# CALCULUS AB

4-8 thru 5-5 /17 AP Review cycle

4/7–We will go over the MC questions that you missed on the recent AP exam.

4/6–Hope to be finished grading your 4 FR non calculator questions by tomorrow; if not (and I am going to work until I am tired), we will go over the MC questions part A and B. Most of you did well on part B.

4/5–4 FR questions (1 hour), no calculators..This should conclude our first AP test.

4/4..Part 2 tomorrow: graphing calculator required, make sure you have batteries, please be on time as you will be working 80 minutes.

4/3–AP testing cycle commence demain!

3/31–pg. 432: 60 a, b; 61 a, b, c

3/30–Google Paul’s notes, Khan Academy, LinMcMullen or simply type, “solids with known cross sections”. Find any problems you like suitable for discussion? Bring them on (Kyle Marcon). See any FR questions you like? Share them with the class. HWK: pg. 430, 59b, 60 a

3/28–It is your responsibility to ask about specific problems assigned for hwk–don’t expect me to go over every prob unless you have questions. I recommend you do 32, 34 and (suggested by Parker Byars, #47

3/3³–The Mackeys are celebrating Big Mac’s 18th; his quiz grade.–well, a different story, more like lamenting it. Quiz grades were a HUUUGE disappointment..Calculuator, means use your calculator, Gwen Freeze et al…let the calculator do all the work. HWK for tomorrow: pg. 428: 5, 6, 13, 15,18, 21, 25, 27

3/24–Same as 3/23

3/23–pg. 428: 1-4; 7-10

3/22–same as 3/20

3/20–pg. 419: 32, 38, 46, 50, 60 (*)

3/17–pg. 418, 1-6; 15, 25, 26, 29 (follow examples, check out Paul’s notes and /or Khan Academy on topic)

3/16–Read 6.1

3/15–Test tomorrow

π day–Should have given you a FR involving Π..never too late, peut etre demain? Merci, Abbas pour la tartte aux noix de pecan..on va la manger demain pendant le dejeuner avec Parker, Patrick, Megan et des autres. Alors, pour le devoir: pg. 393: ; 11, 17, 18, 9, 30, 32, 51, 52, 54, 56.

3/10–If you are not doing your hwk or asking questions in class, there will be consequences; your latest test grades attest to that fact. HWK; pg. 378: 56-68, even

3/9–le meme devoir de hier.

3/8–Test tomorrow (5.1-5. 5), application of rules + FR. Now HW: (I may not get to run off the test either b/c I may not have time to run off the test or because Wikileaks has hacked my archives) pg. 377: 33-54, multiples of 3 (if you so it tonight, it may help you to review for the test tomorrow).

3/7–pg. 366:1-16, all

3/6–pg. 357 (three consecutive odd nos..SWAG!) 41-55 (0dd), 52,54, 59, 60, 62-68 (even), 69, 70, 92

2/22-Any lingering questions from 2/21? Like they say at the altar, “Now is the time to speak or hold your tongue forever”…well, not forever, as we’ll be revisiting some of these topics between now and AP Exam Day. HW: Read 5.4, do pg. 349–87-109, odd; 111-115 (Print slope fields from website..certainly hope you have been doing the slope field problems–don’t be blindsided). We are focusing on the anti derivative of f(x) = e ^x, since we already covered d(e^x)/dx (probs. 39-73, review your notes). Perhaps we should do another density problem? Allie and Parker seem to have a different approach; mine is more Reimanesque (made-up word, meaning “in a Reimann sum style..sort of nerdy). Kyle Marcon, don’t forget the probs from the practice book on how to find the derivative of an inverse function (perhaps we should revisit the formula). I think I’m writing too much..this feels like a blog.

2/21–41, 42 (print from website); 43-49 (odd), 54 (see ex. 9), 55 (Allie, it has your name),68, 79-83–et c’es tout pour aujourdhui, alors, Abbas, n’oublies pas manger, je sais que tu as faim (eat, Abbas! you are hungry!).

2/14–Read 5.2; do 2-40 (all).

2/9–ATTENZIONE! After consulting with Omar, Harper, Khan, Fuentes et al, the test will be rescheduled for Monday, 2/13 (I meant to give you the test as Valentine’s present; instead you’ll get your grade in red ink). It is the consensus that the trapezoid rule is easy and you are set to go. The real reason the date has been moved to Monday has to do with the soccer game. (What does Brandon care? It is not baseball). Our soccer players will leave after second and travel to Alexandria for an afternoon match, coming back late on Monday night. It was at their request that the test be moved. If you are in the soccer team and have advisory at first, you may want to start a bit earlier. Format of the test: 10 MC, no calculator (20 min); The second part of the test is calculator active, consisting of 9 MC (25 min)+ 2 FR (3o minutes) for a total of 75 min (20 + 25 + 75); it is quite possible that you will finish in less time. Each part will be graded individually and the four grades averaged on a 4 pt. scale. If you have any questions, email me during the weekend. I’ll be available Mon morning during C1 (Omar, Kyle Marcon, Gurangi).

2/8–pg. 297: 28, 30, 32, 39, 40, 74, 80, 92, 94, 95, 96,104

2/3–Integration by u-sub. Look for ∫ f(g(x) g'(x) ..usually let u= g(x), then u’ = g'(x) dx…solve for x so that you can write integral in terms of u. For hwk: pg. 297: 2-8 (even). I also recommend that you read 4.5 and follow examples, that way you will be prepared for further discussions on Monday, 2/6.

2/2–Time to do motion probs..pg. 287: 103-105 (Expect this kind of prob on the AP and in future FR questions).

2/1–pg. 286: 69, 73, 75, 82, 83, 87, 88, 92, 93,94,

1/30 pg. 130:– 285: 46, 48, 50, 52, 63

1/27–Read pp. 278-287

1/26–pg. 273: 21 (Mackys); 41-46; pg. 284: 2-32 even.

1/24–Read pp.267-269. Do 4, 9-12

1/23–39-44 (Try to write as an integral)..you are finding the area below the curve, 49, 57, 63.

1/19–pg. 251: 69, 79, 80 and pg. 261: 15, 19, 21, and (try) 29. For the quiz tomorrow you will be well advised, in fact it behooves you to review inverse trig functions and their derivatives (sorry, Kyle, not every thing is L’Hopital). Remember, if in a pinch you can derive the derivatives of the inverse trig functions like Parker, Abbas, Allie and I do: use implicit differentiation and draw a triangle. What’s on the quiz? Well, I just told you.

1/18–pg. 251: 73 (compliments of Garcia), 76 (Escape velocity–what you experience in this class when the bell rings to go to C3 or what I experience when I see Parker Pottinger approachint), 77

1/17–pg. 249: 23-41 (odd) + 38, 42, 52, 55, 62, 64, 67, 68. Also: visit www.mathgraphs.com: select the pix that matches your book cover; pick Ch 4, section 1, print ex 45-48 and 53, 54 (come prepared to discuss these probs).

1/13–pg. 340: 73; 77, 78 (part d only), 81, 82 (two different methods). Read 4.1

1/12–Read 5.3

1/11–pg. 387: 56, 59, 80, 64; pg. 357: 41-56

1/9–pg. 386: 41-52

1/6–Read 5.8

1/5–pg. 537: 6-36, even nos. (omit 22)

1/4–Read Section 7.7 L’Hopital Rule (aka Kyle Marcon’s rule)

12/13–Let’s try it again: pg. 322: 72, 74, 76, 80, 87 (use log diff); pg. 348: 46, 51, 54, 58, 59, 61, 70 73 (good optimization prob), 79

12/9–pg. 322 (compliments of Parker Hernandez): pg. 322: 45-59 (odd); 63, 64 (why absolute value signs?).

12/8–pg. 216: 11, 14, 15 (compliments of Mr. Wms), 23

12/7–pg. 216:2, 5, 8, 16-18, 24-26

12/6–Read 3. 7..Optimization is nothing more than finding the critical value and evaluating the equation in a real-life situation using either the first or second derivative test..most of the probs in the book are algebraically involved, something you seem to be allergic to, but life is not always sweet.

12/5–Test tomorrow (since Luisa will be absent Th and Friday): 3 MC, 3 t/f , 5 constructed response. ALL the content has been discussed in class. No graphing calculator. 2 Bonus questions. You will have the whole period. Don’t expect the test back until later this week..maybe next Monday. and 1 FR (interpret a graph, similar to the one discussed in class today. Don’t be a distracted deriver.

11/30– pg. 209: 31, 34, 41, 59

11/29–Using the guidelines discussed in class (handout) and in your text (pg. 202) do pg. 208, 1-6; 12, 23, 25. Omar was given a DUI on his way home (“deriving under the influence”).

11/28–Read 3.6

11/16–Test tomorrow–You will be busy! Familiarize yourself wiht the conditions when EVT, IVT, and MVT apply. No surprises, no questions are particularly difficult. Format: 6 MC questions; 5 FR (with multiple parts–you seem to do well on this type of question) and a graph that you need to analyze for inc/dec and concavity. We have addressed all the questions in class/hwk (and this morning during our discussion of sample AP questions). Remember that AP questions are 1 pt. each. You will need a scientific calculator.

11/15–pg. 190: 61

11/14–27, 32, 36, 37, 39, 43-48, and 49- 52 (access the graphs trough www.mathgraphs.com ) . Please come to class with the graphs printed.

11/11–Same as 11/10

11/10–Read 3.4–pay attention to Second Derivative Test (at test for min/max, sometimes useful in lieu of the first derivative test). Do: pg. 189: 1-10; 18-20; 24, 26.

11/9–Test

11/8–Holiday (Election Day)

11/7–What to expect on the test? BRING A SCIENTIFIC CALCULATOR. Test will take whole class period.

Review: Implicit differentiation, how to find max/min, interpret a position graph, relationship among f(x), f ‘ (x) and f” (x) from a graph . Related rate prob (done in class)..fine tune your algebra skills..lots of algebra on this test.

11/4–We have pending hwk to discuss (see below). After the fiasco from the quiz on 11/3, the test will be postponed until Wed @ the earliest. We need to zero in on increasing/decreasing and the first derivative test.

11/3–pg. 181: 112, 18, 19, 27, 29, 32, 36, 43-48

11/2-pg. 181: 1-4; 9, 10

10/31–pg. 172: Read 3.2: 1, 2, 5, 9, 11, 14, 23

10/28- pg. 165: 13, 19, 25, 27

10/27–pg. 166: 40, 42

10/26–pg. 165: 1-6; 33-34, 51-54 (justify your answer).

10/25–Read 3.1 (Increasing/Decreasing functions).

10/24– You have the whole period to work ont the test tomorrow. PLEASE BRING A SCIENTIFIC CALCULATOR!

A couple of limit probs (deja vu); four probs relating the graphs of f(x) with f ‘ (x), finding derivatives using tabular values and derivatives rules, + 5 related rate probs (done in class, probs are reflective of the Haynes community, particularly the senior class ??). The rr problems constitute the bulk of the test, time wise and point wise.

10/21–Monday is related rates day, we will tie up loose ends, go over hwk probs that need to be addressed. Add the following to your hwk assignment:, 29, 30,31,32, 34, 43, 44. Test on Tuesday (more info will be posted Monday as to format/content, know that related rates will play a big role).

10/20- If we have a test tomorrow, the material covered is similar to the last test: interpret graphs for differentiability, implicit differentiation, derivative rules, a motion problem, average reate of change, change rule, second derivative, tangent lines, finding the derivative by using the limit definition, def of derivative at a point, one simple related rate prob–80% MV, 20% FR. If we don’t have at test (which as of 5:22 PM is highly probable), then let’s play baseball and throw some shade: pg. 15o: 27, 33, 35 (think similar triangles).

10/18–Take good pictures. In + to probs assigned on 10/17: 22, 24 25 (for Abbas, Alaa, Parker, and Allie + anyone else who likes to be challenged (Fuentes, Eric, Colin, Andrew R(eginelli) are you in that league?)

10/17–pg. 149: 13-21, all; HWQ tomorrow (related rates not included).

10/14–Handout (only first two)..Read section on Related Rates

10/13–Test on derivatives

10/12–Test on derivatives tomorrow (2X)..What should you study? All of Ch 2 except Related Rates. What should I know? Limit def of derivative, def of derivative at a point (pg. 99) Recognize and apply the rules (pg. 133); How can we tell from a graph what is the derivative (Adam Ditchara) or when it does not exist and why? How do we evaluate the derivative using technology (HINT: NDER); Given f(x), f ’(x), g(x) and g ‘ (x), find h(x) (table format), find the equation of a tangent line..no bonus on this test; calculators allowed. You will have the whole hour. NO MC, no motion probs; Johnny Knotubrite (Parker P’s boyfriend?) will be absent. Please derive carefully; be your own designated deriver.

10/11–HW: same as 10/7

10/7–pg. 142: 40, 43 -48-Test on Tue (probably the last test of the marking period).Content everything we have done so far except implicit differentiation with emphasis on derivatives (rules, relationship among s(t), v(t) and a(t), continuity, eq of tangent and normal lines, average velocity). 13 questions (combo: MC + FR, some questions have multiple parts). No calculator. All probs have been done in class…no surprises..(well, one bonus question)

10/6–pg. 142: 41, 42, 43, 48

10/5–pg. 142: 1-15 (odd); 12; 24, 27, 28

10/4–pg. 135: 81, 87-89, 93, 101, 102, 104 (compliments of Abbas). Read 2.5, “Implicit differentiation”.

10/3–“To give anything less than your best is to sacrifice the gift”..(Jay Mouton’s approach to working out..should be our guide as to how we approach life). Now, give this class your best: HW: pg. 134: 37, 38, 43, 47, 53, 56, 58, 61, 64, 68, 69, 50, 74, 77

9/30–pg. 133: 3-33, multiples of 3

9/29–Omar, the prob you worked on the board was incorrect! Sam pointed this out (Omar -1; Sam +1…Hernandez’ law of conservation of points). As Mackey said, “That’s Omar being Omar”. In prep for the Chain Rule (or as Kyle says, “The Shane Rule”), do pg. 29: 32, 54, 56..also read 2.4. Peut etre on va avoir un petit examen demain. Aishu, now that you know the power rule, I hope you use it when suitable.

9/27– pg. 125: 76, 78, 80, 101

9/23–Be prepared for a test on Mon (it may be postponed, but don’t count on it). T0pics to be covered: limits, continuity, derivatives, equation of tan/normal lines..in short, everything we have done so far–average and instant rate of change. Can we talk about derivatives without talking about limits? Go over your notes and hwk probs and you ‘ll be ready. Now, HWK: pg. 124: 39-53 (odd); 59-62

9/21– Hwk assigned this AM: pg. 116; 102; 107, 109, 111; pg. 124: 16-18; 27-37 (odd–check with BOB)..Parker B: Copy of test?

9/20–pg. 124: 1-12, all Writing the product or quotient rule as applicable for each exercise will ingrain the rule in your brains and will avoid mistakes later on…trust me, by then it should be second nature and you will automatically use them when applying the Chain Rule and doing implicit differentiation…

9/19– pg. 115: 87-95, all

3^3/4^2/4^2–In + to hwk given on 9/15: 37, 38, 51, 78 Re: f ‘ (sin x) = cos x; f ‘ (cos x)= -sin x (Ricky Cruz). Don’t forget Allie on her b-day (her explanation gave some of you 2+ pts and a key, right, Parker?).

9/15–pg. 113: 40-50, even: 56, 64, 66

9/14–Test tomorrow, mainly limits, continuity, IVT, + one bonus question..we haven’t done much on derivatives, so maybe only one question on that topic?

9/13–Read 2.2; we will prove the rules in class tomorrow

9/12–I just had a sandwich for lunch..what about if you join me for a sandwich, calculus wise? Do probs 49, 85 and 93 (we haven’t visited the sandwich theorem in a while and it may show up insidiously, so I want to make sure that you still remember). Additionally, look at the proof for the power rule on pg. 106 (this will assuage Abbas’ concerns and reinforce Cook’s “discovery”). Be a tourist tomorrow and visit my class.

9/9–On Monday we will go over probs assigned on 9/8 pg. 103 # 48. I expect questions on both assignments, otherwise I’ll assume that you have mastered the topic and we’ll move on (only to find out later that is not the case, as the quiz this AM proves). Those that don’t know, ask; those that don’t do, don’t know what to ask.

9/8–If we don’t have a quiz tomorrow, Omar will not be able to relax this weekend, so…draw your own conclusions. HW: pg. 102: 34, 37, 38, 61, 66, 71-80, 86

9/7-HW: pg. 101: 3,5; pg. 102–8, 22, 24, 27, 31, 32 (look for patterns..)

-dy/dx, f'(x), y’–These denote an INSTANT RATE OF CHANGE, i.e., at a point, an instant in time. How is “y” changing with respect to x lim x—>0 (f(x+Δx) -f(x))/Δx..Notice “limit”, since we are approximating the slope of the tangent line (Δx–>0, getting closer and closer, but actually never reaching zero)..This is also known as the DIFFERENCE QUOTIENT, b/c you are taking the difference in y values over the diff in x values. The secant line merely gives us the slope, or average over a period of time (diff in x), not a limit approximation. This morning we found formulas for derivatives using the limit definition (know the process!); tomorrow we will extend the idea to finding the derivative at a point (see pg. 99) and discuss the relationship between continuity and differentiability.

9/6–Read 2.1–Slope of tan line Δy/Δx….Now, Δy= differences in y values; Δx= diff in x values..We Will discuss this further tomorrow. Help? Check out Khan Academy, Paul’s Notes or Lin McMullen’s web site (google “slope of tangent line”). It helps if you are prepared.

9/2–In + to 8/26 and 8/30, do (compliments of Vicki, Isabel and Alligator)–chapter review 31, 48, 51..don’t know about you, but I have reached my limit with limits.

8/30-pg. 199: To the hwk given on 8/26, add 1-6, 25-38 (pick one), 37-40 (pick one in last set).

8/29–Same as 8/26.

8/26–Test Mon 8/9–pg. 199: 19-24, 29-32

8/25–pg. 192-“Limits at infinity” (aka “end behavior”), section 3.5; pg. 86, #64

8/24–pg. 67: 101-104; pg. 78: 84, 86–Read 1.5 (“Limits at infinity”)

8/23–Quiz tomorrow on continuity.

8/22–Wiki is on! (thank you, Ms. Rome!)..Now that you are experts on continuity and IVT (fledgling) 26-46, even ( assigned Fri), 57-60, 62, 66,68

8/17 pg. 66: 67-78. All these probs may be manipulated to a form matching the two limits in th. 1.9; once you do that, you are in. #76 is rather laborious. You may want to use a graphing utility to get an idea what the answer is, BUT you have to do these probs. analytically on the assessment. Josh, let’s discuss the question you asked me after class with the whole class..remember what it is? lim x–>inf (sin x/x).

8/16–Go over 1.3, pay attention to rules pg. 57 and as well as theorems on pg. 59. HIGHLIGHTED INFO IN RECTANGLES IS IMPORTANT. If you don’t understand the jargon/symbols, please ask. “Sandwich theorem” (something we eat?) “Squeeze Theorem” (“Please don’t squeeze the Charming”; what is squeezed? what is doing the squeezing? (squeezing functions?), Check pg. 63, TH. 1.8

HW: pg. 66: 89- 94, all (graph first in a small x-window, close to zero). Now, show how the squeeze th holds algebraically . Tomorrow: posssibly a quiz, provided that I have graded the one you took this AM. Continue with limits, prove analytically lim x–>0 (sinx/x)=1.

8/15–Expect a hwk quiz tomorrow (if you were paying attn in class this AM, you should not have a prob; if not, well…better luck next time and listen when the big man talks). HWK: pg 65: 27-62 (all–expect algebraic difficulties with 56-62)

08/11–Review of familiar fns: On the side that starts with “y=x” use your calculator (if you need to) to complete the chart (domain, range, zeroes, etc). Question: What important fn is not covered but is extensively discussed in calculus? Feliz cumpleanos, Parker B.

## PRE-CALCULUS: 2nd Semester

4/24–Textbook: pg. 558: 21, 22, 25,26, 31-37 (odd)…(Check out ex. 2, 3, and 4)

4/20–pg. 558: 1-18 (omit 10) Hint: try to visualize the point graphically in the Argand plane a + bi (a represents the real or “x” axis; i, the y axis and “b”, Hassan Malik, the distance we are moving along the i axis, so “3i” represents “three units along the i (or y ) axis). HTH.

4/19–Read 6.6

4/18–In order to review for the quiz tomorrow: pg. 562: 63, 64, 66, 67, 69, 71

4/7–pg. 548 in your text: 7- 12, 32, 34,

4/6–Old book, pg. 401: 19-26; 24, 25-28. Remind me to show you how to convert a limaçon to rectangular.

4/5–pg. 400 2-8 (even); 13-16 (discuss symmetry (all these graphs are symmetric (double “m”, Luke!), domain (all real nos in most cases; exceptions are spirals) , range, max value..remember that all these graphs are continuous, bounded (closed). Use hand out given in class.

4/4–Read 6.5..Try pg. 548 1, 2, 21-24. Refer to examples in the text, look for patterns. Work done previously will help you understand. For instance for prob 21, graph y= 2 + 3 cos θ –the amplitude, max, min and period appear in the polar graph; ditto for 23 (graph y = 3 cos 3θ the “3” in front of theta has a meaning..what is it? All these graphs are closed curves and symmetric with either the x-axis (cos), y-axis (sin), or origin (usually flowers). We will investigate different curves over the next two days…refer to hand out (C4, remind me tomorrow about the hand out).

4/3–countdown? pg. 180..56-50..look for patterns..somehow, I have a feeling that you are not getting this, even though you tell me that you are…we shall see.

3/31: pg. 3 π: 35-49 odd

3/30–Read 6.4. Do the following for hwk: pg. 539 1-4; 19-22, 23, 24. Remember: R(x,y) —> P (r, θ) r= (x+y) 6 (1/2); θ= tan‾¹ (y/x); to convert from P(r,θ)—>R(x,y),

x= r cosθ; y=rsinθ Keep these two key relationships as we move through this chapter.

3/3³–Study guide for the test on Wed, 3/29, photocopied, old book. Format of the test: Combination of FR, MC, T/F, Fill in the blank.

3/24- pg. 390 (photocopied) 17-30…solve graphically first, then algebraically. Most of these equations rely on using double angle formulas, however, they can be manipulated (Amy Sigur, the manipulator par excellence) do the obvious…if stuck on a problem, don’t spend too much time (23, 24), some of these probs require the quadratic formula (31?) or synthetic division (either 31 or 29)..not a problem that you may see on a test, but a good opportunity to review some of the skills you learned in Alg II. Expect an easy hwk quiz on Monday, similar to the last quiz (DOK 1). Review formulas..We still plan to have a test on Tuesday.

3/23–If Zunair did his homework last night, will Luke be far behind? HWK: photocopied pg. 384: 19-26 and 39-40. Test on Monday or Tuesday?

3/22- Photocopied pp. 1-18, all (easy); 31-38, all

3/20– Due Wednesday..In your text: Review formulas on pg. 471..Read the rest of the section so that you can be prepared for the discussion on half angles; Do 5-14, pg. 475..Tenth graders, report to room 129 (C3); C4, report to my classroom.

3/17–photocopied: pp. 377-78: 1-14 (all); 18, 20, 24

3/16–pg. 374: 33-38 (#37 done in class), 42, ( 44, for Neel and Suraj…deja vu)

3/15–pg. 373–2-30, even

Π Day–We celebrated by having a test involving π (lame!,suggested by Zunair)..HWk for tomorrow (Π +1?)–read 5.3

3/10–17-26–unusual probs–you may have to complete the square, factor by grouping, multiply by a function, etc (unorthodox approaches). Test on Tuesday, 03/14 aka Π day, a good sign.

3/9–In + to the probs assigned yesterday: 9-16 (some of these probs may be solved analytically, i.e., you may want to give an argument such as #15–think, “for what angles do the sine and cosines have opposite values”?

3/8–pg. 326 (photocopied) 1-8

3/7–pg. 460 9test0 11-20 (all); 26, 28, 34

3/6–Photocopied: pg. 321: 13-24 and pg. 322 29-36 (all)..review algebraic techniques. Do the obvious: common factor, expand (if needed), common denominator, Pythagorean relationships (is any expression squared?),..if in doubt, change everything to sines and cosines (this approach usually works, although it may make the problem longer).

2/22–Review probs for the test on 2/24: photocopied pp 328-329, (1-7).

2/21–Both classes: Assigned earlier: pg. 314 (old book), 15-18 ; assigned today: pp. 299-300 (or 5π/6)–22, 23, 26, 28,30-36

2/14–Both classes: Complete package given on Monday (applications of sinusoids–are you paying attention, Luke Vedros and his posse (PM class); Hassan Malik and his posse (the pseudo soccer players), C3?)

2/10 C3–Textbook (applications of right triangles): textbook pg. 433: 12-16; 25

2/9–pg. 306 (photocopied) 21-26 (22 done in class). Follow directions given on 2/28

2/8–pg. 306–19 (done in class); 20 (use graphing calculator before doing the prob to have an idea or after the problem to confirm your answer); 27 and 28. We will do-21-26 in class tomorrow since they pose new twists.

C4: Remind me to go over the classwork assignment given on Monday and also answer Emin’s question

2/3–photocopied pg. 305, 11-12 (these probs do not have neither a vertical nor a horizontal shift). C4–if you had no time to take a pix, please stop by during lunch.

2/2—Photocopied pg. 313 bottom half, but if you are ambitious, top half as well (write the equation corresponding to a given graph..Need help? Ask David Beach, the new expert).

2/1–pg. 395: 61, 62, 64, 65–Follow directions and graph by hand (may confirm with graphing calculator).

1/27–Quiz on inverse trig functions (both classes)

C4: We will go over the assigned (photocopied) study guide for your test (scheduled for Tuesday, 01/31).

1/26–photocopied page (pg. 17²): Class exercises (#8); Written Ex (5-8). Neel Mondal: Please bring up the question you and I discussed after class. Expect a quiz tomorrow (relax, Bruno, inverse functions are not be included) similar to the one you took today.

1/25–pg. 423: 1-12; 23-32

1/24 Read in your text 4.7 “Inverse Trigonometric Function”; pay close attention to examples–ask yourself, “how do we get the graphs of the inverse trig functions from the graphs of the parent function?” Domain restrictions? Remember, the answer to an inverse trig problem is an angle, but we don’t use the whole circle. For the quiz tomorrow: review unit circle, trig values of special angles, quadrants, and the graphs that we covered yesterday. Inverse trig functions will not be included tomorrow.

1/23–pg. 404: 45, 46 and (MC 51-56–explain reason)

1/20–C3– photocopied pg. 286: 13-18 (all)

C4–text: pg. 404: 29-34

1/19–Photocopied page: 33-40

1/18– C3–see C4, 1/17

C4–see C3, 1/17…now we are even.

1/17–C3–Photocopied pg. 272: 2-20, even

C4–pg. 383: 2-24; 44-48 (even)

1/13–HWK due Tuesday, 1/17: pg. 369: 50-58, even; 61-65; 75, 76 , 62, 63 (applications of right triangle trig ratios, aka SOH CAH TOA–use calculator as needed).

1/12–pg. 369 (mnemonic device: 3+ 6= 9): 29-40 (use calculator)

1/11–pg. 368: 1-17, odd #s.. Remember: if in doubt, draw a right triangle and use the trig ratios of a right triangle (you know this as “SOH CAH TOA). Also, recall the reciprocal relationships ( csc Θ = 1/sin Θ, etc.).

1/9– Photocopied pg 265: 1-14

1/5– HWK: Review def of “radian” as well as formula Θ (angle measured in radians) = s (intercepted arc)/ radius; Know how to convert from radians to degrees and viceversa, know the radian, degree and real number equivalent for key angles in the unit circle (e.g., Π radians ∼ 3.14 radians in real number, since we use 3.14 as an approximation for PI). Your hwk: pg 358: 9-34 (some were done in class).

1/4–Read section 4.1; pay attention to examples..will discuss in class tomorrow.

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1st Semeser

12/13–Photocopied Chapter Test (pg. 365 combien des jours dans un an?) Review for test on Th. We have not discussed #10 (will do tomorrow), but give it a try.

12/12–Green book (this is what C3 wanted): Use the Law of Cosines: pg. 494: 6, 10,11, 12, 18, 30, 31, 35, 36 (any baseball players? ),39 (for the engineers in my class–David Hutton, Megan Marasalone?) , 41 (For the “jocks”–DJ and BK)..sorry, no problems for the messy people (Alex, Bellama)..you create your own problems.

12/9–Both classes: Green book: Read 5.5 (“Law of Sines”)..Follow examples..Remember: Law of Sines is used in the SSA situation, known as the “ambiguous case” since it can lead to one, two or No triangles. If you get a positive value for sine, may give you and angle in quadrant I or Q II. You must investigate if two triangles are possible, by + the given angle to the answer in Q2 (angle in Q1, or the reference angle will always work), to make sure that their sum is < 180 and we have enough left for a 3rd angle. HWK og. 484: 6, 8, 14, 16, 17, 18, 20, 22, 38

12/8 C3–See C4, 12/7

12/7–C3–Test tomorrow, polar coordinates? Need help? See me at 1st period (with your teacher’s permission)

C4–Photocopied: pg. 336: 21-24; 27 (deja vu); pg. 342: 7, 9, 12-15 (good cal prob)..read about the Law of Sines in your textbook (Ben Kirk)

12/6–C3–See C4, 12/5

C4: Test on Polar Coordinates–will be available during lunch to answer questions (2nd half)

12/5–C3– pg. 558: 40, 42. 54, 56, 58, 61 (“unity” means “one)

C4–assigned test review, pg. 415 (photocopied)

12/2-C3: pg. 558: 21, 26, 28, 32, 34, 36

C4: In + to probs listed above: 40, 42. 54, 56, 58, 61 (“unity” means “one).

Why so much hwk? You had Th night off.

11/30– Read pp. 550-551; hwk: pg. 558 (1-17; follow ex 1, pg. 551).

11/29–pg. 62: 69, 70, 71 (Analyze ( means follow directions as given on 11/28) and graph without a graphing calculator. Convert either 69 or 70 to polar. How many times do the graphs cross zero? ). You will be expected to do discuss similar probs on your quiz tomorrow.

11/28–pg. 401: do 25-28 and answer the following: domain, range, continuous? symmetry? bounded? Maximum r value? asymptotes?

11/17–pg. 548: 21, 24, 31, 32, 35-40 (follow examples 5 and 6, pg. 546 as well as handout given in class)..use graphing utility to verify graphs. HWK tomorrow.

11/16–Text: pg. 548–25-28; 33, 34 (last two are cardioids)…you may use your calculator to verify/help you understand the assignment; however, you will not be allowed to use your calculator on your assessments.

11/15–pg. 540 (3Π): 36-50, even (follow directions)

11/14–Photocopied page (pg. 400) 2-12 even, 13-16

11/11–Text: Read 6.4–pay attention to boldfaced/highlighted terms as well as formulas in green rectangles. Do 1-22 (omit 9, 10, 17, 18).

11/10–Photocopied (pg. 390): 18-22; 23, 24, 25

11/9–Test (see 11/7)

11/8–Election Day

11/7–Test on Wed, 11/9–Multiple Choice (28) + Bonus Most of the content covers the formulas with which we have been working, although you will encounter questions from material previously covered. Since all the answers are exact, you won’t need a calculator at all.

11/4–pg. 384: 31- 40 (37 and 38 were done in class). Use double angle and half-angle formulas in order to prove the identities.

11/3–pg. 384 C3: same as C4 below (11/2) + 11, 12, 23-26.

C4: Same as 11/2; add 11, 12, 23-26.

11/2–pg. 383: C3– Class exercises (1-10); Written exercises (1-6).

C4–photocopied page (pg. 384): 7-10, 13-18, 19-22

10/31– pg. 378: 7-14 (omit 10), 20, 24-26. Two days to do your hwk; don’t be scared to do your hwk; ( Alex Edwards always is); be prepared (David Hutton always is).

10/28–pg. 374–34-38, 42; pg. 377: 1-6 Written exercises (both pp photocopied from old book)

10/27–pg. 373 (photocopied), odd nos.

10/25–Test tomorrow–shortened period, so please be on time and bring a scientific calculator. 4 equations to solve (done in class and/or assigned for homework), 2 expressions to simplify, 2 identities to prove, 10 MC questions, 1 t/f, 1 discussion, and one bonus question. C3 students may be allowed to stay a few minutes into lunch; C4 you may start a few minutes before class, if you wish.

10/24: Both classes: Finish photocopied page thru #26 (probs after #20 require special techniques such as the quadratic formula and factoring by grouping..good review of algebraic skills learned in Alg II).

10/21–C3: pg. 326 (photocopied 1-16); C4: same page, 9-16

10/20–C4: pg. 326: 1-8

10/18–Good luck on your PSAT. C4–Test tomorrow; C3, test on Th (see below).

10/17: Both classes: we will go over probs on pg. 329 (1-8); be prepared for a short HWQ quiz tomorrow.

C3–Your test will be on Th due to PSAT. Do pg. 322 (photocopied, 29-36).

C4: Your test will be on Wed. HWK (see pg. 329; C3 , above AND pg. 321(photocopied) 13-24).

10/14–Both classes: photocopied page (pg. 321: 1-12)

10/13–C3–pg. 452: 23-32

C4: pg. 451: 9-32

10/12–C3–Textbook: pg. 451: 9-16 Test on Friday.

C4–Photocopied pg 328 (1-8), old book…Test on Friday…

10/11–Π pg (old book, photocopied): 15-18

10/6–Test tomorrow–My advice: Look @ each section, review t/f and mc questions (Ch 4, your text)

10/5–C3: pg. 299: top: 12, 13; bottom: 22, 23, 24

C4: pg. 300: 25-36 (all)

10/3,4–lingering hwk from 9/29 and 9/20—pg. 306, old book (19-26)

9/30–3rd pd..I asked students in C4 to forward the hwk assignment to you: photocopied old book pg. 306 19-26

9/29–Test tomorrow–very similar to the last test + 4 rt Δs probs (similar to hwk given on 9/21). Questions? Stop by during C1 or C3–no lunch tutoring tomorrow. Bring a scientific calculator; you will have the whole period and this test counts twice. I fee that you are prepared.

9/27–pg. 299: 13-21, all

9/21–Test on Friday (focus on graphing). Now, HW for tomorrow (text): pg. 2² 5²: 66; pg. 433: 12-15.

4th pd. We still need to go over the hwk for 9/20 (hand out).

9/20–Finish handout: 3, 4, 5, 6–HWQ tomorrow; test Thursday

9/19–Do first two probs in the handout (“Applications of sinusoids”; answer questions, graphing calculator needed. Additionally, think about the following prob: y = -tan 2π(x-1) -2.. what is the period? vertical displacement? asymptotes? Hint: think, “How do we get the graph of “y” from the graph of f(x) = tan x?

3^2/4^2/4^2-HWQ: Graphing sinusoids (graphs a sinusoid given the equation; given an graph, write the corresponding equation) Hwk: pg. 395: 41, 42, 59, 60, 63. Remember relationship between frequency and period (see pg. 390: frequency= reciprocal of period (or B/(2π)). Also, please remind me how to graph sec, csc, tan and cot with vertical and horizontal shifts as well as modified periods (Katie Charrier’s question).

9/15–1-8, photocopied page; 1-8; (writing equations from the graphs)

9/14–photocopied page (pg. 313, old book)…whole page.

9/13–text, pg.395: 43-52, all (do not graph!)

9/12–pg. 403: 5, 7, 8, 11, 12. Be prepared for a hwk quiz tomorrow.

9/8–Test tomorrow..will be available to answer questions during C1.

9/7– HW: pg. 289 (photocopied), whole page. Expect a quiz tomorrow on inverse trig fns. Study guide questions?

9/6–Test on Friday–study guide (not assigned, but strongly recommended) photocopied today in class. Today we started on inverse trig functions. Highlights: In order to discuss inverse trig functions, their domains must be restricted, so that both the restricted fn and its inverse pass the vertical and horizontal lines tests (i.e., so that they are “one-to-one” functions). We don’t restrict the range. However, the inverses do have restricted ranges..Why? Well, how do we get f‾¹ (x) –we exchange the domain (restricted x value) with the range. Hwk: Read pg. 4.7, pay attention to highlighted green rectangles and definitions, examples 1-4. Do pg. 423, 1-12.

Mort, Hwk posted @ 4:45, before your Reginelli’s shift.

9/1–Continue studying notes…Check chart on pg. 402..nice summary of the basic trig functions..you should know all of the characteristics (Good test/quiz question, “Graph the _____fn and discuss its the characteristics”. Tomorrow we will be doing our pre-test and start on inverse trig functions (I recommend you read 4.7) .

8/30 Bellama is beginning “to get the unit circle”…there is still hope! Review unit circle, focusing on values of key angles. Review graphs discussed in class (sine, cosine and tangent–domain, range, period, symmetry, continuity, end behavior.) Question: How do we obtain the cosecant, secant and cotangent graphs from the sine, cosine, and tangent graphs? We’ll discuss this tomorrow…Remember: hwk quizzes can happen anytime, unannounced…must keep on your toes, so it behooves you to review what we have learned so far.

8/29–11th anniversary of Katrina, a day we all remember. Now, for hwk: photocopied page: 13-18; 23-28. Both set of probs are meant to reinforce your understanding of the unit circle and values of trig fns. Use hand outs as needed…remember: analyze, do not memorize ( Ben Kirk)…How do we find csc 5PI/3? Well, Θ ref = PI/3 (that’s one of the reason we prefer angle in PI radians–we already have the reference angle) and the terminal side (Garret!) is in Q4.

8/26–pg. 383: 21-36

8/25–pg. 274: 33-40; pg. 279 (bottom of the page) 1-4–What did we learn today? How to find reference angles

8/24: Photocopied page: pg. 272, (old book), odd nos.

8/23–pg. 383–43-48, all (check handouts..remember: r = (x + y) ^ (1/2) also, given the information, in what quadrant is Θ?) Expect quiz tomorrow.

8/22–After a week hiatus, my wiki is working thanks to Ms. Rome’s assistance..so here we go:

text: pg. 383–1-20; 37-42 (all–do not use a calculator; draw unit circle on your paper and go from there).

8/15–3rd pd: photocopied Pg 262, old book, 18-30, even

4th pd: pg 261 (photocopied), 2-14, even (+ practice)

8/15–HWK: Review def of “radian” as well as formula Θ (angle measured in radians) = s (intercepted arc)/ radius; Know how to convert from radians to degrees and viceversa, know the radian, degree and real number equivalent for key angles in the unit circle (e.g., Π radians ∼ 3.14 radians in real number, since we use 3.14 as an approximation for PI). Your hwk: pg 358: 9-34 (some were done in class).

08/11–See above, go as far y= √(x² – 1). If confused, or if you have forgotten some of the terminology, don’t worry–we’ll address this in class tomorrow. At this point we are reviewing Alg II content