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, ... (all whole numbers and their negatives)
• Rational Numbers: fractions (e.g. 1/2, 3/4) and decimals (e.g. 0.5, 0.75)
• Irrational Numbers: non-repeating decimals (e.g. π, e)
• Real Numbers: all rational and irrational numbers
• Complex Numbers: numbers with real and imaginary parts (e.g. 3 + 4i)

Algebra

• Variables: unknown values represented by letters (e.g. x, y)
• Constants: known values (e.g. 2, 5)
• Expressions: combinations of variables and constants (e.g. 2x + 3)
• Equations: statements with equal signs (e.g. 2x + 3 = 5)
• Inequalities: statements with greater than, less than, or equal to signs (e.g. 2x + 3 > 5)

Geometry

• Points: locations in space (e.g. A, B, C)
• Lines: sets of points extending infinitely in two directions
• Line Segments: parts of lines with fixed endpoints (e.g. AB, CD)
• Rays: lines extending from a point to infinity (e.g. →AB)
• Angles: formed by two rays sharing a common endpoint (e.g. ∠AOB)
• Triangles: three-sided shapes (e.g. ΔABC)

Calculus

• Limits: values that a function approaches as the input gets arbitrarily close
• Derivatives: rates of change of functions (e.g. dy/dx)
• Integrals: accumulation of quantities over a interval (e.g. ∫f(x)dx)

Statistics and Probability

• Mean: average value of a dataset
• Median: middle value of a dataset when arranged in order
• Mode: most frequently occurring value in a dataset
• Probability: measure of the likelihood of an event occurring (e.g. 0 ≤ P(event) ≤ 1)

Trigonometry

• Angles: measures of rotation (e.g. 30°, 45°)
• Triangles: right-angled triangles (e.g. ΔABC)
• Sine (sin), Cosine (cos), and Tangent (tan) functions relate to triangle sides and angles

Number Systems

• Natural numbers are positive integers: 1, 2, 3, ...
• Whole numbers include 0 and all positive integers: 0, 1, 2, 3, ...
• Integers include all whole numbers and their negatives: ..., -3, -2, -1, 0, 1, 2, 3, ...
• Rational numbers are fractions and decimals: 1/2, 3/4, 0.5, 0.75
• Irrational numbers are non-repeating decimals: π, e
• Real numbers include all rational and irrational numbers
• Complex numbers have real and imaginary parts: 3 + 4i

Algebra

• Variables represent unknown values: x, y
• Constants are known values: 2, 5
• Expressions combine variables and constants: 2x + 3
• Equations are statements with equal signs: 2x + 3 = 5
• Inequalities have greater than, less than, or equal to signs: 2x + 3 > 5

Geometry

• Points are locations in space: A, B, C
• Lines extend infinitely in two directions
• Line segments have fixed endpoints: AB, CD
• Rays extend from a point to infinity: →AB
• Angles are formed by two rays sharing a common endpoint: ∠AOB
• Triangles are three-sided shapes: ΔABC

Calculus

• Limits are values that a function approaches as the input gets arbitrarily close
• Derivatives are rates of change of functions: dy/dx
• Integrals are accumulation of quantities over an interval: ∫f(x)dx

Statistics and Probability

• Mean is the average value of a dataset
• Median is the middle value of a dataset when arranged in order
• Mode is the most frequently occurring value in a dataset
• Probability measures the likelihood of an event occurring: 0 ≤ P(event) ≤ 1

Trigonometry

• Angles are measures of rotation: 30°, 45°
• Right-angled triangles relate to sine, cosine, and tangent functions: ΔABC
• Sine, cosine, and tangent functions relate to triangle sides and angles