Curve sketching is an important application of derivatives. Here’s an example with a polynomial, with pictures to help assist understanding:

## Precalculus Resources: Spring 2017 Midterm II Review

I have gathered quizzes that relate directly to the upcoming midterm, as well as included a sample midterm. Please feel free to use these for practice! If you have trouble with the material, visit this page for additional resources. Don’t forget to grab a free version of wolfram alpha pro to help you if you’re enrolled at San Francisco State University!

## Topics Covered:

- 2.4: Polynomials
- Vertex of a parabola
- Determine the behavior of a polynomial near or

- 2.5: Rational Functions
- Determine the behavior of rational functions near to
- Determine the vertical and horizontal asymptotes of a rational function
- Determine the holes of a rational function, if they exist.

- 3.1: Exponential and Logarithmic Functions
- Their definitions as inverses
- Practice using #23 – #32 in
*Precalculus – Prelude to Calculus, 3rd Ed.*

- 3.2: Power Rule
- Change of Base

- 3.3: Product and Quotient Rule
- Read p.249-p.252 for applications in scientific settings

- 3.4: Exponential Growth
- Compound Interest (
*n*times per year)

- Compound Interest (
- 3.5:
*e*and the Natural Logarithm- Understanding the definition of
*e*will enhance your understanding of proofs later on. For now, we know it’s a real number that is approximately equal to 2.71, and it’s associated with Continuous growth!

- Understanding the definition of
- 3.7: Exponential Growth Revisited
- Read p.304-p.306 for an application of the approximation methods discussed in 3.6 used in financial estimations.
- Focus on Continuous Compound Interest

- 4.1: Unit Circle
- 4.2: Radians
- Make sure you can convert between degrees and radians.

- 4.3: Sine and Cosine
- Definition using unit Circle
- Domain and Range of Sine & Cosine
- If you want a challenge, try answering #45 from this section.

## Quiz 5:

## Review for 2.4 & 2.5

## Khan Academy Videos:

## Reflection: Planning/Time Management

### As a Teacher

- Pre-Calculus
- Lesson Planning is taking a lot less time this time around, since I spent a lot of time documenting the lessons from last year. Over-planning was actually an issue last semeseter; I would never actually complete everything I planned, and that was mildly frustrating. Also, there’s an element of improvisation that happens depending on the mood of the classroom, which means that scripting every sentence is simply not possible anyway.

- Calculus II
- The first two weeks I only prepared by rereading the text on the sections that the lead professor went over, but on the second week students asked me questions that definitely stomped me because I had not seen the problem before hand. Now, I ask students to email me their questions before the TA session, so that I can prepare with care. Planning short lectures on Calculus II material has been easier after that change in preparation, especially with access to great tools.

### As a Student

- Algebra
- I’m really glad to be practicing with SAGE, but I’ve honed in on specific problems and end up spending significant time cleaning up code instead of doing proofs. I need to find a balance in what I’m focusing on when learning.

- Real Analysis II
- I should really be spending more time on this course. The lectures in this cource has been a blessing for preparing for Calculus II TA sessions, since it helps get me into the “mood” to do Calculus. 🙂

- Combinatorics
- Obsessing over the details in this class takes too long. I’m in a similar situation with Algebra, but there’s this one is more like I spend 4-5 hours on one proof and run out of time for the other problems.

There’s a lot of juggling, and I have to get better at this soon before the midterm season.

## Precalculus Resources: Spring 2017 Midterm I Review (Section 0.1 – 2.2)

I have gathered quizzes that relate directly to the upcoming midterm, as well as included a sample midterm. Please feel free to use these for practice! If you have trouble with the material, visit this page for additional resources. Don’t forget to grab a free version of wolfram alpha pro to help you if you’re enrolled at San Francisco State University!

## Quizzes #1 – #4:

## Practice Midterm:

## San Francisco State University Math Resources: Mathematica & Wolfram Alpha Pro

SF State has a site license for Mathematica. Under this site license, Mathematica can be installed without further cost on any computer owned by San Francisco State University, by SF State faculty, or by SF State students. This software works on Windows, Macintosh, and Unix.

Under the terms of the site license negotiated by CSU, free WolframAlpha Pro accounts are also now available to our faculty, students, and staff.

If you are an SFSU student, click here for a free WolframAlpha Pro account.

### Mathematica

If you are a SFSU student and you want to download the *Mathematica* software to your computers, then follow the instructions below:

- Create an account
*(New users only)*:- Go to user.wolfram.com and click “Create Account”
- Fill out form using a @sfsu.edu email, and click “Create Wolfram ID”
- Check your email and click the link to validate your Wolfram ID

- Request the download and key:
- Fill out this form to request an Activation Key
- Click the “Product Summary page” link to access your license
- Click “Get Downloads” and select “Download” next to your platform
- Run the installer on your machine, and enter Activation Key at prompt

For both *Mathematica* and WolframAlpha Pro requests on the links above, **it is important that only sfsu.edu email addresses be used.** Requests from other email addresses will be rejected.

## Reflection- Group Work: Size & Clarity

I’m wondering how group activities can be done with 40+ students; I often give short, paired activities during lecture, which (hopefully) helps with engagement, but if I want to give a longer “exploration” activity in class, there are challenges.

### Group Size

Checking in with each group is takes a significant amount of time, scaling linearly. I tried to keep group size to 3-4 students, but dividing students into groups of 4-5 lead to having about 8-10 groups. The down time caused some groups to finish faster than others. There must be an optimal ratio for the number of students to square foot of classroom. I currently have 40 students, but the rooms are a lot smaller than the previous semester, I must alter the group activity plans. I also had 80 minutes sessions on Tues/Thurs instead of 50 and a much larger classroom for discussions/group work in the 4th hour. My lesson plans will require more adjustments, I suspect.

Some groups had members forging ahead before everyone understood, and that’s always a challenge as well. I wonder if larger groups are a good idea, because conversations between more than 5 students often turn to a few pairs and few solo working in parallel…

### Clarity: Instruction and Feedback

This time around, when I lead the group activity I focused on the clarity of my instructions, and I’m trying a different approach this semester compared to last. Previously, I gave handouts with specific procedure, but it was confusing for some students. This time, I tried a different approach, where I verbally and visually give instructions on the board and forgo all printed handouts in order to allow for students to make their own notes instead of using data sheets. I think I might bring back the data sheet for the later activities, so that the students can know what I specifically expect from them. I should specify that students should use technology to assist in graphing and calculations.

In terms of feedback, I tried to ask questions and check for understanding, but the number of groups is high, which means I must spend less time per group, or make the group size larger. If I maintain that the groups have no more than 5 people, then I will have at least 8 groups – which can cause my feedback to the students to be less precise and more brief. Perhaps I can take a vote with my students, to see if they prefer trying larger groups, given the challenges above?

Looking back, I admire my high school teachers who managed to deal with 30 students at a time, and were able to conduct experiments in labs, with open flames, too.

## Reflection: Following My Passions

When I was in my late teens to early twenties, I knew I liked math but I wanted to try everything that would require application of math: I jumped from applied math to physics to engineering. I loved the process of learning, and I took a lot of different classes, and by the time I was halfway through the second semester of Mechanical Engineering courses, I finally realized that I was only really interested in the math, and talking about the math.

Then today, I went digging through my time-capsules on the internet. I have blogs scattered across a lot of different platforms, and I found this post over on Hubpages that I wrote in 2009. I’m pretty sure this reaffirms that I’ve always wanted to teach math.

Looking back, I’m glad that I took a long, winding path. I needed to grow a lot spiritually and emotionally before I was ready to take on teaching. Hopefully I’ll maintain my capacity for growth in the upcoming years.

## Teacher Evaluations & Reflection, Fall 2016

Teacher Evaluations are out at SFSU. 😀

From my students’ responses, I learned that I can improve in the following ways:

- Plan what I will write on the board in more detail instead of such a rough sketch,
- “Don’t let nerves cause mistakes” – definitely happened 2-3 times where I did a problem incorrectly because I tried to wing it on the board…
- More intensive examples that can tie different concepts together before the midterm (where they do see synthesized word problems),
- On Universal Design:
- Group work that involve manipulatives, geared for kinesthetic/tactile learners,
- Audio / Visual learners balance – I tend to write a conclusion and verbally say a paragraph of explanations.

- On Long Term Planning:
- More group work for inverse trig functions and beyond,
- Maybe building a story that can be used for the concept questions during class?
- Manage expectations earlier – students will need to work and figure out a lot of stuff on their own,
- Create systems that can help students organize all the information – give suggestions on how to take notes, maybe?
- Give more time to do Chapters 4-6, Trigonometry chapters of the book.

- On Class Policy:
- Attendance and participation should be recorded more in detail,
- Be better about grading and returning stuff promptly – I definitely procrastinate on handing back quizzes sometimes. (No one complained about this but I still feel bad about it.)

Looking forward to teaching next semester! I will teach one class of precalculus and TA one section of Calc II. I wonder how different TA’ing for Calculus II will feel. 🙂

## Why a Blog?

So, why start a blog when there is approximately… posts created per day? (Checked @ 8 AM 1/8/17)

For me, this website is a bit more than a collection of math notes and lists of resources. I am aiming to chronicle the challenges of being a student and a teacher at the same time. On the other hand, I want to also document the most fun parts of being in an intensive graduate program!

So this blog will be part survival guide, part chicken-soup-for-the-soul, and part scrapbook.

Oh. By the way, I survived the first semester of graduate school!