AP Calculus AB. Scoring Guidelines

Size: px
Start display at page:

Download "AP Calculus AB. Scoring Guidelines"

Transcription

1 17 AP Calculus AB Scoring Guidelines 17 The College Board. College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home for the AP Program: apcentral.collegeboard.org

2 AP CALCULUS AB/CALCULUS BC 17 SCORING GUIDELINES uestion 1 1 : units in parts (a), (c), and (d) 1 : { (a) Volume A( h) dh ( ) A( ) + ( 5 ) A( ) + ( 1 5) A( 5) cubic feet 1 : left Riemann sum 1 : approximation (b) The approximation in part (a) is an overestimate because a left Riemann sum is used and A is decreasing. 1 : overestimate with reason 1 (c) f( h) dh The volume is 11.5 cubic feet. : { 1 : integral 1 : answer (d) Using the model, V ( h) f dx. dv dv dh dt dh dt h 5 h 5 dh f( h) dt h 5 f ( 5) h : dv : dt 1 : answer When h 5, the volume of water is changing at a rate of cubic feet per minute. 17 The College Board.

3 AP CALCULUS AB 17 SCORING GUIDELINES uestion (a) f ( t) dt pounds of bananas are removed from the display table during the first hours the store is open. : { 1 : integral 1 : answer (b) f ( 7) 8.1 (or ) After the store has been open 7 hours, the rate at which bananas are being removed from the display table is decreasing by 8.1 (or 8.119) pounds per hour per hour. : { 1 : value 1 : meaning (c) g( 5) f( 5).61 < Because g( 5) f( 5) <, the number of pounds of bananas on the display table is decreasing at time t 5. 1 : considers f( 5 ) and g( 5) : 1 : answer with reason 8 8 (d) 5 + g( t) dt f ( t) dt pounds of bananas are on the display table at time t 8. : { : integrals 1 : answer 17 The College Board.

4 AP CALCULUS AB/CALCULUS BC 17 SCORING GUIDELINES uestion 6 (a) f ( 6) f ( ) + f dx 7 f dx f ( 5 ) f ( ) + f dx 7 π + 1 π 1 : uses initial condition : 1 : f ( 6) 1 : f ( 5) (b) f > on the intervals [ 6, ) and (, 5 ). Therefore, f is increasing on the intervals [ 6, ] and [, 5 ]. : answer with justification (c) The absolute minimum will occur at a critical point where f or at an endpoint. : { 1 : considers x 1 : answer with justification f x, x x f( x ) π 5 1 π The absolute minimum value is f ( ) 7 π. 1 (d) f ( 5) 6 ( ) f f ( ) lim and x x f f ( ) lim 1 + x x 1 : f ( 5) : 1 : f ( ) does not exist, with explanation f ( ) does not exist because f f ( ) f f ( ) lim lim. x + x x x 17 The College Board.

5 AP CALCULUS AB/CALCULUS BC 17 SCORING GUIDELINES uestion 4 1 (a) H ( ) ( 91 7) 16 4 H ( ) 91 An equation for the tangent line is y t. 1 : slope : 1 : tangent line 1 : approximation The internal temperature of the potato at time t minutes is approximately degrees Celsius. d H dt 1 dh dt (b) ( )( )( H 7) ( H 7) 1 : underestimate with reason H > 7 for d H 1 t > ( H 7) > for t > dt 16 Therefore, the graph of H is concave up for t >. Thus, the answer in part (a) is an underestimate. (c) dg dt ( ) G 7 dg ( 1) dt ( ) G 7 1 ( G 7) t + C 1 ( 91 7) + C C 1 1 ( G 7) 1 t 1 t Gt ( ) 7 + ( ) for t < 1 The internal temperature of the potato at time t minutes is 1 ( ) degrees Celsius. 5 : 1 : separation of variables 1 : antiderivatives 1 : constant of integration and uses initial condition 1 : equation involving G and t 1 : Gt ( ) and G( ) Note: max 5 [1-1---] if no constant of integration Note: 5 if no separation of variables 17 The College Board.

6 AP CALCULUS AB 17 SCORING GUIDELINES uestion 5 t ( t 1) (a) x P ( t) t t + 1 t t + 1 t t + 1 > for all t. 1 : x P( t) : 1 : interval x P ( t) t 1 xp( t) t < for < 1. Therefore, the particle is moving to the left for t < 1. (b) v ( t) ( t 5)( t ) v( t) t, t 5 : 1 : intervals 1 : analysis using vp( t) and v( t) Note: 1 if only one interval with analysis Note: if no analysis Both particles move in the same direction for 1 < t < and 5 < t 8 since vp( t) xp ( t) and v ( t ) have the same sign on these intervals. (c) a ( t) v ( t) t 8 a ( ) 8 4 : 1 : a ( ) 1 : speed decreasing with reason a ( ) < and v ( ) > At time t, the speed of the particle is decreasing because velocity and acceleration have opposite signs. (d) Particle first changes direction at time t. ( ) ( ) + ( ) 5 + ( ) x x v t dt t t dt t t 4t + 15t 5 + ( ) t 1 : antiderivative : 1 : uses initial condition 1 : answer 17 The College Board.

7 AP CALCULUS AB 17 SCORING GUIDELINES uestion 6 (a) f sin + cos xe sin x : f ( π ) sin π f ( π) sin ( π) + cos π e 1 (b) k h ( f ) f k ( π) h ( f( π) ) f ( π) h ( ) ( 1) 1 1 ( )( 1) : 1 : k 1 : k ( π ) (c) m g ( x) h + g( x) h m ( ) g ( 4) h( ) + g( 4) h ( ) 1 ( 1)( ) + 5( ) : : m 1 : m ( ) (d) g is differentiable. g is continuous on the interval [ 5, ]. g( ) g( 5) 1 4 ( 5) Therefore, by the Mean Value Theorem, there is at least one value c, 5 < c <, such that g ( c) 4. g( ) g( 5) 1 : ( 5) : 1 : justification, using Mean Value Theorem 17 The College Board.

AP Calculus BC. Free-Response Questions

AP Calculus BC. Free-Response Questions 017 AP Calculus BC Free-Response Questions 017 The College Board. College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. 017 AP CALCULUS

More information

AP Calculus AB. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 1. Scoring Guideline.

AP Calculus AB. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 1. Scoring Guideline. 217 AP Calculus AB Sample Student Responses and Scoring Commentary Inside: RR Free Response Question 1 RR Scoring Guideline RR Student Samples RR Scoring Commentary 217 The College Board. College Board,

More information

AP Calculus AB. Free-Response Questions

AP Calculus AB. Free-Response Questions 2018 AP Calculus AB Free-Response Questions College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online

More information

AP Calculus AB 2015 Free-Response Questions

AP Calculus AB 2015 Free-Response Questions AP Calculus AB 015 Free-Response Questions College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online

More information

AP Calculus BC 2013 Scoring Guidelines

AP Calculus BC 2013 Scoring Guidelines AP Calculus BC Scoring Guidelines The College Board The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in 9, the College

More information

AP Calculus BC 2015 Free-Response Questions

AP Calculus BC 2015 Free-Response Questions AP Calculus BC 05 Free-Response Questions 05 The College Board. College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central

More information

Calculus AB 2014 Scoring Guidelines

Calculus 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 information

AP CALCULUS AB/CALCULUS BC 2017 SCORING GUIDELINES

AP CALCULUS AB/CALCULUS BC 2017 SCORING GUIDELINES AP CALCULUS AB/CALCULUS BC 07 SCORING GUIDELINES Question 4 H ( 0) = ( 9 7) = 6 4 H ( 0) = 9 An equation for the tangent line is y = 9 6 t. : slope : : tangent line : approimation The internal temperature

More information

AP Calculus BC. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 5. Scoring Guideline.

AP Calculus BC. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 5. Scoring Guideline. 017 AP Calculus BC Sample Student Responses and Scoring Commentary Inside: RR Free Response Question RR Scoring Guideline RR Student Samples RR Scoring Commentary 017 The College Board. College Board,

More information

Answer Key for AP Calculus AB Practice Exam, Section I

Answer Key for AP Calculus AB Practice Exam, Section I Answer Key for AP Calculus AB Practice Exam, Section I Multiple-Choice Questions Question # Key B B 3 A 4 E C 6 D 7 E 8 C 9 E A A C 3 D 4 A A 6 B 7 A 8 B 9 C D E B 3 A 4 A E 6 A 7 A 8 A 76 E 77 A 78 D

More information

AP CALCULUS BC 2007 SCORING GUIDELINES

AP CALCULUS BC 2007 SCORING GUIDELINES AP CALCULUS BC 2007 SCORING GUIDELINES Question 4 Let f be the function defined for x > 0, with f( e ) = 2 and f, the first derivative of f, given by f ( x) = x 2 ln x. (a) Write an equation for the line

More information

AP Calculus BC. Free-Response Questions

AP Calculus BC. Free-Response Questions 2018 AP Calculus BC Free-Response Questions College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online

More information

AP Calculus BC 2011 Free-Response Questions

AP Calculus BC 2011 Free-Response Questions AP Calculus BC 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 information

AP CALCULUS AB 2017 SCORING GUIDELINES

AP CALCULUS AB 2017 SCORING GUIDELINES AP CALCULUS AB 07 SCORING GUIDELINES Consider the differential equation AP CALCULUS AB 06 SCORING GUIDELINES y =. Question 4 On the aes provided, sketch a slope field for the given differential equation

More information

Answer Key for AP Calculus AB Practice Exam, Section I. Question 23: B

Answer Key for AP Calculus AB Practice Exam, Section I. Question 23: B Answer Key for AP Calculus AB Practice Exam, Section I Question : A Question : D Question : B Question 4: D Question 5: C Question 6: B Question 7: C Question 8: D Question 9: A Question : E Question :

More information

AP CALCULUS AB 2006 SCORING GUIDELINES (Form B) Question 2. the

AP CALCULUS AB 2006 SCORING GUIDELINES (Form B) Question 2. the AP CALCULUS AB 2006 SCORING GUIDELINES (Form B) Question 2 Let f be the function defined for x 0 with f ( 0) = 5 and f, the ( x 4) 2 first derivative of f, given by f ( x) = e sin ( x ). The graph of y

More information

AP Calculus AB 2017 Free-Response Solutions

AP Calculus AB 2017 Free-Response Solutions AP Calculus AB 217 Free-Response Solutions Louis A. Talman, Ph.D. Emeritus Professor of Mathematics Metropolitan State University of Denver May 18, 217 1 Problem 1 1.1 Part a The approximation with a left-hand

More information

AP CALCULUS BC 2008 SCORING GUIDELINES

AP CALCULUS BC 2008 SCORING GUIDELINES AP CALCULUS BC 2008 SCORING GUIDELINES Question 4 A particle moves along the x-axis so that its velocity at time t, for 0 t 6, is given by a differentiable function v whose graph is shown above. The velocity

More information

AP CALCULUS BC 2016 SCORING GUIDELINES

AP CALCULUS BC 2016 SCORING GUIDELINES Consider the differential equation (a) Find in terms of x an. AP CALCULUS BC 06 SCORING GUIDELINES x y. = Question 4 (b) Let y = f ( x) be the particular solution to the given differential equation whose

More information

AP Physics C: Mechanics

AP Physics C: Mechanics 2017 AP Physics C: Mechanics Sample Student Responses and Scoring Commentary Inside: RR Free Response Question 2 RR Scoring Guideline RR Student Samples RR Scoring Commentary 2017 The College Board. College

More information

AP Calculus BC 2003 Free-Response Questions 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 information

AP Physics C: Mechanics

AP Physics C: Mechanics 2017 AP Physics C: Mechanics Scoring Guidelines 2017 The College Board. College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. Visit

More information

AP CALCULUS AB 2011 SCORING GUIDELINES (Form B)

AP CALCULUS AB 2011 SCORING GUIDELINES (Form B) 0 SCORING GUIDELINES (Form B) Consider a differentiable function f having domain all positive real numbers, and for which it is known that f = ( 4 x) x for x > 0. (a) Find the x-coordinate of the critical

More information

Section I Multiple Choice 45 questions. Section II Free Response 6 questions

Section I Multiple Choice 45 questions. Section II Free Response 6 questions Section I Multiple Choice 45 questions Each question = 1.2 points, 54 points total Part A: No calculator allowed 30 questions in 60 minutes = 2 minutes per question Part B: Calculator allowed 15 questions

More information

2017 AP Chemistry Sample Student Responses and Scoring Commentary Inside: Free Response Question 2 Scoring Guideline Student Samples

2017 AP Chemistry Sample Student Responses and Scoring Commentary Inside: Free Response Question 2 Scoring Guideline Student Samples 2017 AP Chemistry Sample Student Responses and Scoring Commentary Inside: RR Free Response Question 2 RR Scoring Guideline RR Student Samples RR Scoring Commentary 2017 The College Board. College Board,

More information

AP Calculus BC 2008 Free-Response Questions Form B

AP Calculus BC 2008 Free-Response Questions Form B AP Calculus BC 008 Free-Response Questions 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 information

AP Calculus AB 2006 Free-Response Questions Form B

AP Calculus AB 2006 Free-Response Questions Form B AP Calculus AB 006 Free-Response Questions 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 information

AP CALCULUS BC 2009 SCORING GUIDELINES

AP CALCULUS BC 2009 SCORING GUIDELINES AP CALCULUS BC 2009 SCORING GUIDELINES Question 5 x 2 5 8 1 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

More information

AP Calculus AB 2008 Free-Response Questions Form B

AP Calculus AB 2008 Free-Response Questions Form B AP Calculus AB 2008 Free-Response Questions 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 information

AP Calculus BC 2011 Free-Response Questions Form B

AP Calculus BC 2011 Free-Response Questions Form B AP Calculus BC 11 Free-Response Questions Form B 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 information

AP CALCULUS AB 2012 SCORING GUIDELINES

AP CALCULUS AB 2012 SCORING GUIDELINES AP CALCULUS AB 12 SCORING GUIDELINES Question 1 t (minutes) 4 9 15 W() t (degrees Fahrenheit) 55. 57.1 61.8 67.9 71. The temperature of water in a tub at time t is modeled by a strictly increasing, twice-differentiable

More information

1998 Calculus AB Scoring Guidelines

1998 Calculus AB Scoring Guidelines 41 Velocity (feet per second) v(t) 9 8 7 6 5 4 1 O 1998 Calculus AB Scoring Guidelines 5 1 15 5 5 4 45 5 Time (seconds) t t v(t) (seconds) (feet per second) 5 1 1 15 55 5 7 78 5 81 4 75 45 6 5 7. The graph

More information

AP Biology. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 5. Scoring Guideline. Student Samples. Scoring Commentary

AP Biology. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 5. Scoring Guideline. Student Samples. Scoring Commentary 2017 AP Biology Sample Student Responses and Scoring Commentary Inside: Free Response Question 5 Scoring Guideline Student Samples Scoring Commentary 2017 The College Board. College Board, Advanced Placement

More information

AP CALCULUS AB/CALCULUS BC 2014 SCORING GUIDELINES

AP CALCULUS AB/CALCULUS BC 2014 SCORING GUIDELINES AP CALCULUS AB/CALCULUS BC 14 SCORING GUIDELINES Question 1 Grass clippings are placed in a bin, where they decompose. For t 3, the amount of grass clippings remaining in the bin is modeled by At ( ) =

More information

AP CALCULUS AB 2004 SCORING GUIDELINES (Form B)

AP CALCULUS AB 2004 SCORING GUIDELINES (Form B) AP CALCULUS AB 004 SCORING GUIDELINES (Form B) Question 4 The figure above shows the graph of f, the derivative of the function f, on the closed interval 1 x 5. The graph of f has horizontal tangent lines

More information

AP Physics C: Electricity and Magnetism

AP Physics C: Electricity and Magnetism 2017 AP Physics C: Electricity and Magnetism Sample Student Responses and Scoring Commentary Inside: RR Free Response Question 2 RR Scoring Guideline RR Student Samples RR Scoring Commentary 2017 The College

More information

AP Calculus Exam Format and Calculator Tips:

AP Calculus Exam Format and Calculator Tips: AP Calculus Exam Format and Calculator Tips: Exam Format: The exam is 3 hours and 15 minutes long and has two sections multiple choice and free response. A graphing calculator is required for parts of

More information

AP CALCULUS AB 2007 SCORING GUIDELINES (Form B)

AP CALCULUS AB 2007 SCORING GUIDELINES (Form B) AP CALCULUS AB 27 SCORING GUIDELINES (Form B) Question 2 A particle moves along the x-axis so that its velocity v at time 2 t is given by vt () = sin ( t ). The graph of v is shown above for t 5 π. The

More information

AP Calculus BC. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 3. Scoring Guideline.

AP Calculus BC. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 3. Scoring Guideline. 208 AP Calculus BC Sample Student Responses and Scoring Commentary nside: Free Response Question RR Scoring Guideline RR Student Samples RR Scoring Commentary 208 The College Board. College Board, Advanced

More information

Physics C: Mechanics 2015 Scoring Guidelines

Physics C: Mechanics 2015 Scoring Guidelines AP Physics C: Mechanics 015 Scoring Guidelines 015 The College Board. College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central

More information

AP CALCULUS BC 2015 SCORING GUIDELINES

AP CALCULUS BC 2015 SCORING GUIDELINES 05 SCORING GUIDELINES Question 5 Consider the function f =, where k is a nonzero constant. The derivative of f is given by k f = k ( k). (a) Let k =, so that f =. Write an equation for the line tangent

More information

AP CALCULUS AB/CALCULUS BC 2016 SCORING GUIDELINES

AP CALCULUS AB/CALCULUS BC 2016 SCORING GUIDELINES The figure above shows the graph of the piecewise-linear function f. For 4, the function g is defined by g( ) = f ( t) (a) Does g have a relative minimum, a relative maimum, or neither at =? Justify your

More information

AP Calculus AB Free-Response Scoring Guidelines

AP Calculus AB Free-Response Scoring Guidelines Question pt The rate at which raw sewage enters a treatment tank is given by Et 85 75cos 9 gallons per hour for t 4 hours. Treated sewage is removed from the tank at the constant rate of 645 gallons per

More information

Note: Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f (x) is a real number.

Note: Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f (x) is a real number. 997 AP Calculus BC: Section I, Part A 5 Minutes No Calculator Note: Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers for which f () is a real number..

More information

AP CALCULUS AB/CALCULUS BC 2015 SCORING GUIDELINES

AP CALCULUS AB/CALCULUS BC 2015 SCORING GUIDELINES AP CALCULUS AB/CALCULUS BC 15 SCORING GUIDELINES Question 3 t (minutes) vt ( ) (meters per minute) 1 4 4 4 15 Johanna jogs along a straight path. For t 4, Johanna s velocity is given by a differentiable

More information

Math 106 Answers to Exam 3a Fall 2015

Math 106 Answers to Exam 3a Fall 2015 Math 6 Answers to Exam 3a Fall 5.. Consider the curve given parametrically by x(t) = cos(t), y(t) = (t 3 ) 3, for t from π to π. (a) (6 points) Find all the points (x, y) where the graph has either a vertical

More information

AP Calculus BC. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 5. Scoring Guideline.

AP Calculus BC. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 5. Scoring Guideline. 018 AP Calculus BC Sample Student Responses and Scoring Commentary Inside: Free Response Question 5 RR Scoring Guideline RR Student Samples RR Scoring Commentary 018 The College Board. College Board, Advanced

More information

AP Calculus AB 1998 Free-Response Questions

AP Calculus AB 1998 Free-Response Questions AP Calculus AB 1998 Free-Response Questions These materials are intended for non-commercial use by AP teachers for course and exam preparation; permission for any other use must be sought from the Advanced

More information

AP Calculus BC 2005 Free-Response Questions

AP Calculus BC 2005 Free-Response Questions AP Calculus BC 005 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 information

AP Physics 1: Algebra-Based

AP Physics 1: Algebra-Based 2017 AP Physics 1: Algebra-Based Sample Student Responses and Scoring Commentary Inside: RR Free Response Question 4 RR Scoring Guideline RR Student Samples RR Scoring Commentary 2017 The College Board.

More information

AP Calculus BC 2005 Free-Response Questions Form B

AP Calculus BC 2005 Free-Response Questions Form B AP Calculus BC 005 Free-Response Questions 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 information

AP Physics 1: Algebra-Based

AP Physics 1: Algebra-Based 2017 AP Physics 1: Algebra-Based Sample Student Responses and Scoring Commentary Inside: Free Response Question 5 Scoring Guideline Student Samples Scoring Commentary 2017 The College Board. College Board,

More information

AP Calculus BC Chapter 4 AP Exam Problems. Answers

AP Calculus BC Chapter 4 AP Exam Problems. Answers AP Calculus BC Chapter 4 AP Exam Problems Answers. A 988 AB # 48%. D 998 AB #4 5%. E 998 BC # % 5. C 99 AB # % 6. B 998 AB #80 48% 7. C 99 AB #7 65% 8. C 998 AB # 69% 9. B 99 BC # 75% 0. C 998 BC # 80%.

More information

AP Calculus AB 2001 Free-Response Questions

AP Calculus AB 2001 Free-Response Questions AP Calculus AB 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 information

AP Physics C: Electricity and Magnetism

AP Physics C: Electricity and Magnetism 2018 AP Physics C: Electricity and Magnetism Sample Student Responses and Scoring Commentary Inside: Free Response Question 2 RR Scoring Guideline RR Student Samples RR Scoring Commentary 2018 The College

More information

Student Study Session Topic: Interpreting Graphs

Student Study Session Topic: Interpreting Graphs Student Study Session Topic: Interpreting Graphs Starting with the graph of a function or its derivative, you may be asked all kinds of questions without having (or needing) and equation to work with.

More information

AP Physics C: Mechanics

AP Physics C: Mechanics 2018 AP Physics C: Mechanics Sample Student Responses and Scoring Commentary Inside: Free Response Question 3 RR Scoring Guideline RR Student Samples RR Scoring Commentary 2018 The College Board. College

More information

AP Physics 1: Algebra-Based

AP Physics 1: Algebra-Based 2017 AP Physics 1: Algebra-Based Sample Student Responses and Scoring Commentary Inside: RR Free Response Question 1 RR Scoring Guideline RR Student Samples RR Scoring Commentary 2017 The College Board.

More information

AP Calculus BC Multiple-Choice Answer Key!

AP Calculus BC Multiple-Choice Answer Key! Multiple-Choice Answer Key!!!!! "#$$%&'! "#$$%&'!!,#-! ()*+%$,#-! ()*+%$!!!!!! "!!!!! "!! 5!! 6! 7!! 8! 7! 9!!! 5:!!!!! 5! (!!!! 5! "! 5!!! 5!! 8! (!! 56! "! :!!! 59!!!!! 5! 7!!!! 5!!!!! 55! "! 6! "!!

More information

Physics C: Mechanics 2014 Scoring Guidelines

Physics C: Mechanics 2014 Scoring Guidelines AP Physics C: Mechanics 14 Scoring Guidelines 14 The College Board. College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central

More information

AP Calculus AB AP Calculus BC

AP Calculus AB AP Calculus BC AP Calculus AB AP Calculus BC Free-Response Questions and Solutions 979 988 Copyright 4 College Entrance Examination Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central,

More information

AP Calculus AB. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 4. Scoring Guideline.

AP Calculus AB. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 4. Scoring Guideline. 018 AP Calculus AB Sample Student Responses and Scoring Commentary Inside: Free Response Question 4 RR Scoring Guideline RR Student Samples RR Scoring Commentary College Board, Advanced Placement Program,

More information

AP CALCULUS AB 28 SCORING GUIDELINES (Form B) Distance from the river s edge (feet) Question 8 14 22 24 Depth of the water (feet) 7 8 2 A scientist measures the depth of the Doe River at Picnic Point.

More information

AP Physics C: Electricity and Magnetism

AP Physics C: Electricity and Magnetism 2017 AP Physics C: Electricity and Magnetism Sample Student Responses and Scoring Commentary Inside: RR Free Response Question 3 RR Scoring Guideline RR Student Samples RR Scoring Commentary 2017 The College

More information

AP Physics C: Electricity and Magnetism

AP Physics C: Electricity and Magnetism 18 AP Physics C: Electricity and Magnetism Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is

More information

AP CALCULUS BC 2010 SCORING GUIDELINES

AP CALCULUS BC 2010 SCORING GUIDELINES AP CALCULUS BC 2010 SCORING GUIDELINES Question 3 2 A particle is moving along a curve so that its position at time t is ( x() t, y() t ), where xt () = t 4t+ 8 and yt () is not explicitly given. Both

More information

CLEP Calculus. Time 60 Minutes 45 Questions. For each question below, choose the best answer from the choices given. 2. If f(x) = 3x, then f (x) =

CLEP Calculus. Time 60 Minutes 45 Questions. For each question below, choose the best answer from the choices given. 2. If f(x) = 3x, then f (x) = CLEP Calculus Time 60 Minutes 5 Questions For each question below, choose the best answer from the choices given. 7. lim 5 + 5 is (A) 7 0 (C) 7 0 (D) 7 (E) Noneistent. If f(), then f () (A) (C) (D) (E)

More information

AP Æ Calculus AB Sample Multiple-Choice Questions

AP Æ Calculus AB Sample Multiple-Choice Questions AP Æ Calculus AB Sample Multiple-Choice 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

More information

LSU AP Calculus Practice Test Day

LSU AP Calculus Practice Test Day LSU AP Calculus Practice Test Day AP Calculus AB 2018 Practice Exam Section I Part A AP CALCULUS AB: PRACTICE EXAM SECTION I: PART A NO CALCULATORS ALLOWED. YOU HAVE 60 MINUTES. 1. If y = ( 1 + x 5) 3

More information

Calculus with the Graphing Calculator

Calculus with the Graphing Calculator Calculus with the Graphing Calculator Using a graphing calculator on the AP Calculus exam Students are expected to know how to use their graphing calculators on the AP Calculus exams proficiently to accomplish

More information

AP Calculus AB. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 1. Scoring Guideline.

AP Calculus AB. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 1. Scoring Guideline. 218 AP Calculus AB Sample Student Responses and Scoring Commentary Inside: Free Response Question 1 RR Scoring Guideline RR Student Samples RR Scoring Commentary 218 The College Board. College Board, Advanced

More information

1969 AP Calculus BC: Section I

1969 AP Calculus BC: Section I 969 AP Calculus BC: Section I 9 Minutes No Calculator Note: In this eamination, ln denotes the natural logarithm of (that is, logarithm to the base e).. t The asymptotes of the graph of the parametric

More information

AP Physics C: Mechanics 2005 Scoring Guidelines

AP Physics C: Mechanics 2005 Scoring Guidelines AP Physics C: Mechanics 005 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

More information

IF (some things are true), then (some other thing is true).

IF (some things are true), then (some other thing is true). Student Notes Student Study Session Topic: Important Theorems Facts, truth, ideas, etc. in mathematics are known as definitions, theorems, and postulates (also known as aioms or assumptions). Theorems

More information

AP Calculus BC. Practice Exam. Advanced Placement Program

AP Calculus BC. Practice Exam. Advanced Placement Program Advanced Placement Program AP Calculus BC Practice Eam The questions contained in this AP Calculus BC Practice Eam are written to the content specifications of AP Eams for this subject. Taking this practice

More information

( ) be the particular solution to the differential equation passing through the point (2, 1). Write an

( ) be the particular solution to the differential equation passing through the point (2, 1). Write an 70. AB Calculus Step-by-Step Name Consider the differential equation dy dx = x +1 y. ( ) be the particular solution to the differential equation passing through the point (2, 1). Write an a. Let f x equation

More information

+ 1 for x > 2 (B) (E) (B) 2. (C) 1 (D) 2 (E) Nonexistent

+ 1 for x > 2 (B) (E) (B) 2. (C) 1 (D) 2 (E) Nonexistent dx = (A) 3 sin(3x ) + C 1. cos ( 3x) 1 (B) sin(3x ) + C 3 1 (C) sin(3x ) + C 3 (D) sin( 3x ) + C (E) 3 sin(3x ) + C 6 3 2x + 6x 2. lim 5 3 x 0 4x + 3x (A) 0 1 (B) 2 (C) 1 (D) 2 (E) Nonexistent is 2 x 3x

More information

Student Session Topic: Average and Instantaneous Rates of Change

Student Session Topic: Average and Instantaneous Rates of Change Student Session Topic: Average and Instantaneous Rates of Change The concepts of average rates of change and instantaneous rates of change are the building blocks of differential calculus. The AP exams

More information

AP Physics 1: Algebra-Based

AP Physics 1: Algebra-Based 018 AP Physics 1: Algebra-Based Sample Student Responses and Scoring Commentary Inside: Free Response Question 1 RR Scoring Guideline RR Student Samples RR Scoring Commentary 018 The College Board. College

More information

Math 113 Final Exam Practice Problem Solutions. f(x) = ln x x. lim. lim. x x = lim. = lim 2

Math 113 Final Exam Practice Problem Solutions. f(x) = ln x x. lim. lim. x x = lim. = lim 2 Math 3 Final Eam Practice Problem Solutions. What are the domain and range of the function f() = ln? Answer: is only defined for, and ln is only defined for >. Hence, the domain of the function is >. Notice

More information

Math 2250 Final Exam Practice Problem Solutions. f(x) = ln x x. 1 x. lim. lim. x x = lim. = lim 2

Math 2250 Final Exam Practice Problem Solutions. f(x) = ln x x. 1 x. lim. lim. x x = lim. = lim 2 Math 5 Final Eam Practice Problem Solutions. What are the domain and range of the function f() = ln? Answer: is only defined for, and ln is only defined for >. Hence, the domain of the function is >. Notice

More information

1985 AP Calculus AB: Section I

1985 AP Calculus AB: Section I 985 AP Calculus AB: Section I 9 Minutes No Calculator Notes: () In this eamination, ln denotes the natural logarithm of (that is, logarithm to the base e). () Unless otherwise specified, the domain of

More information

AP Calculus BC Chapter 4 (A) 12 (B) 40 (C) 46 (D) 55 (E) 66

AP Calculus BC Chapter 4 (A) 12 (B) 40 (C) 46 (D) 55 (E) 66 AP Calculus BC Chapter 4 REVIEW 4.1 4.4 Name Date Period NO CALCULATOR IS ALLOWED FOR THIS PORTION OF THE REVIEW. 1. 4 d dt (3t 2 + 2t 1) dt = 2 (A) 12 (B) 4 (C) 46 (D) 55 (E) 66 2. The velocity of a particle

More information

AP Calculus AB and AP. Calculus BC Exam. ApTutorGroup.com. ApTutorGroup.com SAMPLE QUESTIONS

AP Calculus AB and AP. Calculus BC Exam. ApTutorGroup.com. ApTutorGroup.com SAMPLE QUESTIONS SAMPLE QUESTIONS AP Calculus AB and AP Calculus BC Exam Originally published in the Fall 2014 AP Calculus AB and AP Calculus BC Curriculum Framework The College Board The College Board is a mission-driven

More information

= π + sin π = π + 0 = π, so the object is moving at a speed of π feet per second after π seconds. (c) How far does it go in π seconds?

= π + sin π = π + 0 = π, so the object is moving at a speed of π feet per second after π seconds. (c) How far does it go in π seconds? Mathematics 115 Professor Alan H. Stein April 18, 005 SOLUTIONS 1. Define what is meant by an antiderivative or indefinite integral of a function f(x). Solution: An antiderivative or indefinite integral

More information

Student Performance Q&A: 2001 AP Calculus Free-Response Questions

Student Performance Q&A: 2001 AP Calculus Free-Response Questions Student Performance Q&A: 2001 AP Calculus Free-Response Questions The following comments are provided by the Chief Faculty Consultant regarding the 2001 free-response questions for AP Calculus AB and BC.

More information

AP CALCULUS AB 2011 SCORING GUIDELINES

AP CALCULUS AB 2011 SCORING GUIDELINES AP CALCULUS AB 2011 SCORING GUIDELINES Question 4 The continuous function f is defined on the interval 4 x 3. The graph of f consists of two quarter circles and one line segment, as shown in the figure

More information

AP CALCULUS BC 2009 SCORING GUIDELINES

AP CALCULUS BC 2009 SCORING GUIDELINES AP CALCULUS BC 009 SCORING GUIDELINES Question 6 The Maclaurin series for by f( x) = x e is 3 n x x x x e = 1 + x + + + + +. The continuous function f is defined 6 n! ( x 1) e 1 for x 1 and f () 1 = 1.

More information

AP CALCULUS BC 2007 SCORING GUIDELINES (Form B)

AP CALCULUS BC 2007 SCORING GUIDELINES (Form B) AP CALCULUS BC 2007 SCORING GUIDELINES (Form B) Question 3 The wind chill is the temperature, in degrees Fahrenheit ( F, ) a human feels based on the air temperature, in degrees Fahrenheit, and the wind

More information

AP Calculus AB 2002 Free-Response Questions

AP Calculus AB 2002 Free-Response Questions AP Calculus AB 00 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 be

More information

Calculus BC AP/Dual Fall Semester Review Sheet REVISED 1 Name Date. 3) Explain why f(x) = x 2 7x 8 is a guarantee zero in between [ 3, 0] g) lim x

Calculus BC AP/Dual Fall Semester Review Sheet REVISED 1 Name Date. 3) Explain why f(x) = x 2 7x 8 is a guarantee zero in between [ 3, 0] g) lim x Calculus BC AP/Dual Fall Semester Review Sheet REVISED Name Date Eam Date and Time: Read and answer all questions accordingly. All work and problems must be done on your own paper and work must be shown.

More information

AP Calculus BC 1998 Free-Response Questions

AP Calculus BC 1998 Free-Response Questions AP Calculus BC 1998 Free-Response Questions These materials are intended for non-commercial use by AP teachers for course and exam preparation; permission for any other use must be sought from the Advanced

More information

AP CALCULUS BC 2006 SCORING GUIDELINES (Form B) Question 2

AP CALCULUS BC 2006 SCORING GUIDELINES (Form B) Question 2 AP CALCULUS BC 2006 SCORING GUIDELINES (Form B) Question 2 An object moving along a curve in the xy-plane is at position ( x() t, y() t ) at time t, where dx t tan( e ) for t 0. At time t =, the object

More information

AP Calculus BC Fall Final Part IIa

AP Calculus BC Fall Final Part IIa AP Calculus BC 18-19 Fall Final Part IIa Calculator Required Name: 1. At time t = 0, there are 120 gallons of oil in a tank. During the time interval 0 t 10 hours, oil flows into the tank at a rate of

More information

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA CALCULUS AB SECTION I, Part A Time 55 minutes Number of questions 8 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAM. Directions: Solve each of the following problems,

More information

1993 AP Calculus AB: Section I

1993 AP Calculus AB: Section I 99 AP Calculus AB: Section I 90 Minutes Scientific Calculator Notes: () The eact numerical value of the correct answer does not always appear among the choices given. When this happens, select from among

More information

AP Calculus AB Winter Break Packet Happy Holidays!

AP Calculus AB Winter Break Packet Happy Holidays! AP Calculus AB Winter Break Packet 04 Happy Holidays! Section I NO CALCULATORS MAY BE USED IN THIS PART OF THE EXAMINATION. Directions: Solve each of the following problems. After examining the form of

More information