Quantitative Aptitude Notes on Simplification

Quantitative Aptitude Notes on Simplification



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Welcome to ukssscjob.in. Here we are providing  Notes on Mathmatical Simplification the basics of Quantitative Aptitude. This will helps to build up concepts who are weak in maths section for Candidates get all the MATH STUDY NOTES related to many govt. sector exams like UKSSSC EXAM, RPSC, IAS, RAS, FCI, CLAT, SSC, UPSC, MAT, REET, Patwari, Gram Sevak, NDA, CDS, AAO, LIC, IBPS, Police, Forest Guard, Railway, AAI, Clerk., Kindly make use of this page and do comment about the quality of the content.



BASIC FORMULAE

1. (a+b) 2=a2+b2+2ab

2. (a−b) 2=a2+b2−2ab

3. (a +b) 2− (a−b) 2=4ab  

4. (a+b) 2+ (a−b) 2=2(a2+b2)

5. (a2–b2)= (a+b) (a−b) 

6. (a+b+c) 2=a2+b2+c2+2(ab+bc+ca)

7. (a3+b3) = (a+b) (a2−ab+b2)   

8. (a3–b3) = (a−b) (a2+ab+b2)

9. (a3+b3+c3−3abc)= (a+b+c) (a2+b2+c2−ab−bc−ca)


10. If a+b+c=0, then a3+b3+c3=3abc.


TYPES OF NUMBERS

1. Natural Numbers:

Counting numbers 1, 2, 3, 4, 5 … are called natural numbers

2. Whole Numbers:

All counting numbers together with zero form the set of whole numbers.

Thus,

(I) 0 is the only whole number which is not a natural number.

(II) Every natural number is a whole number.

3. Integers:

All  natural  numbers,  0  and  negatives  of  counting  numbers i.e.,…,−3,−2,−1,0,1,2,3,….. together form the set of integers.

(i) Positive Integers: 1, 2, 3, 4….. is the set of all positive integers.

(ii) Negative Integers: −1, −2, −3… is the set of all negative integers.

(iii) Non-Positive and Non-Negative Integers: 0 is neither positive nor negative.

So,  0,1,2,3,….  represents  the  set  of  non-negative  integers,  while 0,−1,−2,−3,….. represents the set of non-positive integers.

4. Even Numbers:


A number divisible by 2 is called an even number, ex. 2, 4, 6, 8, etc.

5. Odd Numbers:

A number not divisible by 2 is called an odd number. e.g. 1, 3, 5, 7, 9, 11 etc.

6. Prime Numbers:

A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself.

7. Composite Numbers:

Numbers  greater  than  1  which  are  not  prime,  are  known  as composite numbers, e.g., 4,6,8,9,10,12.
Note:

(i) 1 is neither prime nor composite.

(ii) 2 is the only even number which is prime.

(iii) There are 25 prime numbers between 1 and 100.

REMAINDER AND QUOTIENT:


"The remainder is r when p is divided by k" means p=kq+r the integer q is called the quotient.

EVEN ,ODD NUMBERS


A number n is even if the remainder is zero when n is divided by 2: n=2z+ 0 or n=2z.

A number n is odd if the remainder is one when n is divided by 2: n=2z+1.

even X even = even

odd X odd = odd

even X odd = even

even + even = even

odd + odd = even

even + odd = odd

Some important tricks


1.        1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2

2.        (12 + 22 + 32 + ..... + n2) = n ( n + 1 ) (2n + 1) / 6

3.        (13 + 23 + 33 + ..... + n3) = (n(n + 1)/ 2)2

4.        Sum of first n odd numbers = n2

5.        Sum of first n even numbers = n (n + 1)

Quantitative Aptitude Notes on Simplification Quantitative Aptitude Notes on Simplification Reviewed by uksssc on 02:27:00 Rating: 5

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