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Entrance Preparation & Study Plan
A study plan that you develop yourself or center around yourself will go a long way toward helping you reach your goal. Develop a realistic plan that's established according to your needs and schedule, and supports the way you learn. This allows you to stick to your study plan and learn at your own pace, which contributes to the learning process. As the exam nears, you will need to create a plan to help you study effectively and minimize stress. The first step is to figure out how much time and effort you must dedicate to studying for the exam by asking the following questions:

How much material do you need to cover?
How difficult is the material?
How much time is available?
Do you have any other priorities during the study period?
What is the format of the exam?
How important is the exam?
What is your performance target for the exam?

To prepare the study plan, map out all of the material that has to be covered and make a schedule showing what, when and how much you will study each day. If you have kept up with the course work, studying will involve revision of the material that you have already covered. If you are behind in the course, you will have to finish the readings and other uncompleted work before starting the revision (if there isn't enough time to go over everything, you must decide what is most important for the exam).

Here are some tips to follow in creating your study plan
1. budget your time realistically;
2. allocate the study time into several manageable study sessions;
3. divide the course material into small segments and assign them to the study sessions;
4. set clear and specific goals for the study sessions;
5. prioritize to ensure that material weighted more heavily in the exam gets sufficient study time;
6. take into account your familiarity with the material and the difficulty level;
7. don't make the study sessions too long;
8. No noise. A noisy area can increase stress while studying. Avoid studying with the television or radio on. Pick a quiet place like your local library to study.
9. study sessions should have enough variety in terms of topics and activities to prevent boredom and loss of effectiveness;
10. Assess yourself. Take diagnostic or practice tests. Analyze the result. Mark the areas you could consider your weak areas. Concentrate on these areas when you begin studying.
11. avoid cramming before the exam; and
12. don't forget to include regular breaks.

So, understand why the Entrance Test (you are sitting for) is important to you. When preparing for the Exams, prepare through small, well-planned steps. Accomplish each step; build upon them. Then use these accomplishments as additional benefits and motivators to move you closer to the final achievementWish you all the success !

I collected last 7 CAT papers and classified every question according to the topic. Then I summed up the marks for questions in every topic and found the percentage occurrence of marks for each topic. The result for CAT Quant is shown below:
There! You have it. Algebra- 37.6% by marks, Geometry- 22.8% by marks, Number system- 21.6% by marks and ratio and proportion- 11.2% by marks. Enlightenment provided by past 8 CAT papers!
I did the same exercise for the verbal section and the results are summarized below.
Notice that RC again takes 50% of the whole verbal section. Then come grammar and usage, fill in the blanks, and jumbled paragraphs.
I left the DI section as there is fundamental prescribed category for logical questions. Though, I am sure that I can find some sort of classification in the DI section also.
The answer to CAT preparation came in a flash, and it was perfectly logical and full of common sense.

Time Table
Count the duration, in days, from the time you start your CAT preparation to August 31st. After August, you will be busy in taking those mock CATs and you will hardly have any time for studies. Therefore, if you are starting your CAT preparation on 1st of May, you have roughly 120 days of study time.
Assume that you will get 75% of these days for studies. The rest 25% will be lost in sleeping, watching movies or just staring at that nice girl living in the nearby building. Therefore, from May 1st to August 31st you have roughly 90 days of study time.
Assume that you will study 4 hours everyday. These 4 hours are separate from the time spent in reading newspapers or attending any CAT coaching. Also, if you study more, do the calculations in your own way. From those 4 hours, devote 2 hours to quant, 1 hour to Verbal, and 1 hour to DI. Therefore, given 90 days of study time, you have 180 hours to study quant, 90 hours for Verbal, and 90 hours for DI.
Break down those study hours according to percentage breakup of the various topics given in the table above. For example, from 180 hours of quant you should have 22% devoted to Number system. Therefore, you need to devote roughly 40 hours to Number system.
Once you have number of hours, planning becomes simpler. Just start from the highest occurring topic and move to the lowest occurring topic. The beauty of this method is that you would have covered the most important topic at the beginning of your preparations and even if you are not able to cover the least important ones because of lack of time, it would not hurt you so much!
For those who are attending any CAT coaching, if the topics covered in the coaching are different from the ones you are studying according to your plan, then you need to study hard during your coaching classes. Do the class exercises there itself. Pay attention the instructor and study as much as you can in the class itself.
To practice RC passages, download 1000 RC file from the ‘Download’ section of TotalGadha and do 3 RC everyday. Practice the RC techniques I discussed in the ‘RC strategy’ article.

Study Material
Besides the material given in your coaching, you can also follow these to enhance your preparations:
Number System- Lessons and Quizzes on Total Gadha. I am unashamed to say this; the lessons and problems on Total Gadha are one of the best. While I was teaching at a premier CAT coaching institute, my lessons on Number System were unofficially given to Math faculties to help them prepare for their classes. And I keep adding new material whenever I find something interesting.
Geometry- NCERT books VIII, IX and X, and Total Gadha. When it comes to geometry, the NCERT books are matchless. You don’t need to look any further. It is surprising but geometry questions in CAT are still below NCERT level. For higher level questions, refer to Total Gadha.
Algebra- Hall and Knight higher Algebra- The following chapters are a must do from this gem of a book: ratio and proportion, arithmetic progression, geometric progression, logarithms, permutation and combination, quadratic equation, probability and theory of equations. There is also a very good chapter on Number theory for those who want to read more.
General Math- Quantitative Aptitude for CAT by Pradeep Pandey. A good quant book.
Data Interpretation- Those who have never encountered logical reasoning question should certainly finish these:Puzzles and logical reasoning test on Total GadhaPuzzles and Teasers- by George SummersTricky Logic Puzzles- Norman D Willis.Past 5 years CAT Papers.
Grammar- Wren and Martin. Yes I know, most of you have seen this book thousand times in your school. Trust me, do this book 2- 3 times and you will not have to worry about the grammar section in CAT.
Usage- Dictionary of Phrasal Verbs- Collins Cobuild. Read it regularly if you have time. The dictionary gives you different phrasal verbs that can be formed with the same verb. For example, the verb ‘fall’ can give rise to phrasal verbs like fall about, fall apart, fall away, fall back, fall back on, fall behind, fall down, fall for, fall in, fall into, fall in with, fall off, fall on, fall out, fall over, fall through, fall to, and fall under. (Whew!) There are a lot of questions in CAT on usage of phrasal verbs.
Newspaper- The Hindu. There is not a single newspaper that can match the quality of The Hindu. The English is perfect (no puns or slangs), the editorials are very thought-provoking, and the news coverage is done in way that the paper does not take any sides. The paper lets its readers form their own opinions about the news. (My personal favorite is the ‘The Hindu Crossword’ which I’ve been solving for the last 7 years).
Books to read- Pick up the book list from here.
Magazine- The Economist. It is an expensive weekly American magazine but very indispensable if you want to get used to good English. Buy it and see for yourself.
Websites- http://www.epw.org.in/, http://www.sciam.com/, http://www.guardian.co.uk/. There are numerous others, but these three will do given the time that you have.

IMPORTANT FORMULAE AND INSTRUCTIONS
NUMBERS
1. Every prime number greater than 3 can be written in the form of 6k+1 or 6k-1 where k is an integer.
2. Two numbers (which may be prime or composite) are said to be relative primes or co-primes if they do not have any common factor other than one. (Ex: 15 and 16)
Unity is a relative prime to all numbers.
3. A number is said to be a perfect number if sum of all its factors excluding itself (but including 1) is equal to the number itself. (Ex: 28,496,8128)
4. The brackets in an expression have to be opened in the order of vinculum, simplebrackets, curly brackets and square brackets, i.e.,[ { ( - ) } ] to be opened from inside outwards.
5. RULES FOR DIVISIBILITY:
1. Divisibility by 3:
A number is divisible by 3 if the sum of its digits is a multiple of 3.
6. To express a mixed recurring decimal into a vulgar fraction as below:
In the numerator write the entire given number formed by the recurring and non-recurring parts and subtract from it the part of the decimal that is not recurring. In the denominator, write as many nines as the period (i.e., as many nines as the number of digits recurring) and then place next to it as many zeroes as there are digits without recurring in the given decimal.
i.e. 0.ˉ̄
7. The given number N (which can be written as equal to …. Where a, b, c are prime factors of N and p, q, r …. are positive integers) can be expressed as the
product of two factors in different ways. The number of ways in which this can be done
is given by the expression
½ {(p+1) (q+1) (r+1) ….}
To find out the number of ways in which a perfect square can be expressed as a product of 2 factors, we have the following 2 rules
1. As a product of two DIFFERENT factors:
½ {(p+1)(q+1)(r+1) …. -1} ways
2. As a product of two factors :
½ {(p+1)(q+1)(r+1) … +1} ways
7. Sum of all the factors of a number:
If a number N = …. where a, b, c … are prime numbers and p, q, r … are positive integers, then, the sum of all the factors of N (including 1 and the number itself) is:
) ….
8. Numbers of ways of writing a number as product of two co-primes :
If N = …., then, the number of ways of writing N as a product of 2 co-primes is 2^(n-1), where n is the number of distinct prime factors of the given number N.
9. Number of co-primes to N, that are less than N:
If N is a number that can be written as …., then, the number of co-primes of N, which are less than N, represented by Φ (N) is,
N (1-(1/a)) (1-(1/b)) (1-(1/c)) ….
10. Sum of co-primes to N that are less than N:
The sum of the co-primes of N that are less than N is N/2. Φ (N).
11. INVOLUTION:



= + 3ab (a+b)
= -3ab (a-b)
(a+b) (a-b)
(a+b) (a-b)+
(a+b) (
(a-b) (
-3abc
3abc, if a+b+c
12. EVOLUTION:
Any even-root of a positive quantity may be negative or positive
No negative quantity can have an even-root.
Every odd-root will have the same sign as the quantity itself.

1. A number when divided by d leaving a remainder of r is of the form dq+r where q is some integer from 0, 1, 2…
2. The smallest multiple of d which is greater than or equal to N is obtained by adding (d-r) to N, i.e., N+ (d-r) will be the smallest multiple of d which is greater than N.
3. When a division is split into a sum of two divisions (with the same divisor as the original divisor), the original remainder will be equal to the sum of the remainders of the two individual divisions. Similarly, when a division is split into difference of two divisions, the original remainder will be equal to the difference of the remainders of the two divisions.
Ex:
15/6=8/6+7/6
Remainder 3= 2+1
15/6=29/6-14/6
Remainder 3=5-2
4. If the remainder in a division is negative, then add the divisor to the negative remainder to get the positive remainder.
Ex:
15/6=25/6-10/6
Remainder 1-4=-3
13. LCM AND HCF:
1. Product of n numbers = lcm*
2. HCF of fractions =
3. LCM of fractions=
4. HCF by long division:
Take two numbers. Divide the greater by the smaller; then divide the divisor by the remainder; divide the divisor of this division by the next remainder and so on until the remainder is zero. The last divisor is the HCF of the two numbers taken. By the same method find the HCF of this HCF and the third number. This will be the HCF of the three numbers.
5. Any number which when divided by p, q, r leaving the same remainder in each case will be of the form k (LCM of p, q, r)+s where k = 0, 1, 2, ….
6. Any number which when divided by p, q, r leaving respective remainders of s, t, u where (p-s) = (q-t)=(r-u)=v (say), will be of the form k (LCM p, q and r) – v.
7. The largest number with which the numbers p, q or r are divided giving remainders of s, t and u respectively will be the HCF of the three numbers (p – s), (q – t) and (v – u).
8. The largest number with which the numbers p, q or r are divided
9. HCF of (p ~ r) and (q ~ r)
14. THE LAST DIGIT OF ANY POWER:
1. The last digit of
The last digit of
The last digit of
The last digit of
2. The last digit of
The last digit of
The last digit of
The last digit of
3. The last digit of
The last digit of
The last digit of
The last digit of
4. The last digit of
The last digit of
The last digit of
The last digit of
Where ab… is a number ending with 2, 3, 7 or 8.
Suppose we want to find out the last digit of 2357 , we should look at a multiple of 4 which is less than or equal to the power 57. Since 56 is a multiple of 4 , the last digit of 2357 will be the same as the last digit of .

15. FINDING THE REMAINDER IN DIVISIONS INVOLVING POWERS OF NUMBERS:
PATTERN METHOD:
1. Remainder when is divided by 7 is 2
Remainder when is divided by 7 is 4
Remainder when is divided by 7 is 1

Suppose we want to find out the remainder of when divided by 7since 63 is divisible by 3 the remainder is 1.

REMAINDER THEOREM METHOD:
1. In the division /8, the dividend is and the divisor is 8. Since the numerator is in terms of powers of 3, express the denominator also in terms of powers of 3. In this case, 8 can be written as 9 – 1 which is – 1. Now the given problem reduces to finding out the remainder when is divided by – 1. Here, if we consider as x, it is equivalent to finding out the remainder when is divided by (x – 1) which as per remainder theorem, is f (1). So, the remainder will be , i.e., 1.
16. SUCCESSIVE DIVISION:
1. The smallest number which when successively divided by d1 ,d2 and d3 leaves respective remainders of r1, r2 and r3 is [{(r3*d2)+r2}*d1]+r1

D1 d2 d3 divisors
R1 r2 r3 remainders

17. LARGEST POWER OF A NUMBER IN N :
1. To find out the largest power of a number in n we have to successively divide n by that number. Sum of the quotients is the required number.
2. This method is applicable only if the number whose largest power is to be found out is a prime number. If the number is not a prime number, then we have to write the number as the product of prime numbers, find the largest power of each of the factors separately. Then the smallest among the largest powers of all these factors of the given number will give the largest power required.
18. RULES PERTAININGTO :

1. The following rules should be remembered for numbers in the form of
a. It is always divisible by a - b.
b. When n is even it is also divisible by a + b.
c. When n is odd it is divisible by a + b, if a + b is a factor of 2* .
2. The following rules should be remembered for the numbers in the form of .
a. When n is odd it is divisible by a + b.
b. When n is odd, it is divisible by a – b, when a – b is a factor of 2*
c. When n is even, it is divisible by a + b, if a + b is a factor of 2*

Tamil Nadu

ADHIYAMAAN COLLEGE OF ENGINEERING
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RAJALAKSHMI ENGINEERING COLLEGE
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