AP Calculus AB 2003 Scoring Guidelines Form B
|
|
- Aubrey Tyler
- 8 years ago
- Views:
Transcription
1 AP Calculus AB Scoring Guidelines Form B The materials included in these files are intended for use by AP teachers for course and exam preparation; permission for any other use must be sought from the Advanced Placement Program. Teachers may reproduce them, in whole or in part, in limited quantities for noncommercial, face-to-face teaching purposes. This permission does not apply to any third-party copyrights contained herein. This material may not be mass distributed, electronically or otherwise. These materials and any copies made of them may not be resold, and the copyright notices must be retained as they appear here. These materials were produced by Educational Testing Service (ETS ), which develops and administers the examinations of the Advanced Placement Program for the College Board. The College Board and Educational Testing Service (ETS) are dedicated to the principle of equal opportunity, and their programs, services, and employment policies are guided by that principle. The College Board is a national nonprofit membership association whose mission is to prepare, inspire, and connect students to college and opportunity. Founded in 19, the association is composed of more than 4, schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three million students and their parents,, high schools, and,5 colleges through major programs and services in college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT, the PSAT/NMSQT, and the Advanced Placement Program (AP ). The College Board is committed to the principles of equity and excellence, and that commitment is embodied in all of its programs, services, activities, and concerns. For further information, visit Copyright College Entrance Examination Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Vertical Teams, APCD, Pacesetter, Pre-AP, SAT, Student Search Service, and the acorn logo are registered trademarks of the College Entrance Examination Board. AP Central is a trademark owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark jointly owned by the College Entrance Examination Board and the National Merit Scholarship Corporation. Educational Testing Service and ETS are registered trademarks of Educational Testing Service. Other products and services may be trademarks of their respective owners. For the College Board s online home for AP professionals, visit AP Central at apcentral.collegeboard.com.
2 SCORING GUIDELINES (Form B) Question 1 Let f be the function given by fx ( ) = 4 x x, and let be the line y = 18 x, where is tangent to the graph of f. Let R be the region bounded by the graph of f and the x-axis, and let S be the region bounded by the graph of f, the line, and the x-axis, as shown above. (a) Show that is tangent to the graph of y = f() x at the point x =. (b) Find the area of S. (c) Find the volume of the solid generated when R is revolved about the x-axis. (a) f ( x) = 8x x ; f () = 4 7 = f () = 6 7 = 9 Tangent line at x = is y = ( x ) + 9 = x + 18, which is the equation of line. : 1 : finds f() and f() finds equation of tangent line or 1 : shows (,9) is on both the graph of f and line (b) fx ( ) = at x = 4 The line intersects the x-axis at x = Area = ()(9) ( 4 x x ) dx = or OR 4 : : integral for non-triangular region 1 : limits 1 : area of triangular region 1 : answer 4 Area = (( 18 ) ( 4 )) x x x dx + 1 ()(18 1) = or (c) Volume = ( ) 4x x dx = or : limits and constant : 1 : answer Copyright by College Entrance Examination Board. All rights reserved.
3 SCORING GUIDELINES (Form B) Question A tank contains 15 gallons of heating oil at time t =. During the time interval t 1 hours, heating oil is pumped into the tank at the rate 1 H ( t) = + ( 1 + ln( t + 1) ) gallons per hour. During the same time interval, heating oil is removed from the tank at the rate t R( t) = 1 sin gallons per hour. 47 (a) How many gallons of heating oil are pumped into the tank during the time interval t 1 hours? (b) Is the level of heating oil in the tank rising or falling at time t = 6 hours? Give a reason for your answer. (c) How many gallons of heating oil are in the tank at time t = 1 hours? (d) At what time t, for t 1, is the volume of heating oil in the tank the least? Show the analysis that leads to your conclusion. (a) 1 Htdt () = 7.57 or : 1 : integral 1 : answer (b) H(6)(6) R =.94, so the level of heating oil is falling at t = 6. 1 : answer with reason 1 (c) 15 + ( Ht ( )( Rt) dt = 1.5 or 1.6 : 1 : limits 1 : answer (d) The absolute minimum occurs at a critical point or an endpoint. Ht ()() Rt = when t = 4.79 and t = The volume increases until t = 4.79, then decreases until t = 11.18, then increases, so the absolute minimum will be at t = or at 1 : sets Ht ( )( Rt) = 1 : volume is least at : t = : analysis for absolute minimum t = ( Ht ()() Rt) dt = 1.78 Since the volume is 15 at t =, the volume is least at t = Copyright by College Entrance Examination Board. All rights reserved.
4 SCORING GUIDELINES (Form B) Question A blood vessel is 6 millimeters (mm) long Distance with circular cross sections of varying diameter. x (mm) Diameter The table above gives the measurements of the B(x) (mm) diameter of the blood vessel at selected points along the length of the blood vessel, where x represents the distance from one end of the blood vessel and Bx () is a twice-differentiable function that represents the diameter at that point. (a) Write an integral expression in terms of Bx () that represents the average radius, in mm, of the blood vessel between x = and x = 6. (b) Approximate the value of your answer from part (a) using the data from the table and a midpoint Riemann sum with three subintervals of equal length. Show the computations that lead to your answer. 75 Bx () (c) Using correct units, explain the meaning of dx 15 in terms of the blood vessel. (d) Explain why there must be at least one value x, for < x < 6, such that B ( x) =. (a) 1 6 Bx () dx : 6 1 : limits and constant (b) 1 B(6) B(18) B() = 6 1 [ 6( )] = 14 6 : 1 : B(6) + B(18) + B() 1 : answer (c) Bx ( ) Bx ( ) is the radius, so is the area of the cross section at x. The expression is the volume in mm of the blood vessel between 15 : 1 : volume in mm 1 : between x = 15 and x = 75 mm and 75 mm from the end of the vessel. (d) By the MVT, B ( c1) = for some c 1 in (6, 18) and B ( c) = for some c in (4, 6). The MVT applied to B ( x) shows that B () x = for some x in the interval ( c1 c ),. : : explains why there are two values of x where B( x) has the same value 1 : explains why that means B ( x) = for < x < 6 Copyright by College Entrance Examination Board. All rights reserved. 4 Note: max 1/ if only explains why B ( x) = at some x in (, 6).
5 SCORING GUIDELINES (Form B) Question 4 A particle moves along the x-axis with velocity at time t given by v( t) = 1 + e1 t. (a) Find the acceleration of the particle at time t =. (b) Is the speed of the particle increasing at time t =? Give a reason for your answer. (c) Find all values of t at which the particle changes direction. Justify your answer. (d) Find the total distance traveled by the particle over the time interval t. 1 t (a) at () = v() t = e a() = e : 1 : v( t) 1 : a() (b) a () < v() = 1 + e < Speed is increasing since v () < and a () <. 1 : answer with reason 1 t (c) vt () = when 1 = e, so t = 1. vt () > for t < 1 and vt () < for t > 1. Therefore, the particle changes direction at t = 1. : 1 : solves vt ( ) = to get t = 1 1 : justifies change in direction at t = 1 (d) Distance = vt () dt 1 1t t t 1t 1 1t e t e e e 1 1 = ( ) + ( + ) = ( ) ( ) e dt e dt = ( + ) + ( + ) 4 : 1 : limits 1 : antidifferentiation 1 : evaluation = e + 1 e OR OR 1 t () = xt t e x() = e x (1) = x() = e Distance = ( x(1) x() ) + ( x(1) x() ) ( + e) + 1+ e = ( ) = e + 1 e 1 : any antiderivative 1 : evaluates xt ( ) when t =, 1, 4 : 1 : evaluates distance between points 1 : evaluates total distance Copyright by College Entrance Examination Board. All rights reserved. 5
6 SCORING GUIDELINES (Form B) Question 5 Let f be a function defined on the closed interval [,7]. The graph of f, consisting of four line segments, is shown above. Let g be the x function given by gx ( ) = ftdt ( ). (a) Find g (, ) g ( ), and g ( ). (b) Find the average rate of change of g on the interval x. (c) For how many values c, where < c <, is g () c equal to the average rate found in part (b)? Explain your reasoning. (d) Find the x-coordinate of each point of inflection of the graph of g on the interval < x < 7. Justify your answer. 1 (a) g() = f( t) dt = ( 4 + ) = g () = f() = 4 g() = f() = = 4 : 1 : g() 1 : g() 1 : g() (b) g() g() = 1 () ftdt ()(4) + (4 + ) = = ( ) : 1 : g() g() = f( t) dt 1 : answer (c) There are two values of c. We need 7 = g( c) = f( c) The graph of f intersects the line places between and. 7 y = at two 1 : answer of : 1 : reason Note: 1/ if answer is 1 by MVT (d) x = and x = 5 because g = f changes from increasing to decreasing at x =, and from decreasing to increasing at x = 5. 1 : x = and x = 5 only : 1 : justification (ignore discussion at x = 4) Copyright by College Entrance Examination Board. All rights reserved. 6
7 SCORING GUIDELINES (Form B) Question 6 Let f be the function satisfying f ( x) = x f( x) for all real numbers x, where f ( ) = 5. (a) Find f ( ). (b) Write an expression for y = f() x by solving the differential equation dy = x y with the initial dx condition f ( ) = 5. (a) f ( x) = f( x) x f( x) + x = f( x) + fx ( ) f () = = : : f( x) < > product or chain rule error 1 : value at x = (b) 1 dy = x dx y 1 y = x + C 1 5 = () + C ; C = 11 6 : 1 : separates variables 1 : antiderivative of dy term 1 : antiderivative of dx term 1 : constant of integration 1 : uses initial condition f () = 5 1 : solves for y 1 11 y = x ( ) ( 11) y = x + = x Note: max /6 [ ] if no constant of integration Note: /6 if no separation of variables Copyright by College Entrance Examination Board. All rights reserved. 7
AP Calculus AB 2004 Free-Response Questions
AP Calculus AB 2004 Free-Response Questions The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use must be
More informationAP Calculus AB 2003 Scoring Guidelines
AP Calculus AB Scoring Guidelines The materials included in these files are intended for use y AP teachers for course and exam preparation; permission for any other use must e sought from the Advanced
More informationAP Calculus AB 2004 Scoring Guidelines
AP Calculus AB 4 Scoring Guidelines The materials included in these files are intended for noncommercial use by AP teachers for course and eam preparation; permission for any other use must be sought from
More informationAP Calculus BC 2004 Scoring Guidelines
AP Calculus BC Scoring Guidelines The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use must be sought from
More informationAP Calculus AB 2006 Scoring Guidelines
AP Calculus AB 006 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college
More informationAP Calculus AB 2005 Free-Response Questions
AP Calculus AB 25 Free-Response Questions The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to
More informationAP Calculus AB 2011 Scoring Guidelines
AP Calculus AB Scoring Guidelines The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 9, the
More informationAP Calculus BC 2001 Free-Response Questions
AP Calculus BC 001 Free-Response Questions The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must
More informationAP Calculus AB 2010 Free-Response Questions Form B
AP Calculus AB 2010 Free-Response Questions Form B The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity.
More informationAP Calculus BC 2006 Free-Response Questions
AP Calculus BC 2006 Free-Response Questions The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to
More informationAP Calculus AB 2005 Scoring Guidelines Form B
AP Calculus AB 5 coring Guidelines Form B The College Board: Connecting tudents to College uccess The College Board is a not-for-profit membership association whose mission is to connect students to college
More informationAP Calculus AB 2009 Free-Response Questions
AP Calculus AB 2009 Free-Response Questions The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded
More informationAP Calculus AB 2007 Scoring Guidelines Form B
AP Calculus AB 7 Scoring Guidelines Form B The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to
More informationAP Calculus AB 2012 Free-Response Questions
AP Calculus AB 1 Free-Response Questions About the College Board The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in
More informationAP Calculus AB 2001 Scoring Guidelines
P Calculus Scing Guidelines The materials included in these files are intended f non-commercial use by P teachers f course and eam preparation; permission f any other use must be sought from the dvanced
More informationAP Macroeconomics 2003 Scoring Guidelines Form B
AP Macroeconomics 2003 Scoring Guidelines Form B The materials included in these files are intended for use by AP teachers for course and exam preparation; permission for any other use must be sought from
More informationAP Calculus BC 2008 Scoring Guidelines
AP Calculus BC 8 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college
More informationAP Microeconomics 2003 Scoring Guidelines
AP Microeconomics 2003 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and exam preparation; permission for any other use must be sought from the
More informationAP Calculus AB 2011 Free-Response Questions
AP Calculus AB 11 Free-Response Questions About the College Board The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in
More informationAP Calculus AB 2013 Free-Response Questions
AP Calculus AB 2013 Free-Response Questions About the College Board The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded
More informationAP Calculus AB 2010 Free-Response Questions
AP Calculus AB 2010 Free-Response Questions The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded
More informationSample Activity: The Least Expensive Cable
Sample Activity: The Least Expensive Cable from the Pre-AP workshop Pre-AP : Topics for AP Vertical Teams in Mathematics For more information, see apcentral.collegeboard.com/preapworkshops. Copyright 2004
More informationDon't Forget the Differential Equations: Finishing 2005 BC4
connect to college success Don't Forget the Differential Equations: Finishing 005 BC4 Steve Greenfield available on apcentral.collegeboard.com connect to college success www.collegeboard.com The College
More informationAP Calculus BC 2010 Free-Response Questions
AP Calculus BC 2010 Free-Response Questions The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded
More informationAP Calculus BC 2013 Free-Response Questions
AP Calculus BC 013 Free-Response Questions About the College Board The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in
More informationCalculus AB 2014 Scoring Guidelines
P Calculus B 014 Scoring Guidelines 014 The College Board. College Board, dvanced Placement Program, P, P Central, and the acorn logo are registered trademarks of the College Board. P Central is the official
More informationAP Calculus BC 2003 Scoring Guidelines Form B
AP Calculus BC Scorig Guidelies Form B The materials icluded i these files are iteded for use by AP teachers for course ad exam preparatio; permissio for ay other use must be sought from the Advaced Placemet
More informationAP Microeconomics 2002 Scoring Guidelines
AP Microeconomics 2002 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be
More informationAP Human Geography 2004 Scoring Guidelines
AP Human Geography 2004 Scoring Guidelines The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use must be
More informationAP CALCULUS AB 2006 SCORING GUIDELINES. Question 4
AP CALCULUS AB 2006 SCORING GUIDELINES Question 4 t (seconds) vt () (feet per second) 0 10 20 30 40 50 60 70 80 5 14 22 29 35 40 44 47 49 Rocket A has positive velocity vt () after being launched upward
More informationAP Computer Science A 2004 Free-Response Questions
AP Computer Science A 2004 Free-Response Questions The materials included in these files are intended for noncommercial use by AP teachers for course and exam preparation; permission for any other use
More informationAP Macroeconomics 2009 Scoring Guidelines
AP Macroeconomics 2009 Scoring Guidelines The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded
More informationStudent Performance Q&A:
Student Performance Q&A: 2008 AP Calculus AB and Calculus BC Free-Response Questions The following comments on the 2008 free-response questions for AP Calculus AB and Calculus BC were written by the Chief
More informationAP Macroeconomics 2008 Scoring Guidelines
AP Macroeconomics 2008 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to
More informationAP Macroeconomics 2008 Scoring Guidelines Form B
AP Macroeconomics 2008 Scoring Guidelines Form B The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students
More informationAP Microeconomics 2011 Scoring Guidelines
AP Microeconomics 2011 Scoring Guidelines The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded
More informationMark Howell Gonzaga High School, Washington, D.C.
Be Prepared for the Calculus Exam Mark Howell Gonzaga High School, Washington, D.C. Martha Montgomery Fremont City Schools, Fremont, Ohio Practice exam contributors: Benita Albert Oak Ridge High School,
More information2000 Advanced Placement Program Free-Response Questions
2000 Advanced Placement Program Free-Response Questions The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other
More information2008 AP Calculus AB Multiple Choice Exam
008 AP Multiple Choice Eam Name 008 AP Calculus AB Multiple Choice Eam Section No Calculator Active AP Calculus 008 Multiple Choice 008 AP Calculus AB Multiple Choice Eam Section Calculator Active AP Calculus
More informationScoring and Practice Sections
Taking the SAT I: Reasoning Test Scoring and Practice Sections The materials in these files are intended for individual use by students getting ready to take an SAT Program test; permission for any other
More informationAP CALCULUS AB 2007 SCORING GUIDELINES (Form B)
AP CALCULUS AB 2007 SCORING GUIDELINES (Form B) Question 4 Let f be a function defined on the closed interval 5 x 5 with f ( 1) = 3. The graph of f, the derivative of f, consists of two semicircles and
More informationcorrect-choice plot f(x) and draw an approximate tangent line at x = a and use geometry to estimate its slope comment The choices were:
Topic 1 2.1 mode MultipleSelection text How can we approximate the slope of the tangent line to f(x) at a point x = a? This is a Multiple selection question, so you need to check all of the answers that
More informationAP CALCULUS AB 2009 SCORING GUIDELINES
AP CALCULUS AB 2009 SCORING GUIDELINES Question 5 x 2 5 8 f ( x ) 1 4 2 6 Let f be a function that is twice differentiable for all real numbers. The table above gives values of f for selected points in
More informationMark Howell Gonzaga High School, Washington, D.C.
Be Prepared for the Calculus Eam Mark Howell Gonzaga High School, Washington, D.C. Martha Montgomery Fremont City Schools, Fremont, Ohio Practice eam contributors: Benita Albert Oak Ridge High School,
More informationAP Macroeconomics 2011 Scoring Guidelines
AP Macroeconomics 2011 Scoring Guidelines The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded
More informationAP Macroeconomics 2010 Scoring Guidelines
AP Macroeconomics 2010 Scoring Guidelines The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded
More informationAnalyzing Piecewise Functions
Connecting Geometry to Advanced Placement* Mathematics A Resource and Strategy Guide Updated: 04/9/09 Analyzing Piecewise Functions Objective: Students will analyze attributes of a piecewise function including
More informationPRACTICE FINAL. Problem 1. Find the dimensions of the isosceles triangle with largest area that can be inscribed in a circle of radius 10cm.
PRACTICE FINAL Problem 1. Find the dimensions of the isosceles triangle with largest area that can be inscribed in a circle of radius 1cm. Solution. Let x be the distance between the center of the circle
More informationWorksheet 1. What You Need to Know About Motion Along the x-axis (Part 1)
Worksheet 1. What You Need to Know About Motion Along the x-axis (Part 1) In discussing motion, there are three closely related concepts that you need to keep straight. These are: If x(t) represents the
More informationVisualizing Differential Equations Slope Fields. by Lin McMullin
Visualizing Differential Equations Slope Fields by Lin McMullin The topic of slope fields is new to the AP Calculus AB Course Description for the 2004 exam. Where do slope fields come from? How should
More informationMATH 132: CALCULUS II SYLLABUS
MATH 32: CALCULUS II SYLLABUS Prerequisites: Successful completion of Math 3 (or its equivalent elsewhere). Math 27 is normally not a sufficient prerequisite for Math 32. Required Text: Calculus: Early
More informationAP English Literature & Composition 2002 Scoring Guidelines
AP English Literature & Composition 2002 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any
More informationAnswer Key for the Review Packet for Exam #3
Answer Key for the Review Packet for Eam # Professor Danielle Benedetto Math Ma-Min Problems. Show that of all rectangles with a given area, the one with the smallest perimeter is a square. Diagram: y
More informationSolutions to old Exam 1 problems
Solutions to old Exam 1 problems Hi students! I am putting this old version of my review for the first midterm review, place and time to be announced. Check for updates on the web site as to which sections
More informationPre-AP : Interdisciplinary Strategies for English and Social Studies Sample Activity: Dialectical Notebooks
Pre-AP : Interdisciplinary Strategies for English and Social Studies Sample Activity: Dialectical Notebooks Copyright 2004 College Entrance Examination Board. All rights reserved. College Board, Advanced
More informationPractice Final Math 122 Spring 12 Instructor: Jeff Lang
Practice Final Math Spring Instructor: Jeff Lang. Find the limit of the sequence a n = ln (n 5) ln (3n + 8). A) ln ( ) 3 B) ln C) ln ( ) 3 D) does not exist. Find the limit of the sequence a n = (ln n)6
More informationL 2 : x = s + 1, y = s, z = 4s + 4. 3. Suppose that C has coordinates (x, y, z). Then from the vector equality AC = BD, one has
The line L through the points A and B is parallel to the vector AB = 3, 2, and has parametric equations x = 3t + 2, y = 2t +, z = t Therefore, the intersection point of the line with the plane should satisfy:
More informationAP CALCULUS AB 2006 SCORING GUIDELINES (Form B) Question 4
AP CALCULUS AB 2006 SCORING GUIDELINES (Form B) Question 4 The rate, in calories per minute, at which a person using an exercise machine burns calories is modeled by the function 1 3 3 2 f. In the figure
More informationAP CALCULUS AB 2008 SCORING GUIDELINES
AP CALCULUS AB 2008 SCORING GUIDELINES Question 1 Let R be the region bounded by the graphs of y = sin( π x) and y = x 4 x, as shown in the figure above. (a) Find the area of R. (b) The horizontal line
More informationAP Calculus AB First Semester Final Exam Practice Test Content covers chapters 1-3 Name: Date: Period:
AP Calculus AB First Semester Final Eam Practice Test Content covers chapters 1- Name: Date: Period: This is a big tamale review for the final eam. Of the 69 questions on this review, questions will be
More informationAP Human Geography 2006 Scoring Guidelines
AP Human Geography 2006 Scoring Guidelines The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to
More informationAP Calculus AB 2006 Scoring Guidelines Form B
AP Calculus AB 6 Scorig Guidelies Form B The College Board: Coectig Studets to College Success The College Board is a ot-for-profit membership associatio whose missio is to coect studets to college success
More informationEstimating the Average Value of a Function
Estimating the Average Value of a Function Problem: Determine the average value of the function f(x) over the interval [a, b]. Strategy: Choose sample points a = x 0 < x 1 < x 2 < < x n 1 < x n = b and
More informationPROBLEM SET. Practice Problems for Exam #1. Math 1352, Fall 2004. Oct. 1, 2004 ANSWERS
PROBLEM SET Practice Problems for Exam # Math 352, Fall 24 Oct., 24 ANSWERS i Problem. vlet R be the region bounded by the curves x = y 2 and y = x. A. Find the volume of the solid generated by revolving
More informationAP Calculus AB Syllabus
Course Overview and Philosophy AP Calculus AB Syllabus The biggest idea in AP Calculus is the connections among the representations of the major concepts graphically, numerically, analytically, and verbally.
More informationResearch Report No. 2005-5 Nancy K. Scammacca and Barbara G. Dodd
Research Report No. 2005-5 An Investigation of Educational Outcomes for Students Who Earn College Credit Through the College-Level Examination Program Nancy K. Scammacca and Barbara G. Dodd www.collegeboard.com
More informationAP Calculus BC Exam. The Calculus BC Exam. At a Glance. Section I. SECTION I: Multiple-Choice Questions. Instructions. About Guessing.
The Calculus BC Exam AP Calculus BC Exam SECTION I: Multiple-Choice Questions At a Glance Total Time 1 hour, 45 minutes Number of Questions 45 Percent of Total Grade 50% Writing Instrument Pencil required
More informationReadings this week. 1 Parametric Equations Supplement. 2 Section 10.1. 3 Sections 2.1-2.2. Professor Christopher Hoffman Math 124
Readings this week 1 Parametric Equations Supplement 2 Section 10.1 3 Sections 2.1-2.2 Precalculus Review Quiz session Thursday equations of lines and circles worksheet available at http://www.math.washington.edu/
More information2010 The College Board. Visit the College Board on the Web: www.collegeboard.com.
AP CALCULUS AB 21 SCORING GUIDELINES Question 2 A zoo sponsored a one-day contest to name a new baby elephant. Zoo visitors deposited entries in a special box between noon ( t = ) and 8 P.M. ( t = 8. )
More informationAP Physics B 2009 Scoring Guidelines
AP Physics B 009 Scoring Guidelines The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900,
More information