Algebra Concepts and Definitions
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Questions and Answers

What does 'f.o.i.l.' stand for?

  • First, Over, In, Line
  • First, Outer, Inner, Last (correct)
  • First, Over, Integrate, Last
  • Forward, Outer, Inner, Line

    • What is the point-slope form of a line?

    Where m is a slope and (x, y) is a point on the line.

    What is the absolute value?

    How far a number is away from zero on a number line.

    What are real numbers?

    <p>The set including all rational and irrational numbers.</p> Signup and view all the answers

    What are rational numbers?

    <p>Numbers that can be written in the form a/b, where a and b are integers and b cannot equal zero.</p> Signup and view all the answers

    What are irrational numbers?

    <p>Numbers that cannot be written as the quotient of two integers.</p> Signup and view all the answers

    What does the symbol of conclusion indicate?

    <p>Indicates which numbers, variables, and operations are part of the same term.</p> Signup and view all the answers

    What are square roots?

    <p>A number that is multiplied by itself to form a product.</p> Signup and view all the answers

    What does probability describe?

    <p>How likely an event is in percent.</p> Signup and view all the answers

    What is the distributive property?

    <p>A way to simplify expressions.</p> Signup and view all the answers

    What are variable expressions?

    <p>Expressions with letters in them.</p> Signup and view all the answers

    What does translating algebraic expressions mean?

    <p>When you simplify the words into the actual meanings.</p> Signup and view all the answers

    What does combining like terms involve?

    <p>To combine 2 or more fractions or numbers that have the same exponents and/or letters.</p> Signup and view all the answers

    What is a one-step equation?

    <p>An equation that only needs one step to finish.</p> Signup and view all the answers

    What does graphing on a coordinate plane involve?

    <p>Determining whether you have a horizontal or vertical line and then tracing it on a graph.</p> Signup and view all the answers

    What is a two-step equation?

    <p>An equation that takes two steps to solve.</p> Signup and view all the answers

    What are decimal equations?

    <p>Algebraic equations with decimals in them.</p> Signup and view all the answers

    What are relations?

    <p>The way two or more concepts are relevant to each other.</p> Signup and view all the answers

    What are functions in algebra?

    <p>What a number or piece does in an algebraic expression.</p> Signup and view all the answers

    What is a multi-step equation?

    <p>Equations that take three or more steps to solve.</p> Signup and view all the answers

    What does misleading representations of data refer to?

    <p>Not 100% true facts, statistics, and/or data.</p> Signup and view all the answers

    How do you solve equations with variables on both sides?

    <p>Use elimination to get variables on one side and numbers on the other.</p> Signup and view all the answers

    What is a literal equation?

    <p>Where variables represent known values.</p> Signup and view all the answers

    What is a graphic function?

    <p>The collection of all ordered pairs.</p> Signup and view all the answers

    What are rates?

    <p>A measure or quantity.</p> Signup and view all the answers

    What are ratios?

    <p>The quantitative relation between two amounts.</p> Signup and view all the answers

    What are proportions?

    <p>A number considered in comparative relation to a whole.</p> Signup and view all the answers

    What are arithmetic sequences?

    <p>A sequence of numbers that has a constant difference between every two consecutive numbers.</p> Signup and view all the answers

    What are intercepts?

    <p>The points where a line crosses the axes on a graph.</p> Signup and view all the answers

    What is scientific notation?

    <p>A mathematical expression used to represent a decimal number between 1 and 10.</p> Signup and view all the answers

    What is the power property of exponents?

    <p>When multiplying two powers with the same base, just add the exponents.</p> Signup and view all the answers

    What are percent problems?

    <p>Problems that involve calculating percentages.</p> Signup and view all the answers

    What is a rational expression?

    <p>An expression where the numerator and/or denominator are rational numbers.</p> Signup and view all the answers

    What is percent change?

    <p>An increase or decrease in percent.</p> Signup and view all the answers

    What is a measure of central tendency?

    <p>A single value that represents the center of a dataset.</p> Signup and view all the answers

    What is slope-intercept form of a linear equation?

    <p>A way of writing the equation of a line, typically in the form y = mx + b.</p> Signup and view all the answers

    What are polynomials?

    <p>Expressions that consist of several terms.</p> Signup and view all the answers

    What is a linear equation?

    <p>An equation between two variables that gives a straight line when plotted on a graph.</p> Signup and view all the answers

    Study Notes

    Algebra Concepts and Definitions

    • FOIL: Method to multiply two binomials; stands for first, outer, inner, last terms.
    • Point-Slope Form: Equation of a line expressed as (y - y_1 = m(x - x_1)), where (m) is the slope and ((x_1, y_1)) is a point on the line.
    • Absolute Value: Indicates the distance a number is from zero on a number line, always non-negative.
    • Real Numbers: The set that includes all rational (e.g., integers, fractions) and irrational numbers (e.g., square roots of non-perfect squares).
    • Rational Numbers: Numbers that can be represented as (a/b), where (a) and (b) are integers, and (b \neq 0); in decimal form, they either terminate or repeat.
    • Irrational Numbers: Numbers that cannot be expressed as the quotient of two integers; their decimal forms neither terminate nor repeat.
    • Symbol of Conclusion: Symbol that groups numbers, variables, and operations into a single term.
    • Square Roots: A number that, when multiplied by itself, yields a given product.
    • Probability: A measure reflecting how likely an event occurs, typically expressed as a percentage.
    • Distributive Property: A property that allows the multiplication of a term across a sum or difference within parentheses to simplify expressions.
    • Variable Expressions: Algebraic expressions that include letters representing numbers.
    • Translating Algebraic Expressions: The process of converting words into symbolic expressions to enhance understanding.
    • Combining Like Terms: The process of adding or subtracting terms that have identical variables or exponents.
    • One-Step Equations: Equations that can be solved in a single operation.
    • Graphing on a Coordinate Plane: The process of determining the orientation of a line (horizontal or vertical) and plotting it accurately.
    • Two-Step Equations: Equations requiring two steps to isolate the variable and find the solution.
    • Decimal Equations: Algebraic equations that include decimal numbers; converting fractions to decimals for easier solving is a common strategy.
    • Relations: Describes how two or more mathematical concepts interact or are connected.
    • Functions: Describe the role or output of a number in an algebraic expression.
    • Multi-Step Equations: Equations that require three or more operations to solve for the variable.
    • Misleading Representations of Data: Data that is distorted and does not accurately reflect true facts or statistics.
    • Solving Equations with Variables on Both Sides: Requires elimination methods to isolate variables and resolve the equation.
    • Literal Equations: Equations where variables symbolize known quantities.
    • Graphic Function: A collection of ordered pairs representing a function visually.
    • Rates: Measurements that express a quantity in relation to another quantity.
    • Ratios: A quantitative comparison between two amounts reflecting how many times one value contains another.
    • Proportions: A statement that two ratios are equal, expressing a comparative relation to a whole.
    • Arithmetic Sequences: A sequence of numbers with a consistent difference between consecutive terms.
    • Intercepts: Points where a line crosses the axes, integral to understanding linear equations.
    • Scientific Notation: A method to express large or small numbers by using powers of ten, simplifying mathematical computations.
    • Power Property of Exponents: When multiplying like bases, sum the exponents.
    • Percent Problems: Involves expressing quantities as a fraction of 100.
    • Rational Expression: A fraction where both the numerator and/or denominator are polynomials.
    • Percent Change: The rate of increase or decrease represented as a percentage of the original amount.
    • Measure of Central Tendency: A statistic that represents the center of a data set, typically including the mean, median, and mode.
    • Slope-Intercept Form: The equation of a line written as (y = mx + b), where (m) is the slope and (b) is the y-intercept.
    • Polynomials: Expressions consisting of multiple terms combined using addition, subtraction, and multiplication.
    • Linear Equation: An equation involving two variables that results in a straight line when plotted on a graph.
    • Direct Variation: A relationship where two variables change proportionally, typically expressed as (y = kx) where (k) is a constant.

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    Test your understanding of key algebra concepts including the FOIL method, point-slope form of a line, and the differences between rational and irrational numbers. This quiz will assess your knowledge of various definitions and properties related to real numbers and their representations. Perfect for students looking to solidify their algebra foundation!

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