Mistakes are normal in maths. This is during the learning stages.
It will not be acceptable during tests and examinations. This everyone knows!
But human do make mistakes. This is a fact. Therefore, we have to know our weakness and avoid moving towards it (them).
A very common mistake made while doing maths is to use the variable "Z". From the writing, you can see that it is very similar to the number "2".
During examination, we are tensed up and our mind may not see what the eyes received.
2Z may end up as 22 finally. This "22" will then be used for computation and of course results in a BIG shock!
Thus knowing this danger, avoid using variables that are close to number in writing, unless stated by the maths question itself.
Do not choose a similar looking variable and end up with disappointment.
"b" and "6", "l" and "1" or "S" and "5". These are dangerous combination.
Thus look carefully when dealing with these numbers and variables.
Do not cause unnecessary mistakes. Save your effort to deal with better challenging thinking.
:)
Wednesday, 22 April 2009
Saturday, 18 April 2009
Counting With Base Eight
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Number system has an important factor attached to it.
It is the base of the number.
The base defines the quantity of item (in this case, the counted number) before the sequence repeats.
Take for example, base 8.
The count is: 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12 ....., 17, 20, 21, 22, 23,.......
The number "8" does not appear in the base 8 number system.
Once the 7 is reached, the next number increments to 10.
That is, the range is from 0 to 7 only.
How about the addition?
Example 1:
05
03 +
----
10
----
Since 5 + 3 exceed the maximum count of 8, the final added answer is 10, the start of next sequence.
Example 2:
14
05 +
----
11
----
It can be seen from the 2 examples above that the second digit in the addition is added with "1" after the first (right-most) digit shoots over "8".
This counting technique is nothing different from our normal base 10 (decimal) method of addition.
Thus, knowing the meaning of the base in the number system helps in proper counting, and includes addition and subtraction with the respective base.
It is nothing complex and abstract. Just counting with the correct quantity of number.
.
Number system has an important factor attached to it.
It is the base of the number.
The base defines the quantity of item (in this case, the counted number) before the sequence repeats.
Take for example, base 8.
The count is: 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12 ....., 17, 20, 21, 22, 23,.......
The number "8" does not appear in the base 8 number system.
Once the 7 is reached, the next number increments to 10.
That is, the range is from 0 to 7 only.
How about the addition?
Example 1:
05
03 +
----
10
----
Since 5 + 3 exceed the maximum count of 8, the final added answer is 10, the start of next sequence.
Example 2:
14
05 +
----
11
----
It can be seen from the 2 examples above that the second digit in the addition is added with "1" after the first (right-most) digit shoots over "8".
This counting technique is nothing different from our normal base 10 (decimal) method of addition.
Thus, knowing the meaning of the base in the number system helps in proper counting, and includes addition and subtraction with the respective base.
It is nothing complex and abstract. Just counting with the correct quantity of number.
.
Monday, 13 April 2009
Time Calculation May Not Be Easy
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Counting from 1 to 100 is normal for anyone. Just increment by 1. It's that simple.
But counting time may be another story for young math students.
Why is this so?
There is the seconds, the mintes, and the hours to handle. They differ by the umber 60.
The "carry over" through addition is the number SIX!
1 min 30 sec added by 40 sec gives .......
1 min 70 sec?
Here the 70 sec includes 60 sec + 10 sec. You need to understand that for time, 60 sec means one whole minute.
Thus, 70 sec = 60 sec + 10 sec ===> 70 sec = 1 min + 10 sec.
Therefore, 1 min 30 sec add 40 sec gives ==> 2 min 10 sec.
Compare this to adding 30 by 40. Answer = 70. No more analysis.
Time base on 1 hour = 60 min, 1 min = 60 sec concept.
To test true understanding of addition (and subtraction), time is a good gauge and tool to assess learners.
Test it on young kids today to annoy them... *#^&@!
Cheers!
.
Counting from 1 to 100 is normal for anyone. Just increment by 1. It's that simple.
But counting time may be another story for young math students.
Why is this so?
There is the seconds, the mintes, and the hours to handle. They differ by the umber 60.
The "carry over" through addition is the number SIX!
1 min 30 sec added by 40 sec gives .......
1 min 70 sec?
Here the 70 sec includes 60 sec + 10 sec. You need to understand that for time, 60 sec means one whole minute.
Thus, 70 sec = 60 sec + 10 sec ===> 70 sec = 1 min + 10 sec.
Therefore, 1 min 30 sec add 40 sec gives ==> 2 min 10 sec.
Compare this to adding 30 by 40. Answer = 70. No more analysis.
Time base on 1 hour = 60 min, 1 min = 60 sec concept.
To test true understanding of addition (and subtraction), time is a good gauge and tool to assess learners.
Test it on young kids today to annoy them... *#^&@!
Cheers!
.
Saturday, 11 April 2009
Common Mistake Of Gaps and Length
.
There are some maths questions that will be out to catch the careless learner.
A common one is that which require you to calculate the distance or length given the gap of items.
Look at the diagram below for an example.
Here, can you find the length from the left-most pillar to the 8th pillar, given the distance from start to 3rd pillar is 30m?
Solution: (Wrong slip-of-the-mind working)
Since the distance is 30m for 3rd pillar, answer to 8th pillar has to be 80m.
Seems to be right and logical. ==> Careful here!
Why?
Look at the step distance in between pillar. It is 30m / 2 = 15m.
As the gap between pillar from start to 8th pillar is only 7 gaps,
the actual correct distance is 7 x 15m = 105m.
Interestingly tricky question, right?
Be careful and alert for this "step" or "gap" maths problem.
Slamp down this carelessness, and mistake will eventually disappear (for this type).
.
There are some maths questions that will be out to catch the careless learner.
A common one is that which require you to calculate the distance or length given the gap of items.
Look at the diagram below for an example.
Here, can you find the length from the left-most pillar to the 8th pillar, given the distance from start to 3rd pillar is 30m?
Solution: (Wrong slip-of-the-mind working)
Since the distance is 30m for 3rd pillar, answer to 8th pillar has to be 80m.
Seems to be right and logical. ==> Careful here!
Why?
Look at the step distance in between pillar. It is 30m / 2 = 15m.
As the gap between pillar from start to 8th pillar is only 7 gaps,
the actual correct distance is 7 x 15m = 105m.
Interestingly tricky question, right?
Be careful and alert for this "step" or "gap" maths problem.
Slamp down this carelessness, and mistake will eventually disappear (for this type).
.
Friday, 10 April 2009
Constants and Variables
In maths, you will encounter many "letters". This "letters" are the symbols used to form equations and mathematical expressions.
("letters" here may mean symbols like the theta, beta, etc)
Some of these symbols are constants and some represent variables.
Knowing what are constants and variables is crucial for mastery of maths learning.
What are constants?
Constants, as the word literally means, are items that have number that never change.
What are variables?
Variables are symbols that changes in value.
Example A:
y = 3 x + 2
y and x are variables, and 3 and 2 are obviously constants.
Example B:
log x = 5y
x and y are variables , and 5 is constant.
Example C:
y = mx + c ( for straight line equation)
y and x are variables, and m and c are constants.
This may be confusing to some maths students when they start plotting graphs.
Here, the straight line is continuously moving with the value of x and y.
So why is the "m" identified as constant?
You need to know that "m" represents the "GRADIENT" of the line.
The line has the same slope at any value of x and y.
Thus "m" is a constant.
This is a typical concept that commonly goes wrong.
Therefore when you really understand what changes are considered "variables" and those that remain stable are known as "constants", you are in line for good maths study!
.
("letters" here may mean symbols like the theta, beta, etc)
Some of these symbols are constants and some represent variables.
Knowing what are constants and variables is crucial for mastery of maths learning.
What are constants?
Constants, as the word literally means, are items that have number that never change.
What are variables?
Variables are symbols that changes in value.
Example A:
y = 3 x + 2
y and x are variables, and 3 and 2 are obviously constants.
Example B:
log x = 5y
x and y are variables , and 5 is constant.
Example C:
y = mx + c ( for straight line equation)
y and x are variables, and m and c are constants.
This may be confusing to some maths students when they start plotting graphs.
Here, the straight line is continuously moving with the value of x and y.
So why is the "m" identified as constant?
You need to know that "m" represents the "GRADIENT" of the line.
The line has the same slope at any value of x and y.
Thus "m" is a constant.
This is a typical concept that commonly goes wrong.
Therefore when you really understand what changes are considered "variables" and those that remain stable are known as "constants", you are in line for good maths study!
.
Thursday, 2 April 2009
Algebra | Moving Forward in Usage
'
In the study of algebra, symbolic representation of number or unknown is key concept to solving mathematical equations.
The letter "x" or "y" are examples.
Other symbols can also be used as long as the usages are understood.
In the expression, x + 0.5 = 3.
This meant that the unknown "x" added to 0.5 will give a total of 3.
"x" here is nothing other than an unknown item to be solved.
It should be a number that relates to that maths equation. Nothing more, nothing less.
Another example:
x2 + 2x - 1 = 0
This "x" again is an unknown number to be found out.
Thus this algebraic expression and its "x" are just mathematical item representing a relationship.
Many students learning maths, when faced with this "x" always look puzzled.
With this post, the queries of this "x" (or "y", etc) should be cleared.
With this knowledge of the symbolic representation of unknowns, other areas of maths can be explained easily.
Topics like the trigonometry and logarithm will be expanded from this symbolic concept.
Cos A and log B will thus be finalised to a number, with this "A" and "B" yet to be solved.
Equation like
cos A + 2 = 2.4
will then be nothing more than to relate this unknown "A" to the expression.
It is also an easier way to explain and express this relationship between the unknown (A) and the other number (2 and 2.4).
Similarly,
log x + log 2 = 3
means that "x" is related to the 2 and 3 according to the given equation.
From the above few examples, the question now of what really is this "letter" doing forms meaning, right?
Maths starts off easy when this concept is clear.
Alot of the maths study involves this simple "trick" of presenting unknowns.
You notice how clever past mathematicians were now?
The use of simple symbol to pass off as number to carry on with maths solving.
Without this algebraic presentation, maths will not be as interesting as now.
Alot of guessing will have to be done and .... guess what? Maths will be HELL then.
Enjoy this symbolic concept in maths.
Enjoy your maths.
:-) (-:
In the study of algebra, symbolic representation of number or unknown is key concept to solving mathematical equations.
The letter "x" or "y" are examples.
Other symbols can also be used as long as the usages are understood.
In the expression, x + 0.5 = 3.
This meant that the unknown "x" added to 0.5 will give a total of 3.
"x" here is nothing other than an unknown item to be solved.
It should be a number that relates to that maths equation. Nothing more, nothing less.
Another example:
x2 + 2x - 1 = 0
This "x" again is an unknown number to be found out.
Thus this algebraic expression and its "x" are just mathematical item representing a relationship.
Many students learning maths, when faced with this "x" always look puzzled.
With this post, the queries of this "x" (or "y", etc) should be cleared.
With this knowledge of the symbolic representation of unknowns, other areas of maths can be explained easily.
Topics like the trigonometry and logarithm will be expanded from this symbolic concept.
Cos A and log B will thus be finalised to a number, with this "A" and "B" yet to be solved.
Equation like
cos A + 2 = 2.4
will then be nothing more than to relate this unknown "A" to the expression.
It is also an easier way to explain and express this relationship between the unknown (A) and the other number (2 and 2.4).
Similarly,
log x + log 2 = 3
means that "x" is related to the 2 and 3 according to the given equation.
From the above few examples, the question now of what really is this "letter" doing forms meaning, right?
Maths starts off easy when this concept is clear.
Alot of the maths study involves this simple "trick" of presenting unknowns.
You notice how clever past mathematicians were now?
The use of simple symbol to pass off as number to carry on with maths solving.
Without this algebraic presentation, maths will not be as interesting as now.
Alot of guessing will have to be done and .... guess what? Maths will be HELL then.
Enjoy this symbolic concept in maths.
Enjoy your maths.
:-) (-: