9th Grade Algebra Flashcards

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.