Geometry

Geometry in English derives from Greek word :                             
Geo- earth and metron- measurement

According to historians, the geometrical ideas shaped up                        
in ancient times, probably due to the need in art, architecture and measurement. These include occasions when the boundaries of cultivated lands had to be marked without giving room for complaints. Construction of magnificent palaces, temples, lakes, dams and cities, art and architecture propped up these ideas.

  
For competitive exams we can divide the geometry sections into the following chapters:
1.  Lines and Angles.
2. Triangles
3. Polygons
4. Quadrilaterals
5. Mensuration
6. Co-ordinate Geometry
7. Trigonometry

For basic concepts and theories refer only NCERT Class 6-10 mathematics, rest you need to practice. More you practice more you remember. Always get your basics clear otherwise practice doesn't matter.
Books you can refer to for practicing:
best book is

 1.Quantum CAT by Sarvesh K Verma (Arihant Publication).

Table of Contents
XAT Solved Paper 2012
IIFT Solved Paper 2011
SNAP Solved Paper 2011
1. Fundamentals
2. Averages
3. Alligations
4. Ratio, Proportion & Variation
5. Percentages
6. Profit, Loss and Discount
7. Cl/SI/Installments
8. Time and work
9. Time, Speed and Distance
10. Mensuration
11. Trigonometry
12. Geometry
13. Elements of Algebra
14. Theory of Equations
15. Set Theory
16. Logarithm
17. Functions and Graph
18. Sequence, series and Progressions
19. Permutations & Combinations
20. Probability
21. Co-ordinate Geometry
CAT Solved Papers (2003-2008)

2. Manhattan GMAT Guide Geometry

Table of Contents

PART 1 General:

1.Polygons

2.Triangles & diagonals

3.Circles and cylinders

4.Lines and angles

5.Co-ordinate Plane

6. Strategy for Data Sufficiency

7. Official Guide Problems part 1 

PART 2 Advanced:

1. Advanced Geometry

2. Official Guide Problems part 2

3. Quantitative Aptitude for the CAT by Arun Sharma TMH Publication

Table of Contents

BLOCK -- I

1. NUMBER SYSTEMS

2. PROGRESSIONS

BLOCK -- II

3. AVERAGES

4. ALLIGATIONS

BLOCK -- III

5. PERCENTAGES

6. PROFIT AND LOSS

7. INTEREST

8. RATIO, PROPORTION AND VARIATION

9. TIME AND WORK

10. TIME, SPEED AND DISTANCE

BLOCK -- IV

11. GEOMETRY AND MENSURATION

PART I: GEOMETERY

PART II: MENSURATION

12. COORDINATE GEOMETRY

BLOCK -- V

13. FUNCTIONS

14. INEQUALITIES

15. QUADRATIC EQUATIONS

16. LOGARITHMS

BLOCK -- VI

17. PERMUTATIONS AND COMBINATIONS

18. PROBABILITY

19. SET THEORY

MOCK TEST PAPERS

QA shortcuts

Simple Maths shortcuts, which only takes practice. You can invent your own method too. Just practice...

1. 11 multiplication

We all know the trick when multiplying by ten – add 0 to the end of the number, but did you know there is an equally easy trick for multiplying a two digit number by 11? This is it:

Take the original number and imagine a space between the two digits (in this example we will use 52:

5_2

Now add the two numbers together and put them in the middle:

5_(5+2)_2

That is it – you have the answer: 572.

If the numbers in the middle add up to a 2 digit number, just insert the second number and add 1 to the first:

9_(9+9)_9

(9+1)_8_9

10_8_9

1089 – It works every time.

2. Quick Square

If you need to square a 2 digit number ending in 5, you can do so very easily with this trick. Mulitply the first digit by itself + 1, and put 25 on the end. That is all!

252 = (2x(2+1)) & 25

2 x 3 = 6

625

3. Multiply by 5

Most people memorize the 5 times tables very easily, but when you get in to larger numbers it gets more complex – or does it? This trick is super easy.

Take any number, then divide it by 2 (in other words, halve the number). If the result is whole, add a 0 at the end. If it is not, ignore the remainder and add a 5 at the end. It works everytime:

2682 x 5 = (2682 / 2) & 5 or 0

2682 / 2 = 1341 (whole number so add 0)

13410

Let’s try another:

5887 x 5

2943.5 (fractional number (ignore remainder, add 5)

29435



4. Multiply by 9

This one is simple – to multiple any number between 1 and 9 by 9 hold both hands in front of your face – drop the finger that corresponds to the number you are multiplying (for example 9×3 – drop your third finger) – count the fingers before the dropped finger (in the case of 9×3 it is 2) then count the numbers after (in this case 7) – the answer is 27.

5. Multiply by 4

This is a very simple trick which may appear obvious to some, but to others it is not. The trick is to simply multiply by two, then multiply by two again:

58 x 4 = (58 x 2) + (58 x 2) = (116) + (116) = 232

6. Percentage

here is the easy way to do it. Work out 10% (divide the number by 10) – then add that number to half its value and you have your answer:

15% of $25 = (10% of 25) + ((10% of 25) / 2)

$2.50 + $1.25 = $3.75

7. Tough Multiplication

If you have a large number to multiply and one of the numbers is even, you can easily subdivide to get to the answer:

32 x 125, is the same as:
16 x 250 is the same as:
8 x 500 is the same as:
4 x 1000 = 4,000



8. Dividing by 5

Dividing a large number by five is actually very simple. All you do is multiply by 2 and move the decimal point:

195 / 5

Step1: 195 * 2 = 390
Step2: Move the decimal: 39.0 or just 39

2978 / 5

step 1: 2978 * 2 = 5956
Step2: 595.6

9. Subtracting from 1,000

To subtract a large number from 1,000 you can use this basic rule: subtract all but the last number from 9, then subtract the last number from 10:

1000
-648

step1: subtract 6 from 9 = 3
step2: subtract 4 from 9 = 5
step3: subtract 8 from 10 = 2

answer: 352

10. Assorted Multiplication Rules

Multiply by 5: Multiply by 10 and divide by 2.
Multiply by 6: Sometimes multiplying by 3 and then 2 is easy.
Multiply by 9: Multiply by 10 and subtract the original number.
Multiply by 12: Multiply by 10 and add twice the original number.
Multiply by 13: Multiply by 3 and add 10 times original number.
Multiply by 14: Multiply by 7 and then multiply by 2
Multiply by 15: Multiply by 10 and add 5 times the original number, as above.
Multiply by 16: You can double four times, if you want to. Or you can multiply by 8 and then by 2.
Multiply by 17: Multiply by 7 and add 10 times original number.
Multiply by 18: Multiply by 20 and subtract twice the original number (which is obvious from the first step).
Multiply by 19: Multiply by 20 and subtract the original number.
Multiply by 24: Multiply by 8 and then multiply by 3.
Multiply by 27: Multiply by 30 and subtract 3 times the original number (which is obvious from the first step).
Multiply by 45: Multiply by 50 and subtract 5 times the original number (which is obvious from the first step).
Multiply by 90: Multiply by 9 (as above) and put a zero on the right.
Multiply by 98: Multiply by 100 and subtract twice the original number.
Multiply by 99: Multiply by 100 and subtract the original number.


Percentage:
Find 7 % of 300. Sounds Difficult?

Percents: First of all you need to understand the word “Percent.” The first part is PER , as in 10 tricks per list-verse page. PER = FOR EACH. The second part of the word is CENT, as in 100. Like Century = 100 years. 100 CENTS in 1 dollar… etc. Ok… so PERCENT = For Each 100.

So, it follows that 7 PERCENT of 100, is 7. (7 for each hundred, of only 1 hundred).
8 % of 100 = 8. 35.73% of 100 = 35.73
But how is that useful??

Back to the 7% of 300 question. 7% of the first hundred is 7. 7% of 2nd hundred is also 7, and yep, 7% of the 3rd hundred is also 7. So 7+7+7 = 21.

If 8 % of 100 is 8, it follows that 8% of 50 is half of 8 , or 4.

Break down every number that's asked into questions of 100, if the number is less then 100, then move the decimal point accordingly.

EXAMPLES:
8%200 = ? 8 + 8 = 16.
8%250 = ? 8 + 8 + 4 = 20.
8%25 = 2.0 (Moving the decimal back).
15%300 = 15+15+15 =45.
15%350 = 15+15+15+7.5 = 52.5

Also it's useful to know that you can always flip percents, like 3% of 100 is the same as 100% of 3.

35% of 8 is the same as 8% of 35.

1. " Percent " implies " for every hundred".
2.The base used for the sake of percentage change calculations is always the original quantity unless otherwise stated.
3. In general, if the percentage increase is p%, then the new value is [(p/100) +1]
4. If the new value is k times the old value, then the percentage increase is (k-1) x 100
Eg1: If the percentage increase is 300%, the new value is 4 times the old value.
If the new value is 4 times the old value, the percentage increase is 300%.
5. If there are successive increases of p%, q% and r% in three stages, the effective percentage increase is
= {[(100+p) /100] [(100+q)/100] [ (100+r)/100] -1} x 100
Eg2: The percentage increase in the value of exports of apples of a country is as follows:
2001- 2002 => 25 %; 2002-2003 => 20 %; 2003-2004 => 10%
What is the percentage increase in the value of exports of apples of the country from 2001 to 2004?
Ans : Let the value of exports in 2001 be 100 units.
Then total percentage increase is:
= {[(100+25)/100] [ (100+ 20)/ 100] [ (100+10)/100] - 1} x 100
= {(1.25) (1.20) (1.10) -1} x 100
= [1.65-1.00] x 100
= [0.65] x 100
= 65
________________________________________
6. If the price of an item goes up by x %, the percentage reduction required to bring it down to the original price is:
= {100x / (100+x)} %
Eg3: If the price of an item goes up by 10%, by what percentage should the new price be reduced to bring it down to the original price?
Ans: Percentage reduction = {100 x 10/ (100 + 10)} %
= (1000/110) %
= 9.09 %
________________________________________
7. If the price of an item goes down by x %, the percentage increase required to bring it back to the original price = {(100 x 10) / (100 - x)} %.
8. If A is x % more/ less than B, then B is {(100 x 10) / (100 - x)} % less/ more than A.
9. If the price of an item goes up by x %, then the quantity consumed should be reduced by {100x /(100 +x)} % so that the total expenditure remains the same.
10. If the price of an item goes downs by x %, then the quantity consumed should be increased by {100x /(100 -x)} % so that the total expenditure remains the same.
Eg4: If the price of tea goes up by 10%, then what should be the percentage decrease in the quantity consumed so that the total expenditure on tea remains the same?
Ans: Required Percentage decrease = { (10 x 100) / (100+10) }%
= (1000/110) %
= 9.09%

11. If A's income is x% more than that of B, then B's income is less than that of A by [(100r)/(100+r).
12. If B's income is x% less than that of A, then A's income is more that of B by [(100x)/(100-x)]


Wait for some more useful tricks on Maths and VA....

Tairak Melas of the Mughals (Article from The Hindu)

One result of pollution and the scanty water in the Yamuna is the virtual end of the annual swimming fairs. The Delhi Gazetteer of 1883-1884 recorded the number of fairs in Delhi at 33, though originally there were 104 which included (besides the bathing ones) mostly those in honour of local deities, the pankha melas, the Moharram processions and the urs at various shrines. Among the fairs that attracted both Muslims and Hindus were the tairaki melas, first started by the Mughals during the rainy months, when the river was full and flowed right under the walls of the Red Fort. Nets had to be thrown in it to catch crocodiles that were swept thither by the flood. There may be some exaggeration in such accounts, though it is a fact that occasionally ensnared crocs found their way to Macchliwalan, the fish market near the Jama Masjid, where oil was extracted from their carcasses and, like their skin and teeth, fetched a high price, along with the snout that was mounted by taxidermists for the drawing rooms of the nawabs and nawabzadas . Until the late 19th Century crocodiles were found basking near the Purana Quila in winter and shot by British sentries, according to the Gazetteer.

Here is an account written in the mid-20th Century. For most Delhiwallahs the swimming season begins with the onset of the monsoon and not at modern swimming pools. There was a time when swimmers floated on their backs with iron spits on their chests on which kababs, paranthas and jalebis were fried. In Mughal days the art of swimming reached its zenith with tairaks from Turkey, Iran, Armenia, Central Asia and Afghanistan coming to compete here. A noted swimmer from Agra was given the title of Mir Macchli by Jahangir. It is said that when, as Prince Salim, he was initiated into the sport, tons of roses were thrown into the Yamuna, then in flood. A similar story is told about Shah Jahan, which only goes to show how popular river swimming was in those days even for princes.” Up to the early 1940s there were four swimming fairs on the four Thursdays of Sawan. Parties of swimmers from the Walled City marched to the river to the beat of drums, headed by a flag-bearer (the Nishan Nashin), and singing the songs of Barsat of poet Nazir. There were separate groups of Muslim and Hindu swimmers. For the former the ustad was the chief and for the latter the Khalifa (colloquially pronounced Khalipa). This was strange since the word Khalifa has Arabic origins and got converted into the Anglicized “Caliph”. How come then that a non-Muslim group had adopted it? One reason could be that in former times the trainers of both communities were of Turkish descent and so when “ustad” became popular with one group, the other one decided on retaining “Khalifa”.


Parmal Khalifa was actually a fat, paunchy vegetable seller who walked with difficulty. But when he entered the river he was grace sublime, braving the current and leading his team into the most tricky parts of the Yamuna. Ghafoor Ustad was a balding pigeon-fancier who used to jump from the old Yamuna Bridge into the flood water, holding the Nishan in one hand and swimming with the other — a tight-fitting cotton Lucknavi cap on his head. Both Muslim and Hindu groups swam across the river and when they reached the other side they offered “Chiraghi”. One on a mazar and the other under a pipal tree. The groups returned home with the drums beating again and the Nishan fluttering in the monsoon breeze to cries of “Nare Taqbi” and “Har har Mahadeva,” as per their belief. But if a group lost a swimmer (a rare occurrence) then the drums were not played and it trooped home silently. Because of this fear little girls and boys were posted on the road to bring word to the zenana that all was well and that their group was returning with “deecham-deecham” (joyous drumbeats) and mad Razzak dancing in a frenzy. It was then that kheel-batasha or sweat nuktidana (boondi) were distributed to all and sundry. In the case of a mishap the group did not return without the body of the drowned member, even if it took hours to recover it from usually the “bhanwar” or the treacherous circular river current that was a virtual death-trap.

One remembers meeting Munne Mian, an old ustad staying in Kucha Chelan in the 1960s, who had a host of stories to relate in his spare time. Though he had stopped swimming, his son had taken over the ustadi and the turban that went with it. One story concerned Masoom, a boy of 16 who was presumed drowned in the last fair of Sawan. The group searched for him but couldn’t find the body and wanted to return home. Munne Mian however was not the one to give up and eventually found the boy caught in the bhanwar. He carried him to the Yamuna bank, put him on his stomach and squeezed the water out of his lungs. He then massaged the body till breath returned and then the Nishan was hoisted and the group returned triumphantly, with Masoom being carried in a sort of relay throughout. One hardly hears of such fairs now!