Test 3 Study Guide: 9.4, 9.5, 10.1, 10.2, 10.3, 10.4, 11.1, 11.2, 11.3, 11.4, Applications, test 1 and test 2 material and related material from prior classes

At the Test

  • NO calculators will be allowed.
  • I'll bring scratch paper. Ask me if you need more.
  • I will staple a copy of the series theorems sheet and the Algebra, Geometry, Trigonometry and Derivative Review to your test.
  • You may make yourself a cheat sheet on the small card I hand out (additional cards are on my door if you need to rewrite it). The reference card must be handwritten. Think of the card as a way to include some important examples or concepts that you aren't as comfortable with. You won't have room for everything, and you should try to internalize as much as you can.
  • You may have out food, hydration, ear plugs, or similar if they will help you (however any ear plugs must be stand alone--no cell phone, internet or other technological connections)
  • Your grade will be based on the quality of your responses in a timed environment. All tests must be turned in when class ends.
  • The test will have more pages than test 1 and test 2. You may use the entire time period or you may leave if you are finished early.

    Topics to Study

  • This test will cover sections 7.1, 7.2, 7.4, 7.5, 7.6, 8.1, 8.2, 8.4 (density only), 8.5 (work only), 9.1, 9.2 and 9.3, 9.4, 9.5, 10.1, 10.2, 10.3, 10.4, 11.1, 11.2, 11.3, 11.4, applications, as well as related material from prior classes.
  • This test is comprehensive, although there will be more problems from newer material than from previous material. Approximately 1/3 of the material will be from Chapters 7 and 8, and 2/3 from 9,10 and 11. I will separate the test into a section that has material from Chapters 7 and 8, and then another section that has material from Chapters 9, 10 and 11.
  • Questions will be the same (or very similar) to those you have seen before from class notes, homework, quizzes 1-12, test 1 and test 2, group work or clicker questions. The class highlights page shows our day-to-day activities.
  • Detailed solutions to part 2 of Wiley practice are on ASULearn.
  • Online Test 3 Practice Problems (optional) are up on Wileyplus, and the Test 1 and Test 2 Practice Problems (optional) remain available too.

    The new material since test 2 includes more series tests (see the series theorems sheet), radius or interval of convergence of a power series or Taylor series, Taylor polynomials and series, finding new series from known ones, the error bound formula, whether a function solves a differential equation, finding a particular solution with an initial condition, slope fields and equilibrium points, Euler's method, separation of variables, and setting up differential equations related to real-life applications. Test 2 topics included length and arc length, areas and volumes by slicing, volume by surface of revolution, density, work, sequences, geometric series and series in 9.3 including partial sums and the integral test. Test 1 material included integrals from calc 1 such as the FTC on a known derivative, and splitting up a numerator into its sums, as well as substitution, parts, partial fractions, trig sub, improper integrals, and numerical integration.

    Test Instructions

    See instructions on prior tests and quizzes. The vast majority of the exam will be phrased like those. Here are a few additional big picture types of questions, to help you make connections:
  • One of the four main educational goals at Appalachian is local to global perspectives, and it is also a theme in Calculus II. Discuss one of the following in this context where assembling a whole (global) from pieces (local) was important:
    numerical integration via rectangles
    area between two curves via rectangles
    volume by cylindrical disk or rectangular box slices
    total work via the work for each slice = force for each slice x displacement of that slice
    series diverges when sequence terms do not get smaller
    slope fields in DEs
  • Another theme in Calculus II and Analytic Geometry is in understanding infinity. Discuss ____ in this context. For example, the blank could be topics like improper integrals that give finite area OR the harmonic series OR population growth in DEs, just to name a few.
  • Another theme in Calculus II and Analytic Geometry is approximation. Discuss ____ in this context. For example, the blank could be topics like numerical integration OR Taylor series OR Euler's method, just to name a few.