Number Systems and Operations

Numbers and Operations

• Number Systems:
  • Natural Numbers (1, 2, 3, ...): positive integers
  • Whole Numbers (0, 1, 2, ...): non-negative integers
  • Integers (...,-2, -1, 0, 1, 2, ...): positive and negative whole numbers
  • Rational Numbers (fractions, decimals, percentages): can be expressed as a/b, where a and b are integers
  • Irrational Numbers (π, e, ...): cannot be expressed as a finite decimal or fraction
  • Real Numbers: includes rational and irrational numbers
• Operations:
  • Addition (+)
  • Subtraction (-)
  • Multiplication (×)
  • Division (÷)
  • Exponentiation (^)
  • Roots (√)

Algebra

• Equations and Inequalities:
  • Linear Equations (ax + by = c)
  • Quadratic Equations (ax^2 + bx + c = 0)
  • Inequalities (>, <, ≥, ≤)
• Functions:
  • Domain and Range
  • Linear Functions (f(x) = ax + b)
  • Quadratic Functions (f(x) = ax^2 + bx + c)
• Graphing:
  • Cartesian Coordinates (x, y)
  • Graphing Linear and Quadratic Functions

Geometry

• Points, Lines, and Planes:
  • Midpoint Formula
  • Distance Formula
  • Slope Formula
• Angles and Measurements:
  • Degree Measures (acute, right, obtuse, straight)
  • Radian Measures
  • Trigonometric Ratios (sin, cos, tan)
• Shapes and Solids:
  • Properties of 2D Shapes (triangles, quadrilaterals, polygons)
  • Properties of 3D Shapes (pyramids, prisms, spheres)

Calculus

• Limits:
  • One-Sided and Two-Sided Limits
  • Properties of Limits
• Derivatives:
  • Rules of Differentiation (power rule, product rule, quotient rule)
  • Geometric Interpretation of Derivatives
• Integrals:
  • Definite and Indefinite Integrals
  • Substitution Method and Integration by Parts

Numbers and Operations

• Natural Numbers are positive integers, starting from 1, such as 1, 2, 3, and so on.
• Whole Numbers are non-negative integers, including 0, such as 0, 1, 2, and so on.
• Integers include both positive and negative whole numbers, such as ..., -2, -1, 0, 1, 2, ...
• Rational Numbers are fractions, decimals, or percentages that can be expressed as a/b, where a and b are integers, such as 1/2, 0.5, or 25%.
• Irrational Numbers are numbers that cannot be expressed as a finite decimal or fraction, such as π or e.
• Real Numbers include both rational and irrational numbers, making it a comprehensive set of numbers.

Algebra

• Linear Equations are equations of the form ax + by = c, where a, b, and c are constants, and x and y are variables.
• Quadratic Equations are equations of the form ax^2 + bx + c = 0, where a, b, and c are constants, and x is a variable.
• Inequalities are statements that compare two expressions using greater than (()), less than (<), greater than or equal to (≥), or less than or equal to (≤) symbols.