Basic Math Concepts and Operations

Variables: Symbols representing numbers (e.g., x, y).
Equations: Mathematical statements with an equal sign (e.g., 2x + 3 = 7).
Functions: Relationships between variables (e.g., f(x) = x + 2).
Linear Equations: Equations that graph as a straight line (e.g., y = mx + b).

Shapes: 2D (e.g., squares, circles) and 3D (e.g., cubes, spheres).
Area: Measurement of space within a shape (e.g., Area of a rectangle = length × width).
Perimeter: Distance around a shape (e.g., Perimeter of a rectangle = 2(length + width)).
Volume: Space occupied by a 3D object (e.g., Volume of a cube = side³).

Angles: Measured in degrees (°) or radians.
Sine, Cosine, Tangent: Ratios in right triangles (e.g., sin(θ) = opposite/hypotenuse).
Pythagorean Theorem: a² + b² = c² for right triangles.

Probability: Likelihood of an event occurring (e.g., P(A) = number of favorable outcomes/total outcomes).
Independent Events: One event does not affect another.
Dependent Events: One event affects the outcome of another.

Prime Numbers: Numbers greater than 1 with no divisors other than 1 and itself.
Factors: Numbers that divide another number without leaving a remainder.
Multiples: Products of a number and an integer.

Symbols: Common symbols include + (addition), - (subtraction), × (multiplication), ÷ (division), = (equals).
Inequalities: Express relationships (e.g., <, >, ≤, ≥).

Addition involves combining numbers to achieve a total, exemplified by 2 + 3 resulting in 5.
Subtraction is the process of deducting one number from another, as shown in 5 - 2 which equals 3.
Multiplication is essentially repeated addition; for instance, 4 multiplied by 3 (4 × 3) results in 12.
Division breaks down a number into equal segments; for example, 12 divided by 3 (12 ÷ 3) equals 4.

Variables are symbols like x and y used to represent unknown values in equations.
Equations are mathematical statements that assert the equality of two expressions, such as 2x + 3 = 7.
Functions define relationships that associate inputs to outputs, illustrated by f(x) = x + 2.
Linear equations illustrate straight-line graphs, following the format y = mx + b where m is the slope and b is the y-intercept.

Shapes can be categorized as two-dimensional (2D) such as squares and circles, or three-dimensional (3D) like cubes and spheres.
Area quantifies the space contained within a shape, calculated for a rectangle as length multiplied by width.
Perimeter measures the total distance around a shape; for a rectangle, this is computed as 2(length + width).
Volume describes the quantity of space a 3D object occupies, for example, the volume of a cube is calculated as side³.

Angles are assessed in degrees or radians, with various applications in geometry.
Sine, cosine, and tangent are fundamental ratios derived from the sides of right triangles; for example, sin(θ) = opposite/hypotenuse.
The Pythagorean Theorem provides a fundamental relation in right triangles: a² + b² = c², where c is the hypotenuse.

Limits explore the behavior of functions as they approach a specific point.
Derivatives signify the rate of change of a function, representing the slope of a curve at a point.
Integrals compute the cumulative area beneath curves, facilitating techniques in area and accumulated change.

Mean conveys the average of a data set, calculated by summing values and dividing by the total count.
Median indicates the middle value of an ordered data set, providing insight into central tendency.
Mode identifies the most frequently appearing value within a data set, useful for understanding distribution.
Standard deviation measures how spread out the values in a data set are, reflecting variability around the mean.

Probability defines the chance of an event occurring, calculated as P(A) = number of favorable outcomes divided by total outcomes.
Independent events are situations where the outcome of one event does not influence another.
Dependent events indicate scenarios where one event's outcome affects the probabilities of subsequent events.

Prime numbers are integers greater than 1 that have no positive divisors other than 1 and themselves.
Factors are integers that can divide another integer without leaving a remainder.
Multiples are the products obtained when a number is multiplied by integers.

Common symbols include + for addition, - for subtraction, × for multiplication, ÷ for division, and = for equal relationships.
Inequalities express comparative relationships between values using symbols like <, ≤ and ≥.

Identifying the problem is crucial to understanding what needs to be solved.
Devising a plan involves selecting an appropriate strategy, such as diagramming or algebraic methods.
Carrying out the plan means implementing the chosen strategy effectively.
Reviewing and extending involves checking results and considering additional implications or questions that arise.