Number Systems Basics

Numbers and Operations

• 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, decimals, percentages): can be expressed as a/b, where a and b are integers and b ≠ 0
  • Irrational Numbers (π, e, √2, ...): cannot be expressed as a simple fraction
  • Real Numbers: includes rational and irrational numbers
  • Complex Numbers: includes real and imaginary numbers (a + bi, where a and b are real numbers and i is the imaginary unit)

• Basic Operations:

  • Addition (+)
  • Subtraction (-)
  • Multiplication (×)
  • Division (÷)
  • Exponents (^)
  • Roots (√)

Algebra

• Equations and Inequalities:

  • Linear Equations (ax + by = c): degree 1, graph is a straight line
  • Quadratic Equations (ax^2 + bx + c = 0): degree 2, graph is a parabola
  • Systems of Equations: multiple equations with multiple variables
  • Inequalities: statements with <, >, ≤, ≥, or ≠

• Functions:

  • Domain: set of input values
  • Range: set of output values
  • Composition: combining functions
  • Inverse: reversing the input and output

Geometry

• Points, Lines, and Planes:

  • Points: locations in space, represented by coordinates (x, y, z)
  • Lines: sets of points, can be extended infinitely
  • Planes: flat surfaces, can be extended infinitely

• Angles and Measurement:

  • Angle: formed by two rays sharing a common endpoint
  • Types of Angles: acute, right, obtuse, straight, reflex
  • Measurement: degrees, radians, minutes, seconds

Data Analysis and Statistics

• Data Types:

  • Quantitative: numerical data (e.g., height, weight)
  • Qualitative: categorical data (e.g., gender, color)

• Graphs and Charts:

  • Types: bar, histogram, box plot, scatter plot, pie chart
  • Purpose: visualize and understand data distributions

• Descriptive Statistics:

  • Measures of Central Tendency: mean, median, mode
  • Measures of Variation: range, variance, standard deviation

Numbers and Operations

• Natural Numbers are positive integers (1, 2, 3,...)
• Whole Numbers are non-negative integers (0, 1, 2, 3,...)
• Integers include positive and negative whole numbers (...,-3, -2, -1, 0, 1, 2, 3,...)
• Rational Numbers can be expressed as a/b, where a and b are integers and b ≠ 0 (fractions, decimals, percentages)
• Irrational Numbers cannot be expressed as a simple fraction (π, e, √2,...)
• Real Numbers include rational and irrational numbers
• Complex Numbers include real and imaginary numbers (a + bi, where a and b are real numbers and i is the imaginary unit)
• Basic Operations include Addition (+), Subtraction (-), Multiplication (×), Division (÷), Exponents (^), and Roots (√)

Algebra

• Linear Equations are degree 1 and graph as a straight line (ax + by = c)
• Quadratic Equations are degree 2 and graph as a parabola (ax^2 + bx + c = 0)
• Systems of Equations involve multiple equations with multiple variables
• Inequalities are statements with , ≤, ≥, or ≠
• Domain is the set of input values for a function
• Range is the set of output values for a function
• Composition involves combining functions
• Inverse involves reversing the input and output of a function

Geometry

• Points are locations in space, represented by coordinates (x, y, z)
• Lines are sets of points and can be extended infinitely
• Planes are flat surfaces that can be extended infinitely
• Angles are formed by two rays sharing a common endpoint
• Angle types include acute, right, obtuse, straight, and reflex
• Measurement units include degrees, radians, minutes, and seconds

Data Analysis and Statistics

• Quantitative Data is numerical (e.g., height, weight)
• Qualitative Data is categorical (e.g., gender, color)
• Graph types include bar, histogram, box plot, scatter plot, and pie chart
• Graphs are used to visualize and understand data distributions
• Measures of Central Tendency include mean, median, and mode
• Measures of Variation include range, variance, and standard deviation