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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.

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

Collingwood 44

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

Collingwood 45

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

Collingwood 46

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

Collingwood 47

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

Collingwood 48

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

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

Collingwood 51

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.

Homework 4.

Chapters 15-18: Trigonometry

Machine Learning unit. Genetic optimization, principles of learning.

Homework 8