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Vol. 1: Number System & Arithmetic

Glossary

Natural Numbers: 1, 2, 3, 4….. Whole Numbers: 0, 1, 2, 3, 4….. Integers: ….-2, -1, 0, 1, 2 ….. Rational Numbers: Any number which can be expressed as a ratio of two integers for example a p/q format where ‘p’ and ‘q’ are integers. Proper fraction will have (pq) Factors: A positive integer ‘f’ is said to be a factor of a given positive integer 'n' if f divides n without leaving a remainder. e.g. 1, 2, 3, 4, 6 and 12 are the factors of 12. Prime Numbers: A prime number is a positive number which has no factors besides itself and unity. Composite Numbers: A composite number is a number which has other factors besides itself and unity. Factorial: For a natural number 'n', its factorial is defined as: n! = 1 x 2 x 3 x 4 x .... x n (Note: 0! = 1)

Absolute value: Absolute value of x (written as |x|) is the distance of 'x' from 0 on the number line. |x| is always positive. |x| = x for x > 0 OR -x for x < 0 Tip: The product of ‘n’ consecutive natural numbers is always divisible by n! Tip: Square of any natural number can be written in the form of 3n or 3n+1. Also, square of any natural number can be written in the form of 4n or 4n+1. Tip: Square of a natural number can only end in 0, 1, 4, 5, 6 or 9. Second last digit of a square of a natural number is always even except when last digit is 6. If the last digit is 5, second last digit has to be 2. Tip: Any prime number greater than 3 can be written as 6k 1. Tip: Any two digit number ‘pq’ can effectively be written as 10p+q and a three digit number ‘pqr’ can effectively be written as 100p+10q+r.

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Laws of Indices

Last digit of an

n(Right) a(Down) 0 1 2 3 4 5 6 7 8 9 1 0 1 2 3 4 5 6 7 8 9 2 0 1 4 9 6 5 6 9 4 1 3 0 1 8 7 4 5 6 3 2 9 4 0 1 6 1 6 5 6 1 6 1 Cyclicity 1 1 4 4 2 1 1 4 4 2

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