singaporeolevelmaths

Simple Tips for Better Maths Results!

Archives for November 2008

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.

Where To Look For Jobs Suitable For Students

Update: Fight for part—time jobs gets tougher (Students looking for part time jobs might face a little more challenges with more workers getting retrenched in this financial turmoil, be positive and hold the faith)

I overheard a group of youngsters mentioning about the different types of jobs available for them. They were on handphone with their guy friend. The few girls ask him to consider being a waitor or a cashier at one of the major supermarkets.

I remember I started my first job after my A Levels. I guess the trend has changed; with more toys to play, more clothes to buy, heavier handphone bill to foot. Youngsters have to find means to support their lifestyle, isn't it?

It is so common to see a youngster with at least some if not all of the following items:

  • Handphone (s)
  • PSP
  • ipod
  • Camera
  • Laptop

So we can imagine the amount of $ required to support the gadgets lifestyle when parents decide not to be part of their ATM supporters anymore.

It is no wonder that more students are quickly finishing holiday jobs to make more pocket $, know more students and be more finanically and mentally independent; the pursuit of adults lifestyle.

Youth.sg has teamed up with Jobscentral to provide more suitable jobs for students. I thought this is really a brilliant idea! Cheers! More details here

Enjoy your work stint and have fun!