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Archives for 2008

My Revision Workshop Covers 40% of the GCE 'O' Level A-Math Papers

Slide1 Many parents called me to ask "What is the workshop all about?"

Well, this workshop as the name suggests, Essential Concepts Revision Workshop, not Sec 4 jumpstart lessons (Differentiation and the the rest of the Sec 4 topics will be taught next year in the Ultimate Leap Programme)

Essential Concepts Revision Workshop will cover extensively the following modules

  • Surds
  • Indices
  • Logarithms
  • Quadratic Equations & Functions
  • Trigonometry (*All time "favourite"!)

If you happen to have the latest GCE 'O' level A-Math exam papers, 40% of the marks!( It's heavy) are solely devoted to testing students on the mentioned modules! All these are Sec 3 modules which students MUST have the solid foundation before they even talk about What's Up in Sec 4 A-Math.

More details are available here >>> http://www.WinnersEducation.com/holidaya-math.html

Important Equations Everyone Must Know But Never Taught In School

This equation should be taught in all A-Math and E-math classes! (But never taught in school)

From a strictly mathematical viewpoint it goes like this:

What Makes 100%?

What does it mean to give MORE than 100%?

Ever wonder about those people who say they are giving more than 100%?

We have all been to those meetings where someone wants you to give over 100%.

How about achieving 103%? What makes up 100% ! in life?

Here's a little mathematical formula that might help you answer these questions:

If:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z is represented as:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26.

Then:

H-A-R-D-W-O-R-K
8+1+18+4+23+15+18+11 = 98% !

and
K-N-O-W-L-E-D-G-E
11+14+15+23+12+5+4+7+5 = 96%

But,

A-T-T-I-T-U-D-E
1+20+20+9+20+21+4+5 = 100%

So, one can conclude with mathematical certainty that While Hard work and Knowledge will get you close, and Attitude will get you there.

Email courtesy of Nzm

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:

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

Features of each type of Log Equations

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

Examples for each type as stated above:

  1. [pmath]log_2 \{3x+1}/{2x-7} = 3[/pmath]
  2. [pmath]log_3 (2x+1) - log_3 (x-7) = 2[/pmath]
  3. [pmath]log_4 3y - 2log_2 x = 1[/pmath]
  4. [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.