Shormann Prealgebra Exam 2 Definitions

Mathematical Concepts

• Comparison Symbols: Used to compare values and establish inequalities.
• Set: A collection of distinct objects or numbers used mathematically.
• Open Circle (○): Indicates exclusion of a value on a graph or number line.
• Closed Circle (): Indicates inclusion of a value on a graph or number line.

Absolute Value

• Finding the Absolute Value: Absolute value is represented as |a|, meaning the distance from zero on a number line, regardless of sign.
• Absolute Value Definition: Enclosed by vertical bars, |a| signifies the non-negative value of a number.

Variables and Numbers

• Descriptive Variable: A letter or letters used in equations to represent specific quantities, making expressions more relatable.
• Real Number Chart: Real numbers can be split into rational (can be expressed as a ratio) and irrational (cannot be expressed as a ratio).

Rational and Irrational Numbers

• Rational Number: Can be expressed as a fraction; decimal form displays a repeating pattern.
• Irrational Number: Cannot be expressed as a fraction; decimal form is non-repeating and non-terminating.

Algebra Basics

• Algebra Definition: A method of solving equations using symbols and letters representing quantities.
• Coefficient: The numerical factor in a term, e.g., in 3x², the coefficient is 3.
• Like Terms: Terms that have the same variable factors and powers can be combined in algebraic expressions.

Algebraic Properties

• Additive Property of Equality: If a = b, then a + c = b + c holds true for any real numbers a, b, and c.
• Multiplicative Property of Equality: If a = b, then ac = bc for any real number c.
• Algebraic Subtraction: Can be expressed as a + (-b).

Geometry

• Perimeter: The total distance around a shape. Formulas include:
  • Rectangle: 2(l + w)
  • Square: 4s
  • Circle: 2πr or πD
• Circumference: Distance around a circle.
• Triangle Properties:
  • The sum of interior angles equals 180°.
  • Opposite angles of equal sides are also equal.

Euclidean Geometry

• Axioms and Postulates: Basic assumptions in geometry, such as a unique line through two points and the equality of right angles.

Angles

• Angle Relationships:
  • Vertical angles formed by intersecting lines are equal.
  • Complementary angles sum to 90°.
  • Supplementary angles sum to 180°.

Temperature Conversion

• Temperature Formula: F = 1.8C + 32 establishes the relationship between Fahrenheit (F) and Celsius (C).

Probability

• Probability (P): Represents the likelihood of an event occurring, quantified as a fraction or decimal between 0 and 1.

Exchange Rates (2020)

• Values of the US dollar against several currencies include:
  • 0.92 Euros (EU)
  • 75.9 Rupees (India)
  • 1.41 Dollars (Canada)
  • 73.6 Rubles (Russia)

Additional Mathematical Concepts

• Scale Factor: A ratio that describes how a figure is enlarged or reduced proportionally.
• Polynomial Definition: An expression consisting of variables and coefficients combined using addition, subtraction, and multiplication.

Creativity and Discovery

• Inductive Reasoning: The process of recognizing patterns to formulate rules.
• Deductive Reasoning: Applying known rules to explore new situations.
• Creativity: The ability to generate original ideas and solutions.