# 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
- Chapter 11 Notes - Mr H. Notes - Introduction to Calculus

## Sample Tests and Reviews, 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.

- 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.
- 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.
- 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.
- 2021-22 Chapter 3 Sample Test - Problems and Solutions – Practice test and step-by-step solutions for Exponents and Logarithms.

- Chapters 4, 5, and 6 cover Trigonometry. Sample tests are also on the Trigonometry page.
- 2021-22 Chapter 4 Part 1 Sample Test and Solutions - Trigonometric Functions and Analytic Trigonometry
- 2021-22 Chapter 4 Part 2 Sample Test and Solutions - Trigonometric Functions and Analytic Trigonometry
- 2021-22 Chapter 5 Sample Test and Solutions - Analytic Trigonometry (angle addition, double angle, half angle, Trigonometric equations)
- 2021-22 Semester 1 Review Problems and Solutions - Covers Semester 1 Precalculus and Trigonometry topics.
- Semester 1 Cumulative Test solutions will be posted after the test is handed in.

- 2021-22 Chapter 6 Sample Test and Solutions - Additional Topics (Laws of Sines and Cosines, Oblique Triangles, Polar Coordinates and Forms, Vectors)
- 2021-22 Chapter 7 Sample Test and Solutions – Systems of Non-Linear Equations and Partial Fraction Decomposition.
- Chapter 9 Companion – a subset of the Algebra Handbook that deals with Conic Sections - includes some very useful charts.
- Chapter 9 Test solutions will be posted after the test is handed in.
- 2021-22 Chapter 10 Sample Test and Solutions – Sequences and Series.

- 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.
- 2021-22 Semester 2 Review Problems and Solutions - Covers Semester 2 Precalculus and Trigonometry topics.

## Handbooks

- Algebra and PreCalculus Handbook version 3.5 – Covers two years of Algebra and one year of Pre-Calculus.
- Trigonometry Handbook version 2.3 – Covers High School Trigonometry.

- 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.