Algebra 1 Flashcards
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Questions and Answers

What are the zeros of the function?

The x-intercepts of the graph of a function.

What does the zero-product property state?

  • If $ab=1$, then neither $a$ nor $b$ can equal zero (correct)
  • If $a+b=0$, then $a=-b$
  • If $ab=0$, then $a=0$ or $b=0$ (correct)
  • If $a*b=1$, then $a=1/b$
  • What is the y-intercept?

    The y-coordinate of the point where the line crosses the y-axis.

    What does the y-coordinate indicate?

    <p>The value on the y-axis used to locate a point on the coordinate graph.</p> Signup and view all the answers

    What is the y-axis?

    <p>The vertical axis on a coordinate plane.</p> Signup and view all the answers

    What is the x-intercept?

    <p>The x-coordinate of the point where a line crosses the x-axis.</p> Signup and view all the answers

    What does the x-coordinate represent?

    <p>The value on the x-axis used to locate a point on the coordinate graph.</p> Signup and view all the answers

    What is the x-axis?

    <p>The horizontal axis on a coordinate plane.</p> Signup and view all the answers

    What are whole numbers?

    <p>All positive integers (including zero).</p> Signup and view all the answers

    What is the vertical-line test used for?

    <p>A test used to determine whether a relation is a function.</p> Signup and view all the answers

    What are vertices?

    <p>The point of intersection of two sides of a polygon.</p> Signup and view all the answers

    What is a vertex?

    <p>The common endpoint of two sides of a polygon.</p> Signup and view all the answers

    What is a variable?

    <p>A symbol (like x or y) that is used in mathematical or logical expressions.</p> Signup and view all the answers

    What are unlike radicals?

    <p>Radical expressions that do not have the same radicands.</p> Signup and view all the answers

    What is a unit rate?

    <p>A rate that has a denominator of 1.</p> Signup and view all the answers

    What is unit analysis?

    <p>The process of selecting conversion factors to produce the appropriate units.</p> Signup and view all the answers

    What is a union in set theory?

    <p>The set that contains all of the elements of two or more sets.</p> Signup and view all the answers

    What is uniform motion?

    <p>The motion of an object moving at a constant rate.</p> Signup and view all the answers

    What is a trinomial?

    <p>A polynomial with three terms.</p> Signup and view all the answers

    What are trigonometric ratios?

    <p>The ratios of corresponding sides of similar right triangles.</p> Signup and view all the answers

    What is a trend line?

    <p>A line on a scatterplot that helps show the correlation between data sets.</p> Signup and view all the answers

    What is translation in geometry?

    <p>A transformation that shifts a graph horizontally, vertically, or both.</p> Signup and view all the answers

    What is theoretical probability?

    <p>The ratio of the number of favorable outcomes to the number of possible outcomes.</p> Signup and view all the answers

    What is a term in mathematics?

    <p>A number, variable, or the product or quotient of a number and one or more variables.</p> Signup and view all the answers

    What is a term of a sequence?

    <p>Any number in a sequence.</p> Signup and view all the answers

    What is a tangent in trigonometry?

    <p>Ratio of the opposite to the adjacent side of a right-angled triangle.</p> Signup and view all the answers

    What is a system of linear inequalities?

    <p>Two or more linear inequalities with the same variables.</p> Signup and view all the answers

    What is a system of linear equations?

    <p>Two or more linear equations using the same variables.</p> Signup and view all the answers

    What is the substitution method?

    <p>A method of solving a system of equations by replacing one variable.</p> Signup and view all the answers

    What is a stem-and-leaf plot?

    <p>A data display that shows groups of data arranged in order by place value.</p> Signup and view all the answers

    What is the standard form of a quadratic function?

    <p>The form of a quadratic equation written $ax^2 + bx + c$ where $a$ does not equal 0.</p> Signup and view all the answers

    What is the standard form of a polynomial?

    <p>The form of a polynomial in which the degree of the terms decreases from left to right.</p> Signup and view all the answers

    What is the standard form of a linear equation?

    <p>$Ax + By = C$, where $A$, $B$, and $C$ are real numbers and $A$ and $B$ are not both zero.</p> Signup and view all the answers

    What is standard deviation?

    <p>A measure of how data varies from the mean.</p> Signup and view all the answers

    What is a square root function?

    <p>A function that contains the independent variable in the radicand.</p> Signup and view all the answers

    What is a square root?

    <p>A number that when multiplied by itself equals a given number.</p> Signup and view all the answers

    What is the solution of an inequality with two variables?

    <p>Any ordered pair that makes the inequality true.</p> Signup and view all the answers

    What is the solution of an inequality with one variable?

    <p>Any value or values of a variable that makes the inequality true.</p> Signup and view all the answers

    What is the solution of an equation?

    <p>Any value or values that make an equation true.</p> Signup and view all the answers

    What is the solution of a system of linear inequalities?

    <p>Any ordered pair that makes all of the inequalities in the system true.</p> Signup and view all the answers

    What is the solution of a system of linear equations?

    <p>Any ordered pair in a system that makes all the equations of that system true.</p> Signup and view all the answers

    What is slope-intercept form?

    <p>An equation written in the form $y = mx + b$.</p> Signup and view all the answers

    What is slope?

    <p>The steepness of a line, equal to the ratio of vertical change to the corresponding horizontal change.</p> Signup and view all the answers

    What is sine?

    <p>Ratio of the opposite side to the hypotenuse of a right-angled triangle.</p> Signup and view all the answers

    What is simulation in probability?

    <p>A model of a real-world situation used to find probability.</p> Signup and view all the answers

    What does it mean to simplify an expression?

    <p>Replace an expression with its simplest name or form.</p> Signup and view all the answers

    What is simple interest?

    <p>Interest paid only on the principal.</p> Signup and view all the answers

    What are similar figures?

    <p>Figures that have the same shape, but not necessarily the same size.</p> Signup and view all the answers

    What is a set in mathematics?

    <p>A well-defined collection of elements.</p> Signup and view all the answers

    What is a sequence?

    <p>A number pattern.</p> Signup and view all the answers

    What is scientific notation?

    <p>A method of writing or displaying numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10.</p> Signup and view all the answers

    What is a scatter plot?

    <p>A graph with points plotted to show a possible relationship between two sets of data.</p> Signup and view all the answers

    What is a scale factor?

    <p>The ratio of dimensions of the new image to those of the original figure.</p> Signup and view all the answers

    What is a scale drawing?

    <p>A drawing that uses a scale to represent an object as smaller or larger than the original object.</p> Signup and view all the answers

    What is scale in mathematics?

    <p>The ratio of a distance in a drawing to the actual distance.</p> Signup and view all the answers

    What is a sample space?

    <p>All possible outcomes of an event.</p> Signup and view all the answers

    What are the roots of the equation?

    <p>The solutions of an equation.</p> Signup and view all the answers

    What is a relation in mathematics?

    <p>Any set of ordered pairs.</p> Signup and view all the answers

    What is a reciprocal?

    <p>The inverse of a fraction; when multiplied by the original fraction, it results in a product that equals one.</p> Signup and view all the answers

    Study Notes

    Zeros and Intercepts

    • Zeros of the function: The x-intercepts where the graph crosses the x-axis.
    • X-intercept: The x-coordinate where a line intersects the x-axis.
    • Y-intercept: The y-coordinate where a line crosses the y-axis.

    Coordinates and Axes

    • X-coordinate: The first value in an ordered pair used to locate a point on the x-axis.
    • Y-coordinate: The second value in an ordered pair used to locate a point on the y-axis.
    • X-axis: The horizontal line on a coordinate plane.
    • Y-axis: The vertical line on a coordinate plane.

    Number Types and Properties

    • Whole numbers: All positive integers, including zero.
    • Unlike radicals: Radical expressions with different radicands.
    • Trinomial: A polynomial consisting of three terms.

    Motion and Rates

    • Uniform motion: Motion at a constant speed.
    • Unit rate: A ratio with a denominator of 1, illustrating a per unit measure.
    • Unit analysis: Choosing conversion factors to yield the correct units.

    Algebraic Concepts

    • Variable: A symbol representing an unknown quantity in expressions.
    • Term: A number, variable, or combination of both in an expression.
    • Solution of an equation: Values that satisfy the equation's conditions.

    Functions and Relations

    • Vertex: The common endpoint of two sides in polygons or edges in solids.
    • Vertical-line test: A method for determining if a relation is a function by checking if it intersects a vertical line more than once.
    • Relation: A collection of ordered pairs.

    Graphing and Transformations

    • Trend line: A line on a scatterplot illustrating the correlation between datasets.
    • Translation: A graph transformation that shifts either horizontally, vertically, or both.

    Probability and Statistics

    • Theoretical probability: The ratio of favorable outcomes to all possible outcomes, assuming equal chances.
    • Standard deviation: A measure describing how much data varies from the mean.

    Geometry

    • Similar figures: Shapes that are proportional in dimension but differ in size.
    • Scale factor: Ratio comparing the dimensions of an image to the original figure.
    • Scale drawing: A representation where the object is resized, larger or smaller.

    Inequalities and Systems

    • System of linear equations: Multiple equations using the same set of variables.
    • Solution of a system of linear inequalities: An ordered pair that satisfies all inequalities in the system.

    Functions

    • Square root function: A function where the independent variable appears under a square root.
    • Standard form of a polynomial: Arranged in descending order of degree.

    Miscellaneous

    • Simulation: A model simulating real-world scenarios to assess probability.
    • Roots of the equation: The solutions derived from an equation or its factors.
    • Reciprocal: A fraction's inverse that results in a product of one when multiplied by the original fraction.

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    Test your knowledge of key concepts in Algebra 1 with these flashcards. These cards cover essential terms such as zeros of functions, the zero-product property, and the y-intercept. Perfect for students looking to reinforce their understanding of algebraic fundamentals.

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