Questions and Answers
What is a variable?
What are integers?
Whole numbers and their opposites
What is the Order of Operations?
The process for evaluating a math problem
What defines real numbers?
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What is the Additive Inverse of a number?
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What does it mean to evaluate an expression?
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What does simplify mean?
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What are Equivalent Expressions?
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What is an algebraic expression?
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What is a coefficient?
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What is meant by 'like terms'?
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What is a quantity?
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What is a numerical expression?
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What is a power in mathematics?
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What is an exponent?
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What is the base in an expression?
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What is a radicand?
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What is a radical?
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What is a rational number?
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What are natural numbers?
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What defines whole numbers?
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What is an irrational number?
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What is absolute value?
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What is the opposite of a number?
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What is the reciprocal or multiplicative inverse?
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What is the Distributive Property?
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What is a constant in algebra?
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What is an open sentence in mathematics?
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What is an equation?
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What is a solution of an equation (one variable)?
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What is a solution of an equation (two variables)?
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What is a square root?
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What is a perfect square?
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What is an inequality?
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Study Notes
Key Algebra Concepts
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Variable: Symbol (typically a letter) representing one or more numbers. Essential for forming equations and expressions.
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Integers: Collection of whole numbers including both positive and negative values, along with zero.
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Order of Operations: Established process to evaluate mathematical expressions (often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
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Real Numbers: Complete set of numbers encompassing both rational (fractions, integers) and irrational numbers (non-repeating, non-terminating decimals).
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Additive Inverse: For any number 'a', its additive inverse is '-a', such that their sum equals zero.
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Evaluate: Substituting numbers for given variables and simplifying the expression.
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Simplify: Process of reducing a mathematical expression to its most basic form.
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Equivalent Expression: Different expressions that yield the same value for their respective variables.
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Algebraic Expressions: Composed of numerical values, variables, and operations, these phrases do not have an equality sign.
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Coefficient: Number in front of a variable in a term, indicating how many times the variable is multiplied.
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Term: Units in an expression that can be a single number, variable, or a combination of numbers and variables.
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Like Terms: Terms that share exactly the same variable(s) raised to the same power, allowing for them to be combined.
Types of Numbers
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Quantity: A measurable or countable amount.
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Numerical Expression: Consists solely of numbers and operational symbols without any variables.
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Power: Represents a number multiplied by itself a defined number of times, characterized by a base and an exponent.
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Exponent: Indicates how many times to multiply the base by itself.
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Base: The number that is repeatedly multiplied in a power expression.
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Radicand: The number or expression located under a radical sign, indicating the value to extract the root from.
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Radical: Symbol used to denote the square root or other roots of a number.
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Rational Number: Any number expressible as a fraction where both numerator and denominator are integers.
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Natural Numbers: Counting numbers starting from 1 (1, 2, 3,...).
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Whole Numbers: Combination of natural numbers and zero (0, 1, 2, 3,...).
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Irrational Number: Cannot be expressed as a fraction of two integers; represented by non-terminating, non-repeating decimals.
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Absolute Value: The distance of a number from zero on a number line, always expressed as a positive value.
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Opposite: Two numbers that are symmetrically located relative to zero on the number line.
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Reciprocal (Multiplicative Inverse): For any non-zero number, the reciprocal is a number which when multiplied with the original equals one (e.g., the reciprocal of 2/3 is 3/2).
Key Algebra Properties
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Distributive Property: A critical algebraic principle that allows for distribution of multiplication over addition (a(b + c) = ab + ac).
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Constant: A value that remains fixed; it does not change or contain any variables.
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Open Sentence: An equation featuring one or more variables, indicating that it may hold different truths based on the variable's value.
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Equation: A mathematical statement asserting that two expressions are equal (represented with an equals sign).
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Solution of an Equation (one variable): Specific value assigned to a variable that makes the equation valid.
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Solution of an Equation (two variables): Any ordered pair (x,y) that satisfies the equality of the equation.
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Square Root: A value which, when multiplied by itself, retrieves the original number (e.g., √4 = 2).
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Perfect Square: The result of squaring a whole number (e.g., 1, 4, 9 are perfect squares).
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Inequality: Mathematical expressions that show the comparative relationships between two values or expressions using inequality symbols (>, <, ≥, ≤).
Studying That Suits You
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Enhance your understanding of the foundational concepts of algebra with these flashcards covering key terms like variables, integers, and the order of operations. Perfect for students starting their journey in algebra, this quiz will help reinforce essential definitions and concepts. Test your knowledge and get ready for more advanced topics!