AP MC Review – Limits Continuity Diff Eq April 5-7 Do Now Solve the differential equation

Plan for rest of classes up to AP Exam Every 3ish days, MC packet and FRQ quiz on one of four topics – Limits, Diff eq, Continuity Ch 2 and 9.1/9.3 – Differentiation and Applications Ch 3-4 – Anti-Derivatives and techniques Ch 5 – Accumulation (Definite Integrals and Applications) Ch 6 and 5.5

After AP Exam Each week after the AP exam there will be a project centered around a topic we learned – First day of week: Intro/Lecture – Middle days: work on project / presentation – Last day of week: presentations (groups of 1-3) (5 min max) The week before prom: First chance to take the final – Monday – Wed – MC Calc, MC No Calc, FRQ No calc – If you don’t take it then, you take it on the scheduled June date

Show other AP powerpoints

Cont/Diff, Limits, Diff EQ Tuesday: review 1 st part of packet (Cont/Diff) Cont/Diff part for HW Wed: review 2 nd part (Limits) Limits part for HW Thurs: review 3 rd part (Diff EQ) Diff EQ part for HW Friday: Quiz from packet

Problems to skip Limits - Page 2 #45 Page 3 #41 Cont + Diff – none Differential Eq – page 1 #44, 37 page 2 #32 page 4 #5, page 5 #24 page 6 #7 page 7 #24 – Page 1 #31 typo: f’(x) = -f(x)

Limits To evaluate a limit, substitute the value x is approaching If 0/0 or inf/inf, [factor, conjugates, etc] or use L’Hopitals – L’Hopitals = derivative of top and bottom – Any indeterminate form must be rewritten as a 0/0 or inf/inf If #/0 -> undefined, or +/- inf Limit definition of Derivative – Determine the function, differentiate it, and plug any #

MVT Given a continuous [a,b], differentiable (a,b) function between a and b, there must exist a c in between s.t. f’(c) = the slope between a, f(a) and b, f(b)

Continuity and Piecewise Continuous = right and left limits approach the same defined value Differentiability = the right and left limits of the derivative approach the same value

Review Let’s review

Closure (one of these days) Describe the importance of limits, continuity, or differential equations in mathematics and possibly real life applications. Only choose one for each closure HW: Continuity due Wed Limits due Thurs Diff EQ due Fri Quiz Fri

AP Review – Differentiation April Do Now Pick up FRQ Quiz OR Have questions about derivatives

Do Now Find the derivative of f(x) = [sin(1/x)]^2

Goals for this week 2008 MC Proctor (not graded) Differentiation Packet (1 st half) should be worked on SKIP: Differentation: Pg5 #14, Pg8 #30, Pg11 #15, Pg14 #4,6, Pg17 #2, Pg18 #77 Pg21 #1 Applications: Pg5 #4, Pg8 #15, Pg10 #34, Pg12 #12, 25, Pg 13 #28, Pg17 #18, Pg21 #10,

Related Rates What rate is given? What rate do we need to solve for? Write an equation using those variables – Don’t use any constants unless that measure never changes Differentiate with respect to T Solve for the missing rate – May need to use the orig equation to find other measurements

Optimization Identify what variable you are optimizing Write an equation variable = – If optimizing area, A = f(x) – Single variable equation Differentiate then set = 0 – Don’t worry about denominators when solving If there are endpoints, test your zeros and your endpoints

Review Let’s review

Closure (one of these days) Describe the importance of derivatives in mathematics and possibly real life applications. Only choose one for each closure HW: (1 st half) Deriv packet due Mon Applications Packet due Tues 4/19 and Wed 4/20 Quiz Thurs 4/21

AP Review – Anti-derivatives April Do Now – Integrate

April Tuesday: Anti Derivatives Quiz Packet pages: p.1-7 Fri, p8-14 Mon Tues MC Packet: SKIP anything labeled BC, and Pg3 #25, Pg 5 #45, Pg15 #11, Pg18 #11, Pg21 #25

Things to think about Fundamental Theorem of Calculus – Part 1: Definite Integral [F(b)-F(a)] – Part 2: Derivative of Integral Substitution – Compositions, products – Change the bounds

Review Let’s review

Closure (one of these days) Describe the importance of anti-derivatives in mathematics and possibly real life applications. Only choose one for each closure HW: Antiderivative Packet p.1-7 due Fri P.8-14 due Mon P due Tues Antiderivative Quiz Tues

AP – Review – Accumulation April 27 – 29 Do Now The velocity of a particle is given by v = 10t – 2t^2. Find the distance traveled in the interval [1,10]

Goals for this week Friday: Accumulation Quiz Packet HW: 12 pts total p.1-8, p.9-16, 17a-22 SKIP: Pg1 #33, Pg2 #9, 43, Pg3 #22, Pg4 #10, Pg5 #40, Pg7/8 #24, 35, 41, Pg9 #30, Pg11 #23, 33, Pg13 #20, Pg14 #19, 23, Pg17a #84, Pg 17b #15, 21, Pg18 #77, Pg21 #19, Pg22 #21, 80 Note: Page 7 and 8 are the same

Review? Area between 2 curves – With respect to x (higher – lower) and y (right – left) – Approximations: left, right, midpoint, trapezoidal Not every subinterval has to be the same Volume – Cross sections – Solids of Revolution Displacement/distance traveled – Set up of integral is most important

Closure (one of these days) Describe the importance of definite integrals and accumulation in mathematics and possibly real life applications. Only choose one for each closure HW: p.1-8 due Wed p.9-16 due Thurs P.17a-22 due Fri Quiz Friday

Last Days before exam May 4 Do Now Come up with last minute questions (anything from packets, FRQ, textbook, etc)