AP Calculus AB - Final Exam Topics
Exam #1 – Integration Techniques (MC and FR)
1. Integration – all rules and properties
2. Relationship of graphs of
3. 1st and 2nd FTC
4. Riemann Sums
5. Trapezoidal Rule
6. Average value of a function
Exam #2 – Differentiation Techniques
(MC and FR)
1. Differentiation – all rules and properties
2. Implicit differentiation
3. Tangent line
4. Derivatives of inverse functions
5. Identification of extrema, inflection points, concavity,
and intervals of increasing/decreasing
Exam #3 – Applications of Integration (MC and FR)
1. Area and volume problems
2. Motion problems
3. Word problems
Exam #4 – Applications of Differentiation (MC and FR)
1. Identification of extrema and increasing/decreasing
intervals - graphically , analytically, and with word
problems
2. Identification of inflection points and concavity –
graphically, analytically, and with word problems
3. Related rates
4. Motion Problems
5. Dif Eq’s and Slope Fields
6. MVT, IVT, and EVT
Exam #5 – Limits and Continuity (MC and FR)
1. Limits
2. Definition of the derivative as a limit
3. Continuity
4. Differentiability
**Note – Topics listed on earlier exams may also be
included in subsequent exams.
Review Materials for AP Calculus BC Final Exams and AP Exam Preparation, due 05/23 for test bonus. Items marked *** are
mandatory bonus.
1. Your note cards, notes, and homework!
2. Workbook - Fast Track to a 5 Preparing for the AP Calculus AB and Calculus BC Examinations (do not write in book!)
a. Complete Diagnostic Test p. 15; AB Practice Test 1, p. 225; AB Practice Test 2, p. 255
b. Complete the multiple choice and free response questions at the end of Chapter 4 (Integration); Chapter 5
(Applications of Integration – skip arc length); Chapter 7 (Differential Equations – slope fields and separation of
variables only)
c. Review work completed for semester exam – Chapter 1 (Limits); Chapter 2 (Differentiation); and Chapter 3
(Applications of Derivatives)
3. ***1997 Multiple Choice Questions and Solutions(skip #90); key and solutions at end of document; make sure you are
answering the questions for the AB exam and not the BC exam; follow exam directions regarding calculator use
Available at: http://crunchymath.weebly.com/uploads/8/2/4/0/8240213/ap_multiple_choice.pdf
***1998 Multiple Choice Questions and Solutions; key and solutions at end of document; make sure you are answering
the questions for the AB exam and not the BC exam; follow exam directions regarding calculator use
Available at same site as the 1997 exam:
4. ***2003 Multiple Choice Questions available at https://cszymanski.wikispaces.com/file/view/2003-AB-EXAM-MC.pdf
5. Free Response Questions and Scoring Guidelines 1998 – 2012, 2014 (After May 11th). Do not look at 2013 questions as
you will complete those during your practice exam.
Available at AP Central:
http://apcentral.collegeboard.com/apc/members/exam/exam_information/1997.html
6. “Gateway” derivative and integration problems Pitt students must be able to solve:
http://calculus.math.pitt.edu/Gateway/23/23gw/23gw.html. Answers can be verified with your calculator.
Note: Integration problems skip #40-45
Questions from 1997,1998, and 2003 exams to study for each test.
Test
#1 – Integration
Techniques
#2 – Differentiation
Techniques
#3 – Integration
Applications
#4 – Differentiation
Applications
#5 – Limits and
Continuity
1997 AP Exam
1,3,6,11,18,20,24,78
*Skip #25!
2,4,5,7,10,12,13,14,17,19,
22,76
8,9,16,23,83,84,87
1998 AP Exam
2,3,5,7,9,11,15,20,21,23,
27,79,82,85,88
1,6,8,10,16,17,18,19,22,28,
89,91
14,24,25,84,92
2003 AP Exam
2,5,7,8,10,11,19,21,22,23,
28,92
1,4,9,14,15,16,17,18,24,26,
27, 81,89
77,82, 83,85,86,88,90
77,80,81,82,85
26,77,78,89,86,87,90
12,25,76,78,84,87,91
15,21,79
4,12,13,76,81,83
3,6,13,20,79,80