Number Systems and Basic Operations

Study Notes

Number Systems:
- Natural Numbers (1, 2, 3, ...)
- Whole Numbers (0, 1, 2, 3, ...)
- Integers (...,-3, -2, -1, 0, 1, 2, 3, ...)
- Rational Numbers (fractions, decimals)
- Irrational Numbers (cannot be expressed as a fraction)
- Real Numbers (includes rational and irrational numbers)
- Complex Numbers (includes real and imaginary parts)
Operations:
- Addition (+)
- Subtraction (-)
- Multiplication (×)
- Division (÷)
- Exponents (powers)
- Roots (√)

Variables and Expressions:
- Variables (letters/symbols that represent unknown values)
- Expressions (combinations of variables, constants, and operations)
- Equations (expressions with equal values)
- Inequalities (expressions with unequal values)
Linear Algebra:
- Equations with multiple variables
- Matrices (arrays of numbers)
- Vectors (quantities with magnitude and direction)

Points, Lines, and Planes:
- Points (locations in space)
- Lines (sets of points extending infinitely in two directions)
- Planes (flat surfaces)
Angles and Measurements:
- Angles (formed by two rays sharing a common endpoint)
- Types of Angles (acute, obtuse, right, straight, reflex)
- Measurement units (degrees, radians)

Limits:
- Concept of approaching a value
- Rules for evaluating limits
Derivatives:
- Rate of change of a function
- Rules for differentiating functions
Integrals:
- Accumulation of a function over an interval
- Rules for integrating functions

Data Analysis:
- Types of data (quantitative, qualitative)
- Graphical representations (histograms, box plots, scatter plots)
Probability:
- Events (outcomes of experiments)
- Probability rules (addition, multiplication)
- Conditional probability

Natural Numbers: 1, 2, 3, ... (counting numbers)
Whole Numbers: 0, 1, 2, 3, ... (includes 0 and natural numbers)
Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (includes negative and positive whole numbers)
Rational Numbers: fractions (e.g., 3/4), decimals (e.g., 0.5)
Irrational Numbers: cannot be expressed as a fraction (e.g., π, e)
Real Numbers: includes rational and irrational numbers
Complex Numbers: includes real and imaginary parts (e.g., 3 + 4i)

Variables: letters/symbols that represent unknown values (e.g., x, y)
Expressions: combinations of variables, constants, and operations (e.g., 2x + 3)
Equations: expressions with equal values (e.g., 2x + 3 = 5)
Inequalities: expressions with unequal values (e.g., 2x + 3 > 5)
Linear Algebra: equations with multiple variables, matrices (arrays of numbers), and vectors (quantities with magnitude and direction)

Points: locations in space
Lines: sets of points extending infinitely in two directions
Planes: flat surfaces
Angles: formed by two rays sharing a common endpoint
Angle Types: acute (less than 90˚), obtuse (greater than 90˚), right (90˚), straight (180˚), reflex (greater than 180˚)
Measurement Units: degrees, radians

Limits: concept of approaching a value
Limit Rules: sum, product, chain, and power rules
Derivatives: rate of change of a function
Differentiation Rules: power rule, product rule, quotient rule
Integrals: accumulation of a function over an interval
Integration Rules: substitution, integration by parts, integration by partial fractions