AP Calculus BC
Summer Work 2016
•
•
due date:
estimated time:
third day of class
10 hours (for planning purposes only; work until you finish)
Dear AP Calculus BC Students,
This assignment is designed for you to review all of your precalculus and calculus skills and make sure
you are well prepared for the start of AP Calculus BC in the fall. We anticipate that the work will take
about 10 hours to complete.
Summer work is due on the third day of class. Most math classes will have a short quiz with problems
taken directly from their summer assignment; we will have a different arrangement, which is described
on the next page.
The AP Calculus BC exam requires you to know all the material learned in AP Calculus AB, in addition to
new material learned in Calculus BC. For this reason, we will spend the first four weeks of school
reviewing Calculus AB material.
Questions? Email any of us at the following:
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
Page 1 of 4
AP Calculus BC Summer Math due the third day of class:
1. Answer all of the free response questions from the 2011 AP Calculus AB Exam. Your
answers will be graded for correctness. There are Khan Academy videos about these very
problems, which you may use to help you answer the questions.
2. Complete 40 of the 63 Khan Academy Skills listed in the chart beginning on page 3. In order
to “complete” a skill, you need to have “practiced” this skill. The chart below states the
minimum number of consecutive questions that must be answered correctly in order for a
skill to be considered “practiced.” The website should give you a smiley face and play happy
music to celebrate a skill being practiced. Complete the 40 skills of your choice during the
summer. You will eventually need to complete all 63 skills, but will be given time during the
month of September to complete the other 23 skills.
• Be sure to sign in to your Khan Academy Account before answering questions, or
there will be no record of your doing the questions.
• Be sure you know your Khan Academy password in September once school starts!
Our IT Department will need to add me to your Khan Academy account as a “coach,”
so that I can verify what topics you have completed. You may need to access your
account in September to help make this happen.
• For your own information: Any topic that has a star next to it has questions that one
can answer. Do not mix that up with topics that have an arrow next to it, which are
videos.
There will be a mini-quiz of sorts on the third day of class.
• Half of the mini-quiz grade will be the free-response questions (#1 above), graded for
correctness.
• Half of the mini-quiz grade will be the completion percentage of the 40 Khan Academy skills
(#2 above).
Page 2 of 4
Complete 40 of the following 63 skills.
AP Calculus BC
Khan Academy Skills
Finding limits numerically
One-sided limits from graphs
Two-sided limits from graphs
Two-sided limits using algebra
Two-sided limits using advanced algebra
Continuity
Limits at infinity where f(x) is unbounded
Limits at infinity where x is unbounded
Squeeze Theorem
Slope of secant lines
Tangent slope is limiting value of secant slope
The formal and alternative form of the derivative
Derivative intuition
Recognizing slope of curves
Graphs of functions and their derivatives
Visualizing derivatives
Symbolic differentiation
Power rule (basic)
Power rule (advanced)
Special derivatives quiz
Special derivatives
Chain rule on two functions
Chain rule on three functions
Product rule
Quotient rule
Combining the product and chain rules
Implicit differentiation
Derivatives of inverse functions
Logarithmic differentiation
Applications of derivatives: tangent and normal lines
Applications of derivatives: motion along a line
Critical numbers
Extreme values from graphs
Extreme value theorem
Recognizing concavity
Concavity and the second derivative
Page 3 of 4
Min. consecutive
questions required
to be answered
correctly
4
1
1
4
5
5
4
5
3
3
5
4
1
3
5
5
5
5
4
5
5
5
3
5
5
5
3
3
3
3
3
5
5
3
5
3
Points earned
for correctly
answering these
questions
400
175
175
400
475
475
400
475
325
325
475
400
175
325
475
475
475
475
400
475
475
475
325
475
475
475
325
325
325
325
325
475
475
325
475
325
Second derivative test
Optimization
Applications of differentiation in biology, economics, etc.
Related rates
Mean value theorem
L’Hopital’s rule
Local linearization
Finding antiderivatives
Graphs of antiderivatives
Finding the constant of integration
Area under a rate function equals net change
Using rectangles to approximate area under a curve
Riemann Sums and sigma notation
Trapezoid Rule
The definite integral as the limit of a Riemann Sum
Evaluating a definite integral from a graph
Properties of integrals
Functions defined by integrals
The Fundamental Theorem of Calculus
Area between a curve and an axis
Evaluating definite integrals
Integration by u-substitution
Integration by the reverse chain rule
Area between two curves
Average value of a function
Volumes of solids of known cross section
Volumes of solids of revolution, discs, and washers
Page 4 of 4
3
3
3
3
3
5
3
3
5
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
325
325
325
325
325
475
325
325
475
325
325
325
325
325
325
325
325
325
325
325
325
325
325
325
325
325
325