Algebra 2 Final Exam Flashcards

Questions and Answers

What is a relation?

A set of ordered pairs.

What is the domain of a relation?

All of the x-coordinates of a relation.

What is the range of a relation?

All of the y-coordinates of a relation.

What is a function?

A relation in which each element of the domain is paired up with exactly one element of the range. Signup and view all the answers

What does FOIL stand for?

Find the product of two binomials. Signup and view all the answers

What is the distributive property?

a(b + c) = ab + ac. Signup and view all the answers

What are similar figures?

Figures that have the same shape, but not necessarily the same size. Signup and view all the answers

What are congruent figures?

Figures that have the same size and shape. Signup and view all the answers

What are variables?

Letters or symbols used to represent an unknown quantity. Signup and view all the answers

What is an algebraic expression?

An expression with at least one variable. Signup and view all the answers

What is the order of operations?

Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction. Signup and view all the answers

What are rational numbers?

Numbers that can be expressed as a ratio, a/b. Signup and view all the answers

What are irrational numbers?

Numbers where the decimal form neither terminates nor repeats. Signup and view all the answers

What are perfect squares?

Square roots that are rational numbers. Signup and view all the answers

What are integers?

{..., -3, -2, -1, 0, 1, 2, 3,...}. Signup and view all the answers

What are whole numbers?

{0, 1, 2, 3,...}. Signup and view all the answers

What are natural numbers?

{1, 2, 3,...}. Signup and view all the answers

What is the commutative property of addition?

The order in which you add numbers does not change the sum. Signup and view all the answers

What is the commutative property of multiplication?

The order in which you multiply numbers does not change the product. Signup and view all the answers

What is the associative property of addition?

The way in which you group terms does not affect the sum - (a + b) + c = a + (b + c). Signup and view all the answers

What is the associative property of multiplication?

The way in which you group factors does not affect the product a( b c ) = (a b) c. Signup and view all the answers

What is the identity property of addition?

When zero is added to any number, the sum is the number. Signup and view all the answers

What is the identity property of multiplication?

When any number is multiplied by one, the product is the number. Signup and view all the answers

What is the additive inverse?

When a number is added to its opposite, the result is zero. Signup and view all the answers

What is the multiplicative inverse?

When a number is multiplied by its reciprocal, the result is one. Signup and view all the answers

What is an equation?

A mathematical sentence stating that two expressions are equal. Signup and view all the answers

What is the addition property of equality?

Adding the same number to both sides of an equation produces an equivalent equation. Signup and view all the answers

What is the multiplication property of equality?

Multiplying both sides of an equation by the same number produces an equivalent equation. Signup and view all the answers

What is absolute value?

A number's distance from zero. Signup and view all the answers

What is a linear equation?

An equation whose graph is a straight line. Signup and view all the answers

What is the standard form of a linear equation?

Ax + By = C. Signup and view all the answers

What is an x-intercept?

The point at which a graph crosses the x-axis. Signup and view all the answers

What is a y-intercept?

The point at which a graph crosses the y-axis. Signup and view all the answers

What is slope?

A ratio that compares the vertical change to the horizontal change. Signup and view all the answers

What is the equation for slope?

m = (y2 - y1)/(x2 - x1). Signup and view all the answers

What is slope-intercept form?

y = mx + b. Signup and view all the answers

What does m represent in slope-intercept form?

The slope in the slope-intercept form of a line. Signup and view all the answers

What does b represent in slope-intercept form?

The y-intercept in the slope-intercept form of a line. Signup and view all the answers

What is point-slope form of a line?

y - y1 = m(x - x1). Signup and view all the answers

What is a positive slope?

A slope that rises as we move from left to right. Signup and view all the answers

What is a negative slope?

A slope that falls as we move from left to right. Signup and view all the answers

What is zero slope?

A slope that is horizontal, meaning it has no rise. Signup and view all the answers

What is undefined slope?

A slope that is vertical, meaning it does not have a defined ratio. Signup and view all the answers

What is a constant function?

f(x) = c. Signup and view all the answers

What is an identity function?

y = x. Signup and view all the answers

What is an absolute value function?

f(x) = |x|. Signup and view all the answers

What is a quadratic function?

y = ax^2 + bx + c. Signup and view all the answers

What is a system of linear equations?

Two or more equations with the same variables. Signup and view all the answers

What is a matrix?

A rectangular array of variables or constants in rows and columns, usually enclosed in brackets. Signup and view all the answers

What is a quadratic equation?

An equation where the greatest exponent is 2. Signup and view all the answers

What is a parabola?

The graph of a quadratic equation. Signup and view all the answers

What is the axis of symmetry?

A line through the graph of a parabola that divides the graph into two congruent halves. Signup and view all the answers

What is the vertex of a parabola?

The minimum or maximum point of a parabola, located on the axis of symmetry. Signup and view all the answers

Study Notes

Key Definitions in Algebra

Relation: A collection of ordered pairs that defines a relationship between elements.
Domain: Represents all possible x-coordinates from a relation.
Range: Encompasses all possible y-coordinates from a relation.
Function: A special type of relation where each domain element maps to exactly one range element.

Algebraic Properties

FOIL: A method used to find the product of two binomials.
Distributive Property: States that a(b + c) equals ab + ac, demonstrating distribution across addition.
Commutative Property:
- Addition: The sum remains unchanged irrespective of the order of addends.
- Multiplication: The product remains unchanged irrespective of the order of factors.
Associative Property:
- Addition: Grouping of addends does not affect the sum.
- Multiplication: Grouping of factors does not affect the product.
Identity Properties:
- Addition: Adding zero to any number leaves it unchanged.
- Multiplication: Multiplying any number by one leaves it unchanged.
Inverses:
- Additive Inverse: The sum of a number and its negative equals zero.
- Multiplicative Inverse: The product of a number and its reciprocal equals one.

Numbers and Sets

Rational Numbers: Can be expressed as a fraction a/b where both a and b are integers.
Irrational Numbers: Numbers whose decimal representation is non-terminating and non-repeating.
Perfect Squares: Square roots that result in rational numbers.
Integers: The set of whole numbers including negatives, zero, and positives.
Whole Numbers: Non-negative integers starting from zero.
Natural Numbers: Positive integers starting from one.

Algebraic Expressions and Equations

Algebraic Expression: Combines numbers, variables, and operations, containing at least one variable.
Linear Equation: Expresses a straight line graphically; typically takes the form Ax + By = C.
Standard Form: Refers to the form Ax + By = C for linear equations.

Graphing Concepts

X-Intercept: The point where the graph intersects the x-axis.
Y-Intercept: The point where the graph intersects the y-axis.
Slope: Indicates the steepness of a line, calculated as the ratio of vertical change to horizontal change, expressed by m=(y2-y1)/(x2-x1).

Types of Functions

Constant Function: A function where output remains constant f(x)=c.
Identity Function: Defined as y=x, reflecting that every input produces the same output.
Absolute Value Function: Expressed as f(x)=|x|, which returns the distance from zero.
Quadratic Function: Formulated as y=ax^2 + bx + c, resulting in a parabola on a graph.

Geometry and Data Analysis

Parabola: The U-shaped graph produced by a quadratic equation.
Axis of Symmetry: A vertical line through the vertex of the parabola, dividing it into two symmetrical halves.
Vertex: The highest or lowest point on a parabola, located at the axis of symmetry.

Systems and Matrices

System of Linear Equations: Consists of two or more linear equations involving the same variables.
Matrix: A rectangular arrangement of numbers or variables presented in rows and columns, typically enclosed by brackets.

Graphing Relationships

Positive Slope: Indicates an upward trend in a graph.
Negative Slope: Indicates a downward trend in a graph.
Zero Slope: Represents a horizontal line, indicating no change.
Undefined Slope: Generally occurs with vertical lines where a change in x does not exist.

These notes consolidate essential algebra concepts and serve as a quick reference for study and revision.

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Prepare for your Algebra 2 final exam with these comprehensive flashcards. Each card presents key terms and definitions essential for understanding relations, functions, and more. Use this resource to reinforce your knowledge and boost your confidence before the test.