# PreCalculus

## Introduction

This page contains resources that may be of interest to students studying Pre-Calculus. The number of resources on this page will grow as additional items are developed. If you have any questions or special requests, please contact Earl at mathguy.us@gmail.com.

## Chapter Notes

#### Teacher Notes for PreCalculus

- Chapter 1 Examples - Mr H. Notes - Review of Algebra 2
- Chapter 2 Notes - Mr H. Notes - Polynomials, Rational Functions
- Chapter 3 Notes - Mr H. Notes - Exponential and Logarithmic Functions
- Chapter 4 Part 1 Notes - Mr H. Notes - Angles and Radian Measure, Arc Length, Right Angle Trigonometry, Unit Circle, Trig Functions of Any Angle
- Chapter 4 Part 2 Notes - Mr H. Notes - Graphs, Inverse Trig Functions, Applications, Simple Harmonic Motion
- Chapter 5 Notes - Mr H. Notes - Identities, Formulas, Equations
- Chapter 6 Notes - Mr H. Notes - Laws of Sines and Cosines, Area formulas, Vectors
- Chapter 6 Notes - Mrs A. Notes - Laws of Sines and Cosines, Area formulas, Vectors
- Chapter 7 Notes - Mr H. Notes - Simultaneous Equations and Inequalities, Partial Fraction Decomposition
- Chapter 9 Notes - Mr H. Notes - Conic Sections, Parametric Equations
- Chapter 10 Notes - Mr H. Notes - Sequences, Series, Parametric Equations
- 2024 Chapter 10 Notes - Mrs A. Notes - Sequences, Series, Parametric Equations
- 2024 Chapter 10 Notes Filled In - Mrs A. Notes Filled In - Sequences, Series, Parametric Equations
- Chapter 11 Notes - Mr H. Notes - Introduction to Calculus

## Sample Tests, Reviews, Alternate Assignments, and Solutions

#### Problems related to Precalculus

The value of reviewing these sample problems and solutions is twofold. The more obvious benefit relates to problems that a student has difficulty solving themselves; a solution is provided. Less obvious is the set of techniques used in our solutions; some of the techniques used on the sample problems may not be taught in the classroom. We concentrate on efficient solutions and shortcuts; so a review of the solved problems may present new techniques that enable a student to be more efficient in their approach to solving problems.

- DRHS Math Precalculus Page
- Graph paper - Catesian and Polar - Design and print your own with easy point and click. Install the program on your PC, then have at it. Defaults may work well for you, or change them as desired. After you design the graph paper, use Windows' snipping tool to copy it into your own document.

#### Chapter 1

- 2017 Chapter 1 Sample Test Problems and Solutions (by Havel) - Previous year practice test and step-by-step solutions for Quadratics, Zeros of Polynomials, and Graphing Polynomials. Includes a generalization of asymptotic curves of rational functions.
- 2024 Chapter 1 Review Problems and Solutions - Functions, domain, range, piecewise functions, composition of functions, forms of lines, graphs.

#### Chapter 2

- 2013 Chapter 2 Previous Sample Test - Problems and Solutions – 2013 practice test and step-by-step solutions for Quadratics, Zeros of Polynomials, and Graphing Polynomials. Includes a generalization of asymptotic curves of rational functions.
- 2022 Chapter 2 Sample Test Problems and Solutions (by Havel) - 2022 practice test and step-by-step solutions for Quadratics, Zeros of Polynomials, and Graphing Polynomials.
- 2024 Chapter 2 Review Problems and Solutions - Functions, domain, range, piecewise functions, composition of functions, forms of lines, graphs.

#### Chapter 3

- 2021-22 Chapter 3 Sample Test - Problems and Solutions – Practice test and step-by-step solutions for Exponents and Logarithms.
- 2024 Chapter 3 Review Problems and Solutions - Exponential and logarithmic functions, their graphs, and applications.

#### Chapters 4, 5, and 6 cover Trigonometry. For additional Sample Tests and Reviews, go to the Trigonometry page.

- 2024 Chapter 4 Part 1 Review and Solutions - Trigonometric Functions and Their Values
- 2021-22 Chapter 4 Part 2 Sample Test and Solutions - Trigonometric Functions and Analytic Trigonometry

- 2024 Chapter 5 Alternative Assignments - Analytic Trigonometry (angle addition, double angle, half angle, Trigonometric equations)
- 2024 Chapter 5 Alternative Assignments - Solutions - Analytic Trigonometry (angle addition, double angle, half angle, Trigonometric equations)

- 2021-22 Chapter 5 Sample Test and Solutions - Analytic Trigonometry (angle addition, double angle, half angle, Trigonometric equations)
- 2021-22 Chapter 6 Sample Test and Solutions - Additional Topics (Laws of Sines and Cosines, Oblique Triangles, Polar Coordinates and Forms, Vectors)

#### Semester 1 Review

- 2021-22 Semester 1 Review Problems and Solutions - Covers Semester 1 Precalculus and Trigonometry topics.
- 2020-21 Semester 1 Cumulative Problems and Solutions - Covers Semester 1 Precalculus and Trigonometry topics. Multiple choice practice exam.
- 2021-22 Semester 1 Cumulative Problems and Solutions - Covers Semester 1 Precalculus and Trigonometry topics. Multiple choice practice exam.

#### Chapter 7

- 2021-22 Chapter 7 Sample Test and Solutions – Systems of Non-Linear Equations and Partial Fraction Decomposition.

#### Chapter 9

- 2024 Chapter 9 Review Worksheet and Solutions – Conic Sections.
- Chapter 9 Companion – a subset of the Algebra Handbook that deals with Conic Sections - includes some very useful charts.

#### Chapter 10

- 2021-22 Chapter 10 Sample Test and Solutions – Sequences and Series.

#### Chapter 11

- 2021-22 Chapter 11 Part 1 Review and Solutions – Introduction to Calculus: Limits.
- 2021-22 Product Rule Worksheet and Solutions – Introduction to Calculus: Product Rule - solutions provided by Kula Software.
- 2021-22 Quotient Rule Worksheet and Solutions – Introduction to Calculus: Quotient Rule - solutions provided by Kula Software.
- 2021-22 Chapter 11 Part 2 Review and Solutions – Introduction to Calculus: Derivative Rules and their applications to polynomials.
- 2024 Chapter 11 Review and Solutions – Introduction to Calculus: Limits and Derivatives.

#### Semester 2 Review

- 2021-22 Semester 2 Review Problems and Solutions - Covers Semester 2 Precalculus and Trigonometry topics.
- 2024 Semester 2 Review Problems and Solutions - Covers Semester 2 Precalculus and Trigonometry topics. Pages 1-25 are review for the 2024 semester final. Pages 26-42 contain problems from prior Semester 2 Reviews.

## Handbooks

- Algebra and PreCalculus Handbook version 3.5 – Covers two years of Algebra and one year of Pre-Calculus.
- Trigonometry Handbook version 2.4 – Covers High School Trigonometry. Special thanks to Butterfly Hall for discovering and developing the Butterfly Method for solving the Ambiguous Triangle (Chapter 6).

- Calculus Handbook version 5.6 – Covers High School Calculus as well as additional topics that may be of interest.

For more information on the handbooks, , including download instructions, go to the Math Handbook page.

## PC Apps

- Algebra (Main) App version 0.8c – Covers topics in Algebra up to and including Pre-Calculus.
- Trigonometry App version 0.7g – Covers topics in Trigonometry.
- Probability and Statistics App version 0.7p3 – Covers topics in Probability and Statistics.

For more information on the PC Apps, including download instructions, go to the PC Apps page.

## Miscellaneous Topics

- Reflection Property of a Parabola – A 2-page description and proof that lines perpendicular to the directrix of a parabola reflect off the surface of the parabola and meet at its focus.