Algebra Class: Variables and Expressions

Variables and Expressions

• Variable: A letter or symbol that represents a value capable of changing.
• Constant: A fixed value that remains unchanged.
• Numerical Expression: Comprises only constants and mathematical operations.
• Algebraic Expression: Includes variables, constants, and operations.

Evaluation and Properties

• Evaluate: The process of determining the value of an expression.
• Absolute Value: Represents the distance of a number from zero on the number line.
• Opposites: Two numbers that sum to zero, e.g., 3 and -3.
• Additive Inverses: A number paired with its opposite.
• Reciprocals: Two numbers whose product equals one.
• Multiplicative Inverses: A number and its reciprocal.

Powers and Roots

• Power: An expression with a base and an exponent; can represent its value.
• Base: The number being multiplied in a power expression.
• Exponent: Indicates how many times the base is multiplied by itself.
• Square Root: A number which, when multiplied by itself, yields a product.
• Perfect Square: A number with a whole number as its positive square root.

Number Sets

• Real Numbers: All numbers that can be illustrated on a number line.
• Natural Numbers: Counting numbers starting from 1 (1, 2, 3...).
• Whole Numbers: Natural numbers plus zero (0, 1, 2, 3...).
• Integers: Whole numbers and their negatives (-3, -2, -1, 0, 1, 2, 3...).
• Rational Numbers: Expressible as a fraction (a/b) where a and b are integers, and b ≠ 0.
• Terminating Decimals: Rational numbers with a finite decimal representation (1.5, 2.75).
• Repeating Decimals: Rational numbers with a repeating sequence in decimal form (1.333...).
• Irrational Numbers: Cannot be expressed as a fraction; include non-repeating, non-terminating decimals and square roots of non-perfect squares (√2, π).

Operations and Expressions

• Order of Operations: The sequence for executing mathematical operations.
• Terms: Components of an expression that are added or subtracted.
• Like Terms: Terms that share the same variables raised to identical powers, including constants.
• Coefficient: A numerical factor multiplied by a variable.

Coordinate Geometry

• Coordinate Plane: Formed by two intersecting perpendicular number lines called axes.
• Axes: The horizontal (X-axis) and vertical (Y-axis) lines that create the coordinate plane.
• Origin: The intersection point of the X-axis and Y-axis, designated as (0, 0).
• Ordered Pair: Specific point on the coordinate plane represented by (x, y).
• Quadrants: Four regions created by dividing the coordinate plane with the axes.

Functions

• Input: The value substituted for x in an equation.
• Output: The resulting value for y in an equation after substitution.