Log of Updates

P. 30, 15c. Inverse incorrect. Thanks to Nancy Swenson for spotting this.

P. 172 #2. Inside integral should be q(x), not Q(x).

P. 179, #5. Table is now included.

Thanks to Elise Jacobs.

Unit 7, page 13. Reworded problem.

Unit 7, page 20, horizontal line test - it is a function if it is not possible to draw a horizontal line passing through the curve in more than one point. Thanks to Nancy Swenson.

p. 90, #19 ii) should use sqrt (340)

p. 92. #26, dx/dt is negative

Thanks to Josh Ipock for finding these.

p. 5, # 16 - rounding error

p. 8, # 24 - 322.31

p 13, # 13 - reference angle is 28 degrees changing answers

p. 17, #17 - 51.170

Thanks to Kristie Hubbard

Page 109, #3. Terms incorrect

Page 109, #9. Error = -1/42 and range corrected.

Page 76, #7.  52.79 instead of 42.79 in the work shown.

Page 102, #10. Answer is pi^2^/8.

Page 106, # 2. Problem changed to match solution.

HW 11e. Coordinates reversed.

HW 12d. Quadrant II so angles chage.

Thanks to William Preston.

Test Your Strength SAT's

Student & Solutions

We have made some changed to some problems. Many are typos although some are major.

11, 25, 32, 33, 38, 48, 55, 57, 66, 67, 72. Suggest you redownload the student version.  Thanks to Lori Freed.

Chapter 35 Inverse Functions:

Changes to solutions 1a, 1b.

Question 2e changed.

Question 3 now matches solution.

Thanks to William Preseton for spotting these.

Page 108: Definition of Conditional and absolute convergence missing. Thanks Anthony Grabowski.

Integral Puzzle

#13: problem shoudl ask for an absolute minimum. Solutions OK.  Affects #18 in scrambed version. Thanks to Peggy Frisbie.

Integral Puzzle

#41 - v(e) = 0  (affects #27 scrambled)

# 42 - changed conditions of problem (affects # 16 scrambled)

Test Your Strength Precalc Student & Solutions

#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

#58 - choice iii should be -a. Also affects #38 in scrambled version

#68 - choices in different order. Also affects #19 in scrambled version

Section 15 differentiability, #8 HW. Slight typos in solutions for b,c,d,e,f,h. Thanks to Keith Pigeon and his students.

#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.

#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.

#21. Changed original function to a numerator of 2 and changed one of the choices. #23, changed choice A.  Thanks to Peggy Frisbie.

#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.

Ch 26 HW #1. Parentheses shoudl read x - 2.

Ch 31 HW #6: x² 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.

Exam 3: FR#5. Slighly revised answer b and changed answer d.

Exam 4: FR#2. answer b is 16.910.

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.

Page 181, c. F(14) = 9, F(16) = 9.5.

Page 181, l. added the caveat that day > 2.

Thanks to Lori Freed.

Page132, #5.  Solution should say x not equal to -1. Thanks to William Preston.

BC Student and Solution Manual

Page 193, #1b should be asking for relative max/min.

Thanks to Tony Grabowski.

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.

Page 85, #3. Derivative incorrect but solution correct.

Page 86, #7.  Clarified solution.

Thanks to Steve Clinton.

Page 20, #13e.  Answer is -3.

Page 20, #16. Student manual should be for -1, not 1.

Page 17, #10.  Middle term of problem should be -11x²

Page 19, #1b.  Point should be (5, 1).

Thanks to LaWanda King-Butler.

P. 183, #12.  Second fraction in numerator of problem should be 1/x.

P. 184, #7. Answer should be 6pi.

Thanks Anthony Grabowski.

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

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 2017-2018 school year begins, for teachers just to download the student and solution versions and they are guaranteed that they will have the most up-to-date version.

For teachers who purchased solutions, concat me at team@mastermathmentor.com for the links.

#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.

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.

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.

Highs and Lows $400. Question should ask for minimum, not maximum.

Derivatives $300. First line in solution corrected.

Thanks to Vicki Carter.

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.

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.

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..

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 (x⁴)

#11. Problem changed to match solution.

Power series AP type: general term for g(x) corrected.  Thanks, Dick.

#76. Answer should be B.

This also effects 4 AP Exams - Exam #3. Part A, #26. Thanks Megan Simoneau.

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.

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.

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.

Page 216, #5b.  Answer is 2pi.

Page 216, #5c.  Second integral goes from 1 to e. Answer changed to 1.437pi.  Thanks Wes Davis.

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.

Page 207, #4d. denominator should have square root (1 - x).

Page 208, #13.  3 in the denominator for a, not 5. 

Thanks Lori.

Exam 4: #4. Changed choices and answer.

#15. Answer should be a. (affects Demystifying AB MC #141).

Page 206, #3. Final answer missing x in numerator.

Page 206, #17. Problem should be integral of square root of 8x - x². Thanks Lori Freed.

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.

Page 217: 7c: Mentioned is should be an isosceles right triangle.

Page 216, 8d: Answer is 33.510. Thanks Lori Freed.

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.

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.

Page 120, #6. Corrected the expansion of the series. Solution correct.

#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.

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.

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 x² 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

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.

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.

Page 91: First term in solution is 2/3.

Page 101: #2. 4th term should be 1/e³. Same in solution. Thanks Dick.

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.

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 semi-circle.

#3c: Correct answer is 1.

#4b: Problem should go out to 45 minutes.

#6b: Quadrant should be IV.

#6c: Point should be (3,4).

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.

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/sec².

Page 94, #7. Extra terms are -1/(n + 1) and -1/(n + 2).

Page 96, #9. The term should be -8/125.

Thanks Dick.

Curve 6, Part o. Quadrifolium is r²=32 cos 4 theta. Affects answer.

Curve 11, part d. Should be x² in parentheses, not x³.   Thanks to Jerry Glaser.

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.

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.

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.

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.

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.

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.

#29, Location. CD = 13.  (doesn't affect answer).

#25: Occupation.  Functions in solution don't match student version. Now they do.

Exam 1, #8. Answer hasn't changed but it is more involved than shown. Necessary to change to sines and cosines.

Exam Ch 2-4, #8. Student version changed and solution version matches it. Thanks to Stefan San Miguel.

Page 166, 2c: Equation after integration should be in h.

Page 167, 12. First integral result is 308.22 in-oz.

Thanks Dick Stibor.

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.

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 air-conditioner changing integral limits. Answer changed affecting 6b.

Page 164, 9.  Table values corrected.

Thanks to Dick Stibor.

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.

#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.

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.

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.

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.

Section 35 - inverse trig

Changes in the pictures for 2d and 3c. Answers not affected. Thanks to Michael Morton.

Epsilon-delta quiz:  #3, epsilon = 0.003 - solution

changed.  #4 - solution changed.

Exam chapters 2-4

#7.  2nd term absolute value should be x + 3

#11: -2 after integrating inestead of 2

#13: changed solution slightly

Thanks to Dick Stibor

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.

Page 145: Corrections in solutions of #1, #2.

Thanks to Dick Stibor.

Occupation #6:  Changed the possible answers.

Occupation # 28:  Change the problem because as stated, it was impossible.

Thanks to Nancy Garnan.

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.

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.

All on Exam D:

Def Integrals/Accumulation Quiz (28-29): #15: 23

FTC Exam (30-32): #16: 6

Area Quiz Student: 1a) Chart should ask for F(x)

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.

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 (18-21): 5d is a relative minimum.
Optimization Exam (22-23): Extra credit answer changed slightly.

Optimization Take Home (22-23):  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.

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.

Page 92, #:. 1 - 1 + 1 - 1 ...

Page 94, #7:  S_n = 1.5 - 1/(n + 2) - 1/(n + 3)

Page 94, #8: 2/(2n-1) - 2/(2n+1)

Thanks Dick Stibor.

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.

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.

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.

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.

Page 82, #6.  Constant should be 13/2. 

Page 82, #8. f ''' (x) =  -2/(x + 1)³ ...Thanks to Dick Stibor's class.

Exam 1, 2a should be -31/24 = - 1.292.

Prac Quiz (2-3), 5b should say Inst. Vel.

Quiz (2-3), 5b should say Inst. Vel.

Quiz (4), 5a - d should be the limit as x approaches 1 on the student version.

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.

Download B. Midterm #4. Choice III has changed.

Midterm #10: Solution slighly changed although answer remains the same. Thanks Dick Stibor.

#29. Table of values was missing.

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.

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.

Page 69, #7b: t ? ?/2, 3?/2, ...

Page 70, #1b: Solution: 1 + 1/t.

Thanks Dick Stibor.

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.

Related Rates solutions: #3a: answers in ft/sec.

7:  not dy/dy, dy/dt.

Thanks to Bruce Hartman.

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.

Page 90, #20. Solution reworked.

Page 105, #5. Solution is 8/9, not 9/8.

Thanks to Sarah Browning.

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.

Page 87, #12. Solution changed.

Page 89, #17. r = 3.25, not 3.75. Thanks to Bruce Hartman.