MATHEMATICS

• Absolute Value


  The distance of the number from 0 on the number line
• Linear Inequality


  A mathematical statement that shows that an expression is either greater than or less than the other
• Inequality Symbols


  • ≠ (not equal to)
  • > (greater than, more than)
  • ≥ (greater than or equal to, at least)
  • < (less than, fewer than)
  • ≤ (less than or equal to, at most)
• Solving Linear Inequalities

  • Solution is any value of the variable that makes the inequality true
  • Solution set is the set of all solutions enclosed in braces {}
• Properties of Inequality

  • Addition Property: The inequality remains the same when the same number is added to both sides
  • Multiplication Property: The inequality remains the same when a positive number is multiplied by both sides, but changes when a negative number is multiplied to both sides
• Undefined Terms

  • Point: An indication of a specific location in space, has no length, width, nor thickness
  • Line: A set of points that extends endlessly in opposite directions, has infinite length but no thickness and width
  • Plane: A two-dimensional figure that has length and width but no thickness
• Naming Undefined Terms

  • Point: Named by a capital letter (e.g. Point A)
  • Line: Represented by a straight line with arrowheads, named using a lowercase script letter or two capital letters (e.g. Line l or Line AB)
  • Plane: Named using a single script capital letter or by three distinct points on the plane (e.g. Plane K or Plane ABC)
• Defined Terms


  • Collinear Points: Three or more points that lie on the same line
  • Noncollinear Points: Three or more points that do not lie on the same line
  • Coplanar Points: Three or more points that lie on the same plane
  • Noncoplanar Points: Three or more points that do not lie on the same plane
• Line Segment


  A subset of a line consisting of two endpoints and the set of all points between them
• Ray


  A subset of a line consisting of an endpoint and the set of all points on one side of that endpoint
• Opposite Rays


  Two rays with a common endpoint that extend in opposite directions and form a straight line
• Intersection


  The point common between two or more lines
• Postulate


  A statement assumed to be true even without proof, universally acceptable and does not need confirmation of its truthfulness
• Theorem


  A statement that can be proven using valid reasoning
• Coordinate


  Every point corresponds to a real number
• Number line


  Used to illustrate the concept of measuring a segment
• Measuring segments


  Using a number line
• Segments


  • Find the length of the following segments using the given number line