Apex Algebra 2 Flashcards Semester 1

Mathematical Expressions

• A mathematical expression is a meaningful arrangement of numbers and operations.
• Algebraic expressions contain one or more variables and may not include numerals.

Types of Expressions

• An expression combines numbers, variables, and operations without equal or inequality signs (e.g., 3x + 4y).
• An equation states that two expressions are equal (e.g., 2x = 6).
• An inequality involves expressions separated by inequality signs (e.g., 4x - 5 ≥ 11), with rules for solving including flipping signs when multiplying/dividing by negatives.

Variables & Patterns

• Variables represent unknown values, typically denoted by letters like x and y (e.g., 4x - 5y = 9).
• Patterns demonstrate consistent relationships, such as each number in a sequence being multiplied by a constant (e.g., 2, 6, 18,... multiplies by 3).

Tables & Coordinates

• Tables organize data systematically in rows and columns.
• Coordinates denote the location of points in a Cartesian plane, expressed as ordered pairs (e.g., (4, -3)).

Algebraic Components

• Factors are numbers or expressions that combine to yield a product (e.g., 8 and 3 in 8 x 3 = 24).
• Terms are parts of an algebraic expression, separated by + or - signs, and may contain numbers, variables, or exponents (e.g., 5x² + 2x + 7).

Coefficients & Constants

• Coefficients are the numbers multiplying variables in an expression (e.g., 4 and 6 are coefficients in x²y² + 4x + 6y + 10 = 0).
• Constants are fixed values that do not change (e.g., 10 and 0 in the same expression).

Linear Equations

• A linear equation's graph is a straight line and can be expressed in slope-intercept form (y = mx + b), with no exponents on variables (e.g., y = 2x - 3).
• Solving linear equations involves applying the distributive property, simplifying, and isolating variables through inverse operations.

Inequalities & Absolute Values

• Compound inequalities combine simple inequalities (e.g., -3 < x < 15) and can be graphed with arrows indicating direction.
• Absolute value measures distance from zero, always resulting in a positive number (e.g., |x| = 3 for both 3 and -3).
• Rules for absolute values include potential for one, two, or no solutions based on equation set to a negative value.

Functions

• A function pairs each input (x-value) with a unique output (y-value), denoted in functional notation y = f(x).
• The domain consists of all possible x-values, while the range includes y-values resulting from the function.

Literal Equations & Formulas

• Literal equations feature two or more variables, allowing for expressions like 20x + 5y = 40.
• Formulas describe crucial mathematical relationships (e.g., perimeter of a rectangle: P = 2l + 2w).

Solving Techniques

• Solving literal equations requires isolating the desired variable using reverse operations.
• Simplifying expressions involves reducing terms and fractions to their simplest forms (e.g., 8/10 simplifies to 4/5).

Unions & Intersections

• The union denotes all solutions in an "or" statement, while the intersection represents numbers appearing in both solution sets of inequalities.

Test your knowledge with these flashcards for Apex Algebra 2, Semester 1. Explore key concepts like mathematical expressions, algebraic expressions, and more. Enhance your understanding of algebraic terminology and improve your skills in manipulating expressions.