Number Systems and Basic Operations

Numbers and Operations

• 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 (√)

Algebra

• 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)

Geometry

• 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)

Calculus

• 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

Statistics and Probability

• 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

Numbers and Operations

• 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)

Algebra

• 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)

Geometry

• 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

Calculus

• 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

Statistics and Probability

• Data Analysis: types of data (quantitative, qualitative)
• Graphical Representations: histograms, box plots, scatter plots
• Probability: events (outcomes of experiments)
• Probability Rules: addition rule, multiplication rule, conditional probability