HW: Complete the Rotations/Cross Sections packet, including the last page. Bring your 2012 FRQs and any questions on the odds. Students can now complete FRQ #2. Quiz 7.2 on volume by revolutions is tomorrow.
Students completed 2 warm-up questions, find the area of a region and then computing the volume of the region given the cross-sections (as semi-circles, squares, or equilateral triangles). We went over these in class. We also went over questions from the Volume by Rotations/Cross Sections packet. We completed question 1 on the rotations III page.
HW: Complete the Rotations/Cross Sections packet, including the last page. Bring your 2012 FRQs and any questions on the odds. Students can now complete FRQ #2. Quiz 7.2 on volume by revolutions is tomorrow. We discussed our last topic today, finding the volume of a solid with a known cross section. We reviewed the area formulas for square, equilateral triangle, and semicircle. Using animations we were able to see that the volume was an accumulation of particular cross sections. We used the integral to sum up these cross sectional pieces. We completed our notes and 5 examples in class.
Use the videos for more examples http://www.youtube.com/watch?v=N_50DlV9v24 http://www.youtube.com/watch?v=puSlVA6mwNQ HW: Complete WS Cross Sections I & II and the MC Questions attached to your notes. AP Exam Review on Monday, 4/24. Students completed 2 warm-up questions on volume of revolution. We worked out both of these problems together. Students also had the opportunity to complete the WS Circuit Training Volume by Revolution and the packet form Monday. We also went over a couple of problems in the Circuit Training.
HW: The packet from Monday (contained volume questions with the answers in parentheses & had multiple choice questions) should be completed by the end of class tomorrow. Please note, there is an optional page for more practice. We went over the first 5 problems (with some variations too) from the WS Circuit Training Volume of Revolution. Students had the last 15 minutes to complete their Quiz 7.1.
HW: Complete the WS Circuit Training Volume of Revolution and make your plan for AP Exam Prep. Use getafive.com and/or your Fast Track to a Five Book. AP Exam review tomorrow after school in C215 from 3:00 - 3:50. We looked at the set up of Problems 1 & 2 (parts a - d on both) using geometer's sketchpad to visualized the solid. Students used the last 15 minutes for their quiz 7.1.
HW: Complete the first 9 - 10 problems on the WS Circuit Training - solids of revolution. Only 3 weeks to the AP Exam - review sessions on Wednesday & Thursday this week; 3:00 - 4:00 in room C215. Make a study plan as you cannot cram for the AP Exam. Use getafive.com and your Fast Track to a Five Book. We started with 2 warm-up questions that asked for the area of the region and then the volume formed by rotating that region about the x or y axis.
Then we completed our notes on finding the volume of a solid formed by rotation around a horizontal or a vertical line. Today we looked at the region having some gap between it and the axis of rotation. The cross section ends up being a washer, so we need to determine the outer and inner radii. Use the video links below for more examples of the washer method. http://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/solid_of_revolution/v/solid-of-revolution--part-4 http://www.youtube.com/watch?v=E5OOMbz5jZk http://www.youtube.com/watch?v=ithgZfRKMHI http://www.youtube.com/watch?v=lE814ngFt3I HW: Quiz 7.1 (area between curves) is tomorrow. Complete the front side (1 -4) of the 7.2 packet from today. AP Exam review tomorrow and Thursday after school in C215. We went over the even 2012 FRQs. We checked the set up for 2a and went over all parts of #4 and #6. We also discussed the grading rubric, each FRQ is 9 points and students should attempt all parts of the question.
HW: Do 1, 3, & 5 in the 2012 FRQs and check with the grading rubric. We will discuss any questions on Monday. HW: Complete Worksheet 1 - 3 doing parts "A" and "b" only. On the 2012 FRQ packet please complete #2 part A and questions 4 or 6. Allow 15 minutes per FRQ.
Check your FRQs with the link below. https://secure-media.collegeboard.org/ap-student/pdf/calculus-ab/ap-2012-calculus-ab-scoring-guidelines.pdf We spent a second day setting up integrals that gave the area between 2 curves. We also showed how to use the calculator to find the intersection points and store those values (in "a" and "b") so that they are easily used in the evaluation of the integral. We also showed how to use the name of the function (VARS button) in the set up.
We also checked 1 - 5 (worked out #4) on WS 7.1 and did 66a (with the calculator). HW: Complete WS Finding Area I, II and III. The 2012 FRQs will be discussed in class the next 2 days (evens tomorrow and odds on Thursday). We reviewed and completed our notes and 4 examples on area between 2 curves. We used our understanding of the integral as the area under the curve to help us come up with formulas for given areas. We found that if we are accumulating slices from left to right the integrand is top - bottom and if we accumulates slices from bottom to top the integrand is right - left.
Use the link below for additional help: http://www.youtube.com/watch?v=DRFyNHdVgUA http://www.youtube.com/watch?v=70NQ3ISYihw http://www.youtube.com/watch?v=Xne6Hv9useE http://tutorial.math.lamar.edu/Classes/CalcI/AreaBetweenCurves.aspx More Examples: http://www.dummies.com/how-to/content/how-to-find-the-area-between-two-curves.html Student were given the last 15 minutes to complete their Test 6.1 - 6.3. HW: Complete the attached WS 7.1 and Step by Step worksheet (66 a, b and 67 a) |
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