Fundamental Math Concepts

Fundamental Math Concepts

• Arithmetic involves basic operations: addition, subtraction, multiplication, and division. These are foundational for more advanced concepts.
• Algebra uses variables and equations to represent and solve unknowns. It manipulates equations and formulas to find variable values.
• Geometry studies shapes, sizes, and properties of figures in two and three dimensions, including lines, angles, triangles, circles, and volumes.
• Calculus studies change, encompassing differential calculus (rates of change) and integral calculus (accumulation of quantities).
• Trigonometry examines relationships between angles and triangle sides using trigonometric functions (sine, cosine, tangent).
• Statistics involves collecting, analyzing, and interpreting data using measures of central tendency (mean, median, mode) and dispersion (variance, standard deviation).
• Probability quantifies the likelihood of events, using sample spaces, events, and probability calculations.

Arithmetic Operations

• Addition combines quantities to find a sum.
• Subtraction finds the difference between quantities.
• Multiplication repeatedly adds a quantity to get the product.
• Division distributes a quantity into equal parts to find the quotient.

Algebraic Equations

• Variables represent unknown values, often letters (x, y).
• Equations show the equality of two expressions, containing variables and constants.
• Solutions to equations are the variable values that satisfy the equation.
• Linear equations have a degree of 1 (e.g., y = mx + b).
• Quadratic equations have a degree of 2 (e.g., ax² + bx + c = 0).

Geometric Shapes

• Lines are one-dimensional figures extending infinitely in both directions.
• Angles are formed where two lines or rays meet at a common point, measured in degrees or radians.
• Triangles have three sides and three angles; types include equilateral, isosceles, and scalene.
• Circles are defined by a fixed center and radius.
• Polygons are closed two-dimensional shapes with straight sides.

Calculus Concepts

• Derivatives represent instantaneous rates of change.
• Integrals represent accumulated quantities.
• Limits determine the behavior of a function as its input approaches a specific value.

Trigonometric Identities

• Fundamental relationships connect trigonometric functions (sine, cosine, tangent).
• Pythagorean identities link trigonometric functions via a relationship similar to the Pythagorean Theorem.
• Angle sum and difference identities calculate trigonometric functions of sums or differences of angles.

Statistical Measures

• Mean is the average of a data set.
• Median is the middle value in a sorted data set.
• Mode is the most frequent value in a data set.
• Standard deviation measures data spread around the mean.
• Variance measures data variability.

Probability Definitions

• Sample space lists all possible outcomes.
• An event is a subset of the sample space.
• Probability measures the likelihood of an event.
• Conditional probability is the probability of an event given another event has occurred.
• Independent events are events whose occurrences do not affect each other's probabilities.