Math 151 Final Exam Information


Administrative Details
  • The exam will be administered Friday, 6 May from 3-5pm in HELD 111 (11:10am lecture) or Wednesday, 11 May from 1-3pm in HELD 111 (2:20pm 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 20 questions (2.4% each) with multiple-choice answers; mark the letter of the best choice on your exam or Scantron (provided if necessary). No work will be graded and no partial credit will be given. Part II will have 5 workout questions (8-14% 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
  • Exact Trig Ratios (App D)
  • Finding Any Trig Ratios given one (App D)
  • Operations with Vectors (1.1)
  • Displacement Vector (between points) (1.1)
  • Magnitude of a Vector (1.1)*
  • Components of a Vector Given Magnitude and Angle (1.1)
  • Dot Product (1.2)*
  • Scalar Projections (1.2)*
  • Evaluating Vector Functions (1.3)
  • Vector Equation of a Line (1.3)*
  • Left and Right hand Limits (2.2)
  • Infinite Limits (2.2)
  • Limits (2.3)
  • Continuity of Piecewise Functions (2.5)*
  • Limits at Infinity (2.6)
  • Definition of Derivative (2.7, 3.1)*
  • Graphical Interpretation of Differentiable (3.1)
  • Derivative Rules (Power, Product, Quotient) (3.2)*
  • Slope/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)
  • Tangent Vectors (3.7)
  • Higher Derivatives (3.8)
  • Patterns in Higher Derivatives (3.8)
  • Linear Approximation (3.11)*
  • Differentials (3.11)*
  • Derivative of ex (4.1)*
  • Exponential Functions as Solutions to Differential Equations (4.1)
  • Inverse Functions (4.2)
  • Properties of Logarithms (4.3)*
  • Solving Exponential Equations with Logarithms (4.3)
  • Derivative of ln x (4.4)*
  • Exponential Growth/Decay (4.5)
  • Computing Inverse Trig Functions (4.6)
  • Derivatives of Inverse Trig Functions (4.6)*
  • L'Hospital's Rule (4.8) (fraction ONLY)
  • Absolute Extrema on Closed, Bounded Interval (5.2)
  • Critical Values (5.2)*
  • Local Extrema (5.2)
  • Intervals of Increasing and Decreasing (5.1, 5.3)*
  • Intervals of Concavity (5.3)*
  • Second Derivative Test (5.3)*
  • Applied Max/Min Problems (5.5)
  • Antiderivative Rules (5.7)*
  • Approximating Integrals with Riemann Sums (6.2)
  • Midpoint Rule (6.3)
  • Computing a Definite Integral from the Definition (6.3)
  • Properties of Definite Integrals (6.3)
  • Interpreting Integrals using Area (6.3)
  • Fundamental Theorem of Calculus, part I (6.4)
  • Fundamental Theorem of Calculus (part II) (6.4)*
    • 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: 27%
    Exam II Material: 27%
    Exam III Material: 27%
    New Material (6.3, 6.4) 20%

    Topics which will NOT appear on the Final:
  • Parallel Vectors (1.1)
  • Finding Unit Vectors (1.1)
  • Geometry of Vector Operations (1.1)
  • Angle Between Vectors (1.2)
  • Vector Projections (1.2)
  • Orthogonal Complement (1.2)
  • Work (1.2)
  • Parametrized Curves (other than Lines) (1.3)
  • Eliminating the Parameter (1.3)
  • Squeeze Theorem (2.3)
  • Continuity from the Left/Right (2.5)
  • Intermediate Value Theorem (2.5)
  • Infinite Limits at Infinity (2.6)
  • Definition of Derivative of a Vector Function (2.7)
  • Graph of f' Given f (3.1)
  • Finding Tangent Lines Which Pass Through Other Points (3.2)
  • Limits of Trig Functions (3.4)
  • Orthogonal Curves/Trajectories (3.6)
  • Unit Tangent Vectors (3.7)
  • Position/Velocity/Acceleration (3.7, 3.8)
  • Angle of Intersection of Curves (3.7)
  • Section 3.9 (Slope of Tangent to Parametrized Curve)
  • Section 3.10 (Related Rates)
  • Quadratic Approximation (3.11)
  • Limits of Exponential Functions (4.1)
  • Derivatives of Inverse Functions (4.2)
  • Limits of Logarithm Functions (4.3)
  • Derivatives of Exp/Log in Other Bases (4.4)
  • Logarithmic Differentiation (4.4)
  • Limits Involving Inverse Trig Functions (4.6)
  • Derivations of Inverse Trig Derivatives (4.6)
  • Graphical Interpretation of Function/Deriv/2nd Deriv (5.1)
  • Sketching Graph of Function Given Information about f, f', and f'' (5.1)
  • Graph of f given f' (5.1)
  • Mean Value Theorem (5.3)
  • Acceleration/Velocity/Position (5.7)
  • Specific Antiderivative Given Initial Data (5.7)
  • Antiderivatives of Vector Functions (5.7)
  • Sigma Notation (6.1)


    Resources Preparing for the Final
  • Previous Final Exams I have given:     Fall 2006     Fall 2007       Fall 2008
  • Answers to said exams
  • Detailed Solutions to relevant problems to said exams
  • Office Hours: Tues 1:30-3:30pm, Wed 2-4pm OBA
  • Final Exam Review Thurs 5 May 2-4pm in HELD 111
  • Read your textbook, including all Examples
  • Read your notes from lecture, including all Examples
  • Suggested Homework Problems from the textbook
  • Online HW
  • Past Common Exams for Math 151
  • Math 151 Week in Review (live from this semester) ("NBD" Tuesday 3 May 7-9pm BLOC 166)
  • Week in Review (video from Fall 2006).

    (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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