Numbers and Algebra Basics

Numbers

• 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 finite decimal)
• Irrational Numbers: cannot be expressed as a finite decimal, e.g. π, e
• Real Numbers: includes rational and irrational numbers

Algebra

• Variables: symbols that represent unknown values, e.g. x, y
• Constants: numbers, e.g. 2, 5
• Expressions: combinations of variables, constants, and mathematical operations
• Equations: statements that two expressions are equal, e.g. 2x + 3 = 5
• Inequalities: statements that one expression is greater than, less than, or equal to another

Geometry

• Points: locations in space, represented by coordinates (x, y)
• Lines: sets of points that extend infinitely in two directions
• Line Segments: parts of lines with a fixed length
• Rays: parts of lines that extend from a point to infinity in one direction
• Angles: formed by two rays sharing a common endpoint

Calculus

• Limits: the value that a function approaches as the input gets arbitrarily close to a certain point
• Derivatives: measures of how functions change as their input changes
• Integrals: measures of the area under curves or the accumulation of a quantity over an interval

Statistics

• Mean: average value of a dataset
• Median: middle value of a dataset when arranged in order
• Mode: most frequently occurring value in a dataset
• Range: difference between the largest and smallest values in a dataset
• Standard Deviation: measure of the spread or dispersion of a dataset

Numbers

• Natural numbers are positive integers, starting from 1 and going up to infinity.
• Whole numbers are non-negative integers, including 0 and all positive integers.
• Integers include both positive and negative whole numbers, as well as 0.
• Rational numbers are fractions that can be expressed as a finite decimal, such as 3/4 or 22/7.
• Irrational numbers cannot be expressed as a finite decimal, like π or e.
• Real numbers encompass both rational and irrational numbers.

Algebra

• Variables are symbols that represent unknown values, such as x or y.
• Constants are numbers, like 2 or 5, that remain unchanged.
• Expressions combine variables, constants, and mathematical operations.
• Equations assert that two expressions have equal values, like 2x + 3 = 5.
• Inequalities compare two expressions, indicating that one is greater than, less than, or equal to the other.

Geometry

• Points are locations in space, defined by their coordinates (x, y).
• Lines extend infinitely in two directions and consist of a set of points.
• Line segments are parts of lines with a fixed length.
• Rays are parts of lines that extend from a point to infinity in one direction.
• Angles are formed by two rays sharing a common endpoint.

Calculus

• Limits determine the value that a function approaches as the input gets arbitrarily close to a certain point.
• Derivatives measure the rate of change of a function as its input changes.
• Integrals calculate the area under curves or the accumulation of a quantity over an interval.

Statistics

• The mean is the average value of a dataset.
• The median is the middle value of a dataset when arranged in order.
• The mode is the most frequently occurring value in a dataset.
• The range is the difference between the largest and smallest values in a dataset.
• The standard deviation measures the spread or dispersion of a dataset.