ITEM 
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COMMENTS 
BC Solution Manual 
2/20/2019 
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P. 208. #7, and 10. Errors in solutions. Thanks to Kristie Hubbard's students at Tennessee Christian School. 
BC Acrostic 
2/18/2019 
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#61. Choice II should go from 2 to n. The answer reflects that. Affects #61 in scrambled vesion. #64  Change in choices and solution. Affects #48 in scrambed version. Thanks to Peggie Frisbie. 
AB Solution Manual 
1/25/2019 
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Page 276, #18. Answer corrected. Thanks to Kristie Hubbard. 
BC Calculus Cache #3 
1/24/2019 
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#4. Choices didn't match on student & solutions. #6. Extra dx in problem. Thanks to Hoa Nguyen. 
AB Solution Manual 
1/21/2019 
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Page 163, #15, Should be cos 5x. Thanks to Kristie Hubbard. 
BC Calculus Manual Student version 
1/9/2019 
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Page 108: Definition of Conditional and absolute convergence missing. Thanks Anthony Grabowski.

Calculus Acrostic AB  Student and Solution 
1/5/2019 
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Integral Puzzle
#13: problem shoudl ask for an absolute minimum. Solutions OK. Affects #18 in scrambed version. Thanks to Peggy Frisbie.

Calculus Acrostic AB  Student and Solution 
1/1/2019 
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Integral Puzzle
#41  v(e) = 0 (affects #27 scrambled)
# 42  changed conditions of problem (affects # 16 scrambled)

Test Your Strength Precalc Student & Solutions

12/30/2018 
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#36  Want f(x 1) + 1.
#41  Switched choices c and d
#42  h is the odd function, not f
#44  changed choices to include iii only

Calculus Acrostic AB  Student and Solution 
12/30/2018 
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#58  choice iii should be a. Also affects #38 in scrambled version
#68  choices in different order. Also affects #19 in scrambled version

AB Manual Solutions 
12/18/2018 
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Section 15 differentiability, #8 HW. Slight typos in solutions for b,c,d,e,f,h. Thanks to Keith Pigeon and his students.

BC Calculus Acrostic Student & Solutions 
12/13/2018 
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#43. All choices changes. Letter answer still correct but solution changed. Affects #45 of scrambled version. Thanks to Peggy Frisbie for picking this up. 
AB Exams and Solutions 
12/11/2018 
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Quarterly exam, #16. Choices b, c, and d should not be in the form y =. Thanks to K. Pigeon's students at New Britain High. 
AB Calculus Acrostic 
11/9/2018 
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#46, added 1/3 in volume formula. Doesn't affect answer.
#47. Changed choices.
#54. Made the problem clearer and changed answer T.
Thanks to Peggy Frisbie.

BC Calculus Acrostic 
10/22/2018 
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#24. Should start with a > 0.
#30. Arc length should be taken from x = 0 to x = 1. Changes affect same problem numbers in scrambled version. Thanks to Peggy Frisbie.

AB Calculus Acrostic Derivatives 
10/19/2018 
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#42. Function refdefined to fit solution. Also affects # 56. Thanks to Peggy Frisbie. 
AP Statistics Descriptive Stats Ex  Soln 
10/16/2018 
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D10, #1c. Answer should be 48%. Thanks to Catherine Cameron. 
Calculus Acrostic BC 
9/28/2018 
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#21. Changed original function to a numerator of 2 and changed one of the choices. #23, changed choice A. Thanks to Peggy Frisbie.

Calculus Acrostic AB 
9/27/2018 
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#25. Mistake in 2nd derivative. Had to change one of the choices. Affected # 59 in scrambled version.
#28. Letter answer right but solution used a^{2sqrt(x)}. Affected #14 in scrambled version.
Thanks to Carolyn Guzman.

BC Solution Manual 
9/18/2018 
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Page 191: # 2: Error in first term  should be 5x^{3}/3. Page 192: the ln term in answer should be positive. Thanks to Anthony Grabowski. 
BC Solution Manual 
9/17/2018 
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Review: R5, p. 189. Function Analysis #4. On f " (x), the first term should be  cos^{2}(x). Thanks to Christy Gallei. 
BC Exams 
9/8/2018 
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BC Exam  Solutions Aa. L'Hospital's Rule Exam. #11 should be 2/pi. #14 had a solution for another problem. It is fixed with the answer 2/pi. Thanks to Kristie Hubbard and her student Jireh Cen. 
AB Solution Manual 
9/7/2018 
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Page 39, # 29. Tangent line is y = 18x + 9. Affects Answer only page as well. In Answers only, page 298, # 35  typo in answers. Thanks to Kristie Hubbard. 
AP Statistics Manual Student and Solutions 
9/7/2018 
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Teacher version, Density Curves: Example 4, c, d, have been changed as well as improving diagram. Thanks to Terri Hipps. 
BC Manual Solutions 
9/6/2018 
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P. 189, #3. Inflection points are plus or minus square root of 2 divided by 5. Thanks to Anthony Grabowski. 
RU Ready Solution version 
6/4/2018 
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U8. Answer is [1, 0.801). Thanks to William Preston. 
AB Solution Manual and AB Answer Key 
5/7/2018 
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Ch 26 HW #1. Parentheses shoudl read x  2.
Ch 31 HW #6: x^{2} shouldn't be in solution.
Ch 32: HW #24. du shouldn't be negative and final answer should be positive.
Ch 34: HW #2b. Denominator in solution step should be 3.
Ch 35: HW #4d.(1  x) should be in radical.
Ch 38: HW #1e. Final answer is 42. Trapezoid should be (1/3)(40 + 20).
Answers: Ch 41, #1b, Answer should be $5826.32.
Thanks to Ashley Moran.

Test Your Srength AB and AB/BC Solutions 
4/26/2018 
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#36. In the solution, the integral should be of e ^ sin x. Doesn't affact answer. This problem is also #36 in AB/BC exam. #46 solution should be an underestimation of f (5.5). Thanks to Jennifer Rich. 
AB Demystifying Solution FR 
4/21/2018 
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#66c. First line of solution should have 1000 in front of integral. Doesn't affect answer. Thanks to Harry Myrick. 
AB Manual Student & Solution 
4/18/2018 
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P. 214, b. Formula slighly changed (radius is squared) and answer changed. Thanks to Chunchi Shen 
BC Calculus Cache 10 Parametrics 
4/16/2018 
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#9. Added a figure, changed the choices and solution. Thanks to Susan Lohr. 
BC Calculus Cache 08 Parametrics 
4/13/2018 
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#6. Analysis correct but ansser is B. 2. Thanks to Susan Lohr. 
BC Solution Manual 
4/6/2018 
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P 189, #3. Forgot the 2x in f''(x). Bu the 2nd derivative is correct. Thanks to Barbara Rothstein. 
Demystifying the BC FR Exam 
4/3/2018 
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#10. Should pe pi(e  2). Thanks to Harry Myrick. 
4 AB Exams Solutions 
4/3/2018 
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Exam 3: FR#5. Slighly revised answer b and changed answer d.
Exam 4: FR#2. answer b is 16.910.

Demystifying the AB MC Exam student & solutions 
3/14/2018 
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Page 25. #52. Not sure why I changed choice A to 0.064 on 3/14. The answer 0.064 is correct which is now choice A. Thanks to Michael Weyer. 
Demystifying the AB MC Exam student & solutions 
3/14/2018 
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Page 25, #52. Choice A. should be 0.064 and is the correct answer. Also affects 4 AP Exams, Exam 2. #11.
Page 25, #54. In answer f(4) = 5. Also affects 4 AP Exams, Exam 4. #18. Thanks to Charlotte Zajac.

BC Solutions Manual 
3/12/2018 
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Page 73, #4. Final solution corrected. Thanks to Tony Grabowski. 
AB Solutions Manual 
3/3/2018 
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Page 221, 8d. Answer is 1024 pi/3. Thanks to John Silcox. 
AB Student & Solution Manual 
2/26/2018 
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Page 181, c. F(14) = 9, F(16) = 9.5.
Page 181, l. added the caveat that day > 2.
Thanks to Lori Freed.

BC Solution Manual 
2/17/2018 
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P. 55, #71. There are no tangent lines at the pole. Thanks to Tony Grabowski. 
AB Solution Manual 
2/14/2018 
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p 179, 1b. decreasing on (5, 8]. 1c. F(5) = 6. Thanks Ethan Roe. 
AB StepbyStep Solutions 
2/9/2018 
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#39, g(x) shouldn't be negative. Thanks Patricia Hill and students. 
AP Stat Solution 
1/29/2018 
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ProbEx, p:16, #14, c ii)/ Answer corrected. Thanks to Lynn Church's students. 
AB Solution Manual 
1/25/2018 
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Page 143, #1. Derivative is 0.2  10s. Thanks to William Preston. 
AB Solution Manual 
1/23/2018 
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Page132, #5. Solution should say x not equal to 1. Thanks to William Preston.

Diving In AB  Student & Solution 
1/17/2018 
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Topic 16, #4. Changed the answer choices and the solution. Thanks to Janice Stadler. 
BC Student and Solution Manual

1/9/2018 
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Page 100. Clarified the Integral test slightly. Thanks to Anthony Grabowski for the suggestion. 
AB Student and Solution Manual 
1/9/2018 
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Section 16  Related Rates. No corrections but I emphasized in certain problems that the rates of change were for that moment in time only. I also added a footnote for classwork #2. 
AP Stat Student & Solution 
1/7/2018 
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Affects InfEx1 and TInfch1 documents. Added a stipulation about sample size when using the Central Limit Theorem. Affects a couple of examples in the exercises. Thanks to Janet Delery for pointing this out. 
BC Solution Manual 
1/4/2018 
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Page 85, #13. The largest value of the 4th derivative of f on [0,1/3] occurs at z = 0 and is cost pi/6. That changes the Lagrange error but not the conclusion. While using 16 as the max value of the 4th derivative is not wrong, it really isn't the Lagrange error. Thanks to Jill Bell. 
AB Student & Solution Manuals 
12/17/2017 
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In Non Essentials, changed the order. Made 24a Advanced L'Hospital's Rule and 24b Newton's Method. This changes the table of contents and also the order of Helpful Hints. 
Across Down Soluttions 
12/15/2017 
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Across 29. N(20) = 8, not 20. Doesn't affect final answer. Thanks to Janet Williams. 
AB Solution Manual 
12/8/2017 
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Page 118: #10, intervals of concavity corrected. #12: fraction should be multiplied by 2/2. Thanks to Dr. Michelle Arnold. 
BC Student Manual 
12/7/2017 
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Page 84, #11. Questions should be asking about the interval [0, 0.1], not [0, 1]. Thanks to Tony Grabowski. 
AB Exams C  Student and Solutions 
12/1/2017 
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Comprehensive midterm: #30, all choices should have angles of ax. 
AB Exams A  Student and Solutions 
12/1/2017 
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Chain Rule, Trig, and Implicit Exam: #18. Point should be (6, 2). Answer changed. Thanks to Keith Taylor's students for finding this. 
BC Manual Solutions 
12/1/2017 
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Page 38, #2c. In denominator in solution's 2nd line, ln 400 should be ln 499. Answer still correct. Thanks Anthony Grabowski. 
Calculus Cache AB 
11/10/2017 
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AB, 15 Related Rates. #22. Choices changed as there was an error in the solution. Thanks to Jesse Ramirez for spotting it. 
Across & Down Solutions 
11/7/2017 
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Across 47. Doesn't affect the final answer but on [0, 2], x = 1/4, 3/4, 5/4, 7/4. 
RU Ready Solution 
10/12/2017 
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Page 44, #7. Sin pi/2 = 1, not 1/2. Thanks LaWanda KingButler. 
AB Solution Manual 
10/4/2017 
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Page 34, 7b. Denominator incorrect. Thanks to Chunchi Shen. 
BC Solution Manual 
10/3/2017 
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Page 198, part b. In the 3 solutions, the right side of the equation should use v instead of a. Thanks to Tony Grabowski. 
BC Manual Student & Solution 
9/24/2017 
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Page 193, #1b should be asking for relative max/min.
Thanks to Tony Grabowski.

AB Student & Solution Manual 
9/17/2017 
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Pages 22 and 24. Footnotes 5a and 5c are moved.
Page 26, #23. Problem should say sin x, not sin pi
Page 20, #17e,f. According to definition on page 17, limits as x approach infinity should be infinity as curve eventually gets higher than any value k.
Page 26, #27. Soln, first limit should start: cos 4pi
Thanks to Lori Freed.

AB Solution Manual 
9/15/2017 
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Page 85, #3. Derivative incorrect but solution correct.
Page 86, #7. Clarified solution.
Thanks to Steve Clinton.

BC Solution Manual 
9/13/2017 
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Page 189, #6. Error in derivation but solution correct. Thanks to Anthony Grabowski. 
AB Student & Solution Manual 
9/13/2017 
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Page 20, #13e. Answer is 3.
Page 20, #16. Student manual should be for 1, not 1.

RU Ready Student & Solutions 
9/12/2017 
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Page 17, #10. Middle term of problem should be 11x^{2}
Page 19, #1b. Point should be (5, 1).
Thanks to LaWanda KingButler.

BC Student & Solution Manual 
8/29/3017 
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P. 183, #12. Second fraction in numerator of problem should be 1/x.
P. 184, #7. Answer should be 6pi.
Thanks Anthony Grabowski.

Demystifying the AP Exam FR Student & Solution 
8/26/2017 
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P. 16, #25b. Answer is IVT, not MVT.
P. 23, #36. Forgot the word searchlight.
P. 30, #46. Changed problem.
P. 34, #57b. Answer should be miles traveled.
P. 43, #71d. Final answer should not include 800.
P. 52, #86 is mislabeled as 88

Demystifying the AP Exam MC Solution 
8/25/2017 
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#175: Answer is C. Work is correct. 
AB Manual Student and Solutions 
8/12/2017 
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A teacher who wishes to remain anonymous has kindly gone over the entire AB manual and found a number of errors. Many are typos, but a typo in math just looks like a wrong answer. He has my undying gratitude.
Rather than spell them all out, it is much easier, as the 20172018 school year begins, for teachers just to download the student and solution versions and they are guaranteed that they will have the most uptodate version.
For teachers who purchased solutions, concat me at team@mastermathmentor.com for the links.

Precalc Student and Solution Manual 
8/3/2017 
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A teacher who wants to remain anonymous found a number of errors in the precalculus manual. It is recommended that you redownload both the student and solution versions so that you have the most accurate version. 
BC Manual Student and Solutions 
7/24/2017 
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Page 11 on student: Tabular method description: x^{n}cos kx. Page 26: changed part b problem and solution. Thanks to Anthony Grabowski. 
BC Manual AB Review pages 181  204 Student & Solutions 
7/25/2017 
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Changes on pages 183 (19), 188 (2), 189 (6), 194 (e), 201 (c), 202 (7a). Suggest you redownload. Thanks to Anthony Grabowski. 
RU Ready Solutions 
7/18/2017 
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Topic F, Assignment, #8. Middle term in trinomial is 20x. 
Jeopardy 1  Student & Solution 
5/12/2017 
Website fixed. Download solutions. 
What's My Area $300 and $400 have had choices and answers changed. Thanks to Leo Hartsock. 
Demystifying AB MC Students & Solutions/BC Exam #3 Solutions 
5/3/2017 
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#141: h'(pi/3)
#148. Initial condition is 68 degrees.
#149: Answer is choice D. This affects BC Exam #3. Problem IB#9.
Thanks Janie Waidelich.

4 BC Exams, Student & Solution Exam 2 
5/2/2017 
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Part IB: #3. Sign of answer is wrong. Had to change the sign choice D to correct answer.
#10: 4th term in solution should have denom = 2.
#11: Inverse should be in terms of y.
Thanks Dick.

Demystifying AB MC Exam Student & Solutions 
5/1/2017 
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#122. Choice c (which should correct) needs a constant a. Thanks to Janie Waidelich. 
4 BC Exams, Student & Solution Exam 1 
4/30/2017 
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Page 16, #13. Student version has no choice.
Solution version: Typos in solutions of Part IA, #1, Part IB, #2, 7, 10 and 14. Also Part II2a and Part II6b. Doesn't affect answers. Thanks Dick Stibor.

Revised Triple Jeopardy BC 
4/28/2017 
Game operates as usual. Redownload Triple Jeopardy BC. 
Polar Equations $300: Graph incorrect. Work correct. Thanks to Vicki Carter. 
Revised Jeopardy 
4/28/2017 
Game operates as usual. Redownload Jeopardy. 
Highs and Lows $400. Question should ask for minimum, not maximum.
Derivatives $300. First line in solution corrected.
Thanks to Vicki Carter.

Revised Jeopardy 
4/27/2017 
Game operates as usual. Redownload Jeopardy. 
Limits $400. e^(1/x) and cos (1/x). Thanks Bruce Hartman. 
Demystifying AB MC Exam Student & Soutions 
4/26/2017 
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#155. Changed choices B and C. C is the correct answer. Also affects practice exam #4, Part A, #21. Thanks John Silcox. 
Test Your Strength AB and AB/BC 
4/24/2017 
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#18 in both exams. The answer is correct. In the solution, a(pi/4) = 6pi which is different from answer key. It is not the correct answer to the problem. But I corrected it and made choice B 6 pi. Thanks to Ferd Schneider. 
Demystifying AB MC Exam  Student & Solution 
4/23/2017 
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#136. Problem incorrect. It has been changed to match the solutions. Thanks to Michele Schempp for spotting it, This also affects the practice exam #4, part B, #9. 
Test Your Strength BC and AB/BC 
4/18/2017 
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Sitting on the deck of a cruise ship with free wifi at the port. Got notification of 2 errors in the BC version and wanted to get them updated. Thanks to Leo Hartsock for spotting them.
BC # 36. The original series should not have a 2 in in. It should be cosine of multiples of pi.
BC # 41. The answers were calculated incorrectly. THey are now right and the answer is D. The grading spreadsheet has been changed. THis affects the AB/BC exam # 41 as well.

BC Exam Solutions 
4/7/2017 
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First Power series quiz (ch 18  24)
slight changes in solutions to #4, 8, 9
Second Power series quiz (ch 18  24). In original problem, f(1) = 0 for continuity.
Change to d (signs of derivatives changed meaning a relative minimum). Thanks Dick.

BC Test Your Strength Student & Solution 
4/5/2017 
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BC, Part A, #21. The limit for #I changed as x approaches pi/2 from the left insuring that the function is defined. Doesn't affect solution. Thanks to Ferd Schneider. 
AB/BC Test Your Strength Gradesheet 
4/5/2017 
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The gradesheet for AB/BC had #29 and #30 misclassified. Doesn't affect grading but you want to use the new grading spreadsheet. Thanks to Brianne Allbee for spotting this. 
BC Solution Manual 
4/3/2017 
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Page 131, #2  typo 2nd line of solutions
Page 133, #11  typo last line of solution
Page 133, #12  error in general term sokution
Page 133, #15  error 0.0129
Thanks Dick..

Test Your Strength AB/BC Version Student & Solution 
4/03/2017 
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AB/BC exam #10 and BC#10 in Part A. Ferd Schneider picked up an error in the soution. Turns out that the solution is fine  it's just the x part of the given parametric has a coefficient of 4 for both terms rather than just for the first. 
BC Exams Student & Solution 
4/02/2017 
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First Power series quiz (ch 18  24), #7 problem changed to match solution.
Second Power series quiz (ch 18  24), #3. 2nd line of solution changed to sin (x^{4})
#11. Problem changed to match solution.
Power series AP type: general term for g(x) corrected. Thanks, Dick.

BC Demystifying MC Solution and BC Practice Exam #3 
4/02/2017 
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#76. Answer should be B.
This also effects 4 AP Exams  Exam #3. Part A, #26. Thanks Megan Simoneau.

BC Solution Manual 
3/28/2017 
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Page 129, #18. Small typos corrected
Page 130, #20: All left side of equations are e^{ix}.
Page 131, #2b. Several small errors corrected.
Page 133, #15. Error = 0.0129. Thanks Dick.

AB Student and Solution Manual and Hints. 
3/29/2017 
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Page 17. Expounded on oscillating curve at bottom right of page and changed footnote 4a. 
AB Student and Solution Manual 
3/29/2017 
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Thanks to Wesley Conner, student of Stan Gibby at Scottsboro High school for discovering the fact that the problem situation for #6 on page 220 is not realistic. He investigated and we adjusted the problem so that the number of gallons of fuel in a wing makes sense for this type of plane. 
Test Your Strength AB Solution 
3/29/2017 
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#50. Slight change in solution wording. No change to answer. Thanks Vesna Kukic. 
BC Manual Student 
3/28/2017 
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Page 105, #3 and #4. Comparison series changed. Thanks Rich Kleinschmidt. 
BC Manual Student & Solutions 
3/28/2017 
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Page 124, #4. First term is ln 4.
Page 125 #1 Change student problem to be (x/2)^n
Page 125: 1/x = 1  (x  1) + (x  1) ^2 + ...
Page 126: 1st parabraph: last term is 8.5^6/6!. Thanks Dick.

Test Your Strength 
3/28/2017 
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For the AB and AB/BC exams, Peggy Fribie felt my use of the word range was incorrect on problems 20 and 32. I clarified things my asking the difference between the maximum and minimum values. The solutions haven't changed. On the AB exam, I simplified the graph on #31 to emphasize that the graph oscillates. Thanks Peggy. 
AB Solution Manual 
3/28/2017 
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Page 212: #13: Answer is 12 + 10 = 22. Thanks Lori Freed. 
Test Your Strength 
3/27/2017 
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AB Student and solution, part A, #18. Slight change in the wording to make more sense. Answer unaffected.
AB/BC Student & solution. Same correction as above. Also, #27. Answer had different limits than problem itself. We changed the problem to reflect the answer. So Grading spreadsheet unaffected but student & solution version is. Thanks to Brett Baltz.

AB Solution Manual 
3/27/2017 
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Page 216, #5b. Answer is 2pi.
Page 216, #5c. Second integral goes from 1 to e. Answer changed to 1.437pi. Thanks Wes Davis.

BC Manual, Student & Solutions 
3/26/2017 
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Page 120; #3 and 4 answer is (infinity,infinity).
Page 121: Slight typos in solutions to 8, 8, 10 and 12. #12 solution to different problem. Changed problem to match solution.
Page 122: 4th derivative  last term is (x  c)^{4}
Page 123, #1. Denominator should have (2n+1).
Page 124. #3. Problem changed as solution was different from problem.
Thanks Dick.

Test Your Strength Solutions AB/BC and BC 
3/25/2017 
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#1, both exams. Series 3 should have 1/2 as 2nd term. Doesn't affect answers. Thanks Jaime Garcia. 
BC Solution Manual 
3/23/2017 
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Page 119, Ex 8.Third term is x^{3}/4 and fourth term is x^{4}/5. Thanks, Dick. 
AB Manual Solution 
3/22/2017 
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Page 207, #4d. denominator should have square root (1  x).
Page 208, #13. 3 in the denominator for a, not 5.
Thanks Lori.

4 AB Exams 
3/20/2017 
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Exam 4: #4. Changed choices and answer.
#15. Answer should be a. (affects Demystifying AB MC #141).

AB Student & Solution Manual 
3/20/2017 
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Page 206, #3. Final answer missing x in numerator.
Page 206, #17. Problem should be integral of square root of 8x  x^{2}. Thanks Lori Freed.

4 AB/BC Exams Student & Solutions / Demystifying AB MC 
3/18/2017 
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Exam 1:
Free response, 2d. Eliminate the 100. Answer is 34.045.
Exam 2:
#7 (AB): Student problem doesn't match solution problem. Answer should be B. (affects Demystifying #10)
#19 (AB/BC): Choices weren't A, B, C, D.
#20 (AB): Correct answer is B. Work correct. (affects Demystifying #137).
#7 (AB/BC) , #19 (AB/BC) and 20 (AB) corrected in answers in back.

AB Manual Solutions 
3/17/2017 
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Page 217: 7c: Mentioned is should be an isosceles right triangle.
Page 216, 8d: Answer is 33.510. Thanks Lori Freed.

Ahead of the Curve 
3/16/2017 
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Page 20, part e. Formula uses x^{2}, not x^{3}. Answer is 4(1.457)=5/629. 
BC Manual Student & Solutions 
3/16/2017 
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Page 79. Reference to L1, L2, L3 and L4 on th3 calculator should be Y1, Y2, Y3, Y4. Thanks Rich Kleinschmidt. 
BC Manual Solutions 
3/16/2017 
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Page 114, #1. Limit comparison not applicable. Thanks, Dick. 
Diving In AB Solutions 
3/14/2017 
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#9, Fundamental Thm, #4. Correct work but ansser is B, not D. Thanks Dave Hale. 
BC Manual Solutions 
3/14/2017 
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Page 112. Slight changes in solutions to 1, 2, 3 a,d 7. Thanks Dick. 
Demystifying AB Exam MC Student & Solutions 
3/13/3017 
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#9. Problem changed. Solution still correct. Affects 4 AP exams (Exam #2), #5. Thanks to Bucky Garner. 
AB Solution Manual 
3/13/2017 
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Page 202, #8: F(2) = 14. Lower limit of integral should be 4. Thanks Lori Freed. 
BC Manual Student & Solutions 
3/13/2017 
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Page 105, # 5: Reworded to make more sense.
Page 105, #9: Limit is 1/4. Same conclusion.
Page 106, #11: Divergent.
Page 106, #8L 100 cos 0 =100.
Page 106, #12: no need for L'Hospital's rule.
Page 107: #1: should state that it converges,
Page 107, #3: 1st line should say 4/1 + 4/2 ...
Page 108. Reworded first paragraph.
Page 111, #5. Reworked solution.
Page 111, #7. Last fraction should have numerator of n = 2. Limit is 1/e.
Page 112: Reworked solution.
Thanks Dick.

AB Solution Manual 
3/10/2017 
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Page 185, 3b: du = 2dx and upper limit in 2nd line is pi/2.
Page 198, #6i: 2nd line is positive 78.289.
Page 215, #3a: dx, not dz.
#3d: Iy  1), not (y  4)
Page 221: #7; x = 0 not neccesary in problem.
Page 222, #33c. Double radius: 16.554 is diamater.
Thanks Lori Freed.

AB Solution Manual 
3/10/2017 
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Page 91, #24. Forgot to square (5/3). Answer changed. Thanks Megan Simoneau. 
BC Solution Manual 
3/9/2017 
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Page 120, #6. Corrected the expansion of the series. Solution correct.

AB Solution Manual 
3/7/2017 
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P. 197, #3. Last line should read (32/3). Thanks Lori Freed. 
Diving In AB  08 Solutions 
3/7/2017 
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Integration w/trig functions, #1. Answer is A. Work correct. Thanks Dave Hale. 
Demystifying BC Exam MC 
3/7/2017 
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#27: Solution had typos. Answer still correct. Affects BC Exam #1, #21 as well.
#64. Choice B written incorrectly. Answer still correct.
Affects BC Exam #2, #13 as well.

AB Solution Manual 
3/6/2017 
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Page 196, #7: Distance for t = 45 = 0.53 and t = 55 = 0.25.
Page 220, #5a: delete 0.133 pi + 0.089 pi.
Page 220: #5c: Integrand squared.
Page 224, e. Need equal sign after p(30)
Thanks Lori Freed.

AB Student & Solution Manuals 
3/4/2017 
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Page 179, c. F(5) = 6 so mas ix 6.
d. Inf pts at 3, not 3.
Page 180: a. F(1) = 1.9.
c. Minimum is pi, not pi
Page 181, d: Add inf pt at x = 12
e. Graph changed (conc up on (12,13))
Graph given more room on student manual
j. Days 14 and 15.
Page 211: 2nd function should have x^{2} in numerator in solution.
Page 220: a. Integral from 0 to 2
b. Integral from 0 to 4.
c. Integral from 0 to 2 and graph changed.
Thanks Lori Freed

BC Exam Solutions 
2/28/2017 
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Sequence & Series Test (Ch 16  19). #3. 5th term is 1/60. #6 is 2^{n}/n!. Thanks Dick. 
AB Manual Solutions 
2/25/2017 
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Page 193, #20. Slight change in solution not affecting answer.
Page 193, #23. Solution changed.
Page 194, #25. Second line of solution  integral from 1 to 3.
Page 197: #1  2nd line in answer should be 12  3t.
Page 198, #6: b: v(2) = 200 ft/sec. c: 8 2/3 sec
e: 6 1/3 sec. Thanks Lori Freed.

Calculus Cache  Student & Solution 
2/2t/2017 
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BC Topic 11 (Taylor polynomials). #15. The function has been changed to match the solution. Thanks Lloyd Connors. 
BC Exam Solutions 
2/24/2017 
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Exams B: Sequences & Series (16  19), #13: first line of solution is 2/ln(3x + 1).
#22: Result of integration is 1/3.Thanks Dick.

BC Student & Solution Manuals 
2/24/2017 
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Page 91: First term in solution is 2/3.
Page 101: #2. 4th term should be 1/e^{3}. Same in solution. Thanks Dick.

BC Solution Manual 
2/21/2017 
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Page 95, #2. 5th term should be 9/25.
Page 95, #8. Derivative is 2^n ln 2.
Page 98, #15. Series should be from 1 to infinity. Thanks Dick Stibor.

AP Stat student & Solution 
2/21/2017 
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InfTch2: Chisquare example 2 solution was slighly corrected. 
4 AP Exams, Student & Solution 
2/21/2017 
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Exam 4:
#5. Option II missing a +x at thd end.
#12: Question should be at ?/3 to match solution.
#21. Choices changed and new answer is D.
Calculator
#4: Answer is B. Work correct
#8: Initial condition should be 68.
#12. One of the expoents was wrong is problem.
Free response:
#2b: Need an extra 1/2 for semicircle.
#3c: Correct answer is 1.
#4b: Problem should go out to 45 minutes.
#6b: Quadrant should be IV.
#6c: Point should be (3,4).

4 AP Exams, Student & Solution 
2/20/2017 
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Exam 3:
#3. First line of solution: 3d should be 4d. Answer unaffected.
#22: Answer C should state at x = 1.
#26. Given interval should include 6.
Part B: #3. Height instead of length.
#10: Answer is D. Work correct.
Free Response 2. Problem rewritten with given functions as a(t) and m(t) instead of using Caps.

4 AP Exams, Student & Solution 
2/20/2017 
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Exam #1: Free response, #3. Rather than saying the height is increasing at a negative rate, say that it is decreasing.
Free response, #6d. Given units should be 2 yards/sec^{2}.

BC Solution Manual 
2/20/2017 
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Page 94, #7. Extra terms are 1/(n + 1) and 1/(n + 2).
Page 96, #9. The term should be 8/125.
Thanks Dick.

AB Student Manual 
2/16/2017 
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Page 18, #5. Limit questions as x approaches 1. Thanks Olena Kapatsyna. 
Diving In AB Students and Solution 
2/15/2017 
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Topic 37, #4. Problem slighly changed. 
Ahead of the Curve  Student & Solution 
2/14/2017 
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Curve 6, Part o. Quadrifolium is r^{2}=32 cos 4 theta. Affects answer.
Curve 11, part d. Should be x^{2} in parentheses, not x^{3}. Thanks to Jerry Glaser.

BC Student & Solution Manuals 
2/14/2017 
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Page 92, #1. Sum is 2 + 4 + 8 + ...
Page 95. #8: 2nd line of solution changed.
Page 95, #9. Series missing from lim.
Thanks Dick Stibor.

AB Student & Solution Manuals 
2/14/2017 
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Page 141, #9: 576, not 476 (answer unaffected).
Page 170, 1d: LRS = 1.095. Trap = 0.997.
Page 171, 7th line should say figure to the right.
Page 173, g and h. Altered solution (still correct).
Page 194, #28: Last line: F(6) = ...
Page 194, #30: Question should say F(1) =
Page 194, #31. Last line: F(1) =
Thanks to Lori Freed.

BC Student & Solution Manuals 
2/13/2017 
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Page 178, #11. x bar = 1.246 and ybar has same denominator as x bar.
Page 178, #12. Base measurement = 9.
Page 178, #13. Base measurement of 5 missing in student manual. Thanks Dick Stibor.

AB Manual & Solutions 
2/9/2017 
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Page 107, #23. Teresa Cox picked up that the problem needs to be redfined as 1 = January, 2 = February. And the avareg rate of change is [S(12)  S(1)] / (12  1). 
AB Exams Solutions 
2/8/2017 
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Exams d: Area & Volume takehome (3637). Part b Answer is 922.272. Thanks to Megan Simoneau. 
AB Solution Manual 
2/7/2017 
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Page 192, #6. Final exponent should be 2/3.
Page 194, #32. Answer is 18.855.
Page 198, #6b. Answer is 200 ft/sec.
Thanks to Kristie Hubbard.

BC Solution Manual 
2/7/2017 
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p 169, 2d. Integral changed to make it easier to understand. Old integral was OK.
Page 170, 4e. Integral from 2 to 2.
Page 171, #5. L = 2x
Page 171, #6. Integral: 1,523.278.
Page 172, #8, #11: x = sqrt (y)
Page 172, #12. Answer is 852.188
Page 176, #6: 2nd line: integral from 2 to 1.
Page 176, #7. Rounding error: y bar: 0.604.
Page 177, #6. X bar = 3.
Thanks Dick Stibor.

BC Solution Manual 
2/6/2017 
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Page 175, 4a: 2nd rectangle centroid is (2.5, 1) affecting answer 4b.
Page 176, 5c. ybar turns out to be (128/5)(3/32). Answer of 2.4 still correct.
Thanks Dick Stibor.

SAT Clue Student & Solution 
2/6/2017 
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#29, Location. CD = 13. (doesn't affect answer).
#25: Occupation. Functions in solution don't match student version. Now they do.

BC Exam Solutions 
2/4/2017 
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Exam 1, #8. Answer hasn't changed but it is more involved than shown. Necessary to change to sines and cosines.
Exam Ch 24, #8. Student version changed and solution version matches it. Thanks to Stefan San Miguel.

BC Solution Manual 
2/4/2017 
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Page 166, 2c: Equation after integration should be in h.
Page 167, 12. First integral result is 308.22 inoz.
Thanks Dick Stibor.

AB Student and Solution Manuals 
2/3/2017 
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Page 122: function at top of page should have in parentheses (x  c). Thanks to Tony Grabowski. 
AB Student and Solution Manuals 
2/2/2017 
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Page 204, #6. Hypotenuse should have square root.
Page 205, #7d. Student version changed to x arc tan x to match solutions.
Thanks to Kristie Hubbard.

BC Student & Solution Manuals 
2/1/2017 
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Page 161, 6c: figures transposed: 11,980. Dinal integral missing a y.
Page 161, 7d: Answer should have comma, not period.
Page 162, 3a: Final integral answer is 952.4
Page 163, #6a. The chain should be coiled on to of the airconditioner changing integral limits. Answer changed affecting 6b.
Page 164, 9. Table values corrected.
Thanks to Dick Stibor.

AB Solution Manual 
2/1/2017 
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Page 200: #4: Last term of of trap rule is (5/2)(20 + 5).
Page 200: #5a and b. The constant should be +2/3.
Thanks to Kristie Hubbard.

4 AP Exams (AB and BC) Solutions  Exam # 1 
1/31/2017 
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#2c. A mention was made about addressing the endpoints although technically not necessary.
#2d. Answer changed because of initial 100 gallons in tank. Thanks to student Peri M. in Paul SooHoo's class.

BC Manual Student and Solutions 
1/31/2017 
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Page 158, #2c; Solution denominators should have e^{2x/5}.
Page 159, #3. Globe should be labeled 12,000 miles.
Page 159, #3c. Denominator is 3,750,000 giving 20%.
Thanks Dick Stibor.

4 AP BC Exams Student & Solutions 
1/31/2017 
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Exam 2, Free Response # 2. Julio Avasan's class noticed an error on this problem. Without gong into detail, the problem is sketchy because the solution to DEQ will be undefined at x = 2. So parts a, b, c are changed. Thanks to your students, Julio.

Diving In  Student & Solution 
1/30/2017 
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Diving In #6  Straight Line Motion #4. Choice D should be 0.60. The student version still had 5 choices. It has been changed to 4. Thanks to Dave Hale. 
AB Student & Solution Manual 
1/30/2017 
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Page 220, #6. Problem should have a denominator of 150, not 100. Thanks to Michael Morton. 
BC Manual Solutions 
1/26/2017 
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Page 153, halfway down; integral from 3 to 5 should equal 3. Thanks Dick Stibor. 
Demystifying BC Exam MC  student and solutions 
1/26/2017 
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Problem #35. Changed because there are two solutions. Thanks to Kim Thomas. 
BC Manual Solutions 
1/24/2017 
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Page 153, last example first line. Last two terms ... +4f(8) + f(9)
Page 154, Ex 1; (70  30)/3(8) [ ...
Page 155, Ex 6. Limits should be 0 to ?
Page 156, 3rd and 4th derivative changed.
Thanks to Dick Stibor.

AB Manual Solutions 
1/23/2017 
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Page 169: #7. Final answer changed. Thanks to Monika Daugherty. 
AB Manual Solutions 
1/21/2017 
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Section 35  inverse trig
Changes in the pictures for 2d and 3c. Answers not affected. Thanks to Michael Morton.

BC Exam Solutions 
1/21/2017 
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Epsilondelta quiz: #3, epsilon = 0.003  solution
changed. #4  solution changed.
Exam chapters 24
#7. 2nd term absolute value should be x + 3
#11: 2 after integrating inestead of 2
#13: changed solution slightly
Thanks to Dick Stibor

BC Solution Manual 
1/18/2017 
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Page 145, #4. Corrected 2nd line of soluion.
#7. Corrected plot
Page 148, #6. Eliminated dx on v
Page 149, #2. Corrected A and B.
#3. Corrected A and B.
Page 150, Numerous changes to #6.
Thanks to Dick Stibor.

Demystifying AB Multiple Choice Exam Student & Solution 
1/17/2017 
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#133 and #135. Should say quartercircles, not semicircles. Thanks to Kevin H. for finding this. 
BC Student & Solution Manual 
1/11/2017 
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Page 146. Wrote answer to example on top in terms of cosine to match example 1 below. Elininated erroneous first line of example 1. 
AB Solution Manual 
1/11/2017 
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Page 160, #18. Last term should have coefficient of 2, not 4. Thanks to Wes Davis. 
BC Solution Manual 
1/10/2017 
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Page 145: Corrections in solutions of #1, #2.
Thanks to Dick Stibor.

SAT Clue Student & Solutions 
1/10/2017 
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Occupation #6: Changed the possible answers.
Occupation # 28: Change the problem because as stated, it was impossible.
Thanks to Nancy Garnan.

Probability Student & Solutions 
1/8/2017 
Download Student and Solutions. 
P1. VennDiagrams
1c: 5/90
1d: Cellphone but no landline: 42/90.
1h) 40/82
P3. Tree Diagrams
1x: .0388/.1156 = .3356
8. AP Stat Practice Quiz
3d: 2.375
3d: 0.625
Thanks to Janet Williams.

AB Solution Manual 
1/6/2017 
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Page 170, #3. Trap rule answer should be 11.875 miles. Thanks to Dianne Nurrenbern. 
AB Exams Student & Solution 
1/3/2017 
Download Student and Solutions. 
Holiday Packet. Changed function on #37. Thanks to Lori Freed. 
AB Solution Manual 
1/2/2017 
Download Student and Solutions. 
Page 77, 9b: Denominator should have a 2.
Page 102: #16. Clarified the question.
Pointed out that we should have some absolute extrema with open intervals. Page 132: #5 interval is (1,8] and Page 133: #4 interval is [2,3).
Page 136: #1: Chart for #1. At x = 1, y = 39.
Thanks to Lori Freed.

AB Exams Student & Solution 
1/2/2017 
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All on Exam D:
Def Integrals/Accumulation Quiz (2829): #15: 23
FTC Exam (3032): #16: 6
Area Quiz Student: 1a) Chart should ask for F(x)

AB Exam Solutions 
1/1/2017 
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All on Exam C. Answers are correct, but the wrong letter answer given in multiple choice.
Holiday take home: #35: a
Midterm Samples: #28: C
Midterm I: #19: d, #24: a, #25: c, #32: d
Midterm Part 2: 3d, answer changed.

AB Exams Student & Solution 
12/31/2016 
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All on Exam B;
Straight line motion (17): a) boxes didn't match.
3 Impt Thms (18) c. Solutions now match graphs.
Abs Extrema AP (19, 20, 21). Function on student version now matches solution.
Function Analysis Practice (1821): 5d is a relative minimum.
Optimization Exam (2223): Extra credit answer changed slightly.
Optimization Take Home (2223): 5b: wording changed: so that the surface area is in terms..."
5e: Changed stats: U.S. uses 200 milion cans a year. Changes final answer.

AB Exams Student & Solution 
12/29/2016 
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Chain Rule #9 practice exam: #4, last factor in solution is (2x + 1). Also #8 and 9 do not match solutions. Student version changed for those problems.
5 AP type problems (1  9): #4 f '(1)= 5/18.

BC Exams Student & Solution 
12/21/2016 
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Midterm exam: #14, choices b and d are the same. b was changed. Free response: 1a) point clarified. 1b) question clarified. Thanks to Dave Hale. 
AB Exams Student & Solution 
12/20/2016 
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Exam C. Midterm sample exam. #11 had no choices. #13 had no table. Corrected. Thanks to Hope Pramuk. 
AB Exams Student & Solution 
12/20/2016 
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Exam C, Midterm exam, #20. Sharpened the problem a bit to reduce ambiguity. Thanks Kevin Barhorst. 
AB Solution Manual 
12/19/2016 
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Page 127, possible graph for f and g changed. Thanks to Lori Freed. 
BC Exams Student & Solution 
12/19/2016 
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Exam B. Midterm. Free response #2. The given info should be t = 0, not t = pi. Thanks to Dave Hale. 
AB Exams Solution 
12/15/2016 
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Exam C Midterm: #8 inadvertently had the same solution s #9. Changed solution to b, also at teh chart at the end. Thanks to Janet Williams. 
AB Exams Student & Solution 
12/14/2016 
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Exams C: Midterm, Part 2, #3. All questions and solutions should be at the point (1, 2). Doesn't change answers  as there was a typo in the point. Thanks Janet Williams. 
BC Solution Manual 
12/13/2016 
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Page 92, #:. 1  1 + 1  1 ...
Page 94, #7: S_{n} = 1.5  1/(n + 2)  1/(n + 3)
Page 94, #8: 2/(2n1)  2/(2n+1)
Thanks Dick Stibor.

BC Exams Student & Solution 
12/13/2016 
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Midterm, #15. Choice a and b were the same. a has been changed. Thanks Dick Stibor. 
BC Solution Manual 
12/12/2016 
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Page 39, #4. Left side, 4th line...e should have a coefficient of 59. Thanks Dick Stibor. 
AB Solution Manual 
12/12/2016 
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Page 106, #6. c = (a + b)/2.
Page 110, #2. Critical values as x = 0, 2 (not 3).
Page 116, #4. Relative maximum at x = pi/4.
Page 123, d. The critical pts for f(x) are 4, 2, 4.
Thanks to Lori Freed.

AB Exams Student & Solutions 
12/8/2016 
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Exams C: Holiday take home  #27. Mistake in solution necessitating change in choices. Thanks to Stephen Lange and his student Valentin Z for spotting this. 
BC Student & Solution Manual 
12/6/2016 
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Page 86, #2. Solutions should have denominators of 1  x.
Page 87, # 11 and #12. In problem changed Lagrange error to remainder to make it clearer.
Page 88, #14. Derivatives (sines and cosines) were fixed. Solution unchanged.
Thanks Dick Stibor.

BC Student & Solution Manual 
12/5/2016 
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Page 91: Solutions checked on #1, 2, 3,6
#10: Problem should be 1/(n+1)
#11: exponent in answer should be n  2
#14: Problem should not have the plus/minus
#21: Problem changed to match solutiom.
Thanks Dick Stibor.

BC Student & Solution Manual 
12/3/2016 
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P. 86. #1 Signs should be +,,+,,+,
P 86, #4, Signs should be +,+,+
P 87, #8. P3(x) should start with ?
P 87, #12 R_{n}(x) should be 0.0000286193
P 87, #13 Line 3 shoudl be e^{1/2}
P 89, #3b. Problem should be .
Thanks Rich Stibor.

BC Solution Manual 
11/30/2016 
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Page 82, #6. Constant should be 13/2.
Page 82, #8. f ''' (x) = 2/(x + 1)^{3} ...Thanks to Dick Stibor's class.

AB Student & Solution Exams 
11/30/2016 
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Exam 1, 2a should be 31/24 =  1.292.
Prac Quiz (23), 5b should say Inst. Vel.
Quiz (23), 5b should say Inst. Vel.
Quiz (4), 5a  d should be the limit as x approaches 1 on the student version.

AB Solution Manual 
11/29/2016 
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Page 132, #6. Absolute max occurs at x = 2. Thanks to Wes Davis. 
Revised BC Exams  student & solutions 
11/28/2016 
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Midterm exam: #12: end line of solution changed.
#15: 2nd line of solution changed.
#19. Original problem has positive numerator.
#25. Eliminate word is.
Thanks Rich Stibor.

Demystifying AB MC  Student & Solution 
11/26/2017 
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#133. In decreasing order, the answer is C. This also affects 4 AP Exams, Exam 1, part II, #8. Thanks to Megan Simoneau. 
Demystifying AB MC  Student & Solution 
11/21/2017 
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#102. Choice II needs + x at the end. This also affects 4 AP Exams, exam #1, part I, # 8. 
AB Student & Solution Manual 
11/19/2016 
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Page 106, #1. This problem needed to be stated more clearly. Thanks Stephanie Mader. 
Demystifying AB MC  Student & Solution 
11/17/2016 
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#65. Changed choices I and II. This also affects 4 AP Exams, Exam #4. 
BC Student & Solution Manuals 
11/16/2016 
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In chapter 14, I incorporated arc lenth for vectorvalued functions for several problems. 
BC Exams Student & Solution 
11/16/2016 
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Download B. Midterm #4. Choice III has changed.
Midterm #10: Solution slighly changed although answer remains the same. Thanks Dick Stibor.

Demystifying AB MC  Student & Solution 
11/16/2016 
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#48. Choices and answers changed. This also affects 4 AB Exams: Exam #4, Problem 12. 
Demystifying AB MC  Student & Solution 
11/15/2016 
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#29. Table of values was missing.

AB Manual & Solutions 
11/14/2015 
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Page 100, #9. Now gives answers in both feet and meters.
Page 100, #10. 16,000 should be 1,600.
Page 101, #13. Car, not Gar.
Thanks to Bruce Hartman.

BC Exam Solutions 
11/14/2016 
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Exam 1, #4. Answer of 0 left out. Thanks Rich Stibor. 
BC Solution Manual 
11/14/2016 
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Page 64, #7: Total force is 86.972 tons.
Page 67, #23. Magnitude and angle of vector changed.
Page 73, #4. s(0) = i + 2j in solution.
Page 73, #5. Change v(0) = i  j.
Thanks to Richard Sibor.

Diving In BC Solutions 
11/11/2016 
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6. Euler's Method # 4. Answer should be B as y(1) = 0.375 by Euler. Thanks to Dave Hale for spotting this. 
BC Solution Manual 
11/11/2016 
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Page 115, #11. This is divergent by the limit comparison test. It telescopes when using log rules but the terms are not decreasing. Thanks to Tess Rivero's wonderful students at Bellbrook High School, Ohio, for finding this. 
BC Solution Manual 
11/7/2016 
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Page 69, #7b: t ? ?/2, 3?/2, ...
Page 70, #1b: Solution: 1 + 1/t.
Thanks Dick Stibor.

BC Student & Solution Manual 
11/5/2016 
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Page 67, #24. 4th line: solution is 6.325
Page 68, #1c. t ? ?(2n + 1)/2
Page 68, #2. At t = 5, force is 1.
Thanks to Dick Stibor.

AB Exams Solutions 
11/4/2016 
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Related Rates solutions: #3a: answers in ft/sec.
7: not dy/dy, dy/dt.
Thanks to Bruce Hartman.

BC Student & Solution Manual 
11/3/2016 
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Page 61, #14. Missing words in problem and answer should have a decimal pt, not a commas.
Page 61, #20. 2nd line of solution should not have 2 theta, just theta. Final asnwer changed
Page 64, #5. Problem improved in explanation and w should be 13i  4j. Thanks Dick Stibor.

AB Solution Exams 
11/3/2016 
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Related Rates Exam  #6. Answer should be in ft/min. Thanks to Bruce Hartman. 
AB Solution Manual 
11/2/2016 
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Page 90, #20. Solution reworked.
Page 105, #5. Solution is 8/9, not 9/8.
Thanks to Sarah Browning.

AB Student & Solution Manual 
11/2/2016 
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Page 85, #6. Problem changed so answer makes more sense.
Page 86, #7. dy/dt = 3/8 ft/sec = 4.5 in/sec
Page 86, #8. Work correct, final answer corrected.
Page 89, #16. Numerator of dh/dt should be 9 dV/dt.
Page 91. Should be solving for dy/dt.
Thanks to Wes Davis.

AB Student & Solution Manual 
11/1/2016 
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Page 69, #6. I should be asking for f(0.99) and f (1.01). Thanks Melissa Dubin. 
AB Solution Manual 
11/1/2016 
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Page 87, #12. Solution changed.
Page 89, #17. r = 3.25, not 3.75. Thanks to Bruce Hartman.

BC Solution Manual 
11/1/2016 
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Page 55, 6b: 4th line on left should have a factor (4 cos^2 2 theta  3) changing the next line to cos theta = plus or minus square root 3 over 2. Answers correct. Thanks Dick Stibor. 