BJU Press - Algebra 1 Chapter 1 Flashcards

Set Theory and Number Concepts

• Set: A collection of distinct objects, which can be numerical or non-numerical.
• Element/Member: An individual object within a set.
• Empty Set: A set that contains no elements, often denoted by the symbol ∅.
• Union of Sets (U): Combines all elements from two or more sets, including duplicates.
• Intersection of Sets: Identifies common elements present in two or more sets.
• Subset: A set in which every member is also contained in a larger set.

Number Classification

• Rational Numbers: Any number that can be expressed as the quotient of two integers (a fraction).
• Irrational Numbers: Numbers that cannot be expressed as a simple fraction; their decimal representation neither terminates nor repeats.

Graphing Fundamentals

• Origin: The point at which the coordinates are both zero (0, 0).
• Negative Numbers: Values less than zero, found to the left of zero on the number line.
• Graph: A representation of points on a number line, corresponding to real numbers.
• Coordinate: The specific real number associated with a point on the graph.

Number Properties

• Opposite Number: A number located at an equal distance from zero but in the opposite direction on a number line.
• Absolute Value: The non-negative distance of a number from zero on the number line.
• Mathematical Property: A universally true statement or equation for all variable values.

Mathematical Operations

• Subtraction: Removing one quantity from another to obtain a smaller result.
• Unit Multiplier: A fraction representing equivalent measurements, useful for unit conversion.
• Reciprocals (Multiplicative Inverses): Two numbers whose product equals one (e.g., 2 and 0.5).
• Division: Can be conceptualized as multiplying a number by the reciprocal of the divisor.
• Zero Power: Any non-zero number raised to the exponent of zero equals one.
• Negative Exponents: For any nonzero number x and integer a, x^(-a) equals 1/x^a.

Closing Wishes

• Best of Luck!: Encouragement for students in their studies.

Test your knowledge of basic set theory concepts with these flashcards from Algebra 1 Chapter 1. Learn definitions such as sets, elements, empty sets, unions, and intersections through engaging questions. Perfect for revising key terms in mathematics.