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.

Test your understanding of variables, constants, and expressions in algebra. This quiz covers evaluation methods, properties like opposites and reciprocals, and the basics of powers and roots. Assess your knowledge and improve your algebra skills!