# Mathematics Notes

Reese Johnston, *Precalculus*

## Collingwood Homeworks

*Collingwood textbook is available here. Solutions may or may not be correct. In Winter and Spring quarters (chapter 8 and onward) there is only one Collingwood per chapter.*

Chapter 1: “Warming Up”. Rates, times, and distances; the modeling process.

Chapter 2: “Imposing Coordinates”. Creating coordinate systems, parametric equations.

Chapter 3: “Three Simple Curves”. Vertical lines, horizontal lines, and circles.

Chapter 4: “Linear Modeling”. Forms of lines, perpendicular and parallel lines.

Chapter 5: “Functions and Graphs”. Definitions, graphs, and manipulations of functions.

Chapter 6: “Graphical Analysis.” Modelling and working with piecewise functions.

Chapter 7: “Quadratic Modelling.” Working with quadratic functions.

- Collingwood 30
- Collingwood 31
- Collingwood 32
- Collingwood 33
- Collingwood 34
- Collingwood 35
- Collingwood 36
- Collingwood 37
- Collingwood 38
- Collingwood 39

Chapter 8: “Composition.” Working with composited functions.

Chapter 9: “Inverse functions.” Finding inverse functions and inverted domains and ranges.

Chapter 10: “Exponential Functions.” Manipulating exponentials with exponent rules.

Chapter 11: “Exponential Modeling.” Constructing exponential models.

Chapter 12: “Logarithmic Functions.” Working with logarithms.

Chapter 13: “Three Construction Tools.” Reflections, dilations, and translations.

Chapter 14: “Rational Functions.” Constructing and modeling rational functions.

Statistics unit.

- Homework 1. Means, quartiles, standard deviation, and confidence intervals.
- Homework 2. Linear regression, RMSE, R2 and Adjusted R2, F-tests.
- Homework 3. Pearson correlation, linear modeling, confidence intervals, F-tests.

Game Theory unit. *Game theory frameworks, strategies, Nash equilibria.*

Chapters 15-18: Trigonometry

Machine Learning unit. *Genetic optimization, principles of learning.*