AP® Calculus AB 2005 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 college success and opportunity. Founded in 1900, the association is composed of more than 4,700 schools, colleges, universities, and other educational organizations. Each year, the College Board serves over three and a half million students and their parents, 23,000high schools, and 3,500 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 excellence and equity, and that commitment is embodied in all of its programs, services, activities, and concerns. Copyright © 2005 by College Board. All rights reserved. College Board, AP Central, APCD, Advanced Placement Program, AP, AP Vertical Teams, Pre-AP, SAT, and the acorn logo are registered trademarks of the College Entrance Examination Board. Admitted Class Evaluation Service, CollegeEd, Connect to college success, MyRoad, SAT Professional Development, SAT Readiness Program, and Setting the Cornerstones are trademarks owned by the College Entrance Examination Board. PSAT/NMSQT is a registered trademark of the College Entrance Examination Board and National Merit Scholarship Corporation. Other products and services may be trademarks of their respective owners. Permission to use copyrighted College Board materials may be requested online at: http://www.collegeboard.com/inquiry/cbpermit.html. Visit the College Board on the Web: www.collegeboard.com. AP Central is the official online home for the AP Program and Pre-AP: apcentral.collegeboard.com. www.mymathscloud.com
AP® CALCULUS AB 2005 SCORING GUIDELINES (Form B) Copyright © 2005 by College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for AP students and parents). 2 Question 1 Let f and g be the functions given by ()( )1sin2fxx=+ and ()2.xgxe= Let R be the shaded region in the first quadrant enclosed by the graphs of f and g as shown in the figure above. (a) Find the area of R. (b) Find the volume of the solid generated when R is revolved about the x-axis. (c) The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from ()yfx= to ().ygx= Find the volume of this solid. The graphs of f and g intersect in the first quadrant at ()(),1.13569, 1.76446 .ST=1 : correct limits in an integral in (a), (b), or (c) (a) Area ()()()()()020=1sin20.429SSxfx gx dxxedx=−+−=∫∫2 : 1 : integrand1 : answer⎧⎨⎩(b) Volume ()()()()()()()()()22022201sin24.266 or 4.267SSxfxgxdxxedxππ=−=+ −=⌠⎮⌡∫3 : ()()()22 2 : integrand 1 each error Note: 0 2 if integral not of form 1 : answerbacRxrxdx⎧⎪−⎪⎪⎨⎪−⎪⎪⎩∫(c) Volume ()()()20220221sin2220.077 or 0.078SSxfx gxdxxedxππ−⎛⎞=⎜⎟⎝⎠⎛⎞+−=⎜⎟⎝⎠=⌠⎮⌡⌠⎮⌡3 : 2 : integrand1 : answer⎧⎨⎩www.mymathscloud.com
