AP Calculus AB - Final Exam Topics
Test #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
Test #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
Test #3 – Applications of Integration (MC and FR)
1. Area and volume problems
2. Motion problems
3. Word problems
Test #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. MVT, IVT, and EVT
Test #5 – Limits and Continuity (MC and FR)
1. Limits
2. Definition of the derivative as a limit
3. Continuity
4. Differentiability
Review Materials for AP Calculus BC Final Exams and AP Exam Preparation, due 05/09 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
Available at:
4. https://www.math.ku.edu/~tenkosky/img-APexams69_98-48118_1_158.pdf
5. ***1998 Multiple-Choice Questions and Solutions; key and solutions at end of document
Available at same site as the 1997 exam:
6. https://www.math.ku.edu/~tenkosky/img-APexams69_98-48118_1_158.pdf
7. Free Response Questions and Scoring Guidelines 1998 – 2011. Do not look at 2012 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
8. ***Online Practice Questions (2006 Exam) and key (complete at least one version of the AB exam, both sections)
Available at: http://online.math.uh.edu/apcalculus/exams/index.htm
Questions from 1997 and 1998 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
77,80,81,82,85
26,77,78,89,86,87,90
15,21,79
4,12,13,76,81,83