Algebra Class: Variables and Expressions

Questions and Answers

What is a variable?

A fixed value

A letter or symbol used to represent a value that can change (correct)

A type of constant

None of the above

What is a constant?

A value that does not change.

What is a numerical expression?

May contain only constants and operations.

What is an algebraic expression?

May contain variables, constants, and operations. Signup and view all the answers

What does it mean to evaluate an expression?

To find an expression's value. Signup and view all the answers

What is the absolute value?

A number's distance from zero on a number line. Signup and view all the answers

What are opposites in mathematics?

Two numbers with a sum of zero. Signup and view all the answers

What are additive inverses?

A number and its opposite. Signup and view all the answers

What are reciprocals?

Two numbers whose product is 1. Signup and view all the answers

What are multiplicative inverses?

A number and its reciprocal. Signup and view all the answers

What is a power in math?

An expression written with an exponent and a base or the value of such an expression. Signup and view all the answers

What is the base in an expression?

The number that is used as a factor. Signup and view all the answers

What is an exponent?

The number that tells how many times the base is used as a factor. Signup and view all the answers

What is a square root?

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

What is a perfect square?

A number whose positive square root is a whole number. Signup and view all the answers

What are real numbers?

All numbers that can be represented on the number line. Signup and view all the answers

What are natural numbers?

Are the counting numbers: 1, 2, 3... Signup and view all the answers

What are whole numbers?

Are the natural numbers and zero: 0, 1, 2, 3... Signup and view all the answers

What are integers?

Are whole numbers and their opposites: -3, -2, -1, 0, 1, 2, 3... Signup and view all the answers

What are rational numbers?

Can be expressed in the form a/b, where a and b are both integers and b is not equal to 0. Signup and view all the answers

What are terminating decimals?

Are rational numbers in decimal form that have a finite number of digits: 1.5, 2.75, 4.0 Signup and view all the answers

What are repeating decimals?

Are rational numbers in decimal form that have a block of one or more digits that repeats continuously: 1.33333333... Signup and view all the answers

What are irrational numbers?

Cannot be expressed in the form a/b. They include square roots of whole numbers that are not perfect squares and nonterminating decimals that do not repeat: The square root of 2 ; pi. Signup and view all the answers

What is the order of operations?

Tells you which operation to perform first. Signup and view all the answers

What are terms in an expression?

Are the parts of an expression being added and subtracted. Signup and view all the answers

What are like terms?

Are terms that contain the same variables raised to the same powers; can also be constants. Signup and view all the answers

What is a coefficient?

A number multiplied by a variable. Signup and view all the answers

What is a coordinate plane?

Is formed by the intersection of two perpendicular number lines called axes. Signup and view all the answers

What are axes in a coordinate plane?

Intersect to form a coordinate plane. Signup and view all the answers

What is the origin in a coordinate plane?

The point of intersection on a coordinate plane; is at 0 on each number line. Signup and view all the answers

What is the x-axis?

The horizontal number line in a coordinate plane. Signup and view all the answers

What is the y-axis?

The vertical number line in a coordinate plane. Signup and view all the answers

What is an ordered pair?

A point on the coordinate plane that consists of an x-coordinate and a y-coordinate, and is written (x, y) Signup and view all the answers

What are quadrants?

What the axes divide the coordinate plane into. Signup and view all the answers

What is input in an equation?

The value substituted for x in an equation. Signup and view all the answers

What is output in an equation?

The value generated for y in an equation. Signup and view all the answers

Study Notes

Variables and Expressions

Variable: A letter or symbol that represents a value capable of changing.
Constant: A fixed value that remains unchanged.
Numerical Expression: Comprises only constants and mathematical operations.
Algebraic Expression: Includes variables, constants, and operations.

Evaluation and Properties

Evaluate: The process of determining the value of an expression.
Absolute Value: Represents the distance of a number from zero on the number line.
Opposites: Two numbers that sum to zero, e.g., 3 and -3.
Additive Inverses: A number paired with its opposite.
Reciprocals: Two numbers whose product equals one.
Multiplicative Inverses: A number and its reciprocal.

Powers and Roots

Power: An expression with a base and an exponent; can represent its value.
Base: The number being multiplied in a power expression.
Exponent: Indicates how many times the base is multiplied by itself.
Square Root: A number which, when multiplied by itself, yields a product.
Perfect Square: A number with a whole number as its positive square root.

Number Sets

Real Numbers: All numbers that can be illustrated on a number line.
Natural Numbers: Counting numbers starting from 1 (1, 2, 3...).
Whole Numbers: Natural numbers plus zero (0, 1, 2, 3...).
Integers: Whole numbers and their negatives (-3, -2, -1, 0, 1, 2, 3...).
Rational Numbers: Expressible as a fraction (a/b) where a and b are integers, and b ≠ 0.
Terminating Decimals: Rational numbers with a finite decimal representation (1.5, 2.75).
Repeating Decimals: Rational numbers with a repeating sequence in decimal form (1.333...).
Irrational Numbers: Cannot be expressed as a fraction; include non-repeating, non-terminating decimals and square roots of non-perfect squares (√2, π).

Operations and Expressions

Order of Operations: The sequence for executing mathematical operations.
Terms: Components of an expression that are added or subtracted.
Like Terms: Terms that share the same variables raised to identical powers, including constants.
Coefficient: A numerical factor multiplied by a variable.

Coordinate Geometry

Coordinate Plane: Formed by two intersecting perpendicular number lines called axes.
Axes: The horizontal (X-axis) and vertical (Y-axis) lines that create the coordinate plane.
Origin: The intersection point of the X-axis and Y-axis, designated as (0, 0).
Ordered Pair: Specific point on the coordinate plane represented by (x, y).
Quadrants: Four regions created by dividing the coordinate plane with the axes.

Functions

Input: The value substituted for x in an equation.
Output: The resulting value for y in an equation after substitution.

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Description

Test your understanding of variables, constants, and expressions in algebra. This quiz covers evaluation methods, properties like opposites and reciprocals, and the basics of powers and roots. Assess your knowledge and improve your algebra skills!