Application of Algebra

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I have seen lower primary school kids learning mathematics.
They are exposed to many logic "games" which tested their mathematically analytical skill.

One of them is the math Word problem topic.

Here they are always given a scenario and asked to give an answer.
They are not taught algebra, however.
The expectation is for them to think out logically.

This is good in a way.

But along the journey of learning mathematics, they will sooner or later be told of an exciting area called the "Algebra".

Here, algebra comes in helpful for those who did not do well in the logical word problem questions.

Why?

It is because, in algebra, the unknown can be replaced by a symbol, normally a letter.

This solves the poor kid the time to "guess" the answers, with iteration of checking and re-trying at times.

With the use of algebra, the kid can attach the unknown to a letter and proceed with the calculation.

When this algebra concept is not mastered at a later stage while studying math, the learner will face tremendous obstacles along the way. The meaning of the "letter" will be an alien to him, not knowing the power of its usage, and thus the magic of algebra application.

Thus, in conclusion, any math student has to die-die, managed simple algebra in order to have a good time learning math.

Hope this advise and information helps.

:-)

Not Knowing Maths Is OK

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Anxiety is caused by not being able to fulfill your desire but strongly wishing for it.

Maths anxiety is likewise. Wanting to master maths but is unable to grasp the concepts.

Don't worry. It is not the end of the world!

Maths is just a tool for you to solve problems easily.
Maths lets you have a systematic approach in solving questions.

But if you do not understand maths, does it mean that you cannot solve problems?
You still can, but maybe only through more guessing (that is, non-systematical).

While learning or doing your maths homework, forgo the idea to quickly master the topic.
Forcing your learning through at a faster pace than you are able to handle does not serve any purpose.

Learning needs time to digest and analyse information. It is just like eating a meal.
Eating too fast will get you indigestion!
Same to learning maths, as well as other subjects.

Just understand that not knowing maths is OK.
Knowing maths is a privilege, a bonus.

With this mindset, you will find maths interesting.
It is a tool only for helping you find answers in an "education" and impressive way.

Life still goes on without you knowing maths.
(In fact, you actually use it, except that you did not know that it is called maths!).

Does this message make you feel better?
Hope it does.
Let maths be your slave.
And not you being the slave to maths.

Cheers! :D
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Simple Way to Master Indices Maths Question

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Have you seen many mistakes like the below?


Question 1:
3^x = 27

Solution:
3^x = 3⁴ ===> x = 4

Question 2:
9^x = 3³

Solution:
3^3x = 3³ ===> 3x = 3 ===> x = 1

Why the error?

A simple explanation is that the maths learner is not familiar with the basic multiplication of repeated numbers.

3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49

2 x 2 x 2 = 8
3 x 3 x 3 = 27

2 x 2 x 2 x 2 = 16

etc.....

Once you have mastered this basic repeated multiplications, you can rest assure that indices question will not be there to haunt you.

How about solving "x" in this 9^{x + 1} + 2(3^x) - 3 = 0 ?

I bet that if you understood the above criteria of learning indices, the equation can be easily solved for x (using quadratic formula as a hint).

All complex things start off with simple things.
Do you agree this applies to maths?

:D

Application of Maths - A Surprising One !

It just came to my mind that maths is a special subject.

Why do I say that?

How do you gauge whether you have mastered a subject or topic?

Your teacher will award you marks for the assessment done to check your understanding, right?

What is this process? It is maths!

Maths learning is being monitored through itself!
Applying maths to learn maths.

Giving marks is counting, logical thinking and judging. These are related to maths.

Thus you see that maths is interesting in that it checks itself like no subject does.

*** : - ) ****

Math Challenge 17

This is one that I came across and found to be exciting.

You have to solve using the number 1 to 9 only once.

_ _ _ _ _

0 _ _ _ _ (minus)

3 3 3 3

Any one dare to try?

Quadrant Identification for Trigonometrical Questions

For question regarding trigonometry, quadrant is one of the key parameter to obtain correct answers.

What is this quadrant about?
A complete cycle (360 degree) is divided into 4 quarters.
They are zones defined for specific trigonometric functions.

The first quarant (0 to 90 degree) gives positive sign for ALL trigonometric functions.
The second quarant (90 to 180 degree) allows only "sine" to have positive number.
For the thrid quarant (180 to 270 degree), "tangent" has positive number only.
Lastly, the fourth quarant (270 to 360 degree), "cosine" gives positive number only.

So, you can see that given a sign of a trigonometrical operation, the specific quadrant can be found or identified.

Example:

sin X = - 0.5 ===> Identifies quadrant as 3rd and 4th.

tan X = 0.2 ===> Identifies the 1st and 3rd quadrant.

This is simple, right?

However, do note the below example.
It causes a mistake that is common!

Example of potential error:

sin 2X = -0.5 ====> which quadrants ?

The answer is not that direct!

Why?

Now the math question is not on "X", but on "2X".

To identify the quadrant, you need to start off from the "2X", working as per normal.
But, after identifying the 2 quadrants, you have to compute the "2X" reference angle.
Using the reference angle, you have to obtain the 2 angles.
After which, you need to divide the angles obtained by 2.
The divided angles is then the final angles lying within the quadrants.

Confused? Never mind. See the numerical solution below.....

Solution:
2X = sin^-1 (0.5) = 30⁰
This is the reference angle used to compute the actual answers.

Final answers are (Quad 3)= 180 + 30 = 210⁰
and (Quad 4) = 360- 30 = 330⁰.

Common mistake is to obtain reference "2X" angle and straight away divide it by 2.
Using this newly found "X", you proceed to identify the angles of the quadrant identified using the "2X". THIS IS INCORRECT!

Do not confuse double angle with single angle.
When the problem is "2X", solve all the way using the "2X" first until reaching the end.
After which, you then divide the angles by 2 to get to the final answers.

Maths is simple if you follow the rules accordingly.
If you mess up double angle with single angle while solving, you just literally mess up the workings.

Maths forces you to follow rules set out. It punishes only if you do not obey orders.

Maths is interesting isn't it? Never expect that maths can police your behaviour while practicing it, right?

:-)