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Maths > Integers 7 > Flashcards

Integers 7 Flashcards

1
Q

Product of 11 negative integers and3 positive integers

A

Negative

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2
Q

Product of even no of negative no

A

Positive

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3
Q

X/0 is

A

Undefined

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4
Q

0/x is

A

0

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5
Q

Vulgar fractions

A

Not decimal fractions

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6
Q

Mean is denoted by

A

X bar

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7
Q

Squares of numbers won’t end in

A

2,3,7,8

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8
Q

To find the sum of first n natural numbers

A

n (n+1) / 2

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9
Q

To find the sum of first n square numbers

A

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

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10
Q

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

A

Argument

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11
Q

Imaginary numbers are represented by

A

i = √-1

√-2 = √2 i

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12
Q

Who introduced the concept of logarithm for the first time

A

John Napier

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13
Q

Who prepared a and published the logarithm tables

A

Henry Briggs

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14
Q

The log of a number has 2 parts

A

Characteristic and Mantissa

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

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15
Q

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

A

4

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16
Q

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

A

Logarithm table

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17
Q

How can you find antilog

A

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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18
Q

If the log of a number is negative -

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

A

_

3.5477

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19
Q

To find sum of first n perfect cubes

A

[ n(n+1)/2 ] ²

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20
Q

Common logarithms are represented by

A

Log N

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21
Q

Natural logarithms are represented by

A

In n

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22
Q

Common logarithms have base -

A

10

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23
Q

Natural logarithms have base

A

e = 2.71

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24
Q

Total no of factors of a number

A

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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25
Q

Total no of prime factors of a number

A

E.g. Take a number 648

     648 = 2³ x 3⁴ Total no of prime factors for 648 = 3 + 4
                                                = 7 factors
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26
Q

Perfect squares contain ………. no of factors

A

Odd

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27
Q

Relation between HCF and LCM of 2 numbers

A

Product of 2 numbers = HCF x LCM

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28
Q

HCF and LCM of fractions

A

LCM =
LCM of numerator / HCF of denominator

HCF =
HCF of numerator / LCM of denominator

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29
Q

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

A

Negative

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

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30
Q

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

A

1 or 0

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31
Q

Geometric progression formula

A

[a(rⁿ - 1)] / r-1

a - 1st term
r - common ratio
n - total no of terms

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32
Q

Product of n consecutive numbers is

A

n!

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33
Q

Total no of terms in (a + b)ⁿ

A

n + 1

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34
Q

Total sum of coefficients in (a + b)ⁿ

A

n²

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35
Q

0 ! = ….! = ….

A

0! = 1! = 1

36
Q

Sum of odd binomial coefficients =

A

= Sum of even binomial coefficients = 2 ⁿ⁻¹

37
Q

Every prime number greater than 3 can be expressed as

A

6k +/- 1

38
Q

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

A

(x - a)

39
Q

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

A

(x - a) and (x+a)

40
Q

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

A

x + a

41
Q

Divisibility rule of 7

A

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

42
Q

Divisibility rule of 13

A

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

43
Q

Divisibility rule of 17

A

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

44
Q

Divisibility rule of 19

A

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

45
Q

Fermat’s little theorem

A

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

46
Q

Father of numbers

A

Pythagoras

47
Q

Father of Indian mathematics

A

Aryabhatta

48
Q

Integers are represented by

A

Z or I

49
Q

Twin primes

A

Pair of prime numbers with only composite no between them.

E.g. 3,5 ; 5,7

50
Q

Complex numbers

A

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

51
Q

Irrational numbers represented by

A

Q’ or T

52
Q

Decimal fractions

A

Fractions having denominator as 10

53
Q

Common decimals

A

Fractions having denominator not as 10

54
Q

Compound fractions

A

Fractions whose both numerators and denominators are fractions.

55
Q

Mixed recurring decimal

A

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

56
Q

Bar bracket also called

A

Vinculum

57
Q

Total no of terms in (a + b)ⁿ

A

n + 1

58
Q

Total sum of coefficients in (a + b)ⁿ

A

n²

59
Q

0 ! = ….! = ….

A

0! = 1! = 1

60
Q

Sum of odd binomial coefficients =

A

= Sum of even binomial coefficients = 2 ⁿ⁻¹

61
Q

Every prime number greater than 3 can be expressed as

A

6k +/- 1

62
Q

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

A

(x - a)

63
Q

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

A

(x - a) and (x+a)

64
Q

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

A

x + a

65
Q

Divisibility rule of 7

A

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

66
Q

Divisibility rule of 13

A

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

67
Q

Divisibility rule of 17

A

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

68
Q

Divisibility rule of 19

A

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

69
Q

Fermat’s little theorem

A

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

70
Q

Father of numbers

A

Pythagoras

71
Q

Father of Indian mathematics

A

Aryabhatta

72
Q

Integers are represented by

A

Z or I

73
Q

Twin primes

A

Pair of prime numbers with only composite no between them.

E.g. 3,5 ; 5,7

74
Q

Complex numbers

A

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

75
Q

Irrational numbers represented by

A

Q’ or T

76
Q

Decimal fractions

A

Fractions having denominator as 10

77
Q

Common decimals

A

Fractions having denominator not as 10

78
Q

Compound fractions

A

Fractions whose both numerators and denominators are fractions.

79
Q

Mixed recurring decimal

A

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

80
Q

Bar bracket also called

A

Vinculum

81
Q

Founder of modern number theory

A

Pierre de Fermat

82
Q

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

A

Carl Friedrich Gauss

83
Q

Most ancient device used for calculation purposes

A

Abacus

84
Q

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

A

= [y/x] + [y/x²] + [y/x³] ……

[ ] represents that the integral value is only taken

85
Q

To convert octal to binary

A

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

86
Q

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

A

Down to top

87
Q

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

A

(n(n+1)/2)²

Maths (21 decks)

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