Test 3 Study Guide

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 reference notes 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 exam is cumulative so it will have more pages than exam 1 and exam 2. You may use the entire time period or you may leave early if you are finished early.

Topics to Study

This exam 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.

Many questions will be the same (or very similar) to those you have seen before from class notes, homework, quizzes 1-9, 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, and I'll also post "ready for prime time" videos there too.

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.

Material from previous classes includes slope directions, the tangent line, above or below the x-axis via the sign of the function value, increasing or decreasing via the sign of the first derivative, concave up or down via the sign of the second derivative, graphs of functions, left and right sums, limits, L'Hopitals rule, divide by the highest term in limits, and earlier sequences and series from middle or high school.
series convergence convergence tests slides and clickers, review slides and clickers, Group Work Target Practice, 9.4 Group Work solutions
power series slides and clickers, 9.5 group sols
Taylor polynomials and series, calculations and convergence slides and clickers, animation, Taylor in Maple Solutions, 10.2 solutions
new Taylor series from old, error bounds slides and clickers, finding and using Taylor series practice, 10.3 group work sols, Taylor Polynomial Error Bounds in Maple solutions 10.4 solutions
testing a DE, slope fields, equilibrium, stability, Euler's method, separation of variables slides and clickers, 11.1 sols, slope field practice, (solutions are in the slides), Maple worksheet solutions, Euler and separation of variable solutions.
applications of des, setting up from real-life scenarios slides, group work target practice, solutions

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.

review handout
Material from previous classes includes graphs of functions, Riemann sums, limits, L'Hopitals rule, divide by the highest term in limits, Pythagorean theorem, similarity of triangles, area of a circle, area of a rectangle, volume of a box and cylinder, and earlier sequences and series from middle or high school.
areas and volumes by slicing 8.1 slides and clicker, practice sheet for area, practice sheet for volume, and group work solutions
volume by surface of revolution and arc length 8.2 slides and clicker, practice sheet, solutions to part 2 of Wiley practice are on ASULearn (like they are for all the sections)
density 8.4 slides and clicker, traffic density, and work 8.5 slides and clicker, practice sheet, and group work solutions
sequences 9.1 slides and clickers, intro in Maple, and geometric series 9.2 slides and clickers
series in 9.3 including partial sums, series divergence when terms not getting smaller, linearity arguments, and the integral test slides and clickers, practice sheet, integral test group work target practice, group work solutions, geometric series versus p-series

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.

review handout
substitution slides and clickers, and solutions to group target practice
parts slides and clickers, and solutions to group target practice
partial fractions slides and clickers, and solutions to group target practice
trigonometric substitution slides and clickers, primer, and solutions to group target practice
improper integrals slides and clickers, group target practice, solutions to group target practice
numerical integration slides and clicker, and group target practice, solutions to group target practice, sample questions
algebra missteps

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.