Summer 2012, Term 1

**Final exam:**The final exam will take place on June 16; it will be 150 minutes in duration.

**Weekly exams:**Instead of a midterm, there are four weekly exams scheduled during the term. These will be in-class exams, tentatively scheduled for May 14, 22, 28, and June 4. If you miss a test for a documented reason, bring me a note (doctor's note, for example) when you return, and the other tests will be weighted more heavily.

**Participation:**In the winter semester, Math 184 has a 1.5 hour workshop each week along with 3 lecture hours. In summer, all these hours are combined into lecture hours (and a summer `week' is equivalent to 2 winter `weeks', which is why we have 9 hours of class per week). Participation (and, to some degree, performance) in in-class activities, surveys, and worksheets will make up the workshop portion of the course.

**Assignments:**~~Online assignments will be given twice weekly.~~Several short online assignments at a time will be given as we cover the topics. Due dates will allow at least 3 days to work on each assignment. The nature of online assignments allows for real-time feedback, which is invaluable during such a fast-paced course.

There will also tentatively be one written assignment each week in which you will be expected to show all your work. This will allow the marker to provide detailed feedback about your thought process and notation.

Assignment due date extensions will not be granted; this course moves quickly, and we won't have time to drag topics out. However, your lowest-scoring online assignment and your lowest-scoring written assignment will be forgiven and will not count towards your grade.

**Week 1 [May 7--11]:**Review of Exponentials, Logarithms, and Inverse Functions; Introduction to Limits; Continuity; Business Terminology. Sections 1.3, 2.2, 2.6, plus business-related notes.

**Week 2 [May 14-18]:**Limit Calculations; Intermediate Value Theorem (IVT); Definition of the derivative; a few Rules of Differentiation. Sections 2.1, 2.3, 2.6 (IVT), 3.1--3.5.

**Week 3 [May 22-25]*:**more Rules of Differentiation; Elasticity; Compound Interest. Sections 3.6, 3.8, 6.8, and elasticity notes.

**Week 4 [May 28-June 1]:**Implicit Differentiation; Related Rates; Optimization Problems. Sections 3.7, 3.10, 4.1, 4.2, 4.4,~~and inventory control notes.~~

**Week 5 [June 4-8]:**Graphing; Linear Approximation. Sections 4.3, 4.5.

**Week 6 [June 11-15]:**Quadratic Approximations; Trig Function and their Inverses. Section 9.1 (up to p.591, not including Taylor polynomials), 3.9.

More details are listed here. This document is based upon the standard protocol for Math 184 final exams.

I've had a few questions about passing the final to pass the class. I asked the course coordinator, and

-Kelly

I've also posted a link to the previous final exams that the department has made available. The link is at the very bottom of this page, under Additional Resources.

(1) Logarithmic and exponential functions, Section 1.3,

(2) Business problems, like the worksheet, the example in class, and the problems listed under suggested problems,

(3) Limit concepts and finding limits from graphs, Section 2.2,

(4) Determining continuity, Section 2.6.

The fifth question is to be determined, and will be a lovely surprise!

To prepare for the quiz, you should be comfortable with all the Suggested problems below, the assignment problems (for assignments a1 through a3), the Worksheets and activities from class (solutions posted below), the material covered in Class notes below, as well as the actual notes you have taken during class this week. The Learning Goals for Week 1 (posted below) are a good guide to what you are responsible for knowing.

Send me your questions by email (kmpaton at math.ubc.ca) before 6PM Sunday and I'll get back to you, but I can't guarantee that emails after 6PM Sunday will be answered in time for the exam.

Also, if the test on the first day made you feel a little unsure of your basic skills, that's okay -- now you know, and you can do something about it. The better your basic skills are, the easier calculus will be, so it's definitely worth taking the time to practice. See the new link in 'Additional Resources' below for some algebra review and practice problems.

Week 1 Learning Goals <---

Week 2 Learning Goals <---

Week 3 Learning Goals <---

Week 4 Learning Goals <---

Week 5 and 6 Learning Goals <---

- Introductory WeBWorK Assignment, a0: available May 8 at noon, due May 11 at 11:59PM.
- First real WeBWorK Assignment, a1: available May 8 at 10PM, due May 11 at 11:59PM.
*For some reason, #15 requires you to input the answers separated by the word 'or': 'x=__ or x=__'. Sorry for this inconsistency. Most questions with multiple answers will accept two values separated by a comma.*

- SHORT Logarithmic and exponential functions WeBWorK Assignment, a2: available May 9 at 7PM, due May 13 at 11:59PM.
- SHORT intro to limits WeBWorK Assignment, a3: available May 10 at 3PM, due May 13 at 11:59PM.
- Continuity WeBWorK Assignment a4continuity: available May 14 at 4PM, due May 18 at 11:59PM.
- Evaluating limits WeBWorK Assignment, a5limits: available May 15 at 10:30AM, due May 18 at 11:59PM.
- Derivative intro (3.1) WeBWorK Assignment a6derivatives1: available May 18, due May 21 at 11:59PM.
- Evaluating derivatives (3.2, 3.3) WeBWorK Assignment, a7derivatives2: available May 18, due May 21 at 11:59PM.
- Written Assignment A:
~~due Wed May 23 in class.~~extended to Thurs May 24, in class. Solutions. - Final derivatives (3.4, 3.5, 3.6, business applications) WeBWorK assignment, a8derivatives3: available May 23, due May 27 at 11:59PM.
- Written Assignment B: due Thurs May 31, in class. Solutions.
- Log differentiation and elasticity (3.8, class notes Tues May 29) WeBWorK assignment, a9: available May 28 2PM, due Thurs May 31 11:59PM.
- Implicit differentiation (3.7, class May 30) WeBWorK assignment, a10impDiff: available May 31, due Sun June 3 11:59PM.
- Related rates (3.10, class May 31) WeBWorK assignment, a11RelatedRates: available May 31, due Sun June 3 11:59PM.
- Maxima and minima (4.1, 4.2) WeBWorK assignment, a12optIntro: available June 4, due Thurs June 7 11:59PM.
- Optimization (4.4) WeBWorK assignment, a13optimization: available June 4, due Thurs June 7 11:59PM.
- Written Assignment C: due Friday June 8 at the start of class. Solutions. DO NOT DO QUESTION 5 (graphing a surge function). It will be moved to the last assignment instead.
*Edited at 9PM Monday June 4. The questions are unchanged, but their order has been altered to closer match the order in which we'll cover the topics.* - Graphing (4.3) WeBWorK assignment, a14graphing: available June 7, due Sunday June 10 11:59PM.
- Linear approximation WeBWorK assignment, a15LinApprox: available June 8, due Tues June 12 11:59PM.
- Final Written Assignment D: due Wednesday June 13 at the start of class. Solutions.
- Taylor approximation WeBWorK assignment, a16taylor: available June 12, due Friday June 15 1 PM.
**For participation points**: Review WeBWorK assignment, aReview, is available now, due Friday June 15 11:59PM (answers available at midnight).

Week 1: (for quiz 1 on Monday May 14)

-Section 1.3: #33, 35, 41, 43, 45, 47, 58, 59, 71, 72. Additional problems: see problems 6, 7, 9, 10, 11, 12, 13, 17, 18 on this website.

-Business problems: Not in the text. Instead, here are some more business problems and their solutions (in addition to the 'A Business Problem' worksheet we did in class, posted under Worksheets below).

-Section 2.2: #2, 3, 5, 7, 9, 11, 17, 19, 23, 35

-Section 2.6 (not including the IVT or complicated limits - these will come next week): 2, 9, 13, 15, 17, 71, 73

-You should be familiar with all the worksheet problems from class (solutions are posted below).

Week 2: (for quiz 2 on

-Section 2.6 (continuity on intervals, L/R continuity): 29, 33a, 75

-Section 2.6 (IVT): 8, 49a, 79a.

-Section 2.3: 5, 10, 23, 25, 31, 32, 37, 39, 44, 45, 47, 64, 73.

-Section 1.2: 25, 26.

-Section 2.1: 3, 4, 5.

-Section 3.1: 1, 2, 4, 5, 8, 9, 11, 13, 15, 17, 21, 29, 39, 41, 42, 43, 45, 48, 51, 59, 71.

-Section 3.2: 3, 6, 7, 9, 19, 21, 23, 28, 33, 37, 41, 43, 47, 51, 68, 75

-Section 3.3: 9, 11, 13, 17, 21, 23, 27a, 29a, 46, 49, 51, 55

Week 3: (for quiz 3 on Monday May 28)

-Section 1.3: Review the properties of logarithmic and exponential functions

-Section 3.4: 6, 15, 16, 17, 19, 21, 33, 34, 50, 55 [derivatives of sin(x), cos(x), or tan(x)]

-Section 3.6: 2-7, 9, 13, 17, 19, 21, 23, 29, 39, 41, 43, 57, 59, 71, 75a, 77a [chain rule]

-Section 3.5: 7, 9, 11, 12, 20, 21, 23, 25, 29, 35, 36, 40, 41. [rates of change]

-Section 3.8: 2, 8, 9, 11, 12, 13, 15, 17, 19, 21, 35, 36, 37, 39, 45, 47, 49, 79. [derivatives of logs and exponential functions; logarithmic differentiation]

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-Extra Business Problems (including marginals) can be found here; solutions are here, and corrections to the solution for question 5 are here.

-The text is lacking in relative rates of change problems so here are a few additional relative rates problems and here are the answers (not full solutions, just answers). Also see the logarithmic differentiation worksheet.

-You should be familiar with all the worksheet problems from class (solutions are posted below).

Week 4: (for quiz 4 on Monday June 4)

-Elasticity: see problems from May 29 notes; also, here are some notes and problems from a different text (by Goldstein) on elasticity; try out problems 9, 10 (this one is on relative rates), 14, 15, 16, 17, 19, 20, 23; here are the solutions to the Goldstein problems.

-Section 6.8: 1, 9, 11, 13, 16, 25, 30, 40; problems #11, 12 from the Goldstein notes in the previous point (solutions included in the same document, previous point); problems from May 29 notes [exponential growth/decay].

-Section 3.7: 2, 3, 5, 7, 9, 15, 19, 21, 23, 27, 31, 47, 49, 51, 53, 61, and the problems from the Implicit Differentiation Worksheet [implicit differentiation]

-Section 3.10: 3, 6, 11, 13, 17, 18, 23, 38, and the problems from the Related Rates Worksheet. Here are some additional business-oriented related rates problems and their solutions. [related rates]

-Section 4.1: 1, 4, 5, 7, 8, 10, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 37, 44, 45, 53, 55, 57. [maxima/minima]

-You should be familiar with all the worksheet problems and activities from class (solutions are posted below)

Weeks 5 and 6:

-Section 4.2: 1, 2, 3, 4, 15, 17, 21, 30, 31, 33, 35, 37, 39, 57, 59, 61, 77, 79. [classifying max/min]

-Section 4.4: 1, 2, 3, 4, 7, (note that #10c was our worksheet problem) 11, 13, 15, 17, 23, 25, 31, 33, 57. [optimization]

-Section 2.4: 6, 9, 11, 17, 19, 23, 36. [infinite limits: vertical asymptotes] answers to #36: aD, eA, fE, bC, cF, dB

-Section 2.5: 9, 21, 23, 25, 39, 43, 53, 54. [limits at infinity: horizontal asymptotes]

-Section 4.3: 3, 4, 11, 13, 15, 17, 19, 22, 29, 31, 32, 43, 55. [graphing]

-Section 4.2: 69, 71, 73. [more graphing]

-Section 4.5: 2, 3, 7, 9, 12, 17, 19, 39, 43, 47. [linear approximation]

--Here are some pencast examples (created by a colleague) of linear approximation, including error estimation:

Linear approximation of e^0.05, with error estimation

Linear approximation of 12-(2.1)^2, with error estimation

Linear approximation of cos(-0.01), with error estimation

-Section 4.5: 23, 25. [linear approximation]

--More pencast examples for linear and quadratic approximations:

Linear and quadratic approx of ln(1+x)

Linear and quadratic approx of cube root of 65

-Section 9.1: 1, 2, 7, 9, 15, 19, 27, 31, 33, 37, 65. [quadratic approx., Taylor polynomials]

Additional Review:

-Practice problems: graphing and word problems. Answers. A few full solutions. Both Math 184 summer sections (us and 921) are using this for practice.

-Past final exams are available on the department website.

-The Chapter Review sections in your textbook at the end of each chapter have a good mix of questions, if you're looking for more practice problems.

Logarithm rules and properties (May 8)

Clarification of how to find the demand equation in the UBC farm example from class (May 9)

This document provides a basic summary of revenue, cost, and profit. (May 9)

This document provides notes and an example for continuously compounded interest. (May 10)

Filled-in notes and worksheets for May 29 (price elasticity of demand, exponential growth).

Solutions to the first-day skills test (May 7)

Solutions to the exponents, logs, and inverse function worksheet (May 8)

Solutions to 'A Business Problem' oPad worksheet (May 9)

Solutions to the compound interest worksheet (May 10)

'The Paint Store' worksheet and solutions (May 11)

Intermediate Value Theorem worksheet and solutions (May 15). A complete and correct solution is indicated in blue font. Red is additional notes.

Tax rate worksheet (May 16)

Graphing derivative worksheet solutions (May 17)

Calculating derivatives worksheet (May 18) This was NOT collected for marks. <---

- Calculating derivatives worksheet solutions: For the first half of the worksheet, you may check your answers using Wolfram Alpha. Here is an example of how to input question #15 into Wolfram Alpha. The second half of the worksheet should also be solvable by wolfram alpha (see here for an example of how to input question #2, and here is an example of how you could input question #3), except for question #5. The solution to question #5 is here.

Marginals worksheet and solutions (May 25). This was NOT collected for marks.

Logarithmic differentiation worksheet and solutions (May 25). This was NOT collected for marks.

See 'Class Notes' above for filled-in notes and worksheets for May 29.

Implicit differentiation worksheet, split into two parts: basic questions solutions and elasticity of demand answers (May 30). This was NOT collected for marks.

Related Rates worksheet, split into two parts: in-class question solution and extra problem solutions with diagrams (May 31).

Maxima/minima worksheet and solutions (June 1). This was NOT collected for marks.

Optimization worksheet and solutions - scan quality is a bit poor for some reason, but still legible (June 5).

Graphing worksheet and solutions (June 7).

Linear approximation in-class worksheet (June 8). This was more of a notes outline than a worksheet, and it was NOT collected for marks.

Taylor polynomials worksheet and solutions (June 13).

Timed practice problems: graphing and a word problem, 45 minutes (June 14).

Selected practice problems and solutions (June 15).

Quiz 1 (May 14, Week 1 material) grading comments and solutions: average 77%

Quiz 2 (May 23, Week 2 material) solutions and grading comments: average 68%

Quiz 3 (May 28, Week 3 material) solutions and grading comments: average 52%

Quiz 4 (June 4, Week 4 material) solutions, and grading comments: average 58%

Past final exams are available on the department website.