# Pre-Calculus, Fall 2013

## Math 1060, Section W31

### Office Hours (312 Waterbury):

• Tuesday and Thursday from 12:00-1:00pm
• Friday from 11:15am-12:30pm

If none of these times, let me know and we will find a time that does!

### Important Resources

• The Syllabus for Math 1060. This is your source for course pacing, book problems, and some helpful hints on group work and calculators.
• You can find your assignment grades using HuskyCT. Just go to our section's page, and click the link for "My Grades" on the left.
• Some suggestions and resources for reviewing algebra.
• A Microsoft Excel spreadsheet that you can use to understand what final grades are possible given your current grades. If you plug in your own personal current grades for the different categories, you can see what grades are possible based on your final exam score. By trying out different possible future quiz averages, exam scores, etc., you can get a better sense of what your final grade might look like.

### Class Summary and Handouts

Class 27: Final Exam Review
We spent today's class working on the "Inverses Review" outline and worksheet. But please remember that Final Exam will be cumulative. You can use the outlines, worksheets, and exams to review the matieral for Exams I and II.

Class 26: Exponential Growth and Decay (Class Notes)
Mathematics gives us a powerful language for discussing the world around us. Using what we know about exponentials and logarithms, we can create and use two of the most common mathematical models: exponential growth and decay.

Class 25: Solving Equations with Exponentials and Logarithms (Class Notes)
We first reviewed the most important properties of logarithms from last time, and used the inverse property of logs to solve exponential equations. We then introduced the three "Laws of Logarithms", and used them to help us solve more tricky exponential equations.

Class 24: Logarithmic Functions (Class Notes)
We briefly reviewed the properties and graphs of exponential functions. We then defined our most important inverses: the logarithmic functions. We studied the graphs of logarithms, and how to compute logarithms of different numbers.

Class 23: Inverse Trig Functions (Class Notes)
Because trigonometric functions are periodic, there is no way to invert the whole function. We discussed how, by restricing the domain, we can invert a part of each trigonometric function. We graphed these inverse functions, and saw how to compute their values for different inputs.

Class 22: Inverse Functions (Class Notes)
The inverse of f is a function that "undoes" f. We discussed what types of functions have inverses, how to compute the inverse point-by-point, and how to algebraically find the inverse of (some) functions.

Class 19: Trig Identities - Part II (Class Notes)
We finished the material from last time, introducing the last few trigonometric formulas. We breifly reviewed "verifying" trigonometric identities, and spent the rest of our time talking about "solving trigonometric equations."

Class 18: Trig Identities - Part I (Class Notes)
We introduced most of the important trigonometric formulas. We used the trigonometric identities in two ways: to compute things like sin(pi/12) and to "verify" trigonmetric identities. You can find a handout summarizing our trig formulas here.

Class 17: Other Trig Functions (Class Notes)

Class 16: Graphing Sine and Cosine (Class Notes)
You can find a worksheet for practicing graphing sine and cosine here. You can check your work using a graphing calculator.

Class 15: Sine and Cosine (Class Notes)
Today, we extend the definition of sine and cosine to all angles. The idea is simple: by drawing the right picture and asking the right questions, we can use triangle trigonometry to find sine and cosine of any angle.

Class 14: Right Angle Trigonometry (Class Notes)
In calculus, we will work with the sine and cosine of all angles. But first, we review trigonometry with triangles.

Class 13: Measuring Angles (Class Notes)
Trigonometry begins with defining and understanding "angles". Radians are the standard angle measurement in mathematics, so our emphasis is on translating our understanding of "degrees" and "amount of rotation" into radian angle measure. We also learned how to use radian measure to find the length of an arc swept out by an angle.
You can practice angles using the day's worksheet. Also begin studying the common angles and the points on the unit circle.

Class 11: Polynomial division and Exam I review (Class Notes)
For the first part of class, we saw how to apply the tool of long division to simplify fractions of polynomials.
Then we worked on the Exam Review Worksheet for the rest of class.

Class 10: Sketching Rational Functions (Class Notes)
We studied two ways to sketch the graph of a rational functions (fractions of polynomials).

Class 9: Sketching Polynomials (Class Notes)
We looked at a few tricks for sketching the graph of a higher degree polynomial.
Quiz #4 and Solutions

Class 8: Combining Functions II (Class Notes)
We covered compositions of functions (including the second page of the Combining Functions handout, and finding the domain of a more complex function). We also quickly defined "inverses", defining log_a(x) to be the function that undoes a^x, and we sketched the graph of log_a(x).
For more practice, do the Combinations of Functions Worksheet (from Storrs).

Class 7: Common Functions II and Combining Functions I (Class Notes)
We covered graphing absolute value and exponential functions (using the same graph transformation tricks as before).
We also covered the first page of the Combining Functions handout.
Quiz #3 and Solutions

Class 6: Quadratic Functions II and Common Functions I (Class Notes)
Completing the square Worksheet (from Storrs) and Partial Solutions

Class 5: Linear Functions and Quadratic Functions I (Class Notes)
An old way to complete the square.
Quiz #2 and Solutions

Class 4: Functions II (Class Notes)
Functions Worksheet (from Storrs) and Solutions

Class 3: Absolute values and Functions 1 (Class Notes Part 1 and Part 2)
Quiz #1 and Solutions

Class 2: Solving Complicated Inequalities (Class Notes)

Class 1: Algebra Review
Algebra Review Worksheets (from Storrs) and Solutions

### Interactive Worksheets:

• A html worksheet exploring general exponential functions. This was created using a free and open source computer algebra system called Sage.
You can modify and run the worksheet "cells" using this free online Sage "Cell Server". Just replace the text in the box with the command you want to run and click "Evaluate".