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E-raamat: 5 Steps to a 5: AP Calculus AB 2023 Elite Student Edition

  • Formaat: 688 pages
  • Ilmumisaeg: 01-Aug-2022
  • Kirjastus: McGraw-Hill Education
  • Keel: eng
  • ISBN-13: 9781264412112
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5 Steps to a 5: AP Calculus AB 2023 Elite Student EditionSuurem pilt
  • Formaat: 688 pages
  • Ilmumisaeg: 01-Aug-2022
  • Kirjastus: McGraw-Hill Education
  • Keel: eng
  • ISBN-13: 9781264412112
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Presents three full-length practice tests, providing a comprehensive overview of topics found on the exam, and offering a self-guided study plan.

AP Teachers’ #1 Choice!

Ready to succeed in your AP course and ace your exam? Our 5 Steps to a 5 guides explain the tough stuff, offer tons of practice and explanations, and help you make the most efficient use of your study time. 5 Steps to a 5: AP Calculus AB Elite is more than a review guide, it’s a system that has helped thousands of students walk into test day feeling prepared and confident.

Everything you Need for a 5:

  • 3 full-length practice tests that align with the latest College Board requirements
  • Hundreds of practice exercises with answer explanations
  • Comprehensive overview of all test topics
  • Proven strategies from seasoned AP educators

Why the Elite edition?

  • 200+ pages of additional AP content
  • 5-minute daily activities to reinforce critical AP concepts
  • AP educators love this feature for bellringers in the classroom!

Study on the Go:

  • All instructional content in digital format (for both computers and mobile devices)
  • Interactive practice tests with answer explanations
  • A self-guided study plan with daily goals, powerful analytics, flashcards, games, and more

A Great In-class Supplement:

  • 5 Steps is an ideal companion to your main AP text
  • Includes an AP Calculus AB Teacher’s Manual that offers excellent guidance to educators for better use of the 5 Steps resources

Preface xi
Acknowledgments xiii
About the Author xv
Introduction: The Five-Step Program xvii
STEP 1 Set Up Your Study Plan
1 "What You Need to Know About the AP Calculus AB Exam
3(5)
1.1 What Is Covered on the AP Calculus AB Exam?
4(1)
1.2 What Is the Format of the AP Calculus AB Exam?
4(1)
1.3 What Are the Advanced Placement Exam Grades?
5(1)
How Is the AP Calculus AB Exam Grade Calculated?
5(1)
1.4 Which Graphing Calculators Are Allowed for the Exam?
6(2)
Calculators and Other Devices Not Allowed for the AP Calculus AB Exam
7(1)
Other Restrictions on Calculators
7(1)
2 How to Plan Your Time
8(9)
2.1 Three Approaches to Preparing for the AP Calculus AB Exam
8(2)
Overview of the Three Plans
8(2)
2.2 Calendar for Each Plan
10(7)
Summary of the Three Study Plans
13(4)
STEP 2 Determine Your Test Readiness
3 Take a Diagnostic Exam
17(20)
3.1 Getting Started!
20(1)
3.2 Diagnostic Test
20(5)
3.3 Answers to Diagnostic Test
25(1)
3.4 Solutions to Diagnostic Test
26(8)
3.5 Calculate Your Score
34(3)
Short-Answer Questions
34(1)
AP Calculus AB Diagnostic Test
34(3)
STEP 3 Develop Strategies for Success
4 How to Approach Each Question Type
37(8)
4.1 The Multiple-Choice Questions
38(1)
4.2 The Free-Response Questions
38(1)
4.3 Using a Graphing Calculator
39(1)
4.4 Taking the Exam
40(5)
What Do I Need to Bring to the Exam?
40(1)
Tips for Taking the Exam
41(4)
STEP 4 Review the Knowledge You Need to Score High
5 Review of Precalculus
45(39)
5.1 Lines
46(4)
Slope of a Line
46(1)
Equations of a Line
46(1)
Parallel and Perpendicular Lines
47(3)
5.2 Absolute Values and Inequalities
50(7)
Absolute Values
50(1)
Inequalities and the Real Number Line
51(1)
Solving Absolute Value Inequalities
52(1)
Solving Polynomial Inequalities
53(2)
Solving Rational Inequalities
55(2)
5.3 Functions
57(13)
Definition of a Function
57(1)
Operations on Functions
58(2)
Inverse Functions
60(3)
Trigonometric and Inverse Trigonometric Functions
63(3)
Exponential and Logarithmic Functions
66(4)
5.4 Graphs of Functions
70(8)
Increasing and Decreasing Functions
70(2)
Intercepts and Zeros
72(1)
Odd and Even Functions
73(2)
Shifting, Reflecting, and Stretching Graphs
75(3)
5.5 Rapid Review
78(1)
5.6 Practice Problems
79(1)
5.7 Cumulative Review Problems
80(1)
5.8 Solutions to Practice Problems
80(3)
5.9 Solutions to Cumulative Review Problems
83(1)
Big Idea 1 Limits
6 Limits and Continuity
84(25)
6.1 The Limit of a Function
85(7)
Definition and Properties of Limits
85(1)
Evaluating Limits
85(2)
One-Sided Limits
87(3)
Squeeze Theorem
90(2)
6.2 Limits Involving Infinities
92(7)
Infinite Limits (as x → a)
92(2)
Limits at Infinity (as x → ±∞)
94(2)
Horizontal and Vertical Asymptotes
96(3)
6.3 Continuity of a Function
99(3)
Continuity of a Function at a Number
99(1)
Continuity of a Function over an Interval
99(1)
Theorems on Continuity
99(3)
6.4 Rapid Review
102(1)
6.5 Practice Problems
103(1)
6.6 Cumulative Review Problems
104(1)
6.7 Solutions to Practice Problems
105(2)
6.8 Solutions to Cumulative Review Problems
107(2)
Big Idea 2 Derivatives
7 Differentiation
109(28)
7.1 Derivatives of Algebraic Functions
110(6)
Definition of the Derivative of a Function
110(3)
Power Rule
113(1)
The Sum, Difference, Product, and Quotient Rules
114(1)
The Chain Rule
115(1)
7.2 Derivatives of Trigonometric, Inverse Trigonometric, Exponential, and Logarithmic Functions
116(5)
Derivatives of Trigonometric Functions
116(2)
Derivatives of Inverse Trigonometric Functions
118(1)
Derivatives of Exponential and Logarithmic Functions
119(2)
7.3 Implicit Differentiation
121(3)
Procedure for Implicit Differentiation
121(3)
7.4 Approximating a Derivative
124(2)
7.5 Derivatives of Inverse Functions
126(2)
7.6 Higher Order Derivatives
128(1)
7.7 L'Hopital's Rule for Indeterminate Forms
129(1)
7.8 Rapid Review
129(2)
7.9 Practice Problems
131(1)
7.10 Cumulative Review Problems
132(1)
7.11 Solutions to Practice Problems
132(3)
7.12 Solutions to Cumulative Review Problems
135(2)
8 Graphs of Functions and Derivatives
137(40)
8.1 Rolle's Theorem, Mean Value Theorem, and Extreme Value Theorem
138(4)
Rolle's Theorem
138(1)
Mean Value Theorem
138(3)
Extreme Value Theorem
141(1)
8.2 Determining the Behavior of Functions
142(12)
Test for Increasing and Decreasing Functions
142(3)
First Derivative Test and Second Derivative Test for Relative Extrema
145(3)
Test for Concavity and Points of Inflection
148(6)
8.3 Sketching the Graphs of Functions
154(3)
Graphing without Calculators
154(1)
Graphing with Calculators
155(2)
8.4 Graphs of Derivatives
157(5)
8.5 Rapid Review
162(2)
8.6 Practice Problems
164(3)
8.7 Cumulative Review Problems
167(1)
8.8 Solutions to Practice Problems
167(7)
8.9 Solutions to Cumulative Review Problems
174(3)
9 Applications of Derivatives
177(25)
9.1 Related Rate
177(6)
General Procedure for Solving Related Rate Problems
178(1)
Common Related Rate Problems
178(1)
Inverted Cone (Water Tank) Problem
179(1)
Shadow Problem
180(1)
Angle of Elevation Problem
181(2)
9.2 Applied Maximum and Minimum Problems
183(5)
General Procedure for Solving Applied Maximum and Minimum Problems
183(1)
Distance Problem
183(1)
Area and Volume Problems
184(3)
Business Problems
187(1)
9.3 Rapid Review
188(1)
9.4 Practice Problems
189(2)
9.5 Cumulative Review Problems
191(1)
9.6 Solutions to Practice Problems
192(7)
9.7 Solutions to Cumulative Review Problems
199(3)
10 More Applications of Derivatives
202(25)
10.1 Tangent and Normal Lines
202(9)
Tangent Lines
202(6)
Normal Lines
208(3)
10.2 Linear Approximations
211(3)
Tangent Line Approximation (or Linear Approximation)
211(2)
Estimating the nth Root of a Number
213(1)
Estimating the Value of a Trigonometric Function of an Angle
213(1)
10.3 Motion Along a Line
214(4)
Instantaneous Velocity and Acceleration
214(2)
Vertical Motion
216(1)
Horizontal Motion
216(2)
10.4 Rapid Review
218(1)
10.5 Practice Problems
219(1)
10.6 Cumulative Review Problems
220(1)
10.7 Solutions to Practice Problems
221(4)
10.8 Solutions to Cumulative Review Problems
225(2)
Big Idea 3 Integrals and the Fundamental Theorems of Calculus
11 Integration
227(20)
11.1 Evaluating Basic Integrals
228(5)
Antiderivatives and Integration Formulas
228(2)
Evaluating Integrals
230(3)
11.2 Integration by U-Substitution
233(8)
The U-Substitution Method
233(1)
U-Substitution and Algebraic Functions
233(2)
U-Substitution and Trigonometric Functions
235(1)
U-Substitution and Inverse Trigonometric Functions
236(2)
U-Substitution and Logarithmic and Exponential Functions
238(3)
11.3 Rapid Review
241(1)
11.4 Practice Problems
242(1)
11.5 Cumulative Review Problems
243(1)
11.6 Solutions to Practice Problems
244(2)
11.7 Solutions to Cumulative Review Problems
246(1)
12 Definite Integrals
247(23)
12.1 Riemann Sums and Definite Integrals
248(5)
Sigma Notation or Summation Notation
248(1)
Definition of a Riemann Sum
249(1)
Definition of a Definite Integral
250(1)
Properties of Definite Integrals
251(2)
12.2 Fundamental Theorems of Calculus
253(4)
First Fundamental Theorem of Calculus
253(1)
Second Fundamental Theorem of Calculus
254(3)
12.3 Evaluating Definite Integrals
257(5)
Definite Integrals Involving Algebraic Functions
257(1)
Definite Integrals Involving Absolute Value
258(1)
Definite Integrals Involving Trigonometric, Logarithmic, and Exponential Functions
259(2)
Definite Integrals Involving Odd and Even Functions
261(1)
12.4 Rapid Review
262(1)
12.5 Practice Problems
263(1)
12.6 Cumulative Review Problems
264(1)
12.7 Solutions to Practice Problems
265(3)
12.8 Solutions to Cumulative Review Problems
268(2)
13 Areas and Volumes
270(45)
13.1 The Function F(x) = ∫xa ƒ(t)dt
271(4)
13.2 Approximating the Area Under a Curve
275(5)
Rectangular Approximations
275(4)
Trapezoidal Approximations
279(1)
13.3 Area and Definite Integrals
280(9)
Area Under a Curve
280(5)
Area Between Two Curves
285(4)
13.4 Volumes and Definite Integrals
289(12)
Solids with Known Cross Sections
289(4)
The Disc Method
293(5)
The Washer Method
298(3)
13.5 Rapid Review
301(2)
13.6 Practice Problems
303(2)
13.7 Cumulative Review Problems
305(1)
13.8 Solutions to Practice Problems
305(7)
13.9 Solutions to Cumulative Review Problems
312(3)
14 More Applications of Definite Integrals
315(32)
14.1 Average Value of a Function
316(3)
Mean Value Theorem for Integrals
316(1)
Average Value of a Function on [ a, b]
317(2)
14.2 Distance Traveled Problems
319(3)
14.3 Definite Integral as Accumulated Change
322(3)
Business Problems
322(1)
Temperature Problem
323(1)
Leakage Problem
324(1)
Growth Problem
324(1)
14.4 Differential Equations
325(5)
Exponential Growth/Decay Problems
325(2)
Separable Differential Equations
327(3)
14.5 Slope Fields
330(4)
14.6 Rapid Review
334(1)
14.7 Practice Problems
335(2)
14.8 Cumulative Review Problems
337(1)
14.9 Solutions to Practice Problems
338(4)
14.10 Solutions to Cumulative Review Problems
342(5)
STEP 5 Build Your Test-Taking Confidence
AP Calculus AB Practice Exam 1
347(28)
AP Calculus AB Practice Exam 2
375(28)
Elite Student Edition 5 Minutes to a 5 180 Activities and Questions in 5 Minutes a Day
403(248)
Appendix 651(6)
Bibliography 657
McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide
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