### Cliffsap Calculus Ab & Bc

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### Full Description

A focused review to help you score high and earn college credit on the Calculus AB & BC Advanced Placement Program exam. This hard-hitting guide features: * Helpful test-taking strategies * Focus sections on specific topic areas, including precalculus, limits and continuity, derivatives, and integrals * Sample multiple choice and free-response questions * A discussion of calculators to use during the exam, including which are the best types Advanced Placement Program and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse this product.

`Preface                                            ixStudy Guide Checklist                              ixPART I: INTRODUCTION  Introduction                                     3  (16)    Questions Commonly Asked About the AP          3  (2)    Calculus AB and BC Exams    Strategies for the Exam                        5  (1)    Multiple-Choice Questions                      6  (2)    Free-Response Questions                        8  (2)    Calculator Questions                           10 (3)    Topics Covered on a Recent AP Calculus AB      13 (6)    or BC Exam      Precalculus                                  13 (1)      Calculus                                     13 (6)PART II: SPECIFIC TOPICS  Precalculus Topics                               19 (56)    Functions and Function Notation                19 (7)      Definition of a Function                     19 (1)      Vocabulary                                   20 (1)      Notation                                     20 (1)      Zeros or Roots                               21 (1)      Symmetry                                     21 (1)      Definition of Even and Old Functions         22 (1)      Graphing a Function                          23 (1)      Shifts and Distortions of Graphs             23 (2)      Absolute-Value Distortions                   25 (1)    Inverse Functions                              26 (2)      Definition of Inverse Functions              27 (1)      Notation                                     27 (1)    Polynomial Functions                           28 (2)      Degree Test                                  29 (1)      Leading Coefficient Test                     29 (1)    Trigonometric Functions                        30 (6)      Graphs, Domain and Range, Periods            30 (1)      Shifts and Distortions for Trig Functions    31 (1)      Trig Identities                              32 (1)      Solving Trig Equations                       33 (1)      Inverse Trig Functions                       34 (2)    Exponential and Logarithmic Functions          36 (4)      Exponential Functions                        36 (1)      Logarithmic Functions                        37 (1)      Special Log Functions                        38 (1)      Properties of Logarithms                     38 (2)      Relationship Between Logs and Exponentials   40 (1)    Rational Functions                             40 (3)      Definition of a Rational Function            40 (1)      Graphing a Rational Function                 41 (2)    Conic Sections                                 43 (3)      Completing the Square                        44 (2)    Algebra                                        46 (2)      Interval Notation                            46 (1)      Lines                                        47 (1)      Interval Testing                             47 (1)      Absolute Value                               48 (1)    Parametric Equations (BC Only)                 48 (1)      Domain of t                                  49 (1)    Eliminating the Parameter                      49 (4)      Particle Problems                            52 (1)    Polar Coordinates and Graphs (BC Only)         53 (8)      Notation                                     54 (1)      Conversion                                   54 (1)      Calculators                                  54 (1)      Polar Graphs                                 55 (1)      Symmetry                                     55 (1)      Intersections                                55 (1)      Converting Equations from Rectangular to     56 (1)      Polar Form      Converting Equations from Polar to           57 (2)      Rectangular Form      Special Polar Graphs                         59 (2)    Vectors and Vector-Valued Functions (BC        61 (5)    Only)      Component Form of a Vector                   61 (1)      Magnitude and Direction of a Vector in       62 (1)      Standard Position      Vectors Operations                           62 (1)      Alternate Component Form                     63 (1)      Magnitude/Direction to Component Form        64 (1)      Vector-Valued Functions                      65 (1)    Sample Multiple-Choice Questions:              66 (3)    Precalculus    Answers to Multiple-Choice Questions           69 (4)    Sample Free-Response Question: Precalculus     73 (1)    Answer to Free-Response Question               73 (2)  Limits and Continuity                            75 (30)    Intutive Definition of a Limit                 75 (4)    Algebraic Techniques for Finding Limits        79 (1)    One-Sided Limits                               80 (3)    Infinite Limits                                83 (2)      Theorem for Infinite Limits                  84 (1)    Limits at Infinity                             85 (5)      Theorem for Limits at Infinity               88 (2)    Special Trig Limits                            90 (1)    Continuity                                     90 (4)      Definition of Continuity at a Point          91 (1)      Definition of Continuity on an Open          92 (1)      Interval      Definition of Continuity on a Closed         92 (2)      Interval    Sample Multiple-Choice Questions: Limits       94 (3)    and Continuity    Answers to Multiple-Choice Questions           97 (3)    Sample Free-Response Questions: Limits and     100(1)    Continuity    Answers to Free-Response Questions             101(4)  Derivatives                                      105(48)    Definition of the Derivative                   105(4)    Differentiation Rules                          109(6)      Constant Rule                                109(1)      Constant Multiple Rule                       109(1)      Sum and Difference Rule                      110(1)      Power Rule                                   110(2)      Trigonometric Rules                          112(1)      Product Rule                                 112(1)      Quotient Rule                                113(2)    The Chain Rule                                 115(4)      Chain Rule                                   116(1)      Alternative Form of the Chain Rule           117(1)      Power Rule with Chain                        118(1)      Trig Rules with Chain                        118(1)      Higher-Order Derivatives                     119(1)    Derivatives of Exponential Functions           119(2)      Exponential Rule                             120(1)      Base-a Exponentials Rule                     120(1)    Derivatives of Logarithmic Functions           121(2)      Natural Log Rule                             122(1)      Base-a Logarithms Rule                       122(1)    Derivatives of Inverse Trigonometric           123(3)    Functions      Inverse Trig Rules                           124(1)      Derivatives of Inverses                      124(2)    Implicit Differentiation                       126(2)    Logarithmic Differentiation                    128(2)    Parametric Derivatives (BC Only)               130(2)      Parametric From of the Derivative            130(1)      Parametric From of the Second Derivative     130(2)    Differentiation with Polar Curves (BC Only)    132(2)      Slope in Polar                               132(2)    Limits and Continuity of Vector-Valued         134(1)    Functions      Limit and Continuity of a Vector-Valued      135(1)      Function    Differentiation of Vector-Valued Function      135(2)    (BC Only)      Derivative of a Vector-Valued Function       135(2)    Differentiability and Continuity               137(3)      Differentiability Implies Continuity         137(3)    Sample Multiple-Choice Questions:              140(4)    Derivatives    Answers to Multiple-Choice Questions           144(7)    Sample Free-Response Question: Derivatives     151(1)    Answer to Free-Response Question               151(2)  Applications of the Derivative                   153(60)    Tangent and Normal Lines                       153(3)    Position, Velocity, and Acceleration           156(5)      Theorem for PVA                              157(4)    Related Rates                                  161(10)      Sample Problem                               161(10)    Relative Extrema and the First Derivative      171(4)    Test      Theorem on Increasing and Decreasing         171(2)      First Derivative Test for Extrema            173(2)    Concavity and the Second Derivative Test       175(6)      Definition of Concavity                      176(1)      Theorem: Test for Concavity                  177(1)      Definition of Point of Inflection            178(2)      Second Derivative Test for Extrema           180(1)    Absolute Extrema and Optimization              181(7)      Extreme Value Theorem                        182(2)      Sample Problem                               184(4)    Rolle's Theorem and the Mean Value Theorem     188(3)      Rolle's Theorem                              188(1)      Mean Value Theorem                           189(2)    Differentials                                  191(2)    L'Hopital's Rule (BC Only)                     193(5)      Theorem: L'Hopital's Rule                    193(4)      Summary of Forms Requiring L'Hospital's      197(1)      Rule    Sample Multiple-Choice Questions:              198(4)    Applications of the Derivative    Answers to Multiple-Choice Questions           202(8)    Sample Free-Response Questions:                210(1)    Applications of the Derivative    Answers to Free-Response Questions             211(2)  Antiderivatives and Definite Integrals           213(46)    Antiderivatives                                213(4)      Definition of an Antiderivative              213(1)      Theorem on Antiderivatives                   213(1)      Notation                                     214(1)      Vocabulary                                   214(1)      Constant Multiple Rule                       214(1)      Sum and Difference Rule                      214(1)      Trig Rules                                   215(1)      Power Rule                                   215(2)    The Chain Rule for Antiderviatives             217(4)      Chain Rule for Antiderivatives               217(4)    Exponential Antiderivatives                    221(2)      Exponential Antiderivative                   221(2)    Antiderivative of Other Exponentials           223(1)    Antiderivatives and the Natural Log            223(3)      Antiderivatives Rule for the Natural Log     224(2)    Trig Integrals                                 226(2)    Antiderivatives of Inverse Trig Functions      228(3)      Inverse Trig Antiderivatives                 229(2)    Integration by Parts (BC Only)                 231(3)      Theorem: Integration by Parts                231(3)    Integration by Partial Fractions (BC Only)     234(2)    Improper Integrals (BC Only)                   236(7)      Examples of Improper Integrals               237(1)      Improper Integrals with Infinite Bounds      238(2)      of Integration      Improper Integrals with Infinite             240(3)      Discontinuities    Sample Multiple-Choice Questions:              243(6)    Antiderivatives    Answers to Multiple-Choice Questions           249(10)  Applications of Antiderivatives and Definite     259(84)  Integrals    The Fundamental Theorem of Calculus            259(2)      Fundamental Theorem of Calculus              259(1)      Notation                                     260(1)    Definition of the Definite Integral            261(8)      Definition of the Definite Integral          261(3)      Theorem: Trapezoidal Rule                    264(2)      Theorem: Area Between Curves                 266(3)    Properties of the Definite Integral            269(5)      Four Properties of the Definite Integral     269(3)      Property for Even and Odd Functions          272(1)      Variable Bounds Property                     273(1)      Average-Value Property                       274(1)    Volume                                         274(18)      Vertical Axis of Revolution                  275(2)      Horizontal Axis of Revolution                277(3)      Known Cross-Sectional Area                   280(1)      Solids of Revolution                         281(8)      Solids with Known Cross Sections             289(3)    Differential Equations                         292(3)    Numerical Solutions to Differential            295(5)    Equations: Euler's Method      Euler's Method as a Recursive Formula        299(1)    Differential Equations and Slope Fields        300(5)    PVA with Antiderivatives                       305(6)      Theorem for PVA                              305(3)      Exponential Decay and Newton's Law of        308(1)      Cooling      Bounded Growth                               309(2)    Logistic Growth (BC Only)                      311(3)      Spread of a Rumor                            312(1)      Spread of a Disease                          312(1)      Population Growth                            312(2)    Work (BC Only)                                 314(7)      Work Along a Strainght Line                  315(3)      Liquid Work                                  318(3)    Length of an Arc (BC Only)                     321(2)      Length of an Arc                             321(2)    Arc Length for Parametric Curves (BC Only)     323(1)      Arc Length in Parametric                     323(1)    Area and Arc Length for Polar Curves (BC       324(5)    Only)      Area in Polar                                324(4)      Arc Length in Polar                          328(1)    Integration of Vector-Valued Functions (BC     329(1)    Only)    Sample Multiple-Choice Questions:              330(3)    Applications of Antiderivatives and    Definite Integrals    Answers to Multiple-Choice Questions           333(8)    Sample Free-Response Question: Applications    341(1)    of Antiderivatives and Definite Integrals    Answer to Free-Response Question               342(1)  Sequences, Infinite Series, and Polynomial       343(56)  Approximations (BC Only)    Sequences                                      343(2)      Using Current Technology                     344(1)    Series                                         345(17)      Tests of Convergence or Divergence of an     346(13)      Infinite Series      Other Useful Information Regarding           359(1)      Infinite Series      Summary of Tests for Convergence or          359(1)      Divergence of Infinite Series      Alternating Series Error Bound               360(2)    Radius and Interval of Convergence of Power    362(3)    Series    Sample Multiple-Choice Questions: Sequences    365(2)    and Infinite Series    Answers to Multiple-Choice Questions           367(7)    Sample Free-Response Question: Sequences       374(1)    and Series    Answer to Free-Response Question               375(1)    Polynomial Approximations of Functions         376(2)    (Taylor and Maclaurin Polynomials)    Differentiation and Integration of Power       378(7)    Series    Lagrange From of the Remainder of a Taylor     385(3)    Polynomial      Taylor's Theorem                             385(2)      Power Series for Some Common Functions       387(1)    Sample Multiple-Choice Questions:              388(2)    Polynomial Approximations of Functions    (Taylor and Maclaurin Polynomials)    Answers to Multiple-Choice Questions           390(3)    Sample Free-Response Question: Polynomial      393(1)    Approximation of Functions (Taylor and    Maclaurin Polynomials)    Answer to Free-Response Question               393(4)PART III: AP CALCULUS AB AND BC PRACTICE TESTS    Answer Sheet for Practice Test 1 - AB          397(1)    Taking and Grading the Practice Exams          398(1)  Practice Test 1 - AB                             399(34)    Section I: Multiple-Choice Questions           399(8)      Section IA                                   399(5)      Section IB                                   404(3)    Section II: Free-Response Questions            407(2)      Section IIA                                  407(1)      Section IIB                                  408(1)    Answer Key for Practice Test 1 - AB            409(2)      Section I: Multiple-Choice Questions         409(1)      Section II: Free-Response Questions          410(1)      Practice Test I Scoring Worksheet            410(1)    Answers and Explanations for Practice Test     411(20)    1 - AB      Section I: Multiple-Choice Questions         411(10)      Section II: Free-Response Questions          421(10)    Answer Sheet for Practice Test 2 - BC          431(2)  Practice Test 2- BC                              433(34)    Section I: Multiple-Choice Questions           433(8)      Section IA                                   433(5)      Section IB: BC                               438(3)    Section II: Free-Response Questions            441(2)      Section IIA                                  441(1)      Section IIB                                  442(1)    Answer Key for Practice Test 2 - BC            443(2)      Section I: Multiple-Choice Questions         443(1)      Section II: Free-Response Questions          444(1)      Practice Test 2 Scoring Worksheet            444(1)    Answers and Explanations for Practice Test     445(22)    2 - BC      Section I: Multiple-Choice Questions         445(14)      Section II: Free-Response Questions          459(8)Appendix: Calculus Dictionary                      467`