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Lake County Schools Investing In Excellence! College and Career Readiness Academic Services April 2013

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AP Seminar For Advanced Placement Calculus AB _______ WELCOME Academic Services April 2013

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Community Builder: Just like me….. 1.One person begins introducing themselves to the group 2.When another person in the audience hears something the previous person shared that is “just like them” they chime in and say “ that’s just like me” 3.The person that chimed in saying “ that’s just like me” begins introducing themselves starting with the connection from the previous person. 4.Repeat step 2 and 3 until all members in the audience have introduced themselves.

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Students will share with the class one strategy or tip they will use on exam day I DO Instructor will review the 21st Century skills and AP success stats with students and make a connection to the AP Seminar Instructor will review specific content for AP course of study WE DO Instructor and students will utilize test taking strategies to answer multiple choice and free response answers YOU DO Students will utilize materials from the AP Seminar to study for AP exam April 6 & April Learning Goal : Learners will understand and implement effective test taking strategies for passing AP exams. Objectiv e Learners will: utilize content knowledge learned in AP courses coupled with effective test taking strategies to increase pass rate by completing practice AP test questions Bellwork: Community Builder Strategic Plan Goal # 1 Increased Student Achievement NEXT STEPS: 1.Utilize new learning and implement on AP exam 2.Continue to study for AP exam Benchmarks: Exit Activity Essential Question: How do we revolutionize the way we teach, lead, and learn for 21 st century success? Common Language: Advanced Placement Effective Strategies

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21 st Century Skills Tony Wagner, The Global Achievement Gap 1. Critical Thinking and Problem Solving 2. Collaboration and Leadership 3. Agility and Adaptability 4. Initiative and Entrepreneurialism 5. Effective Oral and Written Communication 6. Accessing and Analyzing Information 7. Curiosity and Imagination Academic Services

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Positive Statistics Hurray Lake County Schools Lake County Schools…. –Named to the College Board District Honor Roll

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Several #2 pencils and a good eraser - NO MECHANICAL PENCILS! Black or blue colored pens are allowed for the free- response section One or two graphing calculators with fresh batteries A watch so you can monitor your time A simple snack if the test site permits it A light jacket in case the room is cold Tissues ABSOLUTELY NO CELL PHONES or any electronic devices. What to Bring

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How the test is graded: Multiple Choice: 50% of your grade –1.2 points for each correct – 0 points for incorrect/blank Free Response: 50% of your grade –Each question is graded on a scale of 0-9 –No “bald” answers are given credit – show work

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Parts of Test: Multiple Choice: Part A 28 problems in 55 min (NO calculator) Part B 17 problems in 50 min (calculator allowed) Free Response: Part A 2 problems in 30 mins (calculator allowed) Part B 4 problems in 1 hour (NO calculator) * *You may go back and work on first two problems but you may NOT use calculator.

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Multiple Choice Strategies Do easy problems first! Do not linger-let the hard ones go. Read the question carefully. Graph or chart- is it f (x) or f '(x)? Do not round until the final answer Perhaps you can work backwards If all else fails – guess!

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Content Overview Limits and their Properties Derivative Concepts Applications of Derivatives Integration Applications of Integration

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Choose a partner. Have your packet and calculator out. Write yourself notes about what to study before the exam.

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Let’s review Limits. Ready?

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1

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If what can you do?

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Factor Rationalize numerator (conjugate) Simplify Graph Make a table THINK!

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3 ways a limit fails to exist

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Limit from the left is not equal to the limit from the right (break) Unbounded Behavior (vertical asymptote) Oscillating Behavior

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means

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Find horizontal asymptotes rational functions non-rational functions

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Partner Time

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Ready to review derivatives?

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A derivative is

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the slope of the tangent line

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Definition of Derivative (formula)

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3 ways a derivative fails to exist

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1.Discontinuities 2.Sharp turn 3.Vertical tangent

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Instantaneous rate of change

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derivative

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Average rate of change

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slope of secant line

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Acceleration

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a(t) = v ’ (t) a(t) = s ’’ (t)

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Derivative Rules

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Derivatives to Remember!

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cos x

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More Derivatives to Remember

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secxtanx -cscxcotx

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And more derivatives

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Don’t forget derivatives of logs, inverse trig functions…

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Find equation of tangent line

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Find f’(c) m Find ordered pair Plug into

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Related Rates

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Know: Want: when: Eq: Deriv: Don’t forget:

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Partner Time

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Let’s look at applications of derivatives.

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Find Absolute Extrema on [a,b] (also known as global)

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Check endpoints and critical numbers to find extreme y values.

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Relative Extrema (also called local)

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May occur where f ’ =0 or f ’ undefined

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Find inflection points:

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Find f’’(x) to see where concavity changes signs.

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Partner Time

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Here come the integrals!

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Trig Integrals

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More Trig Integrals

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Don’t forget the easy ones!

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And more Integrals

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Applications of Integration

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Solve a differential equation

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Separate and Integrate

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Find a particular solution to a differential equation:

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Separate and Integrate + C Use initial condition to solve for C. Plug C into answer.

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Area under a curve

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Area between two curves

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Partner Time

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Disk Method

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Washer Method

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Solids with known cross sections

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or

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Accumulation Function

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Partner Time

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Particle Motion Total distance = how far did you actually walk? Displacement = how far are you from where you started?

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A particle is at rest when A particle is moving right when Particle changes direction when Speed =

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A particle is at rest when velocity = 0 A particle is moving right when velocity >0 Particle changes direction when velocity = 0 Speed = |velocity|

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Speed increases when velocity and acceleration have same signs Speed decreases when velocity and acceleration have opposite signs

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Partner Time

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Strategies and Practice: Free Response Show all work Do not round partial answers Answers correct to nearest thousandth Attempt all parts of each question Write the equation before using calculator to solve Write the integral before using calculator to solve

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Strategies and Practice: Free Response Don’t erase, just cross out work you don’t want graded. Calculators are only for graphs, derivatives, integrals, and equations Be sure you have answered the question “Justify your answer” means to explain using calculus concepts (sign charts are not justification)

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Be sure you know the theorems! Intermediate Value Theorem Mean Value Theorem Rolle’s Theorem First Derivative Test 2 nd Derivative Test Mean Value Theorem for Integrals Fundamental Theorem of Calculus

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2005 AB Free Response Scores

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Time for Group Work You need a group of 4. Each person will be responsible for working out one part of the problem and explaining it to the others.

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Group Work Free Response 2005 AB1 calculator allowed

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Free Response 2005 AB1

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Group Work Free Response 2005 AB2 calculator allowed

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Free Response 2005 AB2

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Group Work Free Response 2005 AB4 no calculator allowed

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Free Response 2005 AB4

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Group Work Free Response 2005 AB6 no calculator allowed

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Free Response 2005 AB6

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Exit Activity With a shoulder partner, turn and talk about one strategy you will utilize on your AP exam and why.

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Lake County Schools Investing In Excellence! College and Career Readiness Academic Services April 2013

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