Chapters and sections refer to our textbook, *Intermediate
Algebra, a Modeling Approach* by Katherine Yoshiwara.

- 1st Week, Aug. 21-25. Chapter 1: Linear Models (models
based on equations of lines e.g. \(y=mx+b\), \(ax+by=c\) ),
Chapter 2 Applications of Linear Models
- 1.1 Linear Models
- 1.2 Intercepts
- 1.3 Graphs and Equations (of lines)
- 1.4 Slope
- 1.5 Equations of Lines
- 2.1 Linear Regression (estimating "best fit" line for
given data by eye).
- Supplementary material: Using a spreadsheet and its "trendline" feature to graph the line then use the "linest" spreadsheet function to obtain its equation. I used the free web-based "Google Sheets" spreadsheet (just google it to find out how to use it). There's even a free phone app for Google Sheets. Microsoft Excel or any other spreadsheet program works pretty much the same way.

- 2nd Week, Aug. 28 - Sept. 1: Chapter 2 (cont.)
- 2.2 Linear Systems (two linear equations, two
variables).
- Desmos https://www.desmos.com is a free, easy-to-use web-based calculator that solves these problems graphically. There's also a free phone app for it.
*Warning: I don't let people use Desmos on exams!!*

- Desmos https://www.desmos.com is a free, easy-to-use web-based calculator that solves these problems graphically. There's also a free phone app for it.
- 2.3 Algebraic Solutions of Systems (solution must
satisfy two linear equations).
- Wolfram Alpha http://www.wolframalpha.com is a free web-based program that solves these problems (and many others). There's also a very inexpensive phone app for it.
*Warning: I don't let people use Wolfram Alpha on exams!!*

- Wolfram Alpha http://www.wolframalpha.com is a free web-based program that solves these problems (and many others). There's also a very inexpensive phone app for it.
- 2.4 Gaussian Reduction (using elimination to solve large systems of linear equations equations). (Wolfram Alpha will solve these too, very handy!)

- 2.2 Linear Systems (two linear equations, two
variables).
- 3rd Week, Sept. 4-8. Chapter 3 Quadratic Models: (models
based on quadratic equations like \(y=ax^2+bx+c\))
**Labor Day holiday, Monday Sept. 4**- 3.1 Extraction of Roots (solving "perfect square equations" like \(2(5x+3)^2=38\), volume formulas, compound interest)
- 3.2 Intercepts, Solutions and Factors (of quadratic equations, problems involving gravity, area, etc.)

- 4th Week, Sept. 11-15. Chapter 3 (cont.)
- 3.2 (cont.)
- 3.3 Graphing Parabolas (vertex, finding maxima and minima)
- Start 3.4, 4.1 Quadratic formula, completing the square

- 5th Week, Sept. 18-22. Chapter 3 (cont.), Chapter 4
Applications of Quadratic Models
- 3.4 Completing the Square (prelude to the quadratic formula)
- 4.1 Quadratic Formula (\(x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\) solves \(ax^2+bx+c=0\))
- 4.2 The Vertex (highest or lowest point on a parabola)
- Supplementary discussion: how linear regression works (not in the text).

- 6th Week, Sept. 25-29. Chapter 4 (cont.)
- 4.4 Quadratic inequalities (solving \(ax^2+bx+c \geq 0\), \(ax^2+bx+c \lt 0\) etc.)
- Review: Chapters 1-4.
**First Midterm Exam Friday Sept. 29 (Date changed!!)**- (Skip this: 4.3 Curve Fitting -- fitting parabola to given data, quadratic regression.)

- 7th Week, Oct. 2-6. Chapter 4 (cont.), Chapter 5 Functions
and Their Graphs
- 5.1 Functions
- 5.2 Graphs of Functions ("vertical line test")

- 8th Week, Oct. 9-13. Chapter 5 (cont.)
- 5.3 Some Basic Graphs (\(y = \lvert x \rvert\), \(y=\sqrt{x}\), \(y=\sqrt[3]{x}\), \(y=1/x\), \(y=1/x^2\), etc.)
- 5.4 Variation (direct variation, inverse variation, scaling, etc.)
- 5.5 Functions as Models

- 9th Week, Oct. 16-20. Chapter 6 Powers and Roots
- 6.1 Integer Exponents (\(x^{-n}=1/x^n\), \(x^0=1\) -- when this makes sense)
- 6.2 Roots and Radicals (\(x=\sqrt[n]{y}\) solves \(y=x^n\) -- when this makes sense)
- 6.3 Rational Exponents (\(x^{1/n}=\sqrt[n]{x}\) -- when this makes sense)
- 6.4 The Distance and Midpoint Formula (distance between two points in the plane, midpoint of a line segment)

- 10th Week, Oct. 23-27. Chapter 6 (cont.), Chapter 7
Exponential Functions (for example \(y=Ae^x\) very important in
science!)
- 6.5 Working with Radicals
- 6.6 Radical Equations (solving them)
- 7.1 Exponential Growth and Decay

- 11th Week, Oct. 30 - Nov. 3. Chapter 7 (cont.)
- Notes from Monday's lecture: Exponentials and Logs.
- 7.2 Exponential Functions
- 7.3 Logarithms
- 7.4 Properties of Logarithms (key fact: \(\log(A^x)=x\log(A)\) no matter what the base of the logarithm is.)

- 12th Week, Nov. 6-10. Chapter 7 (cont.)
- 7.5 Applications of Exponential Functions and Logarithms (compound interest, growth, power laws, half-life, ... -- there are many more)
**Second Midterm Exam Wednesday Nov. 8 (Date changed!!)**Solutions**Veterans' Day Holiday Friday Nov. 10**

- 13th Week, Nov. 13-17. Chapter 7 (cont.), Chapter 8
Polynomials and Rational Functions (fractions! rational
functions are quotients of polynomials)
- 7.5 (cont.)
- 7.6 Logarithmic Scales (Richter scale, decibels, etc. log-log and semilog scales, log-linear regression)
- 8.1 Polynomial Functions
- Graphs of Polynomial Functions over Very Large and Very Small Intervals (not in the text)

- 14th Week, Nov. 20-24.
- 8.2 Algebraic Fractions (rational functions)
- Graphs of Rational Functions over Very Large and Very Small Intervals (not in the text)
- 8.3 Operations with Algebraic Fractions (addition, subtraction, multiplication, division, and so on)
**Thanksgiving Holiday Thursday, Friday Nov. 23-24**

- 15th Week, Nov. 27 - Dec. 1. Graphs, Supplementary
material, Review
- 8.4 More Operations with Algebraic Fractions (quotients of sums, quotients of differences, etc. of rational functions)
- 8.5 Equations with Fractions (equations with rational functions. In principle this is easy: clear fractions, solve a polynomial equation, check the results. But the calculations can be messy.)
- 9.1 Properties of Lines (parallel and perpendicular lines; back to the beginning!)

- 16th Week, Monday Dec. 4 only.
- Review

**Final Exam Wednesday Dec. 13 11:30am-1:30pm**