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AP Precalculus Premium, 2025: 3 Practice Tests + Comprehensive Review (2025)

Ensure exam success with AP Precalculus Premium, 2025: 3 Practice Tests + Comprehensive Review (2025) , a trusted certification guide packed with high-yield content and practice exercises.

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    THE TRUSTED NAME IN TEST PREP ® y y y @® 3 full-length practice tests with detailed answer explanations ® Online practice with a timed test option and scoring ® Comprehensive review and practice for all topics on the exam ® Expert tips plus Barron's “Essential 5” things you need to know [=] o [w] SCAN NOW TO L, ACCESS PREP INCLUDED WITH Christina Pawlowski-Polanish, M.S. = ! THIS BOOK orgo to 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. + StudyXY

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    Downloaded from StudyXY.com ® + StudyXY Sd Ye. o> \ | iF ’ pr E \ 3 S Stu dy Anything This ContentHas been Posted On StudyXY.com as supplementary learning material. StudyXY does not endrose any university, college or publisher. Allmaterials posted are under the liability of the contributors. wv 8) www.studyxy.com

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    ogy 2025 THE TRUSTED NAME IN TEST PREP

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    Dedication To my Cailey, continue looking up to the sky at the stars, and you can reach them! Love, Mommy To my family, thank you for your time and support. It wouldn’t have been possible without you!

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    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 2024, 2023 by Kaplan North America, LLC, d/b/a Barron’s Educational Series All rights reserved under International and Pan-American Copyright Conventions. By payment of the required fees, you have been granted the non-exclusive, non-transferable right to access and read the text of this eBook on screen. No part of this text may be reproduced, transmitted, downloaded, decompiled, reverse engineered, or stored in or introduced into any information storage and retrieval system, including but not limited to generative artificial intelligence (gen AI) systems and machine learning systems, in any form or by any means, whether electronic or mechanical, now known or hereinafter invented, without the express written permission of the publisher. Published by Kaplan North America, LLC, d/b/a Barron’s Educational Series 1515 West Cypress Creek Road Fort Lauderdale, FL 33309 www.barronseduc.com ISBN: 978-1-5062-9204-5

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    About the Author Christina Pawlowski-Polanish 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 of the Presidential Award for Excellence in Mathematics and Science Teaching and was honored in Washington, D.C.

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    Table of Contents How to Use This Book Barron’s Essential 5 Introduction Unit Outline Exam Format Scoring of the Exam Using Your Graphing Calculator on the AP Exam Prior Knowledge UNIT 1: POLYNOMIAL AND RATIONAL FUNCTIONS 1 Rates of Change 1.1 Relations and Functions 1.2 Rates of Change 1.3 Rates of Change in Linear Functions 1.4 Rates of Change in Quadratic Functions Multiple-Choice Questions Answer Explanations 2 Polynomial Functions 2.1 Polynomial Functions and Rates of Change 2.2 Real and Complex Zeros of Polynomial Functions 2.3 Polynomial Functions and End Behavior

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    2.4 Graphs of Polynomial Functions 2.5 Equivalent Representations of Polynomial Expressions 2.6 Polynomial Inequalities Multiple-Choice Questions Answer Explanations 3 Rational Functions 3.1 Equivalent Representations of Rational Expressions: Long Division 3.2 Rational Functions and Zeros 3.3 Rational Functions and Vertical Asymptotes 3.4 Rational Functions and Holes 3.5 Rational Functions and End Behavior 3.6 Graphs of Rational Functions 3.7 Rational Inequalities Multiple-Choice Questions Answer Explanations 4 Parent Functions 4.1 Graphs and Properties of Basic Functions 4.2 Transformations of Functions 4.3 Function Model Selection, Construction, and Application 4.4 Composition of Functions 4.5 Inverse Functions Multiple-Choice Questions Answer Explanations UNIT 2: EXPONENTIAL AND LOGARITHMIC FUNCTIONS 5 Exponential Functions

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    5.1 Exponential Functions 5.2 Exponential Function Manipulation 5.3 Exponential Function Context and Data Modeling 5.4 Competing Function Model Validation Multiple-Choice Questions Answer Explanations 6 Sequences 6.1 Arithmetic Sequences 6.2 Geometric Sequences 6.3 Change in Linear and Exponential Functions Multiple-Choice Questions Answer Explanations 7 Logarithmic Functions 7.1 Logarithmic Expressions 7.2 Inverses of Exponential Functions 7.3 Logarithmic Functions 7.4 Logarithmic Function Manipulation 7.5 Exponential and Logarithmic Equations and Inequalities 7.6 Logarithmic Function Context and Data Modeling 7.7 Semi-log Plots Multiple-Choice Questions Answer Explanations UNIT 3: TRIGONOMETRIC AND POLAR FUNCTIONS 8 Trigonometric Functions 8.1 Periodic Phenomena 8.2 Sine, Cosine, and Tangent 8.3 Sine and Cosine Function Values

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    8.4 Sine and Cosine Function Graphs 8.5 Sinusoidal Functions 8.6 Sinusoidal Function Transformations 8.7 Sinusoidal Function Context and Data Modeling 8.8 The Tangent Function 8.9 Inverse Trigonometric Functions 8.10 Trigonometric Equations and Inequalities 8.11 The Secant, Cosecant, and Cotangent Functions 8.12 Equivalent Representations of Trigonometric Functions Multiple-Choice Questions Answer Explanations 9 Polar Functions 9.1 Trigonometry and Polar Coordinates 9.2 Polar Function Graphs 9.3 Rates of Change in Polar Functions Multiple-Choice Questions Answer Explanations UNIT 4: FUNCTIONS INVOLVING PARAMETERS, VECTORS, AND MATRICES 10 Parametric Functions 10.1 Parametric Functions 10.2 Parametric Functions Modeling Planar Motion 10.3 Parametric Functions and Rates of Change 10.4 Parametrically Defined Circles and Lines 10.5 Implicitly Defined Functions 10.6 Conic Sections 10.7 Parameterization of Functions Multiple-Choice Questions

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    Answer Explanations 11 Vectors 11.1 Algebraic and Graphical Properties of Vectors 11.2 Vector-Valued Functions Multiple-Choice Questions Answer Explanations 12 Matrices 12.1 Matrix Operations 12.2 The Inverse and Determinant of a Matrix 12.3 Linear Transformations and Matrices 12.4 Matrices as Functions 12.5 Matrices Modeling Context Multiple-Choice Questions Answer Explanations PRACTICE TESTS Practice Test 1 Answer Explanations Practice Test 2 Answer Explanations Glossary of Key Terms Visit Barron’s Online Learning Hub for an additional full-length practice test.

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    How to Use This Book This book provides comprehensive review and extensive practice for AP Precalculus. It is based on the latest AP Precalculus Course and Exam Description published by the College Board. Introduction Start with the Introduction, which contains an overview of the AP Precalculus course and exam. Learn the topics covered within each unit, familiarize yourself with the exam format, and review the guidelines for calculator use on test day. Then read through the Prior Knowledge section, which covers important tools and skills (that you may have learned in previous math classes) that can be applied to solve AP Precalculus problems. This section features key formulas, laws, and steps as well as carefully worked-out examples. Review and Practice Study Chapters 1 through 12, which are organized according to the units of AP Precalculus. Every chapter includes Learning Objectives that will be covered, a review of each topic, dozens of tables and figures that illustrate key concepts, numerous examples with clear solutions, and a set of multiple- choice practice questions (with detailed answer explanations) to check your progress. Throughout these chapters, you’ll also find helpful tips and advice to keep in mind for test day. Note: The last three review chapters in this book focus on Unit 4 topics. While Unit 4 topics will not be tested on the AP Precalculus exam, they may

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    be part of your school’s course curriculum. Furthermore, reviewing these chapters may help build your understanding of topics that you will encounter on the exam. Practice Tests This book concludes with two full-length practice tests that mirror the actual exam in format, content, and level of difficulty. Each test is followed by detailed answer explanations for all questions. Glossary of Key Terms Be sure to consult the Glossary of Key Terms at the end of this book. AP Precalculus is a very vocabulary-based subject, so a strong command of the most frequently used precalculus terms will further prepare you for success on the exam. Online Practice There is also an additional full-length practice test online. You may take this test in practice (untimed) mode or in timed mode. All questions are answered and explained. For Students Students who use this book independently will improve their performance by studying the examples carefully and trying to complete the practice problems before referring to the answer explanations. You are strongly encouraged to read the book from start to finish since each topic builds on the previous ones. However, it is possible to use this book as a reference for specific topics that need review. For Teachers The teacher who uses this book with a class can do so in several ways. If the

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    book is used throughout the year, you can assign all or part of each set of multiple-choice questions after the topic has been covered. These sets can also be used for review purposes shortly before exam time. The practice tests will also be helpful in reviewing toward the end of the year.

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    bd BARRON’S ESSENTIAL 5 As you review the content in this book to work toward earning that 5 on your AP PRECALCULUS exam, here are five things that you MUST know above everything else: 1 Know the mathematical content. It is much better to understand the different mathematical concepts rather than memorizing properties and formulas. By understanding why the properties and formulas work, you will have a firm grasp of the topic, which will enable you to solve the problems. No two math questions are alike, and so it is impossible to memorize your way through a math course, especially an AP math course. This book often goes through the derivations of formulas and gives background explanations of the concepts so that you will understand how the math works. With deeper understanding comes true ownership of the material. 2 Build your vocabulary. Math is its own language with its own notations and terms. Often terms in math can have multiple meanings within the context of the problem. For example: + In trigonometry, tangent refers to the ratio of sides of a right triangle or the ratio of the trigonometric functions, sin cos + In geometry, tangent refers to a line that intersects a circle in only one point. + In calculus, tangent refers to a line that intersects a curve at a point, matching the curve’s slope there.

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    Make sure you understand the specific mathematical meanings of each term, especially those in the Glossary at the end of this book. Most of the multiple-choice questions on the exam measure your knowledge and ability to apply mathematical vocabulary. 3 Mark your model. Since math is its own language, the way you read and approach a problem should be different from how you read in other subject areas. Many problems in math require visualization. If a model is provided, it is important to mark the model with any given information. The markings in the model may 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. 4 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 may 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. 5 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. 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 enhance your study strategies. Study strategies can include: «Spacing your studying over a span of 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.

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