Basic Math and Algebra Concepts

Basic Arithmetic

• Addition (+): Combining two or more numbers to get a sum.
• Subtraction (−): Removing a number from another to find the difference.
• Multiplication (×): Repeated addition of a number.
• Division (÷): Splitting a number into equal parts.

Algebra

• Variables: Symbols (like x, y) representing numbers.
• Expressions: Combinations of numbers and variables (e.g., 2x + 5).
• Equations: Statements that two expressions are equal (e.g., 2x + 5 = 10).
• Solving equations: Finding the value of the variable that makes the equation true.

Geometry

• Shapes: Basic figures (e.g., squares, circles, triangles).
• Perimeter: Total length around a shape.
• Area: Space contained within a shape.
• Volume: Measurement of space in 3D objects.

Trigonometry

• Sine (sin), Cosine (cos), Tangent (tan): Ratios in right triangles.
• Pythagorean theorem: a² + b² = c² (relationship between sides in a right triangle).

Calculus

• Limits: Value that a function approaches as the input approaches a point.
• Derivatives: Measure of how a function changes as its input changes.
• Integrals: Represent accumulation of quantities.

Statistics

• Mean: Average of a set of numbers.
• Median: Middle value in a sorted list.
• Mode: Most frequently occurring number in a set.
• Standard deviation: Measure of data spread around the mean.

Probability

• Probability: Measure of likelihood of an event (0 to 1 scale).
• Independent events: One event does not affect another.
• Dependent events: One event affects the probability of another.

Functions

• Definition: A relation where each input has exactly one output.
• Types of functions: Linear, quadratic, exponential, logarithmic.
• Graphs: Visual representation of functions showing relations between variables.

Number Theory

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves.
• Composite numbers: Natural numbers greater than 1 that are not prime.
• Factors: Numbers that divide another number without leaving a remainder.

Mathematical Logic

• Statements: Declarative sentences that are either true or false.
• Logical operators: AND, OR, NOT (used in constructing logical statements).
• Proofs: Logical arguments that establish the truth of a statement.

Basic Arithmetic

• Addition (+) combines two or more numbers to find their sum.
• Subtraction (−) removes a number from another to find their difference.
• Multiplication (×) is like repeated addition of a number.
• Division (÷) splits a number into equal parts.

Algebra

• Variables act as placeholders for unknown numbers.
• Expressions combine numbers and variables using operations.
• Equations state that two expressions are equal.
• Solving equations involves finding the value of the variable that makes the equation true.

Geometry

• Shapes are basic figures like squares, circles, and triangles.
• Perimeter measures the total length around a shape.
• Area measures the space contained within a shape.
• Volume measures the space occupied by a 3D object.

Trigonometry

• Sine (sin), Cosine (cos), and Tangent (tan) are ratios of sides in right triangles.
• Pythagorean theorem relates the sides of a right triangle: a² + b² = c² (where c is the hypotenuse).

Calculus

• Limits describe the value a function approaches as its input gets close to a specific point.
• Derivatives measure how a function changes as its input changes.
• Integrals represent the accumulation of quantities.

Statistics

• Mean represents the average value of a set of numbers.
• Median is the middle value when a set of numbers is ordered.
• Mode identifies the most frequent number in a dataset.
• Standard deviation measures how data points spread around the mean.

Probability

• Probability measures the likelihood of an event happening, ranging from 0 (impossible) to 1 (certain).
• Independent events don't influence each other's probabilities.
• Dependent events have probabilities that influence each other.

Functions

• A function assigns a unique output to each input.
• Types include linear, quadratic, exponential, and logarithmic functions.
• Graphs visually represent functions and their relationships between variables.

Number Theory

• Prime numbers have only two divisors: 1 and themselves.
• Composite numbers are natural numbers greater than 1 that aren't prime.
• Factors are numbers that divide another number evenly without leaving a remainder.

Mathematical Logic

• Statements are sentences that can be either true or false.
• Logical operators (e.g., AND, OR, NOT) combine statements to create complex expressions.
• Proofs establish the truth of a statement through logical arguments.