Mathematics & Statistics
Texas Tech University
Kent Pearce

Department of Mathematics and Statistics
Texas Tech University
Lubbock, Texas 79409-1042
Voice: (806)742-2566 x 226
FAX: (806)742-1112
Email: kent.pearce@ttu.edu

Math 1350
Analytical Geometry
Fall 2014
Riddle
Analytical Geometry
Brooks/Cole

Review Exam I

Section Content      Suggested Problems
Section 1.1
  • Cartesian Plane
    • Coordinates
      • x coordinate; abscissa
      • y coordinate; ordinate
    • Quadrants
 
Section 1.2
  • Distance Formula
  • Applications
    • Determine whether three points form the vertices of a right triange
    • Determine whether three points are co-linear
    • Determine whether four points form the vertices of a parallelogram
    • Determine whether four points form the vertices of a rhombus
    • Determine whether four points form the vertices of a rectangle
Page 9: 5, 9, 15, 19, 23, 25
Section 1.3
  • Point of Division Formulas
  • Mid-point Formula
Page 18: 3, 9, 15, 21, 23
Section 1.4
  • Inclination and Slope
  • Slope formula
  • Special Cases
    • Slope of a horizontal line
    • Slope of a vertical line
 
Section 1.5
  • Parallel and Perpendicular Lines
  • Criteria for two non-vertical lines to be parallel
    • Slopes are equal
  • Criteria for two lines to be parallel if one of them is a vertical line
  • Criteria for two non-vertical lines to be perpendicular
    • Slopes are negative reciprocals
  • Criteria for two lines to be perpendicular if one of them is a vertical line
  • Applications
    • Determine whether three points form the vertices of a right triange
    • Determine whether three points are co-linear
    • Determine whether four points form the vertices of a parallelogram
    • Determine whether four points form the vertices of a rhombus
    • Determine whether four points form the vertices of a rectangle
    • Determine whether two lines are parallel, co-incident, perpendicular or none of the above
Page 28: 1, 3, 5, 11, 15, 19, 25, 30
Section 1.6
  • Angle from One Line to Another
  • Formula for the tangent of the angle between two non-vertical lines
  • Given two non-vertical lines find the slope of the line which bisects the angle between the two lines
Page 35: 3, 9, 17
Section 1.7
  • Graphs of Equations
  • Points of Intersections of Graphs of Equations
  • Function
    • Domain
    • Range
Page 42: 3, 6, 9, 13, 17, 21, 25, 31
Section 2.1
  • Directed Line Segment
  • Vector
    • Representative
  • Geometric definition of the sum of two vectors
    • Parallelogram law for sum of two vectors
  • Geometric definition of the difference of two vectors
  • Length of a vector
  • Geometric definition of a scalar multiple of a vector
  • Theorem 2.2 Algebraic properties of sum, difference and scalar multiples of vectors
  • Geometric definition of a unit vectors
  • Standard basis vectors
  • Theorem 2.3 Every vector can be written (as a unique) sum of scalar multiples of the standard basis vectors
    • Components of a vector
  • Algebraic rule for the sum of two vectors (in terms of components)
  • Algebraic rule for the scalar multiple of a vector (in terms of components)
  • Algebraic rule for the length of a vector
Page 60: 1, 3, 23, 25, 39, 41
Section 2.2
  • Dot Product
  • Theorem 2.6 Algebraic properties of dot product
  • Angle between two non-zero vectors
  • Theorem 2.7 Relationship between dot product and the angle between two vectors
  • Theorem 2.8 Two non-zero vectors are perpendicular if and only if their dot product is zero
  • Projection of a vector u onto a vector v
Page 69: 1, 9, 13, 17, 21, 29






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Last modified on: Monday, 10-Aug-2015 12:18:41 CDT