Algebra 2 Part 1 Flashcards

Questions and Answers

What does PEMDAS stand for?

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (correct)

Parallel, Energy, Mass, Division, Angle, Speed

Probability, Energy, Motion, Distance, Angular Speed

Potential Energy, Mass, Distance, Acceleration, Speed

What is the Reflexive Property of Equality?

a=a

What does the Symmetric Property of Equality state?

If a=b, then b=a

What does the Transitive Property of Equality state?

If a=b and b=c, then a=c Signup and view all the answers

What is the Addition and Subtraction Properties of Equality?

If a=b, then a+c=b+c and a-c=b-c Signup and view all the answers

What does the Multiplication and Division Properties of Equality state?

If a=b, then ac=bc and a/c=b/c Signup and view all the answers

What is a Relation?

A set of ordered pairs Signup and view all the answers

What is a Function?

A relation where for every x-coordinate there is exactly one y-coordinate. Signup and view all the answers

What is the Domain of a relation?

The set of all x-coordinates of the relation. Signup and view all the answers

What is the Range of a relation?

The set of all y-coordinates of the relation. Signup and view all the answers

What is Standard form in algebra?

ax + by = c Signup and view all the answers

What is a Linear equation?

An equation that represents a line. Signup and view all the answers

What is a 0 slope line?

A horizontal line. Signup and view all the answers

What does a No slope line represent?

A vertical line. Signup and view all the answers

What is the Slope-intercept form of a line?

y=mx+b Signup and view all the answers

What is the Determinant of a 2 by 2 matrix?

ad-bc Signup and view all the answers

What are the Dimensions of a matrix?

The number of rows and columns of the matrix, in that order. Signup and view all the answers

What is the Determinant of a 3 by 3 matrix?

aei+bfg+cdh-gec-hfa-idb Signup and view all the answers

How is the Area of a triangle calculated?

1/2 * | {a, b, 1}, {c, d, 1}, {e, f, 1} | Signup and view all the answers

How do you solve a matrix equation?

The inverse of the first matrix. Signup and view all the answers

What is the Degree of a monomial?

The sum of the exponents of the variables. Signup and view all the answers

What is the Product of Powers rule?

a^m * a^n = a^(m+n) Signup and view all the answers

What is the Product of a Power rule?

(a^m)^n = a^(mn) Signup and view all the answers

What is the Power of a Product rule?

ab^m = a^m * b^m Signup and view all the answers

What is the Quotient of Powers rule?

a^m / a^n = a^(m-n) Signup and view all the answers

What is the Power of Quotients rule?

(a/b)^n = (a^n) / (b^n) Signup and view all the answers

What is the Negative Powers rule?

a^-n = 1/(a^n) and 1/(a^-n) = a^n Signup and view all the answers

What is the Difference of 2 Squares?

a^2 - b^2 = (a - b)(a + b) Signup and view all the answers

What is the Difference of 2 Cubes?

a^3 - b^3 = (a - b)(a^2 + ab + b^2) Signup and view all the answers

What is the Sum of 2 Cubes?

a^3 + b^3 = (a + b)(a^2 - ab + b^2) Signup and view all the answers

What is the Multiplication Property of Radicals?

nth root of ab = nth root of a * nth root of b Signup and view all the answers

What is the Division Property of Radicals?

nth root of a/b = nth root of a / nth root of b Signup and view all the answers

What are Rational Exponents?

b^(m/n) = (nth root of b)^m Signup and view all the answers

What is a Quadratic Equation in Standard Form?

y = ax^2 + bx + c, where a is not 0 Signup and view all the answers

What is a Quadratic Equation in Vertex Form?

y = a(x - h)^2 + k, where a is not 0 Signup and view all the answers

What is the Zero Product Property?

If ab = 0, then a = 0, b = 0, or a and b = 0 Signup and view all the answers

What is the Quadratic Formula?

x = -b ± √(b² - 4ac) / 2a Signup and view all the answers

Study Notes

Order of Operations

The order of operations is abbreviated as PEMDAS, representing Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Properties of Equality

Reflexive Property: a = a
Symmetric Property: If a = b, then b = a
Transitive Property: If a = b and b = c, then a = c
Addition/Subtraction Properties: If a = b, then a + c = b + c and a - c = b - c
Multiplication/Division Properties: If a = b, then a * c = b * c and a / c = b / c

Relations and Functions

A relation is defined as a set of ordered pairs.
A function is a specific type of relation where each x-coordinate corresponds to exactly one y-coordinate.
The domain of a relation is the set of all x-coordinates, while the range is the set of all y-coordinates.

Linear Equations

Standard form of a linear equation: ax + by = c
A linear equation graphically represents a straight line.
A line with 0 slope is horizontal, while a vertical line has no slope.
Slope-intercept form of a linear equation is expressed as y = mx + b, where m is the slope.

Matrices

The determinant of a 2x2 matrix is calculated as ad - bc.
Dimensions of a matrix are defined by the number of rows and columns.
The determinant of a 3x3 matrix is calculated using the formula: aei + bfg + cdh - gec - hfa - idb.

Area and Solving Matrices

The area of a triangle defined by vertices (a, b), (c, d), (e, f) is given by 1/2 * | a b 1 | { c d 1 } { e f 1 }.
To solve a matrix equation, find the inverse of the first matrix.

Monomials and Exponents

The degree of a monomial is the total of the exponents of its variables.
Product of Powers rule: a^m * a^n = a^(m+n)
Power of a Product rule: (ab)^m = a^m * b^m
Quotient of Powers rule: a^m / a^n = a^(m-n)
Negative Powers rule: a^-n = 1/(a^n) and 1/(a^-n) = a^n

Special Factorizations

Difference of 2 Squares: a^2 - b^2 = (a - b)(a + b)
Difference of 2 Cubes: a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Sum of 2 Cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Radicals and Rational Exponents

The Multiplication Property of Radicals states that the nth root of ab equals the nth root of a times the nth root of b.
The Division Property states that the nth root of a/b equals the nth root of a divided by the nth root of b.
Rational exponents can be expressed as b^(m/n) = (nth root of b)^m.

Quadratic Equations

Quadratic equations in standard form: y = ax^2 + bx + c where a ≠ 0.
Vertex form of a quadratic equation is represented as y = a(x - h)^2 + k, where a ≠ 0.
The Zero Product Property states that if ab = 0, then a = 0, b = 0, or both.
The quadratic formula for solving quadratic equations is x = (-b ± √(b² - 4ac)) / (2a).

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Test your knowledge of Algebra 2 concepts with these flashcards. Cover topics like the Order of Operations and various Properties of Equality. Perfect for reinforcing key algebraic principles and improving your mathematical skills.