Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Honors Algebra II > Sections 1.1 - 1.5 > Flashcards

Sections 1.1 - 1.5 Flashcards

1
Q

Complex Numbers

A

Have the form a+bi in which a and b are real numbers and i = the square root of -1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Real Numbers

A

Numbers that have points on the number line

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Imaginary Numbers

A

Square roots of negative numbers, which have no points on the number line.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Negative Numbers

A

Numbers less than 0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Zero

A

Neither positive nor negative

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Positive Numbers

A

Numbers greater than 0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Rational Numbers

A

Can be expressed exactly as a ratio of 2 integers

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Irrational Numbers

A

Cannot be expressed exactly as a ratio of 2 integers, but are real numbers

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Integers

A

Whole numbers and their opposites

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Nonintegers

A

Fractions, or numbers between the integers

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Radicals

A

Involve square roots, cube roots, etc. of integers

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Transcendental Numbers

A

Cannot be expressed as roots of integers (pi)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Odd Numbers

A

Numbers not divisible by 2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Even Numbers

A

Numbers divisible by 2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Digits

A

Numbers from which the numerals are made (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Natural / Counting Numbers

A

Positive integers or counting numbers

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

Field Axioms

A

The properties of algebra

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

Definition of Subtraction

A

a - b = a + (-b)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

Definition of Division

A

a/b = a times 1/b

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Closure

A

The sum / product of any two members of a set must belong to the given set.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Closure under addition

A

a + b is always a unique, real number

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Closure under multiplication

A

ab is always a unique, real number

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

Commutativity

A

Changes the order of the operation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

Commutativity for addition

A

a + b = b + a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

Commutativity for multiplication

A

ab = ba

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

Associativity

A

Changes the groupings and not the order

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

Associativity for addition

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

Associativity for multiplication

A

(ab)c = a(bc)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

Inverses

A

The set must contain the opposite and the reciprocal to be a field.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

Inverse of Addition

A

a + (-a) = 0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

The Additive Inverse

A

Also known as the opposite, it is (-a)

32
Q

Inverse of Multiplication

A

a(1/a) = 1

33
Q

The Multiplicative Inverse

A

Also known as the reciprocal, it is 1/a

34
Q

Vinculum

A

The “division / fraction line”

35
Q

Identity

A

Any field must contain 0 and 1

36
Q

The Identity Property of Addition

A

a + 0 = a

37
Q

The Identity Element of Addition

A

0

38
Q

The Identity Property of Multiplication

A

(a)(1) = a

39
Q

The Identity Element of Multiplication

A

1

40
Q

Distributitivity

A

a (b + c) = ab + ac

41
Q

In order for a set of numbers to be a field . . .

A

The set must fit the requirements of closure, commutativity, associativity, inverses, identity, and distributivity

42
Q

Variable

A

Any symbol that represents an unknown value

43
Q

Expression

A

A collection of variables, constants, operations, and / or grouping symbols that can be simplified and / or evaluated

44
Q

Exponentiation

A

The exponent power determines the amount of bases to multiply together

45
Q

Order of Operations to Simplify

A

Groupings, exponentiation, multiplication (division), addition (subtraction)

46
Q

Order of Operations to Solve

A

Addition (subtraction), multiplication (division), exponentiation, groupings

47
Q

Polynomial

A

An algebraic expression that involves only the operations of addition, subtraction, and multiplication of variables

48
Q

Reasons not to be a Polynomial

A

Variable expression in the denominator, variable expression under radical signs, and variable expression inside absolute value

49
Q

Equation

A

A statement that sets two expressions equal to each other

50
Q

Solution(s)

A

Value(s) that can be substituted for (a) variable(s) and make the statement true

51
Q

Addition Property of Equality

A

If a = b, the a + c = b + c

52
Q

Multiplication Property of Equality

A

If a = b, then ac = bc

53
Q

Reasons for Extraneous Solutions

A

The solution is not a member of the domain, multiplying the equation by an unknown value (0) adds solutions, and dividing the equation by an unknown value (0).

54
Q

Irreversible Steps

A

Multiplying or dividing both sides of an equation by an unknown value.

55
Q

Zero Product Rule

A

If ab = 0, then a, b, or both must equal 0

56
Q

Absolute Value

A

lxl = p

57
Q

If P in Absolute Value is Positive . . .

A

x = p or x = -p

58
Q

If P in Absolute Value is 0 . . .

A

x = 0

59
Q

If P in Absolute Value is Negative . . .

A

No solution

60
Q

Addition property of order

A

If a > b, then a + c > b + c

60
Q

Multiplication Property of Order

A

If a > b, then . . .
If c is positive, ac > ab
If c = 0, then ac = bc
If c is negative, then ac < bc

60
Q

Interval Notation

A

(x, y]

60
Q

Set - Builder Notation

A

{x l e real numbers, x > 2}

60
Q

Or statement

A

l x l > p

60
Q

Negative or situation

A

x < -p

60
Q

Positive Or Situation

A

x > p

60
Q

And Statement

A

l x l < p

60
Q

Negative and situation

A

x > -p

60
Q

Positive and situation

A

x < p

60
Q

Solution to l x l > -p

A

All real numbers

60
Q

Solution to l x l < -p

A

No solution

61
Q

Reflexive Property

A

If x is from a set of real numbers, then x = x

62
Q

Symmetry property

A

If x = y, then y = x

63
Q

Transitive property

A

If x = y and y = z, then x = z

64
Q

Trichotomy

A

If x and y are from a set of real numbers, then one of the following is true:
x > y
x < y
x = y

Honors Algebra II (1 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions