the fact that b^2 - 4ac >0"

How to avoid falling into the trap

Understand the question clearly

" It is THE quadratic graph which is always positive "
For all real values of x is NOT equal to real roots, it just means for all values of x. (No much significance in our solution)

Structure your solution carefully

Draw (A picture says a thousand words)
Write down the 2 conclusions
List your a,b and c
Solve the inequality

2008 O level A-Math Quadratic Equations are also discussed in the video here.
Subscribe (for free) to get your access password.

How To Solve "Clones" Type Of Logarithm Equations

In the previous post, I shared with you on the main Types of Logarithm Equations and How To Identify Them Easily.

Today, I'm going to share with you the step by step approach to solve Clone! type of Logarithm Equations.

Photo by Chris Gin

Clone Dolly

The strategy involving

identifying the clone which is relatively easy since clones are items which look EXACTLY the same.
Let the clone by y (Substitution method)

[pmath](log_5 x)^2 = 2log_5 x [/pmath]

[pmath] Let log_5 x be y [/pmath]

Substitution:

[pmath]y^2 = 2y [/pmath]

Common Mistake! (Canceling y from each side of the equation; So What? : you will miss out 1 answer)

[pmath]y = 2 [/pmath]

Correct Approach (Shift everything to left hand side so that right hand side is 0; So What? :Ready for factorization since it is a quadratic equation)

[pmath]y^2 - 2y = 0 [/pmath]

[pmath]y(y - 2) = 0 [/pmath]

[pmath]y = 0 or y - 2 = 0 [/pmath]

Remember we are interested in the unknown in the question (x) NOT y!

[pmath]log_5 x = 0 or log_5 x = 2 [/pmath]

[pmath]x = 1 or x = 25 [/pmath]

Check validity of answers by substituting values of x into the original given equation. Both values are acceptable.

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.

A-Math: Find Coordinates and Nature of Stationery Point (Plus: Tips to note in Differentiation)

The following question is similar to June 2008 GCE O Level A-Math Paper question which is testing on the following concepts

Differentiation involving exponential (I have written a post on Differentiation of e; post on Basic Differentiation Techniques are available here too )

Finding coordinates and nature of stationary point (Application of Differentiation)

Watch the video for a few more important tips on handling this sort of question.