Algebra 1 Flashcards

Podcast

Play an AI-generated podcast conversation about this lesson

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?

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

What is the y-axis?

The vertical axis on a coordinate plane. Signup and view all the answers

What is the x-intercept?

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

What does the x-coordinate represent?

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

What is the x-axis?

The horizontal axis on a coordinate plane. Signup and view all the answers

What are whole numbers?

All positive integers (including zero). Signup and view all the answers

What is the vertical-line test used for?

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

What are vertices?

The point of intersection of two sides of a polygon. Signup and view all the answers

What is a vertex?

The common endpoint of two sides of a polygon. Signup and view all the answers

What is a variable?

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

What are unlike radicals?

Radical expressions that do not have the same radicands. Signup and view all the answers

What is a unit rate?

A rate that has a denominator of 1. Signup and view all the answers

What is unit analysis?

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

What is a union in set theory?

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

What is uniform motion?

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

What is a trinomial?

A polynomial with three terms. Signup and view all the answers

What are trigonometric ratios?

The ratios of corresponding sides of similar right triangles. Signup and view all the answers

What is a trend line?

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

What is translation in geometry?

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

What is theoretical probability?

The ratio of the number of favorable outcomes to the number of possible outcomes. Signup and view all the answers

What is a term in mathematics?

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

What is a term of a sequence?

Any number in a sequence. Signup and view all the answers

What is a tangent in trigonometry?

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

What is a system of linear inequalities?

Two or more linear inequalities with the same variables. Signup and view all the answers

What is a system of linear equations?

Two or more linear equations using the same variables. Signup and view all the answers

What is the substitution method?

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

What is a stem-and-leaf plot?

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

What is the standard form of a quadratic function?

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

What is the standard form of a polynomial?

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

What is the standard form of a linear equation?

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

What is standard deviation?

A measure of how data varies from the mean. Signup and view all the answers

What is a square root function?

A function that contains the independent variable in the radicand. Signup and view all the answers

What is a square root?

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

What is the solution of an inequality with two variables?

Any ordered pair that makes the inequality true. Signup and view all the answers

What is the solution of an inequality with one variable?

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

What is the solution of an equation?

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

What is the solution of a system of linear inequalities?

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

What is the solution of a system of linear equations?

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

What is slope-intercept form?

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

What is slope?

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

What is sine?

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

What is simulation in probability?

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

What does it mean to simplify an expression?

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

What is simple interest?

Interest paid only on the principal. Signup and view all the answers

What are similar figures?

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

What is a set in mathematics?

A well-defined collection of elements. Signup and view all the answers

What is a sequence?

A number pattern. Signup and view all the answers

What is scientific notation?

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

What is a scatter plot?

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

What is a scale factor?

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

What is a scale drawing?

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

What is scale in mathematics?

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

What is a sample space?

All possible outcomes of an event. Signup and view all the answers

What are the roots of the equation?

The solutions of an equation. Signup and view all the answers

What is a relation in mathematics?

Any set of ordered pairs. Signup and view all the answers

What is a reciprocal?

The inverse of a fraction; when multiplied by the original fraction, it results in a product that equals one. 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.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

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.