Kane and Gierut ∫ Morton East High School ∫ 2014 AP Consortium ∫ J. Sterling Morton East High School Cicero, IL AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Barbara.
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Kane and Gierut ∫ Morton East High School ∫ 2014 AP Consortium ∫ J. Sterling Morton East High School Cicero, IL AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Barbara Kane Patrick Gierut ∫ Collaboration & Support 2004-2005 Everyone Takes the AP Test Kane and Gierut ∫ ∫ Vertical Teaming ∫ 2014 AP Consortium ∫ Calculus at Morton Today AP Calculus…as easy as 3, 4, 5 Morton East High School ∫ 2013-2014 ∫ Morton East High School ∫ ∫ Apply skills to new situations AP Review Sessions Kane and Gierut 2014 AP Consortium AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Summer Work Daily Homework ∫ ∫ Kane and Gierut 2014 AP Consortium ∫ Morton East High School ∫ AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ ∫ Kane and Gierut 2014 AP Consortium ∫ Morton East High School ∫ AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ ∫ Kane and Gierut 2014 AP Consortium ∫ Morton East High School ∫ AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Morton East High School ∫ Suppose that the functions f and g and their derivatives with respect to 𝑥 have the following values at 𝑥 = 0 and 𝑥 = 1. If ℎ 𝑥 = 𝑓 𝑔 𝑥 , evaluate ℎ′(0). 𝒇(𝒙) 𝒈(𝒙) 𝒇′(𝒙) 𝒈′(𝒙) 0 1 1 5.6 8.2 1 3.75 –4.2 –7.9 –5.3 Kane and Gierut x ∫ 2014 AP Consortium New Situation: Apply knowledge of the chain rule using a table of values instead of functions. AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Skill: Chain Rule ∫ Morton East High School 2014 AP Consortium ∫ Kane and Gierut ∫ ∫ AP Calculus…as easy as 3, 4, 5 ∫ ∫ Skill: Definite Integral, Increasing/Decreasing, Average Value, Average Rate of Change ∫ Morton East High School ∫ 2014 AP Consortium 3pm-5pm Sat, March 22 8am-10am Thurs, March 27 3pm-5pm Sat, March 29 8am-10am Thurs, April 10 3pm-5pm Sat, April 12 8am-10am Thurs, April 17 3pm-5pm Wed, April 23 Sat, April 26 8am-9:30am 9:30am-11am 8am-10am Length of Test M/C Non-Calculator 55 min (plus 60min discussion) M/C Calculator 50 min (plus 60min discussion) FRQ Calculator 45 min (plus 60min discussion) FRQ Non-Calculator 45 min (plus 60min discussion) M/C Calculator 50 min (plus 40min discussion) FRQ Non-Calculator 45 min (plus 60min discussion) Kane and Gierut Thurs, March 20 Type of Test ∫ Time AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ DATE ∫ Time M/C Non-Calculator 55 min (plus 60min discussion) M/C Calculator 50 min (plus 60min discussion) FRQ Calculator 45 min (plus 60min discussion) M/C Calculator 50 min (plus 40min discussion) FRQ Non-Calculator 45 min (plus 60min discussion) 10am-12pm Sat, March 22 12pm-2pm 10am-12pm Sat, March 29 ∫ 12pm-2pm Sat, April 12 12pm-2pm 8am-9:30am Wed, April 23 9:30am-11am 10am-12pm Sat, April 26 12pm-2pm ∫ ∫ 2014 AP Consortium 10am-12pm Kane and Gierut Length of Test ∫ Type of Test AP Calculus…as easy as 3, 4, 5 Morton East High School ∫ DATE ∫ ∫ Kane and Gierut 2014 AP Consortium ∫ Morton East High School ∫ AP Calculus…as easy as 3, 4, 5 ∫ ∫ Kane and Gierut ∫ Morton East High School ∫ 2014 AP Consortium Unit/Year Schedules ∫ Consistent Teaching AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Teacher Availability Teach Calculus & prepare for AP Test ∫ Morton East High School ∫ Collegial Support: Before & After School, Lunch/Prep Time, Weekends, Summer ∫ Kane and Gierut 2014 AP Consortium AP Review Sessions: After School & Saturdays AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Tutoring/Homework Help: Before & After School every day ∫ ∫ Kane and Gierut 2014 AP Consortium ∫ Morton East High School ∫ AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Morton East High School ∫ ln 𝑥 2 − 2 1 1 − + 𝑥 2 2 𝑑𝑥 Kane and Gierut ∫ Volume = 1.324 Score Qualifications 0 No work or washer method never used or used incorrectly 1 Outer radius incorrect, limits incorrect 2 Inner radius incorrect 3 Error in computation. (AP-style answer) 4 Error in notation. 5 Proper notation used throughout problem. ∫ 2014 AP Consortium SOLUTION: V = 3.513 1 AP Calculus…as easy as 3, 4, 5 ∫ ∫ QUESTION: Find the volume of the solid formed by revolving the region bounded by the graphs of 𝑦 = ln 𝑥 and 𝑥 − 2𝑦 = 1 about the x-axis. Kane and Gierut ∫ Morton East High School ∫ 2014 AP Consortium ∫ ∫ AP-Style Answer Continuity Differentiability Derivatives Riemann Sums Value Theorems Critical Points Volume BC Topics AP Calculus…as easy as 3, 4, 5 ∫ ∫ • • • • • • • • • ∫ ∫ Kane and Gierut 2014 AP Consortium ∫ Morton East High School ∫ AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ ∫ Kane and Gierut 2014 AP Consortium ∫ Morton East High School ∫ AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ PreCalculus AP Calculus PreCalculus Geometry Algebra Algebra (8th grade) ∫ ∫ Geometry Kane and Gierut Adv Alg ∫ 2014 AP Consortium ∫ Summer Adv Alg AP Calculus…as easy as 3, 4, 5 Morton East High School ∫ AP Calculus ∫ Morton East High School ∫ Geometry Algebra 97 2012-13 82 2011-12 64 2010-11 41 2009-10 38 2008-09 49 2007-08 40 2006-07 29 2005-06 32 2004-05 25 36 BC 61 AB Kane and Gierut 2014 AP Consortium Summer Adv Alg 2013-14 ∫ PreCalculus # Students in Calculus AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ AP Calculus School Year ∫ Morton East High School ∫ PreCalculus Summer Adv Alg Adv Alg Summer Geometry Algebra Kane and Gierut Algebra ∫ 2014 AP Consortium AP Calculus PreCalculus Geometry AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ AP Calculus ∫ Morton East High School ∫ • Solving/Simplifying Logs/Exp • Solving/Simplifying Polynomials Kane and Gierut • Calculator Usage (graphing functions, solving equations, etc) ∫ 2014 AP Consortium • Rational Expressions (including factoring) AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ • Unit Circle/Trig Review ∫ Morton East High School ∫ • Partial Fractions ∫ • Parametric Functions • Vectors Kane and Gierut 2014 AP Consortium AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ • Polar Functions • Limits & Continuity ∫ AP Calculus…as easy as 3, 4, 5 AP Calculus Math 2/3 Math 2/3 Summer Math 2 Math 1/2 Math 1 ∫ ∫ PreCalculus Kane and Gierut PreCalculus ∫ 2014 AP Consortium ∫ Morton East High School ∫ AP Calculus ∫ Avg Score: 3.427 70 Global Avg: 2.96 60 50 Score 5 3 or Higher: 75.61% Score 4 40 Score 3 30 Score 2 Score 1 20 10 0 ∫ 2005 2006 2007 2008 2009 2010 2011 2012 2013 Years Kane and Gierut # of students in AP Calculus Morton East High School ∫ 80 ∫ 2014 AP Consortium AP Calculus…as easy as 3, 4, 5 ∫ ∫ 90 2010 1 2011 0 2012 ∫ 2013 Kane and Gierut ∫ 2 2014 AP Consortium 5 4 3 Morton East High School 6 AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ ∫ 7 ∫ ∫ Kane and Gierut 2014 AP Consortium ∫ Morton East High School ∫ AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ % of students ∫ 35 30 2010 25 2011 20 2012 15 2013 Kane and Gierut 2014 AP Consortium 40 ∫ 10 5 0 Lowest 4th Second 4th Third 4th Highest 4th ∫ ∫ Multiple-Choice AP Calculus…as easy as 3, 4, 5 Morton East High School ∫ 45 ∫ 35 30 2010 25 2011 20 2012 15 2013 Kane and Gierut % of students Morton East High School ∫ 40 ∫ 2014 AP Consortium Free-Response AP Calculus…as easy as 3, 4, 5 10 5 0 Lowest 4th Second 4th Third 4th Highest 4th ∫ ∫ ∫ 45 ∫ ∫ Kane and Gierut 2014 AP Consortium ∫ Morton East High School ∫ AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ ∫ Kane and Gierut 2014 AP Consortium ∫ Morton East High School ∫ AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ ∫ Kane and Gierut 2014 AP Consortium ∫ Calculus Teacher AP Calculus…as easy as 3, 4, 5 ∫ Morton East High School ∫ ∫ Student Interest PreCalc Teachers ∫ Morton East High School ∫ 2014 AP Consortium Kane and Gierut Arc Length, Parametrics, Vectors L’Hôpital’s Rule, Improper Integrals Sequences & Series Convergence of Series Taylor Series Euler’s Method Differential Equations, Logistic Graphs Polar graphs ∫ • • • • • • • • AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Attended College Board AP Summer Institute with Ruth Dover (IMSA) ∫ Morton East High School ∫ Chapter 3 Derivatives • Includes Vectors, Parametric & Polar Functions • Ends early October Chapter 4 Applications of Derivatives • Ends early November Chapter 5 Definite Integral • Includes integration by parts, partial fractions • Ends mid-December Kane and Gierut 2014 AP Consortium • Ends 1st week of school ∫ Chapter 2 Limits & Continuity AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Planned out the schedule for the year ∫ Morton East High School ∫ 2014 AP Consortium • Ends late-February Chapter 9 Infinite Series • Ends late-March Kane and Gierut Chapter 8 L’Hôpital’s Rule & Improper Integrals ∫ Chapter 7 Applications of Definite Integrals • Includes polar curves, lengths of curves, parametric curves, distance traveled in vector • Ends mid-February AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Chapter 6 Slope Fields • Includes Euler’s method & Logistic Growth • Ends January, before Finals ∫ Videos & Website Resources Planning Lessons Kane and Gierut ∫ ∫ Guided Notes ∫ 2014 AP Consortium ∫ Demonstrations AP Calculus…as easy as 3, 4, 5 Morton East High School ∫ Wolfram ∫ ∫ Kane and Gierut 2014 AP Consortium ∫ Morton East High School ∫ AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ ∫ Kane and Gierut 2014 AP Consortium ∫ Morton East High School ∫ AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ ∫ Kane and Gierut 2014 AP Consortium ∫ Morton East High School ∫ AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ www.remind101.com • Math Is Fun www.mathsisfun.com/calculus/index.html apcalculusstillwater.wordpress.com/ap-calculus-videos/ https://sites.google.com/a/lusherschool.org/mrwhitecalc/ www.deeringmath.com/Calculus/calculusbc/ ∫ ∫ • Mr. Landry’s Online Learning Math Center Kane and Gierut • Mr. White’s AP Calculus AB ∫ 2014 AP Consortium ∫ • AP Calculus Stillwater AP Calculus…as easy as 3, 4, 5 Morton East High School ∫ • Remind 101 ∫ Morton East High School ∫ 36 students 55 students Series Review Days Videos 35 students ∫ 3 preps Kane and Gierut 2014 AP Consortium Collegial Support AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Frozen Days ∫ Morton East High School ∫ More Teachers Involved Kane and Gierut More Vertical Teaming ∫ 2014 AP Consortium More AB & BC AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Student Buddy System 100% success rate Kane and Gierut ∫ Morton East High School ∫ 2014 AP Consortium ∫ J. Sterling Morton East High School Cicero, IL AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Barbara Kane Patrick Gierut