Numbers and Operations

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, e.g. 3/4, 22/7
  • Real Numbers (R): includes all rational and irrational numbers, e.g. π, e
• Operations:
  • Addition: combining two or more numbers to get a total or sum
  • Subtraction: finding the difference between two numbers
  • Multiplication: repeated addition, e.g. 3 × 4 = 3 + 3 + 3 + 3
  • Division: sharing a number into equal parts or groups

Algebra

• Variables and Expressions:
  • Variable: a symbol representing a value that can change
  • Expression: a combination of variables, numbers, and operations
  • Equation: a statement that says two expressions are equal
• Solving Equations:
  • Linear Equations: equations in which the highest power of the variable is 1
  • Quadratic Equations: equations in which the highest power of the variable is 2

Geometry

• Points, Lines, and Planes:
  • Point: a location in space, represented by a set of coordinates
  • Line: a set of points extending infinitely in two directions
  • Plane: a flat surface that extends infinitely in all directions
• Angles and Shapes:
  • Angle: formed by two rays sharing a common endpoint
  • Types of Angles: acute, right, obtuse, straight, reflex
  • Types of Shapes: triangles, quadrilaterals, polygons, circles

Measurement and Data

• Units and Conversions:
  • Length: meter (m), centimeter (cm), millimeter (mm)
  • Capacity: liter (L), milliliter (mL)
  • Mass: gram (g), kilogram (kg)
• Data Analysis:
  • Types of Data: qualitative, quantitative
  • Data Representation: tables, charts, graphs, diagrams

Calculus

• Limits:
  • The concept of limits is used to study how functions behave as the input values approach a certain point
• Derivatives:
  • The derivative of a function represents the rate of change of the function with respect to the input
• Integrals:
  • The integral of a function represents the accumulation of the function over a given interval

Number Systems

• Natural Numbers (N) are a set of positive integers starting from 1.
• Whole Numbers (W) include 0 and all positive integers.
• Integers (Z) are a set of all positive and negative whole numbers, including 0.
• Rational Numbers (Q) are fractions, e.g. 3/4, 22/7.
• Real Numbers (R) include all rational and irrational numbers, e.g. π, e.

Operations

• Addition is combining two or more numbers to get a total or sum.
• Subtraction is finding the difference between two numbers.
• Multiplication is repeated addition, e.g. 3 × 4 = 3 + 3 + 3 + 3.
• Division is sharing a number into equal parts or groups.

Algebra

Variables and Expressions

• A variable is a symbol representing a value that can change.
• An expression is a combination of variables, numbers, and operations.
• An equation is a statement that says two expressions are equal.

Solving Equations

• Linear Equations have the highest power of the variable as 1.
• Quadratic Equations have the highest power of the variable as 2.

Geometry

Points, Lines, and Planes

• A point is a location in space, represented by a set of coordinates.
• A line is a set of points extending infinitely in two directions.
• A plane is a flat surface that extends infinitely in all directions.

Angles and Shapes

• An angle is formed by two rays sharing a common endpoint.
• Types of Angles include acute, right, obtuse, straight, and reflex.
• Types of Shapes include triangles, quadrilaterals, polygons, and circles.

Measurement and Data

Units and Conversions

• Length units include meter (m), centimeter (cm), and millimeter (mm).
• Capacity units include liter (L) and milliliter (mL).
• Mass units include gram (g) and kilogram (kg).

Data Analysis

• Types of Data include qualitative and quantitative.
• Data Representation includes tables, charts, graphs, and diagrams.

Calculus

Limits

• The concept of limits is used to study how functions behave as the input values approach a certain point.

Derivatives

• The derivative of a function represents the rate of change of the function with respect to the input.

Integrals

• The integral of a function represents the accumulation of the function over a given interval.