Worksheet Wednesday - Calculus Quizzes Part I

This week I'll be sharing a few quizzes from my 5-credit Calculus I course that meets three days a week. I have students complete a daily quiz that contains fairly simple questions about the material covered in the previous lecture. My intent is to make sure students put in time daily to practice the material and struggle with concepts in the course. So far it has worked fairly well, students seem more capable this term, they understand the expectations I have of them, and their performance on tests is exceptional. I will be doing some rudimentary comparisons of this class with my previous Calc I, so stay tuned for that.

Below are quizzes for a few of the first sections from Stewart's Calculus: Concepts and Contexts 4th edition. We don't cover epsilon delta arguments so a few of the limit questions may seem a bit rudimentary, and in reality they are. I feel uncomfortable asking students to do a lot with limits since we don't cover what is 'really' going on. Then again can we teach it at this level?

Quiz 1 - Review - In this quiz I have them do a few things they should know how to do that are pre-skills for the course; finding the slope of a line, finding the equation of a line that goes through two points, and finding a parallel line.

Quiz 5 - Continuity -

Quiz 6 - Miscellaneous -

Quiz 8 - Definition of a Derivative -

If you have any feedback, or you use them in your class modified or not, please post a comment below! You can also email me at robert dot weston dot 82 at gmail dot com. Thank you for reading!

Worksheet Wednesdays - Complex Numbers, Power Series, and Taylor Series, oh my!

For this week I have another twofer, two in-class activities dealing with complex numbers, power series, and Taylor series.

Complex Numbers and Power Series - Students were introduced to some of the properties of complex numbers, and the first page of this activity has them explore operations and graphs on the complex plane. The second page has students identify the radius of convergence of given power series, with a little analysis of the coefficients on the third page. The last two pages have students graph partial sums of power series, with a hint as to what they approximate.

Taylor Series - In this activity students are given two different functions and are asked to analyze their power series about different points, and look at a very special relationship. The first function is a simple rational function, the second being the exponential function. Students are asked to numerically compare Taylor Polynomial Approximations of the rational function centered at different points, and are asked to provide a basic comparison of the approximations of the exponential function as well. The last page walks students through a derivation of Euler's Identity. For the most part students were pretty impressed with the identity, with the exception of the student asking "Is this going to be on the test?" right after the derivation.

Worksheet Wednesdays - Sequences and Series In-Class Activities

This is the inaugural post of Worksheet Wednesdays where I will post some of the worksheets, in-class activities, quizzes, and other assessment items I have develop in teaching college mathematics courses. Today will be a twofer, two in-class activities for my Calculus III course.

I have students start in-class activities during class, but they are free to complete them afterwards. In order to receive credit for completing them I have them show it to me before the next test. When they do I usually go over it with them, providing for some 1-on-1 feedback and developing a repertoire with them. So far this has worked out well for three of my classes, but as I write this it is only Week 2 so that may change. Anyway, on to the worksheets!

Monotonic and Bounded - This activity walks students through a variety of sequences and introduces the idea of monotonic and bounded sequences. They then classify each of those sequences as monotonic and bounded and then see if these sequences are convergent. Students should identify the pattern that all sequences that are monotonic and bounded are convergent, but it is not necessary for a convergent sequence to be monotonic or bounded.

Integral Test - From lecture it was clear that students' integration skills were a bit rusty, if not a bit poor. Thus I created this in-class activity to get students to practice their indefinite, definite, and improper integration skills, and to use the integral test of convergence of a series. There are a few curve balls, and we had a good discussion of how to deal with them.

If you have any feedback, or if you use these worksheets, let me know! Feel free to post a comment below, or email me directly.