Number Systems

Number Systems

• Natural Numbers: 1, 2, 3, ... (positive integers)
• Whole Numbers: 0, 1, 2, 3, ... (non-negative integers)
• Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (positive and negative whole numbers)
• Rational Numbers: fractions, e.g. 3/4, 22/7 (can be expressed as a ratio of integers)
• Irrational Numbers: non-repeating, non-terminating decimals, e.g. π, e (cannot be expressed as a ratio of integers)
• Real Numbers: includes rational and irrational numbers
• Complex Numbers: includes real numbers and imaginary numbers (e.g. 3 + 4i)

Algebra

• Variables: letters or symbols that represent unknown values
• Constants: numbers that do not change value
• Expressions: combinations of variables, constants, and mathematical operations
• Equations: statements that express the equality of two expressions
• Inequalities: statements that express the relationship between two expressions (e.g. <, >, ≤, ≥)

Geometry

• Points: locations in space, represented by coordinates (e.g. (x, y))
• Lines: sets of points that extend infinitely in two directions
• Rays: lines that extend infinitely in one direction
• Angles: formed by two rays sharing a common endpoint
• Triangles: polygons with three sides and three angles
• Quadrilaterals: polygons with four sides and four angles

Calculus

• Limits: the behavior of a function as the input approaches a certain value
• Derivatives: measures of how a function changes as its input changes
• Integrals: measures of the accumulation of a function over a given interval
• Differentiation: the process of finding derivatives
• Integration: the process of finding integrals

Statistics

• Descriptive Statistics: summary measures of a dataset (e.g. mean, median, mode)
• Inferential Statistics: using sample data to make inferences about a population
• Probability: the study of chance and randomness
• Hypothesis Testing: the process of testing a hypothesis about a population based on sample data

Number Systems

• Natural numbers are positive integers, starting from 1.
• Whole numbers are non-negative integers, including 0.
• Integers are positive and negative whole numbers, including 0.
• Rational numbers are fractions that can be expressed as a ratio of integers, such as 3/4 or 22/7.
• Irrational numbers are non-repeating, non-terminating decimals, such as π or e, and cannot be expressed as a ratio of integers.
• Real numbers include both rational and irrational numbers.
• Complex numbers include real numbers and imaginary numbers, such as 3 + 4i.

Algebra

• Variables are letters or symbols that represent unknown values.
• Constants are numbers that do not change value.
• Expressions are combinations of variables, constants, and mathematical operations.
• Equations are statements that express the equality of two expressions.
• Inequalities are statements that express the relationship between two expressions, such as ≤ or ≥.

Geometry

• Points are locations in space, represented by coordinates, such as (x, y).
• Lines are sets of points that extend infinitely in two directions.
• Rays are lines that extend infinitely in one direction.
• Angles are formed by two rays sharing a common endpoint.
• Triangles are polygons with three sides and three angles.
• Quadrilaterals are polygons with four sides and four angles.

Calculus

• Limits describe the behavior of a function as the input approaches a certain value.
• Derivatives measure how a function changes as its input changes.
• Integrals measure the accumulation of a function over a given interval.
• Differentiation is the process of finding derivatives.
• Integration is the process of finding integrals.

Statistics

• Descriptive statistics are summary measures of a dataset, including mean, median, and mode.
• Inferential statistics use sample data to make inferences about a population.
• Probability is the study of chance and randomness.
• Hypothesis testing is the process of testing a hypothesis about a population based on sample data.