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Chapter III: Answers tothe 2008 AP Calculus AB andCalculus BC Exams
Section I: Multiple Choice• Section I Answer Key and Percent Answering
Correctly• Analyzing Your Students' Performance on the
Multiple-Choice Section• Diagnostic Guide for the 2008 AP Calculus AB and
Calculus BC Exams
Section II: Free Response• Comments from the Chief Reader» Commentary, Scoring Guidelines, and Sample
Student Responses• AB/BC Question 1• AB/BC Question 2
• AB Question 3• AB/BC Question 4• AB Question 5• AB Question 6• BC Question 3• BC Question 5• BC Question 6
Section I: Multiple ChoiceOn the following pages are the correct answers to themultiple-choice questions for Form Q, the percent ofAP students who answered each question correctly byAP grade, and the total percent answering correctly.
Section I Answer Key and Percent Answering CorrectlyCalculus AB
ItemNo.
1
2345678910111213141516171819*202122232425
CorrectAnswer
BDDBAABEDCBDAECDCA-DABEBB
Percent Correct by Grade5 4 3 2 1
889672957474978695909889725093748647-734880508055
778448865955897482799279513082466223-502664265426
687135744946766465698269362572304315-351758173316
585726604039555243586957242361203112-251155121814
363214372430222916354433141841112611-197507913
TotalPercentCorrect
656739704949676160667765402970375022-412262234026
ItemNo.
2627287677787980818283848586878889909192
CorrectAnswer
ACABCBBEEBBCBCDCEACB
Percent Correct by Grade5 4 3 2 1
5370389889978170909690917686849667679258
2952139373916652718876805371558440378145
174168356805438557763643858356523206843
12313
6541614426426148412843214516115241
92033024282814212727141818112110102736
TotalPercentCorrect
2543147357715540566961584355426232306445
'Although 45 multiple-choice items were administered in Section I,item #19 was not used in scoring for statistical reasons. Manystudents who scored well on the exam chose option A or option C,instead of the correct answer E. It is important for teachers toemphasize that when determining the horizontal asymptotes for thegraph of y = f (x), students must examine the limit of / (x) as xapproaches infinity and the limit of / (x) as x approaches negativeinfinity.
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Section I Answer Key and Percent Answering CorrectlyCalculus BC
ItemNo.
1
234567891011121314151617181920212223
CorrectAnswer
BACDCADBDBADBEADBAACAEE
Percent Correct by Grade5 4 3 2 1
9796889594819089969075647563856279596149583180
9592778685617371858048355539633860334123351157
9387677476525856747234254032452745233016237
42
8980556166434339585927212927312137162312166
28
81673640403523263339211623221716281318910515
TotalPercentCorrect
9389738080636968797652425545614259384330381856
Analyzing Your Students' Performance onthe Multiple-Choice SectionIf you give your students the 2008 Calculus AB orCalculus BC Exam for practice, you may want to analyzethe results to find overall strengths and weaknesses in theirunderstanding of calculus. The following diagnostic work-sheets will help you do this. You are permitted to photocopyand distribute them to your students for completion.
1. In each category, students should insert a check mark foreach correct answer.
2. Add together the total number of correct answers foreach category.
ItemNo.
24252627287677787980818283848586878889909192
CorrectAnswer
ABDADDDCDEBEBACCDAEDDB
Percent Correct by Grade5 4 3 2 1
63575683269399947070849393958973918579918590
372735665
8498814556687882867442686055796673
251925523
7294663644566571736228484338624754
1913194125687492733415159544919312924442933
131213282
3669262121243739283513181614221518
TotalPercentCorrect
41353864137793744954657577787147655954716167
3. To compare the student's number of correct answers fora given category with the average number correct forthat category, copy the number of correct answers to the"Number Correct" table at the end of the DiagnosticGuide.
In addition, under each item, the percent of AP studentswho answered correctly is shown, so students can analyzetheir performance on individual items. This informationwill be helpful in deciding how students should plan theirstudy time. Please note that one item may appear in severaldifferent categories, as questions can cover different topics.
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Diagnostic Guide for the 2008 AP Calculus AB Exam
Differential Calculus (Average number correct = 13.0)
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
1
65
24
40
3
39
25
26
5
49
26
25
6
49
27
43
8
61
28
14
11
77
76
73
12
65
77
57
13
40
78
71
14
29
80
40
16
37
82
69
18
22
84
58
20
4J
88
62
21
22
89
32
22
62
90
30
Integral Calculus (Average number correct = 8.9)
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
2
67
4
70
7
67
9
60
10
66
15
70
17
50
23
23
79
55
81
56
83
61
85
43
86
55
87
42
91
64
92
45
Part A—No Calculator (Average number correct = 12.8)
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
1
65
15
70
2
67
16
37
3
39
17
50
4
70
18
22
5
49
20
41
6
49
21
22
7
67
22
62
8
61
23
23
9
60
24
40
10
66
25
26
11
77
26
25
12
65
27
43
13
40
28
14
14
29
Part B—With Graphing Calculator (Average number correct = 9.1)
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
76
73
77
57
78
71
79
55
80
40
81
56
82
69
83
61
84
58
85
43
86
55
87
42
88
62
89
32
90
30
91
64
92
45
Calculator-Active Items (Average number correct = 3.5)
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
78
71
80
40
82
69
83
61
87
42
91
64
93
Diagnostic Guide for the 2008 AP Calculus AB Exam (continued)
Number Correct
Number ofQuestions
AverageNumberCorrect
My NumberCorrect
DifferentialCalculus
28
13.0(46.4%)
IntegralCalculus
16
8.9(55.6%)
Part A — NoCalculator
27
12.8(47.4%)
Part B— withGraphingCalculator
17
9.1(53.5%)
Calculator-Active Items
6
3.5(58.3%)
Diagnostic Guide for the 2008 AP Calculus BC Exam
Calculus AB Topics (Average number correct = 17.0)
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
2
89
77
93
6
63
78
74
8
68
80
54
9
79
81
65
10
76
83
77
13
55
85
71
14
45
86
47
15
61
87
65
17
59
88
59
18
38
89
54
21
38
90
71
25
35
91
61
27
64
92
67
76
77
Calculus BC Only Topics (Average number correct = 9.7)
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
1
93
3
73
4
80
5
80
1
69
11
52
12
42
16
42
19
43
20
30
22
7S
23
56
24
41
26
38
28
13
79
49
82
75
84
78
Differential Calculus (Average number correct = 12.6)
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
1
93
3
73
6
63
7
69
10
76
14
45
15
61
17
59
18
38
21
38
25
35
27
64
28
J3
76
77
78
74
80
54
85
71
89
54
90
77
91
61
92
67
94
Diagnostic Guide for the 2008 AP Calculus BC Exam (continued)
Integral Calculus (Average number correct = 9.7)
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
2
89
5
80
8
68
9
79
11
52
13
55
19
43
22
18
24
41
26
38
77
93
81
65
83
77
86
47
87
65
88
59
Part A—No Calculator (Average number correct = 15.4)
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
1
93
15
61
2
89
16
42
3
73
17
59
4
80
18
38
5
80
19
43
6
63
20
30
7
69
21
38
8
68
22
18
9
79
23
56
10
76
24
41
11
52
25
35
12
42
26
38
13
55
27
64
14
45
28
13
Part B—With Graphing Calculator (Average number correct = 11.4)
Question #
Correct/Incorrect
Percent of StudentsAnswering Correctly
76
77
77
93
78
74
79
49
80
54
81
65
82
75
83
77
84
78
85
71
86
47
87
65
88
59
89
54
90
71
91
61
92
67
Series Items (Average number correct = 4.5)
Question f
Correct/Incorrect
Percent of StudentsAnswering Correctly
4
80
12
42
16
42
20
30
23
56
79
49
82
75
84
78
Calculator-Active Items (Average number correct = 4.2)
Question f
Correct/Incorrect
Percent of StudentsAnswering Correctly
77
93
80
54
83
77
85
71
87
65
91
61
95
Diagnostic Guide for the 2008 AP Calculus BC Exam (continued)
Number Correct
Number ofQuestions
AverageNumberCorrect
My NumberCorrect
CalculusAB
Topics
27
17.0(63.0%)
CalculusBC OnlyTopics
18
9.7(53.9%)
DifferentialCalculus
21
12.6(60.0%)
IntegralCalculus
16
9.7(60.6%)
Part A—No Calculator
28
15.4(55.0%)
Part B—With
GraphingCalculator
17
11.4(67.1%)
SeriesItems
8
4.5(56.3%)
Calculator-Active Items
6
4.2(70.0%)
96