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/Trigonometry - Semester 1

• 2024 Chapter 1 Notes - Functions
• 2024 Chapter 2 Notes - Quadratics, Polynomials, Rational Functions
• 2024 Chapter 3 Notes - Exponential and Logarithmic Functions
• 2024 Chapter 4 Part 1 Notes - Introduction to Trigonometry and the Unit Circle
• 2024 Chapter 7 Notes - Simultaneous Equations and Inequalities, Partial Fraction Decomposition
• 2024 Chapter 10 Notes - Sequences, Series, Parametric Equations

Previous Years Teacher Notes for PreCalculus/Trigonometry

• Old Chapter 1 Examples - Mr H. Notes - Review of Algebra 2
• Old Chapter 2 Notes - Mr H. Notes - Polynomials, Rational Functions
• Old Chapter 3 Notes - Mr H. Notes - Exponential and Logarithmic Functions
• Old Chapter 4 Part 1 Notes - Mr H. Notes - Angles and Radian Measure, Arc Length, Right Angle Trigonometry, Unit Circle, Trig Functions of Any Angle
• Old Chapter 7 Notes - Mr H. Notes - Simultaneous Equations and Inequalities, Partial Fraction Decomposition
• Old Chapter 10 Notes - Mrs A. Notes - Sequences, Series, Parametric Equations
• Old Chapter 10 Notes Filled In - Mrs A. Notes Filled In - Sequences, Series, Parametric Equations

• Old Chapter 4 Part 2 Notes - Mr H. Notes - Graphs, Inverse Trig Functions, Applications, Simple Harmonic Motion
• Old Chapter 5 Notes - Mr H. Notes - Identities, Formulas, Equations
• Old Chapter 6 Notes - Mr H. Notes - Laws of Sines and Cosines, Area formulas, Vectors
• Old Chapter 6 Notes - Mrs A. Notes - Laws of Sines and Cosines, Area formulas, Vectors
• Old Chapter 9 Notes - Mr H. Notes - Conic Sections, Parametric Equations
• Old Chapter 10 Notes - Mr H. Notes - Sequences, Series, Parametric Equations
• Old Chapter 11 Notes - Mr H. Notes - Introduction to Calculus

Sample Tests, Reviews, 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; 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 - Cartesian 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

• 2024 Chapter 1 Review Problems and Solutions - Functions, domain, range, piecewise functions, composition of functions, forms of lines, graphs.
• 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.

Chapter 2

• 2025 Assignments and Solutions - secure section (requires user ID and password).

• 2024 Chapter 2 Review Problems and Solutions - Functions, domain, range, piecewise functions, composition of functions, forms of lines, graphs.
• 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.
• 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.

Chapter 3

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

Chapters 4 (Introduction to Trigonometry. For additional Sample Tests and Reviews, go to the Trigonometry page).

• 2024 Chapter 4 Part 1 Review Problems and Solutions - Introduction to Trigonometry and the Unit Circle
• 2021 Chapter 4 Part 1 Review Problems and Solutions - Angles and Radian Measure, Arc Length, Right Angle Trigonometry, Unit Circle, Trig Functions of Any Angle

Chapter 7

• 2024 Chapter 7 Review Problems and Solutions - Systems of Non-Linear Equations, Partial Fraction Decomposition and Linear Programming.
• 2022 Chapter 7 Review Problems and Solutions – Systems of Non-Linear Equations and Partial Fraction Decomposition.

Chapter 10

• 2024 Chapter 10 Review Problems and Solutions – Sequences and Series.
• 2022 Chapter 10 Review Problems and Solutions – Sequences and Series.

Semester 1 Review

• 2024 Semester 1 Review Problems and Solutions - Covers Semester 1 (Reordered) Precalculus and Trigonometry topics.
• 2021 Semester 1 Review Problems and Solutions - Covers Semester 1 Precalculus and Trigonometry topics.
• 2020 Semester 1 Cumulative Problems and Solutions - Covers Semester 1 Precalculus and Trigonometry topics. Multiple choice practice exam.
• 2021 Semester 1 Cumulative Problems and Solutions - Covers Semester 1 Precalculus and Trigonometry topics. Multiple choice practice exam.

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

• 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)

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 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 - will be revised for Spring 2025

• 2025 Semester 2 Review Problems - No solutions. Look at the solutions for 2024.
• 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.
• 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 2.4 – 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.