Study Guide for Exam I



Administrative Details
  • The exam is Thursday, 19 Feb from 7:30-9:30pm in room HELD 100. Seating charts will be posted by 7:15pm outside the doors.
        (NOTE: REQUESTS FOR LEFT-HANDED SEATS MUST BE MADE NO LATER THAN 5PM FRIDAY, 13 FEB. NO CHANGES WILL BE ALLOWED THE NIGHT OF THE EXAM!)
  • The exam will consist of two parts. Part I will have multiple-choice answers; mark the letter of the best choice on your Scantron. No work will be graded and no partial credit will be given. Part II will consist of workout problems. All answers must be justified with appropriate algebraic work. Partial credit will be given for appropriate work shown.
  • Calculators are not allowed at any time on the exam.
  • Bring: Writing Utensil, Picture ID
    Students without a picture ID will have to bring a picture ID to my office and sign a document allowing them to pick up their exam and have the grade recorded!

    Summary of Topics 1.1-3.3 (asterisks indicate key formulas, theorems, or definitions to know)

  • Vectors and Points
  • Length of a Vector (Magnitude)*
  • Unit Vectors
  • Vector Addition (and Geometry)
  • Scalar Multiplication (and Geometry)
  • Vector Subtraction (and Geometry)
  • i-j Notation

  • Dot Product-definition*
  • Dot Product-computational formula*
  • Angle Between Vectors*
  • Orthogonal Vectors
  • Scalar Projections*
  • Vector Projections*
  • Work*
  • Orthogonal Complements

  • Vector-Valued Functions and Parametrized Curves
  • Vector and Parametric Representations of a Line*
  • Parametrized Equations of Circles/Ellipses
  • Converting Between Vector and Parametric Equations (Eliminating the Parameter)
  • Range Restrictions on Parametrized Curve

  • Concept of a Limit
  • Left- and Right-Hand Limits
  • Vertical Asymptotes
  • Limit of a Vector Function (By components)

  • Computing Limits Algebraically
  • Squeeze Theorem*
  • Limits of Piecewise Functions

  • Continuity at x=a*
  • Continuity from Left/Right
  • Continuity of Polynomials/Rational Functions
  • Intermediate Value Theorem*

  • Limits at Infinity
  • Horizontal Asymptotes
  • Infinite Limits at Infinity (Polynomials)

  • Slopes of Tangent Lines (limit x -> a)*
  • Slopes of Tangent Lines (limit h -> 0)*
  • Tangents of Vector Functions
  • Average/Instantaneous Velocity

  • Definition of Derivative*
  • Differentiability
  • Graphical Interpretation of Differentiable
  • Graph of Derivative given graph of a Function

  • Power Rule*
  • Product Rule*
  • Quotient Rule*
  • Finding the Equation of a Tangent Line
  • Finding a Tangent Line Through Another Point

  • Rates of Change
  • Position->Velocity

    Suggestions for Studying:

  • Read your textbook, including all Examples
  • Read your notes from lecture, including all Examples
  • Suggested Homework Problems
  • Past 151 Common Exams (NOTE: Answers to Fall 2003 available Mon, 16 Feb and Spring 2003 available Wed, 18 Feb)
  • Week in Review/Night Before Drill via streaming video online
  • Live Week in Reviews Sunday (15 Feb) 4-6pm AND Wednesday (18 Feb) 7-9pm in BLOC 102

    • Return to David Manuel's Math 151 Homepage


    Return to Calclab Homepage