precalculus

• BARRON'S is the TRUSTED NAME IN TEST PREP
• This book is for the 2024 AP Precalculus exam
• AP


  Advanced Placement
• AP® is a registered trademark of the College Board, which is not affiliated with Barron's and was not involved in the production of, and does not endorse, this product
• © Copyright 2023 by Kaplan North America, LLC, d/b/a Barron's Educational Series
• All rights reserved. No part of this book may be reproduced in any form or by any means without the written permission of the copyright owner
• Published by Kaplan North America, LLC, d/b/a Barron's Educational Series
• ISBN: 978-1-5062-8863-5
• Kaplan North America, LLC, d/b/a Barron's Educational Series print books are available at special quantity discounts to use for sales promotions, employee premiums, or educational purposes
• Christina Pawlowski-Polanish


  Author, has taught all levels of math, including 10 years of AP Calculus BC at Commack High School in Commack, NY, and College Precalculus for 7 years. She earned a B.A. in mathematics and secondary education and an M.S. in mathematics from Hofstra University. She frequently presents on mathematics literacy at local, state, and national conferences and leads workshops in her district and at colleges. Christina is a member of many organizations, including the National Council of Teachers of Mathematics, Suffolk County Math Teachers' Association, and the Association of Mathematics Teachers of New York State, where she served as recording secretary and is presently a county chair. Christina was accepted into the New York State (NYS) Master Teacher Program and the NYS Academy of Master Teachers. She was chosen as Commack School District's Teacher of the Year and was a finalist for the 2018 NYS Teacher of the Year award. Christina joined the National Network of State Teachers of the Year and has been published on their blog. She was honored by the governor as a recipient of the NYS Empire State Excellence in Teaching Award in 2018. Most recently, Christina was named the 2019 New York State winner for the Presidential Award for Excellence in Mathematics and Science Teaching and was honored in Washington, D.C.
• Table of Contents
• How to Use This Book
• Barron's Essential 5
• Unit Outline
• The Exam
• Prior Knowledge
• UNIT 1: POLYNOMIAL AND RATIONAL FUNCTIONS
• UNIT 2: EXPONENTIAL AND LOGARITHMIC FUNCTIONS
• UNIT 3: TRIGONOMETRIC AND POLAR FUNCTIONS
• UNIT 4: FUNCTIONS INVOLVING PARAMETERS, VECTORS, AND MATRICES
• PRACTICE TESTS
• mark the model with any given information. The markings in the model will tell you about a relationship in the figure that will lead to an equation. If a verbal description is provided, begin by creating a model that can be marked.
• Pause for punctuation. When you are reading a problem and see a comma, period, semicolon, colon, or the words and or is, you should stop and ask yourself, "Why might this break in the problem be important?" The answer to this question will tell you about some equation to focus on, information that will allow you to create an equation, or some important information that will lead to a solution to the problem. Think of these pauses as a way for the question writer to signal to you a list of important givens in an organized manner.
• Improve your study habits. Reaching this level in math means that you have been a student for many years and are not afraid to take on a challenging course title. You might already have your own study strategies in place or may have found math very easy up until now. Studying for the AP Precalculus exam is an opportunity for you to modify your study strategies. Study strategies can include:

  • Spacing your studying over a span of days or weeks as opposed to cramming the days before an exam.
  • Reflecting on topics you struggled with, reading the review material on that section, and answering the practice questions. Repeating a question is a great learning tool to ensure you understand the concept.
  • Using the practice questions at the end of each chapter to test your knowledge.
  • Taking all practice tests to become familiar with the testing format and using them to understand which topics you need to repeat and practice more.
  • Using flashcards to review important vocabulary or equations that need to be better understood. The terms you select to make cards on are ones that are seen often or ones that you are not familiar with.
• This book is intended for students who are preparing to take the Advanced Placement Examination in Precalculus offered by the College Entrance Examination Board and for their teachers. It is based on the April 2022 AP Precalculus proposed framework published by the College Board.
• AP Precalculus is a full-year course designed to prepare students for the math they will encounter at the college level. This course should be taken after a student has completed Geometry and Algebra II or for students who have completed Integrated Math 3. AP Precalculus contains content that is already present in standard high school precalculus courses. This course will develop the student's ability to express functions, concepts, problems, and conclusions analytically, graphically, numerically, and verbally and to understand how these are related. Students will also learn how to use a graphing calculator as a tool for mathematical investigations and problem solving.
• Unit Outline


  • Unit 1: Polynomial and Rational Functions
  • Unit 2: Exponential and Logarithmic Functions
  • Unit 3: Trigonometric and Polar Functions
  • Unit 4: Functions Involving Parameters, Vectors, and Matrices
• The AP Precalculus exam and the course descriptions are prepared by committees of teachers from colleges or universities and from secondary schools. The exam is intended to determine the extent to which a student has mastered the subject matter of the course. The exam is 3 hours long and is comprised of the following sections.
• Section I: Multiple-Choice Questions

  • Part A has 36 multiple-choice questions for which 80 minutes are allowed. The use of calculators is not permitted in Part A.
  • Part B has 12 multiple-choice questions for which 40 minutes are allowed. Some of the questions in Part B require the use of a graphing calculator.
• Section II: Free-Response Questions

  • Part A requires a graphing calculator to answer some questions or parts of questions. After 30 minutes, however, you will no longer be permitted to use a calculator.
  • Part B also is allotted 30 minutes, but you are not allowed to use a calculator.
• Each student is expected to bring a graphing calculator to the AP exam. Different models of calculators vary in their features and capabilities; however, there are three procedures you must be able to perform on your calculator:

  1. Produce the graph of a function within an arbitrary viewing window.

  2. Solve an equation numerically.

  3. Compute regression models numerically.
• Guidelines for Calculator Use

  • For multiple-choice questions in Section I: Part B, you may use any feature or program on your calculator.
  • On the free-response questions of Section II: Part A, remember the following:
  • You may use the calculator to perform any of the three listed procedures. When you do, you need to write only the equation or setup that will produce the solution and then the calculator result to the required degree of accuracy (three places after the decimal point unless otherwise specified).
  • For a solution for which you use a calculator capability other than the three listed above, you must write down the mathematical steps that yield the answer. A correct answer alone will not earn full credit.
  • When asked to "justify," you must provide mathematical reasoning to support your answer. Calculator results alone will not be sufficient.
• Learn the proper syntax for your calculator: the correct way to enter operations, functions, and other commands. Parentheses, commas, variables, or parameters that are missing or entered in the wrong order can produce error messages or yield wrong answers.
• Keep your calculator set in radian mode. Almost all questions about angles and trigonometric functions use radians. If you ever need to change to degrees for a specific calculation, return the calculator to radian mode as soon as that calculation is complete.
• Many calculators do not have keys for the secant, cosecant, or cotangent functions. To obtain these functions, use their reciprocals. For example, sec(1) = 1/COS(1)
• Evaluate inverse functions such as arcsin, arccos, and arctan on your calculator. Those function keys are usually denoted as sin^-1, cos^-1, and tan^-1.
• To achieve three-place accuracy in a final answer, do not round off variables at intermediate steps since this is likely to produce error accumulations. Round off only after your calculator produces the final answer.
• Although final answers expressed in this book are in simplest form, this is not necessary on Section II questions of the AP exam. According to the directions printed on the exam, "unless otherwise specified" (1) you need not simplify algebraic or numerical answers and (2) answers involving decimals should be correct to three places after the decimal point. However, be aware that if you try to simplify, you must do so correctly or you will lose credit.
• Factoring is the process of breaking down a polynomial expression or equation and finding its factors that, when multiplied together, return to the original polynomial. A few different factoring techniques will be reviewed.
• Greatest Common Factor (GCF)


  Greatest common factor factoring refers to dividing out the greatest like term in a polynomial. The greatest common factor can be a number, a variable, or both.