Math 151 Final Exam Information


Administrative Details
  • The exam will be administered Friday, 8 May from 3-5pm in HELD 113 (11:10am lecture) or Wednesday, 13 May from 8-10am in HELD 113 (12:45pm lecture). Seating assignments will be posted at least 15 minutes before official start time.
  • The exam will consist of two parts. Part I will have 11 questions (4% each) with 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 have 6 workout questions (10% each). 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 may have their picture taken and have to bring their ID by my office before I grade their exam!

    Topics Which Can Be Helpful for the Final Exam
        (NOTE: Chapter 6 material presented in its entirety)

  • Operations with Vectors (1.1)
  • Magnitude of a Vector (1.1)*
  • Unit Vectors (1.1)
  • i-j Notation (1.1)
  • Dot Product-Computational Formula (1.2)*
  • Scalar Projections (1.2)*
  • Vector Projections (1.2)*
  • Evaluating Vector Functions (1.3)
  • Eliminating the Parameter (1.3)
  • Vector Equation of a Line (1.3)*
  • Limits (2.3)
  • Continuous Functions (2.5)
  • Limits at Infinity (2.6)
  • Definition of Derivative-Scalar Function (2.7, 3.1)*
  • Derivative Rules (Power, Product, Quotient) (3.2)*
  • Slope and Equation of Tangent Line (3.2)
  • Derivatives of Trig Functions (3.4)*
  • Chain Rule (3.5)*
  • Implicit Differentiation (3.6)
  • Derivatives of Vector Functions (3.7)
  • Tangents to Vector Functions (3.7)
  • Second Derivatives (3.8)
  • Tangents to Parametrized Curves (3.9)*
  • Related Rates (3.10)
  • Derivative of ex (4.1)*
  • Properties of Exponents (4.1)*
  • Inverse Functions-Definition (4.2)
  • Derivatives of Inverse Functions (4.2)*
  • Domain of Logarithmic Functions (4.3)
  • Properties of Logarithms (4.3)*
  • Solving Exponential Equations Using Logarithms (4.3)
  • Derivative of ln x (4.4)*
  • Exponential Growth/Decay (4.5)*
  • Inverse Trig Functions (4.6)
  • Derivatives of Inverse Trig Functions (4.6)*
  • L'Hospital's Rule (4.8)
  • Absolute Extrema (5.2)
  • Extreme Value Theorem (5.2)
  • Critical Values (5.2)*
  • Local Extrema (5.2)
  • Intervals of Increasing and Decreasing (5.1, 5.3)*
  • Intervals of Concavity (5.1, 5.3)*
  • Second Derivative Test (5.3)*
  • Applied Max/Min Problems (5.5)
  • Antiderivative Rules (5.7)*
  • Specific Antiderivative Given Initial Data (5.7)
  • Sigma Notation (6.1)
  • Approximating Integrals with Riemann Sums (6.2)
  • Exact Integrals Using the Definition (6.3-given formulas)
  • Properties of Definite Integrals (6.3)
  • Computing Integrals Using Area (6.2/6.3)
  • Fundamental Theorem of Calculus (part I) (6.4)*
  • Fundamental Theorem of Calculus (part II) (6.4)*
  • Substitution (6.5)
    The above topics may occur on more than one question, and each question can cover more than one topic.

  • Approximate Breakdown of Material:
    Exam I Material: 21%
    Exam II Material: 21%
    Exam III Material: 21%
    New Material (ch 6) 37%

    Topics which will NOT appear on the Final:

  • Geometry of Vector Operations (1.1)
  • Dot Product-Definition (1.2)
  • Angle Between Vectors (1.2)
  • Orthogonal Vectors (1.2)
  • Orthogonal Complement (1.2)
  • Work (1.2)
  • Parametrized Equations of Circles/Ellipses (1.3)
  • Range Restrictions on Parametrized Curves (1.3)
  • Section 2.2 (ALL)
  • Squeeze Theorem (2.3)
  • Limits of Piecewise Functions (2.3)
  • Continuity from Left/Right (2.5)
  • Intermediate Value Theorem (2.5)
  • Horizontal Asymptotes (2.6)
  • Infinite Limits at Infinity (2.6)
  • Definition of Derivative of a Vector Function (2.7)
  • Average/Instantaneous Velocity (2.7)
  • Graph of f' Given f (3.1)
  • Finding a Tangent Line Through Another Point (3.2)
  • Section 3.3 (ALL)
  • Limits of Trig Functions (3.4)
  • Tangent Lines to Implicit Curves (3.6)
  • Orthogonal Curves/Trajectories (3.6)
  • Unit Tangent Vectors (3.7)
  • Velocity/Speed (3.7)
  • Angle of Intersection of Curves (3.7)
  • Derivatives Higher than Second Derivative (3.8)
  • Acceleration (3.8)
  • Patterns in Higher Derivatives (3.8)
  • Horizontal and Vertical Tangents to Parametric Curves (3.9)
  • Eliminating Unknown Variables (3.10)
  • Section 3.11 (ALL)
  • Section 3.12 (ALL)
  • Limits of Exponential Functions (4.1)
  • Differential Equations (4.1)
  • Showing One-to-One Function (4.2)
  • Finding Inverse Functions/Domains (4.2)
  • Solving Logarithmic Equations (4.3)
  • Limits of Logarithmic Functions (4.3)
  • Derivatives of Exp/Log in Other Bases (4.4)
  • Logarithmic Differentiation (4.4)
  • Newton's Law of Cooling and Salt Water Tank Applications (4.5)
  • Derivations of Inverse Trig Derivatives (4.6)
  • Limits of Inverse Trig Functions (4.6)
  • Graph of Function Given Graph of Derivative (5.1)
  • Sketching Graph of Function Given Information about f, f', and f'' (5.1)
  • Mean Value Theorem (5.3)
  • Inflection Points (5.3)
  • Acceleration/Velocity/Position (5.7)
  • Acceleration/Velocity/Position-Vectors (5.7)


    Resources Preparing for the Final

  • Previous Final Exams I have given:     Fall 2005*       Fall 2006     Fall 2007
        *-Missing Graph for #13
  • Read your textbook, including all Examples
  • Read your notes from lecture, including all Examples
  • Suggested Homework Problems from the textbook
  • Past Common Exams
  • Week in Review/Night Before Drill via streaming video online
  • Live Week in Review Problems done this semester

    (NOTE-I recommend looking over your old exams as a starting point. If you were unable to work a particular topic the first time and/or now, I would go back to the Resources above and work a few examples along that topic. If you were able to work a particular topic then and still can do it now, don't worry about doing much of the Homework on that topic.)

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