Numbers and Operations Basics

Numbers and Operations

• Number Systems:
  • Natural Numbers (N): 1, 2, 3, ...
  • Whole Numbers (W): 0, 1, 2, 3, ...
  • Integers (Z): ..., -3, -2, -1, 0, 1, 2, 3, ...
  • Rational Numbers (Q): fractions, decimals, percentages
  • Irrational Numbers: non-repeating decimals, e.g. π, e
  • Real Numbers (R): all rational and irrational numbers
• Operations:
  • Addition (+): combining two or more numbers
  • Subtraction (-): finding the difference between two numbers
  • Multiplication (×): repeated addition
  • Division (÷): sharing or grouping
  • Exponents (^): repeated multiplication
  • Roots (√): inverse operation of exponents

Algebra

• Variables and Expressions:
  • Variables: letters or symbols representing unknown values
  • Expressions: combinations of variables, constants, and operations
• Equations and Inequalities:
  • Equations: statements with equal values, e.g. 2x + 3 = 5
  • Inequalities: statements with unequal values, e.g. 2x - 4 > 0
• Graphing:
  • Coordinate Plane: 2D grid with x-axis and y-axis
  • Functions: relations between input (x) and output (y) values

Geometry

• Points, Lines, and Planes:
  • Points: locations in space, represented by coordinates
  • Lines: sets of points extending infinitely in two directions
  • Planes: flat surfaces extending infinitely in all directions
• Angles and Measurements:
  • Angles: formed by two rays sharing a vertex
  • Degrees: units of measurement for angles
• Shapes and Solids:
  • 2D Shapes: triangles, quadrilaterals, polygons, circles
  • 3D Solids: cubes, spheres, pyramids, prisms

Calculus

• Limits:
  • Concept of approaching a value, but not reaching it
• Derivatives:
  • Rate of change, slope of a function
• Integrals:
  • Accumulation of rates of change, area under a curve

Number Systems

• Natural Numbers (N): 1, 2, 3,...
• Whole Numbers (W): 0, 1, 2, 3,...
• Integers (Z): ..., -3, -2, -1, 0, 1, 2, 3,...
• Rational Numbers (Q): fractions, decimals, percentages
• Irrational Numbers: non-repeating decimals, e.g.π, e
• Real Numbers (R): all rational and irrational numbers

Operations

• Addition (+): combining two or more numbers
• Subtraction (-): finding the difference between two numbers
• Multiplication (×): repeated addition
• Division (÷): sharing or grouping
• Exponents (^): repeated multiplication
• Roots (√): inverse operation of exponents

Algebra

Variables and Expressions

• Variables: letters or symbols representing unknown values
• Expressions: combinations of variables, constants, and operations

Equations and Inequalities

• Equations: statements with equal values, e.g. 2x + 3 = 5
• Inequalities: statements with unequal values, e.g. 2x - 4 > 0

Graphing

• Coordinate Plane: 2D grid with x-axis and y-axis
• Functions: relations between input (x) and output (y) values

Geometry

Points, Lines, and Planes

• Points: locations in space, represented by coordinates
• Lines: sets of points extending infinitely in two directions
• Planes: flat surfaces extending infinitely in all directions

Angles and Measurements

• Angles: formed by two rays sharing a vertex
• Degrees: units of measurement for angles

Shapes and Solids

• 2D Shapes: triangles, quadrilaterals, polygons, circles
• 3D Solids: cubes, spheres, pyramids, prisms

Calculus

Limits

• Concept of approaching a value, but not reaching it

Derivatives

• Rate of change, slope of a function

Integrals

• Accumulation of rates of change, area under a curve