2019 AP® Calculus AB Sample Student Responses and Scoring Commentary Inside: Free Response Question 1 5Scoring Guideline 5Student Samples 5Scoring Commentary © 2019 The College Board. College Board, Advanced Placement, AP, AP Central, and the acorn logo are registered trademarks of the College Board. Visit the College Board on the web: collegeboard.org. $3&HQWUDOLVWKHRƱFLDORQOLQHKRPHIRUWKH$33URJUDP DSFHQWUDOFROOHJHERDUGRUJ
AP® CALCULUS AB/CALCULUS BC 2019 SCORING GUIDELINES Question 1 (a) ³5 Et dt153.457690 0 To the nearest whole number, 153 fish enter the lake from midnight to 5 A.M. 1^: integral 2 : 1 : answer (b) 1 5 ³Lt dt6.059038 500 The average number of fish that leave the lake per hour from midnight to 5 A.M. is 6.059 fish per hour. 1^: integral 2 : 1 : answer (c) The rate of change in the number of fish in the lake at time t is given by EtLt. EtLt0 t6.20356 EtLt !0 for 0 d t 6.20356, and Et Lt 0for 6.20356 dt 8. Therefore the greatest number of fish in the lake is at time t6.204 (or 6.203). — OR — Let Atbe the change in the number of fish in the lake from midnight to t hours after midnight. ³tAtEsLsds 0 AtcEtLt0 tC6.20356 t At0 0 C 135.01492 8 80.91998 Therefore the greatest number of fish in the lake is at time t6.204 (or 6.203). 1 : sets EtLt0 °3 : ® 1 : answer ° ̄ 1 : justification (d) Ec5 Lc5 10.7228 0 Because Ec5 Lc5 0, the rate of change in the number of fish is decreasing at time t5. 1 : considers Ec5 and Lc52 : ® ̄1 : answer with explanation © 2019 The College Board. Visit the College Board on the web: collegeboard.org.
© 2019 The College Board. Visit the College Board on the web: collegeboard.org.
© 2019 The College Board. Visit the College Board on the web: collegeboard.org.
© 2019 The College Board. Visit the College Board on the web: collegeboard.org.
© 2019 The College Board. Visit the College Board on the web: collegeboard.org.
