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5 Steps to a 5: AP Calculus AB 2024 (2024)

Reinforce your learning with 5 Steps to a 5: AP Calculus AB 2024 (2024), a set of structured practice exams tailored for success.

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    = YOUR PERSONALIZED STUDY PROGRAM (ETI TRY PI (1) To Access Your Online Course: @ Create an account at www.mheducation.com/5stepscalc De = on nel —— Br _ | © | REDEEM YOUR | lle E | Access cook | = | mhapcawc245 Fessssesssssntinntntinernnrans mhapawe24s [3] Enter your e-mail address and create a password. © crvescnmt : (4) You're all set to start studying! ‘ = — im : e=="______ | : He alll == ei Se — — Study

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    = YOUR PERSONALIZED STUDY PROGRAM [:RTU I ARR FEI) Customizable Study Plan tracks your daily goals 9 Games Center ° for practice in spare moments —— SEE © miosheiont sweeney Tw oo I . Peer Support [2] . and study tips via social media nN Study Plan Interactive Lessons ee] cover entire book 104 14/40 7% Practice Tests o———————————— [ Jerpmioiby r+ designed to simulate the real thing Practice Questions Ta (Wrenn. mile to build test readiness a © "rc Ovptate Coma Study Tools to focus study where E—— most needed (c] [c] Practice: Number Theory Digital Flashcards © Tres cases ? All to memorize key concepts Advanced Analytics [FF =. = _ from the Intelligent Report Dashboard — Study

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    ems . AP Calculus AB 2024 William Ma Emily Pillar iony Yat Now Ou, Snape ine. Tron

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    Copyright © 2023, 2022 by McGraw Hill. All rights reserved. Except as permitted under the Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of publisher. ISBN: 978-1-26-535162-5 MHID: 1-26-535162-7 The material in this eBook also appears in the print version of this title: ISBN: 978-1-26-535107-6, MHID: 1-26-535107-4. eBook conversion by codeMantra Version 1.0 All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps. McGraw Hill eBooks are available at special quantity discounts to use as premiums and sales promotions or for use in corporate training programs. To contact a representative, please visit the Contact Us page at www.mhprofessional.com. McGraw Hill, the McGraw Hill logo, 5 Steps to a 5, and related trade dress are trademarks or registered trademarks of McGraw Hill and/or its affiliates in the United States and other countries and may not be used without written permission. All other trademarks are the property of their respective owners. McGraw Hill is not associated with any product or vendor mentioned in this book. AP, Advanced Placement Program, and College Board are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, this product.

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    Preface Acknowledgments About the Authors Introduction: The Five-Step Program STEP 1 Set Up Your Study Plan 1 What You Need to Know About the AP Calculus AB Exam 1.1 What Is Covered on the AP Calculus AB Exam? 1.2 What Is the Format of the AP Calculus AB Exam? 1.3 What Are the Advanced Placement Exam Grades? How Is the AP Calculus AB Exam Grade Calculated? 1.4 Which Graphing Calculators Are Allowed for the Exam? Calculators and Other Devices Not Allowed for the AP Calculus AB Exam Other Restrictions on Calculators 2 How to Plan Your Time 2.1 Three Approaches to Preparing for the AP Calculus AB Exam Overview of the Three Plans 2.2 Calendar for Each Plan Summary of the Three Study Plans STEP 2 Determine Your Test Readiness 3 Take a Diagnostic Exam 3.1 Getting Started!

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    3.2 Diagnostic Test 3.3 Answers to Diagnostic Test 3.4 Solutions to Diagnostic Test 3.5 Calculate Your Score Short-Answer Questions AP Calculus AB Diagnostic Test STEP 3 Develop Strategies for Success 4 How to Approach Each Question Type 4.1 The Multiple-Choice Questions 4.2 The Free-Response Questions 4.3 Using a Graphing Calculator 4.4 Taking the Exam What Do I Need to Bring to the Exam? Tips for Taking the Exam STEP 4 Review the Knowledge You Need to Score High 5 Review of Precalculus 5.1 Lines Slope of a Line Equations of a Line Parallel and Perpendicular Lines 5.2 Absolute Values and Inequalities Absolute Values Inequalities and the Real Number Line Solving Absolute Value Inequalities Solving Polynomial Inequalities Solving Rational Inequalities 5.3 Functions Definition of a Function

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    Operations on Functions Inverse Functions Trigonometric and Inverse Trigonometric Functions Exponential and Logarithmic Functions 5.4 Graphs of Functions Increasing and Decreasing Functions Intercepts and Zeros Odd and Even Functions Shifting, Reflecting, and Stretching Graphs 5.5 Rapid Review 5.6 Practice Problems 5.7 Cumulative Review Problems 5.8 Solutions to Practice Problems 5.9 Solutions to Cumulative Review Problems Big Idea 1: Limits 6 Limits and Continuity 6.1 The Limit of a Function Definition and Properties of Limits Evaluating Limits One-Sided Limits Squeeze Theorem 6.2 Limits Involving Infinities Infinite Limits (as x — a) Limits at Infinity (as x — +o) Horizontal and Vertical Asymptotes 6.3 Continuity of a Function Continuity of a Function at a Number Continuity of a Function over an Interval Theorems on Continuity

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    6.4 Rapid Review 6.5 Practice Problems 6.6 Cumulative Review Problems 6.7 Solutions to Practice Problems 6.8 Solutions to Cumulative Review Problems Big Idea 2: Derivatives 7 Differentiation 7.1 Derivatives of Algebraic Functions Definition of the Derivative of a Function Power Rule The Sum, Difference, Product, and Quotient Rules The Chain Rule 7.2 Derivatives of Trigonometric, Inverse Trigonometric, Exponential, and Logarithmic Functions Derivatives of Trigonometric Functions Derivatives of Inverse Trigonometric Functions Derivatives of Exponential and Logarithmic Functions 7.3 Implicit Differentiation Procedure for Implicit Differentiation 7.4 Approximating a Derivative 7.5 Derivatives of Inverse Functions 7.6 Higher Order Derivatives 7.7 L’Hépital’s Rule for Indeterminate Forms 7.8 Rapid Review 7.9 Practice Problems 7.10 Cumulative Review Problems 7.11 Solutions to Practice Problems 7.12 Solutions to Cumulative Review Problems 8 Graphs of Functions and Derivatives

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    8.1 Rolle’s Theorem, Mean Value Theorem, and Extreme Value Theorem Rolle’s Theorem Mean Value Theorem Extreme Value Theorem 8.2 Determining the Behavior of Functions Test for Increasing and Decreasing Functions First Derivative Test and Second Derivative Test for Relative Extrema Test for Concavity and Points of Inflection 8.3 Sketching the Graphs of Functions Graphing without Calculators Graphing with Calculators 8.4 Graphs of Derivatives 8.5 Rapid Review 8.6 Practice Problems 8.7 Cumulative Review Problems 8.8 Solutions to Practice Problems 8.9 Solutions to Cumulative Review Problems 9 Applications of Derivatives 9.1 Related Rate General Procedure for Solving Related Rate Problems Common Related Rate Problems Inverted Cone (Water Tank) Problem Shadow Problem Angle of Elevation Problem 9.2 Applied Maximum and Minimum Problems General Procedure for Solving Applied Maximum and Minimum Problems Distance Problem

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    Area and Volume Problems Business Problems 9.3 Rapid Review 9.4 Practice Problems 9.5 Cumulative Review Problems 9.6 Solutions to Practice Problems 9.7 Solutions to Cumulative Review Problems 10 More Applications of Derivatives 10.1 Tangent and Normal Lines Tangent Lines Normal Lines 10.2 Linear Approximations Tangent Line Approximation (or Linear Approximation) Estimating the nth Root of a Number Estimating the Value of a Trigonometric Function of an Angle 10.3 Motion Along a Line Instantaneous Velocity and Acceleration Vertical Motion Horizontal Motion 10.4 Rapid Review 10.5 Practice Problems 10.6 Cumulative Review Problems 10.7 Solutions to Practice Problems 10.8 Solutions to Cumulative Review Problems Big Idea 3: Integrals and the Fundamental Theorems of Calculus 11 Integration 11.1 Evaluating Basic Integrals Antiderivatives and Integration Formulas

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