Integers 7 Flashcards by joel mammen isaac

Product of 11 negative integers and3 positive integers

Negative

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Product of even no of negative no

Positive

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X/0 is

Undefined

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0/x is

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Vulgar fractions

Not decimal fractions

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Mean is denoted by

X bar

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Squares of numbers won’t end in

2,3,7,8

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To find the sum of first n natural numbers

n (n+1) / 2

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To find the sum of first n square numbers

n (n+1) (2n+1) / 6

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In a logarithmic expression the number other than the base and the exponent is called

Argument

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Imaginary numbers are represented by

i = √-1

√-2 = √2 i

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Who introduced the concept of logarithm for the first time

John Napier

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Who prepared a and published the logarithm tables

Henry Briggs

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The log of a number has 2 parts

Characteristic and Mantissa

Mantissa - part of the no after decimal place
Characteristic - “ “ “ “ “ before decimal place

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We can calculate Log of numbers with a maximum of ………… digits (using log table)

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The value of mantissa in a log of the number can be calculated by using the

Logarithm table

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How can you find antilog

Take the mantissa of the log , and using the table find it’s antilog which is similar to the way in which we find log. After that if the characteristic is 4, then multiply the mantissa with 10⁴

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If the log of a number is negative -

E.g. -3.5477 ,it is actually written as

3.5477

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To find sum of first n perfect cubes

[ n(n+1)/2 ] ²

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Common logarithms are represented by

Log N

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Natural logarithms are represented by

In n

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Common logarithms have base -

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Natural logarithms have base

e = 2.71

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Total no of factors of a number

E.g. Take a number 648

     648 = 2³ x 3⁴ Total no of factors for 648 = (3+1) (4+1)
                                                = 4x5 = 20 factors

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Total no of prime factors of a number

E.g. Take a number 648 648 = 2³ x 3⁴ Total no of prime factors for 648 = 3 + 4 = 7 factors

Perfect squares contain .......... no of factors

Odd

Relation between HCF and LCM of 2 numbers

Product of 2 numbers = HCF x LCM

HCF and LCM of fractions

LCM = LCM of numerator / HCF of denominator HCF = HCF of numerator / LCM of denominator

When we divide a negative number by a positive number , the remainder cannot not be

Negative E.g. -22/7 → quotient : -3. Remainder : -1 This is not correct Instead it should be Q: -4 , R: +6

When a square is divided by 3 or 4 , the remainder is

1 or 0

Geometric progression formula

[a(rⁿ - 1)] / r-1 a - 1st term r - common ratio n - total no of terms

Product of n consecutive numbers is

Total no of terms in (a + b)ⁿ

n + 1

Total sum of coefficients in (a + b)ⁿ

n²

0 ! = ....! = ....

0! = 1! = 1

Sum of odd binomial coefficients =

= Sum of even binomial coefficients = 2 ⁿ⁻¹

Every prime number greater than 3 can be expressed as

6k +/- 1

(xⁿ - aⁿ) is divisible by ........ for all values of n

(x - a)

(xⁿ - aⁿ) is divisible by ........ for all even values of n

(x - a) and (x+a)

(xⁿ + aⁿ) is divisible by ........ for all odd values of n

x + a

Divisibility rule of 7

Number - (2 x last digit) = a no divisible by 7

Divisibility rule of 13

Number + (4 x last digit) = a no divisible by 13

Divisibility rule of 17

Number - (5 x last digit) = a no divisible by 17

Divisibility rule of 19

Number + (2 x last digit) = a no divisible by 19

Fermat’s little theorem

states that if n is a prime number, then for any integer a, the number aⁿ− a is an integer multiple of n.

Father of numbers

Pythagoras

Father of Indian mathematics

Aryabhatta

Integers are represented by

Z or I

Twin primes

Pair of prime numbers with only composite no between them. | E.g. 3,5 ; 5,7

Complex numbers

Numbers with 2 terms in which one term is an imaginary number.

Irrational numbers represented by

Q’ or T

Decimal fractions

Fractions having denominator as 10

Common decimals

Fractions having denominator not as 10

Compound fractions

Fractions whose both numerators and denominators are fractions.

Mixed recurring decimal

A recurring decimal in which at least one digit doesn’t repeat.

Bar bracket also called

Vinculum

Total no of terms in (a + b)ⁿ

n + 1

Total sum of coefficients in (a + b)ⁿ

n²

0 ! = ....! = ....

0! = 1! = 1

Sum of odd binomial coefficients =

= Sum of even binomial coefficients = 2 ⁿ⁻¹

Every prime number greater than 3 can be expressed as

6k +/- 1

(xⁿ - aⁿ) is divisible by ........ for all values of n

(x - a)

(xⁿ - aⁿ) is divisible by ........ for all even values of n

(x - a) and (x+a)

(xⁿ + aⁿ) is divisible by ........ for all odd values of n

x + a

Divisibility rule of 7

Number - (2 x last digit) = a no divisible by 7

Divisibility rule of 13

Number + (4 x last digit) = a no divisible by 13

Divisibility rule of 17

Number - (5 x last digit) = a no divisible by 17

Divisibility rule of 19

Number + (2 x last digit) = a no divisible by 19

Fermat’s little theorem

states that if n is a prime number, then for any integer a, the number aⁿ− a is an integer multiple of n.

Father of numbers

Pythagoras

Father of Indian mathematics

Aryabhatta

Integers are represented by

Z or I

Twin primes

Pair of prime numbers with only composite no between them. | E.g. 3,5 ; 5,7

Complex numbers

Numbers with 2 terms in which one term is an imaginary number.

Irrational numbers represented by

Q’ or T

Decimal fractions

Fractions having denominator as 10

Common decimals

Fractions having denominator not as 10

Compound fractions

Fractions whose both numerators and denominators are fractions.

Mixed recurring decimal

A recurring decimal in which at least one digit doesn’t repeat.

Bar bracket also called

Vinculum

Founder of modern number theory

Pierre de Fermat

‘Mathematics is the queen of the sciences and number theory the queens of mathematics’ was said by

Carl Friedrich Gauss

Most ancient device used for calculation purposes

Abacus

Highest power of x (prime number) dividing a factorial y

= [y/x] + [y/x²] + [y/x³] ...... [ ] represents that the integral value is only taken

To convert octal to binary

Convert each digit in the octal number into 3 binary digits. Replace it , and u have converted it

While converting decimal system into another system the result is taken from the ...... direction

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sum of the first n cubes, 1³ +2³ +...+n³ =

(n(n+1)/2)²