# 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.

## Handbooks

The Algebra Handbook covers numerous areas of study in Pre-Calculus.

- Algebra and PreCalculus Handbook version 3.3 – Covers two years of Algebra and one year of Pre-Calculus.
- Trigonometry Handbook version 2.2 – Covers High School Trigonometry.

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.

## Sample Tests and Solutions

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 2 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.
- Chapter 3 Sample Test - Problems and Solutions – NEW: 2021 practice test and step-by-step solutions for Exponents and Logarithms.
- Chapter 7 Sample Test - Problems and Solutions – 2013 Practice test and step-by-step solutions for Systems of Non-Linear Equations and Partial Fraction Decomposition.
- Chapter 9 Sample Test - Problems and Solutions – 2013 Practice test and step-by-step solutions for Conic Sections.
- Chapter 9 Companion – a subset of the Algebra Handbook that deals with Conic Sections - includes some very useful charts.