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ALGEBRA > ALGEBRA > Flashcards

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 ≠ 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 − 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
Q
  • 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.
A

Identity Property

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26
Q

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.

A

Inverse Property

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27
Q

largest number identified in
the list of common factors is known as

A

GCF

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28
Q

defined as the smallest multiple that two or more
numbers have in common

A

LCM

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29
Q

THEORY OF EQUATIONS

A
  1. The Fundamental Theorem of Algebra
  2. The Remainder Theorem
  3. The Factor Theorem
30
Q

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.

A

The Fundamental Theorem of Algebra

31
Q

If a polynomial f(x) is divided by (x-k) , the remainder is f(k).

A

The Remainder Theorem

32
Q

If (x-k) is a factor of a polynomial f(x), then, the remainder f(k)=0.

A

The Factor Theorem

33
Q

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.

A

Descartes’ Rule of Signs

34
Q

In the quadratic formula, the quantity under radical sign b2 - 4ac is called

A

discriminant

35
Q

the roots are real, rational and unequal

A

Perfect Square

36
Q

the roots are real, irrational and unequal

A

Not a perfect square

37
Q

b2-4ac < 0, then the roots are

A

complex conjugate

38
Q

a set of numbers in a definite or specific order and formed according to a definite rule

A

a SEQUENCE of numbers

39
Q

The numbers of the sequence are called

A

terms

40
Q

It is a sequence of numbers in which each term is obtained from the preceding term in the same way

A

Progression

41
Q

It is a sequence in which there is a common difference “d” between any two consecutive terms

A

Arithmetic Progression

42
Q

It is a sequence in which there is a common ratio of each term to its receding term.

A

Geometric Progression

43
Q

A sequence of terms in which each term is the reciprocal of the corresponding term of a series in arithmetic progression

A

Harmonic Progression

44
Q

It is any well-defined collection of symbols or objects.

A

A set

45
Q

The objects comprising the set are called

A

elements or members

46
Q

It is the set of elements which belong to A or to B or to both A and B

A

Union

47
Q

It is the set of elements which belong to both A and B

A

Intersection

48
Q

If A and B do not have any element in common, it is said to be

A

disjoint

49
Q

It is the set of elements which belong to A but not to B

A

Difference

50
Q

denoted by A raised to c, is the set of elements, which belong to the universal set but not to the set A

A

Complement

51
Q

Coin Value and total value of penny(p)

A

1 cent, p

52
Q

Coin Value and total value of nickel(n)

A

5 cents, 5n

53
Q

Coin Value and total value of dime(d)

A

10 cents, 10d

54
Q

Coin Value and total value of quarter (q)

A

25 cents, 25q

55
Q

Coin Value and total value of half(h)

A

50 cents, 50h

56
Q

If equals are added to equals, the results are equal

A

Axiom

57
Q

A mathematical argument that appears to prove something that we know is incorrect.

A

Fallacy

58
Q

It is an algebraic expression consisting of two terms.

A

Binomial

59
Q

“Googol” is one of the smallest large numbers. What does it stands for?

A

1 followed by hundred 0s or 10 raised to 100

60
Q

Irrational numbers are also known as?

A

transcendental numbers

61
Q

A number which is divisible by the sum of its own digits is called

A

Harshad Number

62
Q

Who introduced the multiplication symbol “X” in mathematics?

A

William Oughtred

63
Q

Who introduced the symbol “=” for equality?

A

Robert Recorde

64
Q

Who invented the symbol “n!” for factorial of n?

A

Christian Kramp

65
Q

Who gave the symbol “i” for √-1?

A

Leonard Euler

66
Q

The number o.123123123… is a/an

A

Rational Number

67
Q

MCMXCIV is the Roman Numeral equivalent to

A

1994

68
Q

Any combination of symbols and numbers related by the fundamental operation of
algebra is called a/an

A

Algebraic Expression

69
Q

What is the identity element for addition?

A

0

70
Q

What is the identity element for multiplication?

A

1

71
Q

If a = b =a. This illustrates which axiom in Algebra?

A

Symmetric Axiom

72
Q

In algebra, the operation of root extraction is called

A

Evolution

ALGEBRA (2 decks)

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