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bryx_math > Algebra > Flashcards

Algebra Flashcards

1
Q

Numbers which allow us to count the objects or ideas in a given collection

A

Cardinal Numbers

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2
Q

States the position of the individual objects in a sequence

A

Ordinal Numbers

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3
Q

Symbols or combination of symbols which describe a number

A

Numerals

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4
Q

Most widely used numerals

A

Arabic and Roman Numerals

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5
Q

What is the Arabic Number equivalent of the following:

I V X L C D M

A

I-1 V-5 X-10 L-50 C-100 D-500 M-1000

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6
Q

How does the romans indicate large numbers?

A

Bracket-multiply 100 times
|V|=500
Vinculum(bar above the number):multiply 1000 times
Doorframe=multiply 100,000 times

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7
Q

A specific symbol used alone or in combination to denote a number

A

Digit

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8
Q

Numbers which are considered as the “Counting Numbers”

A

Natural Numbers

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9
Q

Are all natural numbers, negative of natural numbers and the number zero

A

Integers

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10
Q

Are numbers which can be expressed as a quotient (ratio of two integers). The term rational comes from the word ratio

A

Rational Numbers

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11
Q

Are numbers which cannot be expressed as a quotient of two integers

A

Irrational Numbers e.g. sqrt(2), pi, Euler’s number

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12
Q

The numerical value of the number neglecting the sign

A

Absolute Value

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13
Q

Defined as part of the whole

A

Fractions

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14
Q

A fraction in which the numerator and denominator are both integers. Also known as common fraction

A

Simple Fraction

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15
Q

Is a fraction with unity for its numerator and positive integer for the denominator

A

Unit Fraction

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16
Q

A fraction in which the numerator or denominator, or both are fractions

A

Complex Fraction

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17
Q

Two or more simple fraction where the denominators are similar

A

Similar Fraction

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18
Q

Positive integers that have more than two positive whole number factors

A

Composite Numbers

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19
Q

An integer greater than 1 hat is divisible only by 1 and itself

A

Prime number

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20
Q

What is the fundamental theorem of arithmetic

A

Every positive integer greater than 1 is a prime or can be expressed as a unique product of primes and powers of primes

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21
Q

What is the only prime number that is greater than 1 and even?

A

number 2

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22
Q

numbers that have only two factors: 1 and itself

A

Natural Prime numbers

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23
Q

Set of two consecutive odd prime that differs by two

A

Twin Primes

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24
Q

Pair of prime numbers that are the same distance from a given number in a number line

A

Symmetric Primes/Euler Prime

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25
Q

Prime numbers that remains a prime when its digits are reversed

A

Emirp

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26
Q

Numbers whose greatest common factor is 1

A

Relatively Prime numbers

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27
Q

A number whose factors are prime numbers raised to a certain power

A

Unique Product of power prime

eg: 360=2^3 * 3^2 5^1

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28
Q

An integer that is equal to the sum of all its possible divisors, except the number itself

A

Perfect number

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29
Q

Perfect Number formula

A

2^(p-1)*(2^p-1)

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30
Q

If the sum of the possible divisors is greater than the number

A

abundant number

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31
Q

An integer with the sum of all possible divisor is less than the number itself

A

Deficient number

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32
Q

Refers to two integers where each is the sum of all the possible divisors of the other

A

Amicable/Friendly numbers

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33
Q

Represents the product of all positive integers from 1 to n, inclusive

A

factorial

eg: n!=n(n-1)(n-2),,,3,2,1

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34
Q

The factorial symbol was introduced by who?

A

Christian Kramp

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35
Q

Digits that define the numerical value of a number

A

Significant figure/digit

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36
Q

Forms of approximation

A

Rounding and Truncating

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37
Q

It means replacing the number with another number having fewer significant decimal digits

A

Rounding

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38
Q

Refers to the dropping of the next digits in order to obtain the degree of accuracy beyond the need of practical calculation/aka rounding down

A

Truncation

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39
Q

Closure Property of addition

A

a+b=integer

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40
Q

commutative property of addition

A

a+b=b+a

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41
Q

Associative Property of addition

A

(a+b)+c=a+(b+c)

42
Q

Identity property of addition

A

a+0=a

43
Q

additive identity

A

0

44
Q

multiplicative identity

A

1

45
Q

transitive property

A

if a=b and b=c then a=c

46
Q

What is Zero-Factor property

A

if ab=0, then a=0 or b=0

47
Q

Who first used the symbol of radical

A

Christoff Rudolff, 1525 in Die Coss

48
Q

A radical expressing an irrational number

A

Surd

49
Q

contains no rational number and all its terms are surds

A 
Pure surd
eg sqrt(3)=sqrt(2)
50
Q

a surd that contains at least one rational number

A 
Mixed Surd 
eg 5sqrt(2)
51
Q

an expression of two terms with at least one surd

A

Binomial Surd

eg 5+sqrt(2)

52
Q

Difference of two squares x^2-y^2

A

(x+y)(x-y)

53
Q

Cube of a binomial (x+y)^3

A

x^3+3x^y+3xy^2+y^3

54
Q

difference of two cubes x^3-y^3

A

(x-y)(x^2+xy+y^2)

55
Q

sum of two cubes x^3+y^3

A

(x-y)(x^2-xy+y^2)

56
Q

square of a trinomial (x+y+z)^3

A

x^2+y^2+z^2+2xy+2xz+2yz

57
Q

In proportion, what do you call the first and second term respectively

A

antecedent/consequent

58
Q

Refers to the product of several prime numbers each taken with its greatest multiplicity

A

Least common donominator

59
Q

A number that two other numbers will divide into evenly

A

common multiple

60
Q

Lowest multiple of two numbers

A

least common multiple

61
Q

A factor that divides into a larger number evenly

A

Greatest common factor

62
Q

Logarith comes from the greek words _____ and _____

A

logus=ratio

arithmus =number

63
Q

who invented logarithm?

A

John Napier, 1614 using e=2.718 for its base

64
Q

What do you call a logarithm with base e?

A

Natural logarithm/Napierian Logarithm

65
Q

who improved the logarithm using base 10?

A

Henry Briggs. Its now called common logarithm/Brigssian Logarithm

66
Q

Euler’s number formula

A

e=lim as n->infinity (1+1/n)^n

67
Q

if a polynomial p(x) is divided by the binomial(x-a), the remainder is p(a)

A

Remainder Theorem

68
Q

What is the factor theorem?

A

if the polynomial is divided by x-a, and the reminder is zero, then x-a is a factor of the polynomial

69
Q

who suggested the remainder and factor theorem?

A

Etienne Bezout

70
Q

Sum of two roots formula

A

r1+r2=-B/A

71
Q

Product of two roots formula

A

r1*r2=C/A

72
Q

rth term of the binomial expansion of (x+y)^n

A

rth=nC(r-1)x^(n-r+1)y^(r-1)

73
Q

What is the degree of the polynomial 3x^4y-2x^3z^4=7yz^5?

A
  1. second term, 3+4
74
Q

Work Problems tips

A

solve in man-hours

75
Q

what is the equivalent of the following coins?
Penny, Nickel, Dime
Quarter, Half dollar?

A 
Penny 1c
Nickel 5c
Dime 10c
Quarter 25c
halfdollar 50c
76
Q

magic clock formula

A

degrees=11/2m-30H

77
Q

arithmetic progression formula

A

an=a1+(n-1)d

s=n/2(a1+an)

78
Q

Geometric Progression Formula

A

an=a1r^(n-1)

S= a1(r^n-1)/(r-1)

79
Q

Infinite Geometric Progression Formula

A

S=a1/(1-r)

80
Q

Fibonacci Numbers

A

1 1 2 3 5 18 13

81
Q

Lucas Sequence

A

1 3 4 7 11 1 29

82
Q

A set of ordered pairs

A

Relation

83
Q

A relation where X has one and only y value

A

Function

84
Q

Who introduced matrices?

A

James Joseph Sylvester

85
Q

what is the main/principal diagonal?

A

in square matrices, the diagonal from the upper left to the lower right is the main diagonal. The entries are called diagonal entries

86
Q

What is the trace of a matrix?

A

It is the sum of all diagonal entries of a square matrix

87
Q

Define square matrix

A

has the same number of rows and columns

88
Q

Define Diagonal Matrix

A

Square matrix that has values only in its diagonal

89
Q

Define scalar matrix

A

diagonal matrix where all the entries are equal

90
Q

Define identity/unit matrix

A

a type of scalar matrix whose non-zero elements are equal to 1

91
Q

Define zero/null marix

A

matrix that does not contain any non-zero element

92
Q

Define Triangular Matrix

A

Lower Triangular matrix: diagonal matrix whose entries above the main diagonal are all zero
Upper triangular matrix: diagonal matrix whose entries below the main diagonal are all zero

93
Q

Define Symmetric Matrix

A

The transpose is equal to the original matrix

94
Q

Skew-Symmetric Matrix

A

Transpose is equal to the negative of the original matrix

95
Q

Steps required to get the inverse of a matrix

A
  1. Form the co-factor
  2. Transpose the cofactor
  3. multiply the determinant of the original matrix to the transpose of the cofactor
96
Q

Dot product

A

A*B=|A||B|cos(theta)

97
Q

Cross Product

A

AxB=|A||B|sin(theta)

98
Q

What refers to the operation of root extraction

A

Evolution

99
Q

To compute the vaue of n factorial, in symbolic form (n!), where n is a large number, a formula called ______ is used

A

Stirling’s Approximation

100
Q

*Caltech

in simplifying complex fraction/simplification and rationalization

A

substitute the given using a number and compare the choices using the same number

101
Q

Curvature Formula

A

1/p=(d^2y/dx^2)/(1+(dy/dx)^2)^(3/2)

bryx_math (9 decks)

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