9th Grade Algebra Flashcards

Questions and Answers

What are whole numbers?

Numbers with fractions

Negative numbers

Decimal numbers

Integers without fractions (correct)

What is an integer?

A whole number that is not a fraction.

Define irrational numbers.

Numbers that cannot be expressed as a fraction for any integers.

What is a linear function?

A function whose graph is a straight line. Signup and view all the answers

What is an exponential function?

A function where the value is a constant raised to the power of the argument. Signup and view all the answers

What defines a quadratic function?

It is of the form $f(x) = ax^2 + bx + c$. Signup and view all the answers

What is an absolute value function?

A function that contains an algebraic expression within absolute value symbols. Signup and view all the answers

What are zeros of a function?

Values of the domain that produce an output of zero. Signup and view all the answers

What is meant by roots of a function?

Real numbers that satisfy the equation of the function. Signup and view all the answers

Define area in mathematical terms.

The number of unit squares that can be contained within a flat figure. Signup and view all the answers

What does translation mean in geometry?

A function that moves an object a certain distance without altering its shape. Signup and view all the answers

What is the distributive property?

The property that states you can multiply a sum by multiplying each addend separately and then adding the products. Signup and view all the answers

What does the commutative property state?

Order does not matter in addition and multiplication. Signup and view all the answers

State the associative property.

The way in which numbers are grouped does not change their sum or product. Signup and view all the answers

Define the identity property.

The property stating that multiplying any number by 1 gives the original number. Signup and view all the answers

What is the additive inverse property?

The property that states the additive inverse of a number is what you add to it to yield zero. Signup and view all the answers

What does mode refer to in statistics?

The value that appears most frequently in a data set. Signup and view all the answers

What is mean in mathematics?

The average value found by dividing the sum of a set of numbers by the number of values. Signup and view all the answers

Define a trinomial.

An algebraic expression consisting of three terms. Signup and view all the answers

What is a vertex?

The highest point or apex of a shape or graph. Signup and view all the answers

Define interest.

The state of wanting to know or learn about something. Signup and view all the answers

What is appreciation?

The recognition and enjoyment of the good qualities of someone or something. Signup and view all the answers

Define depreciation.

A reduction in the value of an asset over time. Signup and view all the answers

What is an equation?

A statement that the values of two mathematical expressions are equal. Signup and view all the answers

What does inequality mean?

A difference in size, degree, or circumstances; lack of equality. Signup and view all the answers

Define recursive.

Characterized by recurrence or repetition. Signup and view all the answers

What is an interval?

An intervening time or space. Signup and view all the answers

Define correlation coefficient.

A number between -1 and +1 representing the linear dependence of two variables. Signup and view all the answers

What is range in mathematics?

The area of variation between upper and lower limits on a scale. Signup and view all the answers

What is slope?

A surface where one end or side is at a higher level than another. Signup and view all the answers

Study Notes

Whole Numbers and Integers

Whole numbers are numbers without fractions or decimals, including zero.
Integers are whole numbers that can be positive, negative, or zero, and do not include fractions.

Types of Numbers

Irrational numbers cannot be expressed as fractions. Their decimal forms neither terminate nor become periodic.
Rational numbers are the complement, easily represented as fractions with integers.

Functions

Linear functions produce straight-line graphs and are expressed in the form y = f(x) = a + bx, which involves one independent and one dependent variable.
Exponential functions involve a constant raised to a variable, notably featuring the base e.
Quadratic functions take the form f(x) = ax² + bx + c, producing parabolic graphs when plotted.

Functions Characteristics

Absolute value functions include expressions within absolute value symbols, reflecting distances from zero.
Zeros of a function, also known as roots, are values that make the function output zero, indicating points where the graph intersects the x-axis.

Mathematical Properties

The area measures the amount of unit squares that can fit within a flat figure.
Translations in geometry refer to moving objects a specified distance without altering their shape.
The distributive property allows multiplication of a sum by distributing the multiplier across each addend.
The commutative property indicates that the order of addition and multiplication does not change the result.

More Properties

Associative property involves grouping in addition or multiplication, where the arrangement of numbers does not affect their sum or product.
The identity property states that multiplying any number by one leaves it unchanged.
The additive inverse property asserts that every number a has an opposite -a that, when added together, equals zero.

Statistics and Measurements

The mode is the number that appears most frequently in a data set.
The mean represents the average value in statistics and is crucial for understanding probabilities.

Algebraic Terms

A trinomial consists of three terms, commonly seen in polynomial expressions.
The vertex of a parabola is its highest point or apex.

Financial Concepts

Interest refers to the cost of borrowing money or the reward for saving, reflecting a desire to learn about financial matters.
Appreciation indicates the recognition of valuable qualities, while depreciation denotes a decline in asset value over time due to various factors.

Mathematical Statements

An equation represents the equality of two expressions, demonstrated using the equals sign.
Inequality illustrates differences in size or degree, lacking complete equality among expressions.

Additional Concepts

Recursive definitions involve processes that repeat or return to earlier steps.
An interval signifies the space or time between two points or values.
Correlation coefficients range from -1 to +1, indicating the strength and direction of linear relationships between two data sets.
The range reflects the variation in values between minimum and maximum limits.
Slope describes the steepness of a line, indicating how much one variable changes concerning another.

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Description

Test your knowledge of key algebraic concepts with these flashcards designed for 9th-grade students. Each card presents essential definitions related to numbers, including whole numbers, integers, and irrational numbers. Perfect for students looking to reinforce their understanding of algebraic terms.