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


quadratic-equation-common-mistake

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'

  1. " .... is always positive, oh b^2 - 4ac >0"
  2. " 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

  1. " It is THE quadratic graph which is always positive "
  2. 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

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

2008 O level A-Math Quadratic Equations are also discussed in the video here.
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Day 1 of 'O' level A-Math Essential Concepts Revision Workshop [Photos]


It was awesome start for the 4 days A-Math Essential Concepts Workshop.
Here are some pictures and for those who missed out this workshop, I'll be sharing in the next few posts some of the fatal mistakes (Quadratic Equations, Logarithms) you must NEVER make!

Let's get the house rules right on day 1 before we begin learning.

Happyeeee after the lemon tea drink

What was learnt in Day 1

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

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.