On google knol publishing platform some more articles on algebra are posted.

http://knol.google.com/k/narayana-rao-kvss/knol-sub-directory-algebra-new-knols/2utb2lsm2k7a/1658#

## Wednesday, September 23, 2009

## Saturday, August 22, 2009

### Algebra - New Posts on Google Knol

Knol Sub-Directory - Algebra - New Knols

http://knol.google.com/k/narayana-rao-kvss/-/2utb2lsm2k7a/1658#

More articles or posts are appearing on knol in the area of mathematics.

Yesterday I made a subdirectory of knols on geometry. Today I saw an author writing on combinatorics and number theory. They may not be focussed on JEE but for having a look at a different treatment of the topic they are good. Additional advantage is that you can ask a doubt and the author is likely to respond to your question. That interactive learning is possible when you read knols.

http://knol.google.com/k/narayana-rao-kvss/-/2utb2lsm2k7a/1658#

More articles or posts are appearing on knol in the area of mathematics.

Yesterday I made a subdirectory of knols on geometry. Today I saw an author writing on combinatorics and number theory. They may not be focussed on JEE but for having a look at a different treatment of the topic they are good. Additional advantage is that you can ask a doubt and the author is likely to respond to your question. That interactive learning is possible when you read knols.

## Monday, July 20, 2009

### Mathematics - Interesting Essays

http://knol.google.com/k/narayana-rao-kvss/knol-sub-directory-mathematics/2utb2lsm2k7a/1455#

List of interesting articles on Mathematics.

You can search for more using knol search engine.

List of interesting articles on Mathematics.

You can search for more using knol search engine.

## Friday, May 8, 2009

### IIT JEE Learning Mathematics - Recall Facilitation

Memorizing vs. Rote Learning & Drilling

Ideas of Michael Paul Goldenberg

Ann Arbor, MI, United States

I know of no one who opposes memorization (which by the way is NOT the same as rote learning.)

MINDLESS rote learning of things that can be learned effectively, possibly MUCH more effectively, in other ways needs to be stopped.

Mneomonic methods are, however, extremely easy to understand and put into practical use for a wide range of applications. These methods pay off in inverse proportion to the arbitrariness of the material being memorized. It means is that when faced with , say, a random or arbitrary list of items, dates, facts, etc., the more random the list and therefore the less conceptual links or "common knowledge" might be involved, the more a person using mnemonics would gain from using these techniques. Because otherwise the main option would be some variation on pure rote.

However, less time was needed for memorizing information with more structure, because the "inherent logic" or interconnectedness of the information helped one memorize.

Mathematics already is based on logical and conceptual links. Hence, it is often the case that what needs to be "memorized" in the sense mentioned above is minimal.

What sorts of things would need to be memorized in mathematics? Well, things like Order of Operations, which consists of conventions, not something that simply HAS to be. Terminology. Notation. Axioms. Things that do not follow from first precepts.

Even going beyond that, it is undoubtedly true that we need to "memorize" certain fundamental relationships and identities in specific areas of mathematics in order to not have to tediously look them up for every single instance in which they arise. In trigonometry, for example, understanding the definition of sine, cosine, and tangent in right triangle trigonometry is a key "fact" that one does much better to have at one's mental fingertips than not.

The amount that "must" be memorized is often far smaller than one originally believes, because of underlying relationships and concepts that create natural connections among a smaller set of facts. Anyone who is led to believe that entire chapters of a mathematics book and solutions of all problems need to be memorized by drill or rote is being mistaught.

That which is understood conceptually has a better chance of lasting, and can be more readily recreated through the concepts even if the "at one's fingertips" recall has been weakened or extinguished. Most people are well aware of this through personal experience.

http://rationalmathed.blogspot.com/2009/04/memorizing-vs-rote-learning-drilling.html

Ideas of Michael Paul Goldenberg

Ann Arbor, MI, United States

I know of no one who opposes memorization (which by the way is NOT the same as rote learning.)

MINDLESS rote learning of things that can be learned effectively, possibly MUCH more effectively, in other ways needs to be stopped.

Mneomonic methods are, however, extremely easy to understand and put into practical use for a wide range of applications. These methods pay off in inverse proportion to the arbitrariness of the material being memorized. It means is that when faced with , say, a random or arbitrary list of items, dates, facts, etc., the more random the list and therefore the less conceptual links or "common knowledge" might be involved, the more a person using mnemonics would gain from using these techniques. Because otherwise the main option would be some variation on pure rote.

However, less time was needed for memorizing information with more structure, because the "inherent logic" or interconnectedness of the information helped one memorize.

Mathematics already is based on logical and conceptual links. Hence, it is often the case that what needs to be "memorized" in the sense mentioned above is minimal.

What sorts of things would need to be memorized in mathematics? Well, things like Order of Operations, which consists of conventions, not something that simply HAS to be. Terminology. Notation. Axioms. Things that do not follow from first precepts.

Even going beyond that, it is undoubtedly true that we need to "memorize" certain fundamental relationships and identities in specific areas of mathematics in order to not have to tediously look them up for every single instance in which they arise. In trigonometry, for example, understanding the definition of sine, cosine, and tangent in right triangle trigonometry is a key "fact" that one does much better to have at one's mental fingertips than not.

The amount that "must" be memorized is often far smaller than one originally believes, because of underlying relationships and concepts that create natural connections among a smaller set of facts. Anyone who is led to believe that entire chapters of a mathematics book and solutions of all problems need to be memorized by drill or rote is being mistaught.

That which is understood conceptually has a better chance of lasting, and can be more readily recreated through the concepts even if the "at one's fingertips" recall has been weakened or extinguished. Most people are well aware of this through personal experience.

http://rationalmathed.blogspot.com/2009/04/memorizing-vs-rote-learning-drilling.html

## Thursday, April 30, 2009

### IIT JEE Mathematics Blog Status

I am presently preparing study plans for each chapter based on the text book by R D Sharma. I completed up to chapter 30.

You can see all chapters by clicking on labels revision facilitator or study plan.

Feel free to give your comments on the plans.

You can see all chapters by clicking on labels revision facilitator or study plan.

Feel free to give your comments on the plans.

## Friday, April 10, 2009

### Interesting Arithmetic Relations

1 x 8 + 1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 + 5 = 98765

123456 x 8 + 6 = 987654

1234567 x 8 + 7 = 9876543

12345678 x 8 + 8 = 98765432

123456789 x 8 + 9 = 987654321

-----------------------------

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 +10= 1111111111

-------------------------------

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 = 888888

987654 x 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 x 9 + 0 = 888888888

-------------------------------

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 + 5 = 98765

123456 x 8 + 6 = 987654

1234567 x 8 + 7 = 9876543

12345678 x 8 + 8 = 98765432

123456789 x 8 + 9 = 987654321

-----------------------------

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 +10= 1111111111

-------------------------------

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 = 888888

987654 x 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 x 9 + 0 = 888888888

-------------------------------

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

## Wednesday, March 11, 2009

### Blog Status - IIT JEE Mathematics

Presently developing chapterwise study plans for JEE 2010 and JEE 2011

## Monday, January 26, 2009

## Friday, January 23, 2009

### Concept of Congruency of Triangles

Concept of Congruency

(From 9th Class Text)

(Used in Trigonometry Chapters of XI )

When two triangles have the same size, then they are said to be congruent triangles.

Two congruent triangles are equal in all respects and when one is placed on the other, both exactly coincide. This means each part of one triangle is equal to the corresponding part of the other.

If ABC and DEF are congruent triangles, when DEF is placed over ABC, both will coincide and this proves that they are congruent. This process of proof is known as proof by superposition.

But one need not check for all the six parameters (three sides and three angles) for proving congruency.

Conditions for Congruency

1. If two sides and the included angle of a triangle are equal to the corresponding two sides and the included angle of another triangle, then the triangles are congruent.

2. If two angles and a side of a triangle are equal to the two angles and the corresponding side of another triangle, then the triangles are congruent.

3. If the three sides of the first triangle are equal to the corresponding three sides of the second triangle, then the triangles are congruent.

4. In case of right angled triangles, if the hypotenuse and a side of a triangle are equal to the corresponding side and hypotenuse of another triangle, then the triangles are congruent.

More briefly the rules are

(i) Two sides and the included angle (S.A.S.)

(ii) Two angles and corresponding side (A.A.S.)

(iii) Three sides (S.S.S.)

(iv) Right angle, hypotenuse, and one side (R.H.S.)

(From 9th Class Text)

(Used in Trigonometry Chapters of XI )

When two triangles have the same size, then they are said to be congruent triangles.

Two congruent triangles are equal in all respects and when one is placed on the other, both exactly coincide. This means each part of one triangle is equal to the corresponding part of the other.

If ABC and DEF are congruent triangles, when DEF is placed over ABC, both will coincide and this proves that they are congruent. This process of proof is known as proof by superposition.

But one need not check for all the six parameters (three sides and three angles) for proving congruency.

Conditions for Congruency

1. If two sides and the included angle of a triangle are equal to the corresponding two sides and the included angle of another triangle, then the triangles are congruent.

2. If two angles and a side of a triangle are equal to the two angles and the corresponding side of another triangle, then the triangles are congruent.

3. If the three sides of the first triangle are equal to the corresponding three sides of the second triangle, then the triangles are congruent.

4. In case of right angled triangles, if the hypotenuse and a side of a triangle are equal to the corresponding side and hypotenuse of another triangle, then the triangles are congruent.

More briefly the rules are

(i) Two sides and the included angle (S.A.S.)

(ii) Two angles and corresponding side (A.A.S.)

(iii) Three sides (S.S.S.)

(iv) Right angle, hypotenuse, and one side (R.H.S.)

## Thursday, January 1, 2009

### Ask questions and answer questions about IIT JEE Subjects

KNOWLEDGE QUESTION AND ANSWER BOARD

http://knol.google.com/k/narayana-rao-kvss/-/2utb2lsm2k7a/654#

http://knol.google.com/k/narayana-rao-kvss/-/2utb2lsm2k7a/654#

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