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Hi there,
Welcome to AP Precalculus! I’m Dr. Jason Elsinger, and I’m excited to work with you this year.
To help you start strong, I’ve prepared a summer review with practice problems and instructional videos covering the key algebra and precalculus topics you’ll need. These materials aren’t busy work—they’ll help you honestly assess your readiness and strengthen any areas that need work.
What to do:
Use the diagnostic practice set [see (1) below] to check what you remember and what you need to review. You can also review the learning outcomes for the course.
Do some reading and try some problems with answers [see (2) and (3) below].
Watch the video lessons to review prerequisite topics [see (4) below].
Visit the additional websites for further practice problems and recordings if you’d like more review [see (5) below].
Important notes:
The focus is on understanding math, not just getting the right answer. You’ll learn by showing your work and explaining your reasoning.
Assessments will require you to complete problems without using a calculator/Desmos.
All assessments will be free-response with no multiple-choice questions to develop strong problem-solving and communication skills.
If, after working through the review, you feel you’re not ready for Honors Precalculus, please reach out so we can discuss the best placement for you.
I encourage you to start now and build a solid foundation for the year ahead. I’m looking forward to seeing you in class this fall.
Best regards,
Dr. Jason Elsinger
Mathematics Instructor
C. E. Jordan High School
(1) Summer Review Problems (Start Here)
Preparing for Precalculus Summer Review Problems
This set of problems covers the following topics: combining like terms, rules of exponents, simplifying radicals, factoring techniques and factoring formulas, polynomial operations, error analysis, greatest common divisor (GCD), solving rational equations, solving quadratic equations, solving equations involving square roots, solving equations involving absolute value. This set is borrowed from The Bear Creek School.
Below is the List of Learning Outcomes for Honors Precalculus that will be available on Canvas. I also provide an example assessment for the review topics R1 - R7. This assessment displays the format, to be completed without a calculator/Desmos. In my courses, I refer to exams as a "Celebration of Knowledge."
standards Honors 2.pdfReview.pdfTo help students begin the year prepared for AP Precalculus, I strongly encourage everyone to complete the summer review packet before the first day of class. The packet is designed to refresh the prerequisite algebra, geometry, and function skills that are essential for success in the course.
As an incentive, students who complete both 1) the entire R1-R6 Practice set and 2) at least half of each section (A-D) of the Preparing for Precalculus Summer Review Problems in earnest and submit it on the first day of class will receive the following benefit:
If your final course average is a 59, 69, 79, or 89, I will round your grade up to the next letter grade—no questions asked.
This incentive is intended to reward students who make a genuine effort to prepare for the course before the school year begins. The expectation is that the packet reflects your own honest work and is completed thoughtfully rather than simply copied or rushed. I emphasize that Desmos or other calculators are not allowed in completing this work.
If, after working through the review, you still find that much of the material is unfamiliar or cannot be completed without significant assistance, I encourage you to work through the resources below, which I have tried to prioritize.
(2) Rules of Fractions, Exponents, and Placement of Parentheses
Dr. Elsinger's Review of the Rules of Fractions
Dr. Elsinger's Review of the Rules of Exponents
Dr. Elsinger's Review of the Rules of Parentheses
(3) Reading Resources
Dr. Elsinger's Handout on Functions
This packet is meant to be a Crash Course of the common types of functions studied in precalculus (it is currently a work in progress). Some of the material in this packet is not prerequisite material. To prepare for precalculus, read through the following sections carefully: 1, 2, 3, 4, 5.3, 5.4, 8.2, 8.3, 8.4.
Precalculus with Limits Text by Ron Larson
The appendices in this text is an excellent resource for review of foundational mathematical concepts. Read through pg. 891 (A1) - pg. 947 (A5).
(4) Video Resources
4a) Kahn Academy Precalculus
Unit 1: Composite and inverse functions
4b) The following videos are by Sean Fitzpatrick. It is recommended to watch and take notes.
Review - Algebra: Expanding (whole video)
Review - Algebra: Factoring Formulas (whole video)
Review - Algebra: Factoring by Grouping (whole video)
4c) Lectures from Precalculus at Fordham University (Fall 2019)
While this lecture series is for a college level precalculus course, the instructor mainly reviews high school math that will be expected in honors precalculus and beyond. I have indicated which parts of the video to focus on while the rest can be ignored.
Math 1000-R03 Lecture 0 - Class Intro (7:30 – 28:35)
Math 1000-R03 Lecture 1 - How to be good at Math; The Real Numbers; Fractions (21:00 – end)
Math 1000-R03 Lecture 3 - Domains; Interval Notation; Absolute Values; PEMDAS (whole video)
Math 1000-R03 Lecture 4 - Exponents and Radicals (whole video)
Math 1000-R03 Lecture 6 - Factor by Grouping; Factoring quadratics; ac Method (whole video)
Math 1000-R03 Lecture 14 - Lines, Quadratics, and their graphs (whole video)
Math 1000-R03 Lecture 17 - Piecewise Functions; Inverse Functions; Transformation of functions (6:30 – 41:45)
Math 1000-R03 Lecture 18 - Graphing Inverse Functions; Polynomial Long Division; More Factoring (Start – 56:30)
Math 1000-R03 Lecture 22 - Angles and Trig Functions - An Introduction (whole video)
4d) Videos by Brian Logan
Only focus on videos 2 (solve quadratics), 3 (arithmetic and algebraic operations), and 5 (rational expressions).
Get Ready For Pre Calculus in One Day
This video is 2:39:22 in length and covers a wide range of topics.
(5) Additional (Optional) Resources
1) Algebra Rules Cheat Sheet (not allowed on assessments)
2) The Big Fat Book of High School Algebra 2 (Amazon $12 as of 12/10/26)
Each chapter in this comprehensive workbook aligns with a chapter in the Algebra 2 study guide, providing students the opportunity to reinforce their Algebra 2 skills with extra in-depth practice. Each Workbook chapter begins with a brief recap of concepts and has 10-15 robust practice questions covering all the skills reviewed in each chapter.
3) More by Sean Fitzpatrick
a) Precalculus Review: Functions
4) Paul’s Online Notes: Algebra
An excellent recourse for notes, examples, and problems with solutions for all topics in algebra. You can also check out Paul's other courses!
5) Precalculus at Fordham University (Fall 2019)
Entire series: https://www.youtube.com/playlist?list=PLYoxM3oLTvxK-uD8QszitlemtP7X2g7LN
Course website: https://jhevonorg.wordpress.com/math-1000-r03-precalculus-fall-2019/
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