IB Math SL 2 Spring Semester.

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Unit 4: Integration

Thursday, 1/31 - we introduced the idea of antidifferentiation as the reverse process of differentiation. Here are the slides from class. Your HW is Exercise 14.1 #1-6.

Friday, 2/1 - we practiced finding antiderivatives, especially those of common functions we found from taking derivatives. Here are the slides from class. Here are the calculus formulae from your booklet. Your HW is Exercise 14.1 #7-10, 12, 16-19.

Monday, 2/4 - we have a field trip to Bryant Park and surrounding fun!

Tuesday, 2/5 - we don't have school for Lunar New Year. Happy Year of the Pig!

Wednesday, 2/6 - we're continuing our process of reviewing for our upcoming Math IB Exams and reviewing the topic of sequences and series. Here are the problems from class. Here are the solutions.

Thursday, 2/7 - we are practicing finding antiderivatives in class. Here are the slides from class. Here are the practice problems, including the HW, from class.

Friday, 2/8 - we found complex antiderivatives by the process of substitution, essentially reversing the chain rule. Here are the slides from class. Here is the worksheet with your HW, which is Ex. 14.1 #21-29 odd.

Monday, 2/11 - we continued to practice using the method of u-substitution to find antiderivatives of functions that came from a chain rule application. Here are the slides from class. Here is the worksheet with your HW, which is Ex. 14.1 #22-30 even.

Tuesday, 2/12 - we're continuing our process of reviewing for our upcoming Math IB Exams and reviewing univariate data (cumulative frequency, box and whisker, measures of center and spread, etc.). Here are the problems from class. Here are the solutions.

Wednesday, 2/13 - we approximated areas under curves, and saw some new notation to represent these areas. Here are the slides from class. Here is the worksheet from class.

Thursday, 2/14 - we used the Fundamental Theorem of Calculus to evaluate some definite integrals. We'll see how this idea is related to finding areas with rectangles tomorrow. Here are the slides from class. Your HW is p. 476 (Ex. 14.2) #1-9 odd.

Friday, 2/15 - we watched a video that reviewed what we've learned about integrals so far and motivates why the Fundamental Theorem of Calculus is true. Here is the video. Happy break!

Monday, 2/18 - Friday, 2/22 - it's our Mid-Winter Recess. Happy break!

Monday, 2/25 - we practiced evaluating definite integrals. Here are the slides from class. Here is the worksheet of problems from class. For HW, remember that your Math Exploration is due at 10PM on Friday, 3/8.

Tuesday, 2/26 - we explored some properties of definite integrals. Here are the slides from class. Here is the worksheet from class. For HW, remember that your Math Exploration is due at 10PM on Friday, 3/8.

Wednesday, 2/27 - we evaluated definite integrals using the method of u-substitution. Here are the slides from class. Your HW is Ex. 14.2 #12-20 even, (check on GDC).

Thursday, 2/28 - we explored the idea of using definite integrals to evaluate areas. Here are the slides from class. For HW, remember that your Math Exploration is due at 10PM on Friday, 3/8.

Friday, 3/1 - we practiced problems involving indefinite and definite integrals. Here are the problems from class. For HW, remember that your Math Exploration is due at 10PM on Friday, 3/8.

Monday, 3/4 - Friday, 3/8 - we worked on your Math Exploration in class. Mr. Lao is absent on Wednesday, 3/6, and it's a half-day on Friday, 3/8. Here are some final reminders for submission requirements for your Math Exploration. Your Math Exploration is due at 10PM on Sunday, 3/10.

Monday, 3/11 - we're wrapping up our Internal Assessment in Math SL and reflecting on the whole process. Here are the slides from class. Here is the guided worksheet we went through to reflect on our Math Explorations. Mr. Lao collected these for a grade.

Tuesday, 3/12 - we have a Group Practice Quiz on integration.

Wednesday, 3/13 and Thursday, 3/14 - we did more IB practice problems involving integrals. Here are the problems and their solutions.

Friday, 3/15 - we have our quiz on indefinite and definite integrals.

Monday, 3/18 - we found fancier areas found between two curves. Here are the slides from class. Your HW is Ex. 14.3 #2, 3, 6, 8 and you can find the solutions at the end of the slides.

Tuesday, 3/19 - we found even fancier ares found between two curves that interweave with each other. Here are the slides from class. Your HW is Ex. 14.3 #1, 4, 7, 9.

Wednesday, 3/20 - we practiced finding a variety of fancy areas. Here are the problems from class.

Thursday, 3/21 - Mr. Lao is on the Tenement Museum field trip with Class II. You reviewed the Binomial Distribution with some notes and practice problems.

Friday, 3/22 - we found volumes of solids of revolution with integration. Here are the slides from class. Your HW is Ex. 14.4 #1 & 2.

Monday, 3/25 - we have a workshop about our relationships with technology.

Tuesday, 3/26 - we found volumes of solids of revolutions with holes in them with integration, which is an extension topic for Math SL. Here are the slides from class. Your HW is Ex. 14.4 #5, 6, 8, 10.

Wednesday, 3/27 - it's city-wide SAT Day and you have a field trip. Have fun!

Thursday, 3/28 - we practiced a variety of IB Math SL style volume problems. Here are the slides from class. Here are the problems from class. Here are the solutions to those problems. Did you know that there are YouTube channels dedicated to watching people study? Like, you put on the video, and it's just someone studying their own thing for a few hours and you're supposed to study along with your own thing? What is this world we live in? Does anyone even read this website that I spend too much time editing to provide a resource for too few students? Alas. Also, did you know they're making a live action Dora the Explorer movie? Woah, man. Also, I know lots of you are hearing back from colleges very soon and I have my fingers crossed for all of you. You're all so special and I hope these next few days are filled with surprises and happiness and learning moments. I know there might be some disappointments along the way, too. Whatever the case, I'm here for you in whichever ways I can be, even if it's as simple as an ear to listen while you weigh your options.

Friday, 3/29 - we started our study of kinematics, which for us is using calculus to analyze one dimensional motion. Here are the slides from class.

Monday, 4/1 - we continued our study of kinematics and specifically analyzed how we can determine speed. Here are the slides from class. Your HW is Exercise 11.3 #14 (not b), 21.

Tuesday, 4/2 - it's your last TBLS March Madness day ever! In math class, we saw how integration can help us find total displacement and total distance traveled for kinematics problems. Here are the slides from class. Your HW is Exercise 14.5 #3-5, 8-10.

Wednesday, 4/3 - we combined all our knowledge of derivatives and integrals to solve some kinematics practice problems. Here is a (hopefully) useful sheet of notes summarizing kinematics. Here are the problems from class.

Thursday, 4/4 - we solved more complex kinematics problems. Here are the problems from class. Your Exam on Applications of Integration (area, volume, kinematics) is upcoming on Tuesday of next week. Here are some mixed practice problems that we'll work on in class on Monday should you like to start studying now, and here are the solutions to those problems. You have a group quiz tomorrow for even more practice. Here is a (hopefully) useful sheet of notes summarizing kinematics.

Friday, 4/5 - you have a group quiz on Applications of Integration (area, volume, kinematics). Here is a (hopefully) useful sheet of notes summarizing kinematics.

Monday, 4/8 - we did a variety of mixed review IB Math SL style problems about the applications of integration (area, volume, kinematics). Here again are those problems and here are the solutions to those problems. Your exam (GDC required) is tomorrow. Here is a (hopefully) useful sheet of notes summarizing kinematics.

Tuesday, 4/9 - we have an exam on the applications of integration (area, volume, kinematics) where a GDC is required.