• ...... Exam ID Numbers for 11 am class
  
  
• ...... Exam ID Numbers for 1:10 pm class

EXAM DATES


• ...... Exam 1 -- Monday, October 10, 2011
• ...... Exam 2 -- Wednesday, October 26, 2011
• ...... Exam 3 -- Monday, November 21, 2011
• ...... Final Exam
  • 11 am class -- Friday, December 9, 2011, 6-8 p.m.
  • 1:10 pm class -- Monday, December 5, 2011, 8-10 a.m.

Here are Math 16A HOMEWORK Solutions . . . . . and . . . . . EXAM Solutions .

Here are copies of Worksheets , Supplemental Algebra Problems , and Supplemental Trigonometry Problems .

Here are Supplementary Class Handouts .

Here are Practice Exam 1 and Solutions .

Here are Practice Exam 2 and Solutions .

Here are Practice Exam 3 and Solutions .

Here are Practice Final Exam and Solutions .

These are the OPTIONAL EXTRA CREDIT (NOT AVAILABLE DURING SUMMER SESSION) survey and short paper .

• HW #1 ... (Section 1.1) ... p. 8: 3, 4, 10, 13-16, 19, 23, 26, 28, 31, 32, 35, 36, 41, 43a ... and ... (Section 1.2) p. 21: 3, 5, 7-13, 15, 18, 20, 23, 29, 31, 32, 35, 38, 41, 44, 46, 48, 53, 55, 59, 60, 62, 63, 66
  
  
• HW #2 ... (Section 1.3) ... p. 33: 2, 5, 6, 8, 14, 15, 21, 27, 31, 34, 38, 44, 47, 50, 51, 64, 67, 69, 81, 82, 83, 86, 88 ... and ... (Section 1.4) p. 45: 2, 5, 8, 12, 17, 18, 19, 22, 23, 26, 27, 30, 31, 32, 36, 38, 39, 42, 47, 54, 55, 60, 62, 63, 70, 72, 75 ... and ... Worksheet 1: 1-10 and SuppAlg: SA1, SA3
  
  
• HW #3 ... (Section 1.5) ... p. 58: 2, 6, 9-12, 17, 19, 22, 23, 29, 32, 37, 40, 42, 44, 47, 50-52, 56, 57, 59-62, 64, 68 ... and ... Worksheet 1: 11, 12, 14-16, 19, 23 ... and ... SuppAlg: SA2, SA5
  
  
• HW #4 ... (Section 3.6) ... p. 228: 1, 3, 4, 6, 9-16, 19, 22-24, 26-29, 31, 32, 37, (On the following six problems use x- and y-intercepts and vertical and horizontal asymptotes to sketch each graph. Do NOT use extrema or inflection points) 41, 43, 48, 52, 54, 56, 59, 63, 64 ... and ... Worksheet 1: 13, 17, 18, 20, 26
  
  
• HW #5 ... (Section 1.6) ... p. 69: 3, 5, 11, 14, 21, 25, 27, 30, 39, 44-46, 60 ... and ... Worksheet 2: 1, 2 ... and ... Worksheet 1: 21, 22, 24, 25, 27-29
  
  
• HW #6 ... (Section 8.1) ... p. 555: 9, 10, 13-16, 21-24, 28, 30-34, 36, 37, 40, 41, 47, 48, 50, 53, 54 ... and ... (Section 8.2) ... p. 566: 1, 5, 8, 10, 12, 26, 28-30, 47, 50-52, 55, 63, 65 ... and ... (Section 8.3) ... p. 575: 9, 14, 16, 28, 32, 40, 59, 62 ... and ... Worksheet 3: 1-4 ... and ... SuppTrig: ST1

TYPES OF QUESTIONS FOR EXAM 1 FOR FALL 2011 (subject to change)

• 4 -- limits
• 1 -- domain/range
• 1 -- continuity (using the three-step process at x=a, discussing continuity using shortcuts, or solving for unknown constants using limits and a fake graph)
• 1 -- trigonometry
• 1 or 2 -- functional composition/one-to-one function/inverse function
• 1 -- asymptote
• 1 -- circle
• 2 -- others
• 1 -- OPTIONAL EXTRA CREDIT

HERE ARE SOME RULES FOR EXAM 1.

• 1.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT'S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION.
• 2.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
• 3.) You may NOT use L'Hopital's Rule to compute limits on this exam.
• 4.) You may NOT use shortcuts from the textbook for finding limits to infinity.
• 5.) You need NOT MEMORIZE trigonometry identities. A short list of identities will be provided on the front cover of the exam.
• 6.) Using only a calculator to determine the value of limits will receive little credit.
• 7.) You will be graded on proper use of limit notation.
• 8.) Put units on answers where units are appropriate.
• 9.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.

THE GRADING SCALE FOR EXAM 1 FOR Fall 2011 IS :

A+ ...... 100-110

A ...... 90-99

A-/B+ ...... 84-89

B ...... 70-83

C ...... 50-69

D ...... 35-49

F ...... 0-34

• HW #7 ... (Section 2.1) ... p. 90: 5-12, 14, (Use the limit definition of derivative on the next seven problems) 15, 18, 22, 25, 32, 34, 43, 49, 50, 51 (Use the limit definition of derivative to "prove" that y=x^{2/5} is not differentiable at x=0.), 52-54
  
  
• HW #8 ... I.) Find all points (x, y) on the graph of y = 4x-x^2 with tangent lines passing through the point (2, 5). You may assume that the derivative of y = 4x-x^2 is y'=4-2x. ... and ... Worksheet 4: 1, 2 ... and ... SuppAlg: SA4, SA7, SA9, SA10, SA11
  
  
• HW #9 ... (Section 2.2) ... p. 102: 1, 4-20, 23, 26, 30, 31, 33-36, 40, 44, 45, 48, 49, 51, 53, 61, 65, 66 ... and ... SuppAlg: SA8, SA15
  
  
• HW #10 ... (Section 2.3) ... p. 116: 1, 3, 6, 8, 12, 14-16, 32, 33cde, 43 ... and ... SuppAlg: SA6, SA12
  
  
• HW #11 ... (Section 2.4) ... p. 128: 1, 3, 6, 8, 12, 25, 30, 32, 33, 37, 38, 45-48, 55, 57 ... and ... SuppAlg: SA17
  
  
• HW #12 ... (Section 8.4) ... p. 585: 1-12, 39, 40, 43, 44 ... and ... SuppAlg: SA16

MEMORIZE the following list of derivative rules.

1. D(c) = 0
2. D(mx+b) = m
3. D(f(x) +/- g(x)) = f'(x) +/- g'(x)
4. D(c f(x)) = c f'(x)
5. D(x^n) = n x^(n-1)
6. (Product Rule) ... D(f(x)g(x)) = f(x)g'(x) + f'(x)g(x)
7. (Triple Product Rule) ... D(f(x)g(x)h(x)) = f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)
8. (Quotient Rule) ... D(f(x)/g(x)) = {g(x)f'(x) - f(x)g'(x)}/[g(x)]^2
9. D(sin x) = cos x
10. D(cos x) = - sin x
11. D(tan x) = sec^2 x
12. D(sec x) = sec x tan x
13. D(cot x) = - csc^2 x
14. D(csc x) = - csc x cot x

TYPES OF QUESTIONS FOR EXAM 2 FOR FALL 2011 (subject to change)

• 1 -- limit definition of a derivative
• 1 -- sketch f' from graph of f
• 4 -- various derivatives using above rules (NO SIMPLIFICATION OF ANSWERS)
• 2 -- solve f'(x)=0 for x, one of which is trig
• 1 -- average and instantaneous rate of change using a graph like we did in class
• 1 -- find equation of tangent or perpendicular line
• 2 -- others
• 1 -- OPTIONAL EXTRA CREDIT

HERE ARE SOME RULES FOR EXAM 2.

• 1.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT'S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION.
• 2.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
• 3.) You may NOT use L'Hopital's Rule to compute limits on this exam.
• 4.) You may NOT use shortcuts from the textbook for finding limits to infinity.
• 5.) You will be graded on proper use of limit notation.
• 6.) Put units on answers where units are appropriate.
• 7.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will receive LITTLE or NO credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.

THE GRADING SCALE FOR EXAM 2 FOR FALL 2011 IS :

A+ ...... 100-110

A ...... 90-99

A-/B+ ...... 85-89

B ...... 70-84

C ...... 56-69

D ...... 40-55

F ...... 0-39

• HW # 13 ... (Section 8.4 and 2.5) ... p. 585: (Do not simplify answers. Do not use trig identities. Omit problems 13, 14, 22, 25, 26, 31. These will be covered later in Math 16B.) 15-21, 23, 24, 28, 36, 41, 46 ... and ... p. 138: 17, 22, 23, 30, 38, 39, 49, 59, 64, 67, 70, 73, 74 ... and ... Worksheet 5 ... and ... SuppTrig: 6
  
  
• HW # 14 ... (Section 2.6) ... p. 145: 1, 4, 7, 11, 13, 16, 19, 20, 21, 24 (On next four problems solve f'(x) = 0 and f''(x) = 0 for x.) 34, 35, 38, 40, 41-43, 50abcde
  
  
• HW #15 ... (Section 3.1) ... (Set up a sign chart for y'. Clearly label critical points and y-values and identify relative maximums and minimums.) p. 179: 2, 3, 6, 8, 14, 15, 18, 22, 23, 25, 27, 35a, 40a ... and ...(Section 3.2) ... (Set up a sign chart for y'. Clearly label critical points and y-values and identify relative and absolute maximums and minimums. Sketch the graph.) p. 189: 5, 8, 16 (Also check for vertical asymptote.), 18 (Also check for horizontal asymptote.), 20, 21 (Use interval[-1, 2].), 23 (Use interval [-1, 4].), 44 (Change $100 to $25.), 45
  
  
  • Here are DETAILED GRAPHING INSTRUCTIONS :
    1. State the DOMAIN of the function.
    2. Take the FIRST derivative and set up a SIGN CHART for f'(x). Clearly mark the solutions to f'(x)=0 and their y-values, and identify all RELATIVE and ABSOLUTE maximum and minimum values.
    3. State the OPEN INTERVALS on which f is INCREASING and DECREASING.
    4. Take the SECOND derivative and set up a SIGN CHART for f''(x). Clearly mark the solutions to f''(x)=0 and their y-values, and identify all INFLECTION POINTS.
    5. State the OPEN INTERVALS on which f is CONCAVE UP and CONCAVE DOWN.
    6. Determine all X-INTERCEPTS and Y-INTERCEPTS.
    7. If appropriate, determine all HORIZONTAL ASYMPTOTES (H.A.).
    8. If appropriate, determine all VERTICAL ASYMPTOTES (V.A.).
    9. DRAW a rough SKETCH of the graph of y=f(x) and CLEARLY identify the coordinates of all important points on the graph.
  
  
  
• HW #16 ... (Section 3.3) ... p. 198: 1, 6, 7, (Do DETAILED GRAPHING for the next 8 problems.) 15, 27, 29, 35, 39, 44-46, 65ab
  
  
• HW #17 ... (Section 3.7) ... p. 238: (Do DETAILED GRAPHING for all problems.) 1, 2, 9, 17, 22, 23, 24, 34, 35, 40 ... and ... (Section 3.2) ... p. 189: (Do DETAILED GRAPHING for all problems.) 22, 23 ... and ... (Do DETAILED GRAPHING for all problems except SuppTrig: ST2.) I. f(x)=sinx+cosx on interval[0, pi], II. f(x)=-\sqrt{3}cosx-sinx on interval [0, 2pi] ... and .. Supplementary Trig: ST2, ST3ab.
  
  
• HW #18 ... (Section 2.7) ... p. 152: 1, 4, 6, 10, 15, 18, 22, 24, 30, 34, 36, 40, 45 ... and ... (Section 8.4) ... p. 586: 47, 48
  
  
• HW #19 ... (Section 2.8) ... p. 160: 2, 5, 6, 9, 10, 13, 17ac ... and ... Worksheet 6 ... and SuppTrig: ST4, ST5
  
  
• HW #20 ... (Section 2.8) ... p. 160: 16-20, 23 ... and ... (Chapter 2 Review) p. 169: 99 ... and ... Worksheet 7

Bring it ...

TYPES OF QUESTIONS FOR EXAM 3 FOR FALL 2011 (subject to change)

• 3 -- chain rule
• 1 -- velocity/acceleration
• 2 -- implicit differentiation
• 2 -- related rates
• 1 -- complete detailed graphing
• 1 -- partial detailed graphing
• 1 -- OPTIONAL EXTRA CREDIT

HERE ARE SOME RULES FOR EXAM 3.

• 1.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT'S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION.
• 2.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
• 3.) You will be graded on proper use of derivative notation.
• 4.) Put units on answers where units are appropriate.
• 5.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will receive LITTLE or NO credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.

THE GRADING SCALE FOR EXAM 3 FOR FALL 2011 IS :

A+ ...... 100-110

A ...... 90-99

A-/B+ ...... 85-89

B ...... 69-84

C ...... 50-68

D ...... 39-49

F ...... 0-38

• HW # 21 ... (Section 3.4) ... p. 207: 1, 4, 6-9, 11, 13, 18, 20, 22 ... and ... MaxMinHW: I
  
  
• HW # 22 ... (Section 3.4) ... p. 207: 14, 24, 25c, 26, 28, 35, 39 ... and ... MaxMinHW: II, III
  
  
• HW # 23 ... (Section 3.5) ... p. 219: 19, 20, 23, 25 ... and ... MaxMinHW: IV, V, VI, VII, VIII
  
  
• HW #24 ... (Section 3.8) ... and p. 246: 11, 12, 17, 37-39, 40-42 ... and ... Worksheet 8
  
  
  
  

  The FINAL EXAM is

  • 11 am class -- Friday, December 9, 2011, 6-8 p.m., 212 Veihmeyer
  • 1:10 pm class -- Monday, December 5, 2011, 8-10 a.m., 194 Chemistry
  
  
  
  
  

  BRING A PICTURE ID TO THE EXAM
  AND BE PREPARED TO SHOW IT TO KOUBA OR THE TEACHING ASSISTANTS !!
  
  

  The final exam will cover handouts, lecture notes, and examples from class, homework assignments 1 through 24, and material from sections 1.1-1.6, 2.1-2.8, 3.1-3.4, 3.6-3.8, 8.1-8.4. You are expected to know the 13 rules of differentiation, which were needed on Exam 2. Use your three hour exams, 24 homework assignments, and the practice exams as a guide to your preparing for the final exam.
  
  

  TYPES OF QUESTIONS FOR THE FINAL EXAM FOR FALL 2011 (subject to change)

  • 3 -- limits
  • 3 -- max./min optimization
  • 2 -- related rates
  • 2 -- differentials
  • 1 -- limit definition of derivative
  • 1 -- complete detailed graphing
  • 2 -- solve f'(x)=0 or f''(x)=0 for x
  • 1 -- velocity/acceleration (gravity)
  • 1 -- continuity
  • 1 -- implicit differentiation
  • 1 -- find equation of tangent line or perpendicular line
  • 1 -- OPTIONAL EXTRA CREDIT
  
  
  

  HERE ARE SOME RULES FOR THE FINAL EXAM.

  • 0.) IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION.
  • 1.) No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM.
  • 2.) You may NOT use L'Hopital's Rule to compute limits on this exam.
  • 3.) You may NOT use shortcuts from the textbook for finding limits to infinity.
  • 4.) You need NOT MEMORIZE trigonometry identities. A short list of identities will be provided on the front cover of the exam.
  • 5.) Using only a calculator to determine the value of limits will receive little or no credit.
  • 6.) You will be graded on proper use of limit notation.
  • 7.) Put units on answers where units are appropriate.
  • 8.) Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will NOT receive full credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important.
  
  
  
  

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Your comments, questions, or suggestions can be sent via e-mail to Kouba by clicking on the following address :

kouba@math.ucdavis.edu .