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Archives for 2008

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:

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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.

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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?

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Since we observe that there is a common term (log2 x),
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image Did you observe the fatal mistake (It's #7 Common mistake in Logarithm?

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The correct way to do the substitution would be:
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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]

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

Poll Result for Do You Want To Receive Math Exam Papers Monthly?

This is the result for the poll conducted last month.

98% of the voters want us to send monthly Math exam papers.
We will be looking into this and implement it by Mid Jan'09 for all singaporeolevelmaths.com subscribers.
If you want to receive the Math exam papers (complete with answer keys), ensure you subscribe (it's free!) by entering your name and email address on the right hand side of this website.

Congratulations to all 88 NUS High pioneer batch graduates

All of the 88 National University of Singapore (NUS) High School graduates will get places in universities here or overseas. From Strait Times:

THE PIONEER batch of 88 National University of Singapore (NUS) High School of Mathematics and Science students graduated on Monday and all of them will get places in universities here or overseas.

Principal Hang Kim Hoon said he is confident that their NUS High School diplomas will earn all of them places in universities.

Some of the students have already been admitted to top universities such as King's College London, Cambridge and Oxford universities

Dr Hang said the students' achievements were poignant especially because they took the risk by becoming the first cohort to start on an experimental path of education which specialised in math and science and did away with the O-levels and A-levels.

The students entered NUS High School as year three students when it was still at its temporary location at Mount Sinai. The school has since moved to its permanent campus at Clementi Avenue.

In their three years at the school, they were exposed to a broad-based education which gave them grounding not only in math and science subjects but also allowed them to explore interests in humanities and the fine arts.

The students also worked with mentors from research institutes such as Agency for Science, Technology and Research and Defence Science Technology Agency on research projects based on their interes

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Gifted students were given opportunities to reach their potential. For example, 19 students from the graduating cohort took up university-level modules offered at NUS.

NUS High started off specializing in Math and Science Education for students who exhibit strong inclination towards these 2 major subjects. Based on what was reported, students in NUS High was provided with broad base education other than the 2 core subjects and at the same time explore students to the appreciation of humanities and fine arts subject.

In my opinion, this pioneer batch has shown the success of this initiative with all 88 students being offered places in either renowned overseas or local universities!

All the best for the future endeavors of these students! They have once again done themselves, their family and the nation proud!