Mr. Evans

AP Calculus A

Education B.S. in Mathematics from the

University of Texas at Austin in 1992

M.S. in Education from Wilkes University in 2004

2013 Stem Fellow 14th year here at H-H

Siemens STEM Fellows 2013

Calculus

Functions (piece-wise) Polynomial Functions Continuity and Intermediate Value

Theorem Derivative The Chain Rule, General Power Rule Implicit Differentiation Related Rates Integration

Example : What dimensions for a one liter cylindrical can will use the least amount of material?

We can minimize the material by minimizing the area.

22 2A r rh area ofends

lateralarea

We need another equation that relates r and h:

2V r h

31 L 1000 cm21000 r h

2

1000h

r

22

10 02

02A r r

r

2 20002A r

r

2

20004A r

r

Example : What dimensions for a one liter cylindrical can will use the least amount of material?

22 2A r rh area ofends

lateralarea

2V r h

31 L 1000 cm21000 r h

2

1000h

r

22

10 02

02A r r

r

2 20002A r

r

2

20004A r

r

2

20000 4 r

r

2

20004 r

r

32000 4 r

3500r

3500

r

5.42 cmr

2

1000

5.42h

10.83 cmh

Sample ProblemLuke and Leia are trapped inside a rectangular trash compactor on the Death Star. The side walls are moving apart at 0.1 m/sec, but the end walls are moving together at 0.3 m/sec. If the volume of liquid inside the compactor is a constant 20 cubic meters, find the rate at which the height of the liquid is changing when the side walls are 5 m long and the end walls are 3 m long.

COURSE GOALSCOURSE GOALS

•To complete the course syllabus, as submitted to the College Board

•Calculus AB and Calculus BC are primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications.

•The courses emphasize a multirepresentational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally.

WHAT AP EXAM WHAT AP EXAM GRADES MEAN…GRADES MEAN…

•5: Extremely Well Qualified (A)5: Extremely Well Qualified (A)

•4: Well Qualified (B)4: Well Qualified (B)

•3: Qualified (C)3: Qualified (C)

•2: Possibly Qualified (D)2: Possibly Qualified (D)

•1: No recommendation…statistically 1: No recommendation…statistically dangerous to himself and others…dangerous to himself and others…

THE AP STATS EXAMTHE AP STATS EXAM

•Date: May 5, 2015 Date: May 5, 2015

•Multiple Choice section (90 Multiple Choice section (90 mins)mins)

•Free Response section (90 Free Response section (90 mins)mins)

•Both sections are split into Both sections are split into calculator and non-calculator calculator and non-calculator parts.parts.

•HHSD pays for one AP exam for every student. The AP Exam cost is $92.00. Students are responsible for payment beyond one AP exam.•The AP exam registration and ordering process will be completely online this year.•Mr. Williams will be scheduling a brief meeting/assembly with all AP students the first or second week in October to explain the AP registration process to students •Students will be coming home with a letter from Mr. Williams laying out the very simple registration process for parents as well•The AP registration window will open in October and close sometime in December.

More AP Details:More AP Details:

Homework Policy

HW assigned almost every day Homework will be checked daily

(2 points per assignment) A “best effort attempt” must be made in order to

get any credit for an assignment. Homework = Home + Work Extra Help always available Assignments posted at

http://www.hatboro-horsham.org/hhhs

Grades

Quarter Grades Total points

from all HW, CW, Tests and Quizzes

Semester Grades 1st and 2nd MP

count 40% each Final counts 20%

My Style Interactive, participation

encouraged Lots of Demos (both in class

and online) Work in pairs and groups

daily Calculus can change your

life.