Algebra 1 - Definitions Flashcards

Questions and Answers

What is a bar graph?

A graph that displays percentages

A circular graph

A type of graph in which the lengths of bars represent data (correct)

A graph that uses lines to show trends

What is a frequency table?

A table that lists items together according to their intervals and frequency.

What distinguishes a histogram from a bar graph?

Histograms have bars that touch each other (correct)

Histograms use lines instead of bars

Histograms always have a circular shape

Histograms represent categorical data

What does a numerical expression consist of?

Numbers and operations. Signup and view all the answers

What does it mean to evaluate an expression?

To find the value of the expression. Signup and view all the answers

What is the order of operations?

Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. Signup and view all the answers

What is a variable?

A letter used to represent one or more numbers. Signup and view all the answers

What is a variable expression?

An expression that consists of numbers, variables, and operations. Signup and view all the answers

What is a power?

A number made of repeated factors. Signup and view all the answers

What does an exponent indicate?

The number of times a quantity is multiplied by itself. Signup and view all the answers

What is a base in terms of powers?

The number that is repeatedly multiplied in a power. Signup and view all the answers

What is an equation?

A mathematical sentence with an equal sign showing two expressions are equivalent. Signup and view all the answers

What does solving an equation involve?

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

What is a formula?

An equation that shows a relationship among two or more quantities. Signup and view all the answers

What is perimeter?

The sum of the lengths of the sides of a polygon. Signup and view all the answers

What is area?

The number of square units needed to cover a flat surface. Signup and view all the answers

What are integers?

Positive and negative whole numbers and 0. Signup and view all the answers

What is absolute value?

The distance a number is from 0 on the number line. Signup and view all the answers

What is the additive identity property?

The sum of a number and zero is always that number. Signup and view all the answers

What is the additive inverse property?

The sum of a number and its opposite is zero. Signup and view all the answers

What is the multiplication identity property?

The product of any number and one is that number. Signup and view all the answers

What is mean?

The sum of the values in a data set divided by the number of values. Signup and view all the answers

What does the commutative property of addition state?

In a sum, you can add terms in any order. Signup and view all the answers

What does the commutative property of multiplication state?

The order of the factors does not change the product. Signup and view all the answers

What is the associative property of addition?

Changing the grouping of terms will not change the sum. Signup and view all the answers

What is the associative property of multiplication?

Changing the grouping of factors will not change the product. Signup and view all the answers

What is the distributive property?

a(b + c) = ab + ac Signup and view all the answers

What are terms in an expression?

Parts of an expression separated by addition and subtraction signs. Signup and view all the answers

What are like terms?

Terms that have identical variable parts raised to the same power. Signup and view all the answers

What is a coefficient?

A number in front of a variable. Signup and view all the answers

What is a constant?

A term that has no variable and does not change. Signup and view all the answers

What is a coordinate plane?

A plane divided into four regions by the x-axis and y-axis. Signup and view all the answers

What is an ordered pair?

A pair of numbers (x, y) that indicate the position of a point on a coordinate plane. Signup and view all the answers

What is a quadrant in the coordinate plane?

One of the four sections into which the coordinate plane is divided. Signup and view all the answers

What is an inverse operation?

Operations that undo each other, such as addition and subtraction. Signup and view all the answers

What does it mean to isolate the variable?

To get a variable alone on one side of an equation or inequality. Signup and view all the answers

What are equivalent equations?

Equations that have the same solution. Signup and view all the answers

What is the base of a triangle?

The bottom of a triangle. Signup and view all the answers

What is height in terms of triangles?

The perpendicular distance from the base of a triangle. Signup and view all the answers

Study Notes

Graphical Representations

Bar Graph: Uses lengths of bars to represent and compare categorical data.
Frequency Table: Lists items according to their frequency, showing how often they occur.
Histogram: A specific type of bar graph where bars touch and represent grouped data frequencies.

Mathematical Expressions

Numerical Expression: Combines numbers and operations (e.g., addition, subtraction).
Evaluate: The process of finding the value of an expression.
Variable: A letter or symbol representing one or more numbers in expressions or equations.
Variable Expression: An expression consisting of numbers, variables, and operations.

Exponential Terms

Power: A number formed from repeated multiplication of a base.
Exponent: Indicates how many times a base is multiplied by itself.
Base: The number that is raised to a power.

Equations and Relationships

Equation: A mathematical statement with an equal sign showing two expressions are equal.
Solving an Equation: The process of determining all possible values that satisfy the equation.
Formula: An equation that delineates the relationship between two or more quantities.

Geometric Concepts

Perimeter: The total length of the sides of a polygon.
Area: The measure of the surface enclosed by a shape, quantified in square units.

Number Types and Properties

Integers: Whole numbers including positives, negatives, and zero; not fractions or decimals.
Absolute Value: The distance of a number from zero on the number line, denoted as |n|.

Identity and Inverse Properties

Additive Identity Property: The result of adding zero to any number is the number itself.
Additive Inverse Property: The sum of a number and its opposite (negative) equals zero.
Multiplication Identity Property: The product of any number and one is that number itself.

Statistical Concepts

Mean: The average of a data set, calculated by dividing the sum of values by the number of values.

Properties of Operations

Commutative Property of Addition: The order of terms in addition can be changed without affecting the sum.
Commutative Property of Multiplication: Changing the order of factors in multiplication does not alter the product.
Associative Property of Addition: Rearranging the grouping of addends does not change the result.
Associative Property of Multiplication: Changing the grouping of factors does not affect the product.
Distributive Property: Combining multiplication with addition, e.g., a(b + c) = ab + ac.

Expression Components

Terms: Components of an expression separated by addition or subtraction.
Like Terms: Terms that have identical variable parts raised to the same power.
Coefficient: A numerical factor in front of a variable.
Constant: A term without a variable that does not change.

Coordinate Geometry

Coordinate Plane: Divided into four quadrants by the x-axis (horizontal) and y-axis (vertical).
Ordered Pair: A pair of numbers (x, y) that specifies a location on the coordinate plane.
Quadrant: Each of the four sections created by the intersection of the x and y axes.

Algebra Techniques

Inverse Operation: Operations that reverse each other, such as addition and subtraction.
Isolate the Variable: The process of getting a variable alone on one side of an equation for solving purposes.
Equivalent Equations: Equations that yield the same solution.

Triangle Dimensions

Base: The bottom side of a triangle used for calculating area.
Height: The distance from the base to the top point of a triangle, measured perpendicularly.

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Test your knowledge on key definitions in Algebra 1 with these flashcards. Each card presents a term along with its precise definition, focusing on fundamental concepts like bar graphs, frequency tables, and histograms. Perfect for review and reinforcement of algebra terminology.