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ALGEBRA Flashcards

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1
Q

is an expression involving a combination of real and imaginary numbers. They are written in the form: a + bi

A

Complex Numbers

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2
Q

are the rational and irrational numbers taken together.

A

Real Numbers

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3
Q

are the square roots of negative numbers.

A

Imaginary Numbers

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4
Q

Are numbers which can be expressed in the form m/n, where m and n are integers and 𝑛 β‰  0 .

A

Rational Numbers

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5
Q

are numbers, which cannot be expressed in the form m/n.

A

Irrational Numbers

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6
Q

are the natural numbers, along with their negatives, and
zero (0).

A

Integers

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7
Q

a number that is not a whole number, a negative whole
number, or zero.

A

Non-Integers

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8
Q

are numbers that have a value less than zero. They do not include fractions or decimals. For example, -7, -10 are negative integers.

A

Negative Number

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9
Q

are numbers that are positive and zero.

A

Whole Number

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10
Q

number representing an empty quantity

A

Zero

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11
Q

a whole number not including zero.

A

Natural Number

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12
Q

Types of Natural Number

A
  1. Even Number
  2. Odd number
  3. Composite Number
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13
Q

Are natural numbers that are neither 1 nor a prime number.

A

Composite Numbers

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14
Q

Are natural numbers that are divisible by 1 and itself only.
{2,3,5,7,11,etc.}

A

Prime Number

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15
Q

Types of Prime Numbers

A
  1. Euler primes or Symmetric primes
  2. Twin primes
  3. Emirp
  4. Mersenne primes
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16
Q

are pairs of prime numbers that are equidistant from a given number on a number line.

A

Euler primes or Symmetric primes

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17
Q

are pairs of two consecutive odd prime numbers that differ by 2.

A

Twin primes

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18
Q

are prime numbers that remain a prime when its digits are reversed.

A

Emirp

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19
Q

are prime numbers can be made from the Expression 2𝑛 βˆ’ 1. This method for generating prime numbers works only when n itself is prime, but not always. For example, it works when n = 2, 3, 5 or 7 but not when n is 11, and not when n = 23 as well as several other prime values. (3, 7, and 31, etc.)

A

Mersenne primes

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20
Q

PROPERTIES OF REAL NUMBERS

A

A.) Closure Property
B.) Commutative Property
C.) Associative Property of Addition
D.) Distributive Property
E.) Identity Property
F.) Inverse Property

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21
Q

The set of real numbers is closed under addition, subtraction and multiplication. This means that adding, subtracting or multiplying two or more real numbers always results to another number that belongs to the same set of real numbers.

A

Closure Property

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22
Q

The order of adding two or more numbers of a sum or multiplying two or more
factors of a product does not affect the result.

A

Commutative Property

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23
Q

When two or more real numbers are added or multiplied together, no matter how the numbers are grouped, or associated, when performing the operation the result is not affected.

A

Associative Property of Addition

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24
Q

The product of a number a by the sum of two or more numbers (b +c +d +…) is equal to the sum of the products ab, ac, ad, …

A

Distributive Property

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25
- Additive Identity Property When zero (0) is added to a real number, the sum is the real number itself. - Multiplicative Identity Property When one (1) is multiplied to a real number, the product is the real number itself.
Identity Property
26
Additive Inverse The additive inverse of a real number is its opposite, so that the sum of that number and its additive inverse is 0 Multiplicative Inverse The multiplicative inverse of a real number is its reciprocal, so that the product of that number and its multiplicative inverse is 1.
Inverse Property
27
largest number identified in the list of common factors is known as
GCF
28
defined as the smallest multiple that two or more numbers have in common
LCM
29
THEORY OF EQUATIONS
1. The Fundamental Theorem of Algebra 2. The Remainder Theorem 3. The Factor Theorem
30
States that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers. The roots can have a multiplicity greater than zero. It also states that every single-variable polynomial with complex coefficients has at least one complex root.
The Fundamental Theorem of Algebra
31
If a polynomial f(x) is divided by (x-k) , the remainder is f(k).
The Remainder Theorem
32
If (x-k) is a factor of a polynomial f(x), then, the remainder f(k)=0.
The Factor Theorem
33
Determines the maximum number of positive and negative real roots that a polynomial will have by counting the number of sign variations in the polynomial. The polynomial must have real coefficients and be arranged in terms of descending powers of x.
Descartes’ Rule of Signs
34
In the quadratic formula, the quantity under radical sign b2 - 4ac is called
discriminant
35
the roots are real, rational and unequal
Perfect Square
36
the roots are real, irrational and unequal
Not a perfect square
37
b2-4ac < 0, then the roots are
complex conjugate
38
a set of numbers in a definite or specific order and formed according to a definite rule
a SEQUENCE of numbers
39
The numbers of the sequence are called
terms
40
It is a sequence of numbers in which each term is obtained from the preceding term in the same way
Progression
41
It is a sequence in which there is a common difference "d" between any two consecutive terms
Arithmetic Progression
42
It is a sequence in which there is a common ratio of each term to its receding term.
Geometric Progression
43
A sequence of terms in which each term is the reciprocal of the corresponding term of a series in arithmetic progression
Harmonic Progression
44
It is any well-defined collection of symbols or objects.
A set
45
The objects comprising the set are called
elements or members
46
It is the set of elements which belong to A or to B or to both A and B
Union
47
It is the set of elements which belong to both A and B
Intersection
48
If A and B do not have any element in common, it is said to be
disjoint
49
It is the set of elements which belong to A but not to B
Difference
50
denoted by A raised to c, is the set of elements, which belong to the universal set but not to the set A
Complement
51
Coin Value and total value of penny(p)
1 cent, p
52
Coin Value and total value of nickel(n)
5 cents, 5n
53
Coin Value and total value of dime(d)
10 cents, 10d
54
Coin Value and total value of quarter (q)
25 cents, 25q
55
Coin Value and total value of half(h)
50 cents, 50h
56
If equals are added to equals, the results are equal
Axiom
57
A mathematical argument that appears to prove something that we know is incorrect.
Fallacy
58
It is an algebraic expression consisting of two terms.
Binomial
59
β€œGoogol” is one of the smallest large numbers. What does it stands for?
1 followed by hundred 0s or 10 raised to 100
60
Irrational numbers are also known as?
transcendental numbers
61
A number which is divisible by the sum of its own digits is called
Harshad Number
62
Who introduced the multiplication symbol β€œX” in mathematics?
William Oughtred
63
Who introduced the symbol β€œ=” for equality?
Robert Recorde
64
Who invented the symbol β€œn!” for factorial of n?
Christian Kramp
65
Who gave the symbol β€œi” for √-1?
Leonard Euler
66
The number o.123123123… is a/an
Rational Number
67
MCMXCIV is the Roman Numeral equivalent to
1994
68
Any combination of symbols and numbers related by the fundamental operation of algebra is called a/an
Algebraic Expression
69
What is the identity element for addition?
0
70
What is the identity element for multiplication?
1
71
If a = b =a. This illustrates which axiom in Algebra?
Symmetric Axiom
72
In algebra, the operation of root extraction is called
Evolution

ALGEBRA (2 decks)

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