Math

• Probability


  Experiment, Outcome, Sample Space, Event
• Experiment


  A process of investigation from which results are observed or recorded
• Experiments


  • Tossing a coin
  • Picking a card from deck of cards
  • Rolling a die
  • Choosing a ball from a box
  • Drawing a ball in the lottery
• Formula for probability


  P(E) = number of favorable outcomes / number of possible outcomes
• Outcome


  A possible result in an experiment
• Outcomes of tossing two coins


  • head & tail
  • head & head
  • tail & head
  • tail & tail
• Outcomes of rolling a die


  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
• Sample Space


  The set of all possible outcomes for a probability experiment or activity
• Sample space of rolling a die


  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
• Event


  The subset of all possible outcomes or sample space of an event
• Events of rolling a die


  • {1, 2}
  • {1}
  • {1, 2, 3}
• If-then statement


  The hypothesis is the first, or if, part. The conclusion is the second, or then, part.
• If-then statement


  • If an angle is acute, then its measurement is between 0 degrees and 90 degrees.
• Hypothesis


  The first, or if, part of a conditional statement
• Conclusion


  The second, or then, part of a conditional statement
• Inductive Reasoning


  Conclusion is obtained by observing a pattern or doing several observations
• Deductive Reasoning


  Conclusion is based on facts such as definitions and properties
• Undefined terms


  Cannot be precisely defined (e.g. point, line, plane)
• Defined terms


  Have a formal definition (e.g. collinear points, coplanar points, subsets of a line)
• Axioms/Postulates


  Statements accepted as true without proof
• Theorems


  Statements that cannot be proven
• Point


  A position in space with no dimension, length, width, thickness, and does not occupy an area
• Line


  A straight, continuous arrangement of infinitely many points, extending infinitely in two directions with no thickness
• Plane


  A flat surface that extends infinitely along its length and width, with length and width but no thickness
• Collinear points


  Points that lie on the same line
• Non-collinear points


  Points that do not lie on the same line
• Coplanar points


  Points that lie on the same plane
• Noncoplanar points


  Points that do not lie on the same plane
• Line segment


  A line consisting of two end points
• Ray


  A part of a line with only one endpoint and extending in only one direction
• Opposite rays


  Rays with a common endpoint but extending in opposite directions
• Triangle


  • A 3-sided polygon that consists of 3 sides, vertex and angles
  • Congruent means exactly equal shape and size
  • The shape and size should remain equal, even when we flip turn or rotate the shapes
• SSS (Side Side Side)


  If three sides of a triangle are congruent to the corresponding sides of another triangle, then the two triangles are congruent
• SAS (Side Angle Side)


  Two sides and the included angle of the first triangle are congruent to the corresponding parts of the second triangle
• ASA (Angle Side Angle)


  Two angles and the included side of the first triangle are congruent to the corresponding parts of the second triangle