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.

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.