AP Calculus BC
Summer Assignment 2015
First: Please don’t throw away your Calculus AB stuff!
Second: Your “Summer Assignment” is to refresh Chapters 1-3 of Calculus before coming to school so that you are ready for a Test on those chapters within the first/second week of school. DO NOT DO THIS PACKET IN JUNE!
Third:I will post the solutions in August. You need to check your solutions, try to fix the problems you got wrong and come in with problems highlighted that you still don’t understand. This means the packet is NOT collected-so please don’t copy it from each other. It is for you to use to test yourself and to check your understanding. I will be checking whether or not you do it on the FIRST DAY OF CLASS, but it is NOT a grade. It will, however, help you tremendously on your first test! Please ask for help on it once school starts!
Fourth: Please sign up for Remind for BC Calc. That way I can communicate with you when the assignment solutions are posted and give you a link to the online syllabus we are using.
Fifth:**If you would like to check out a textbook see Ms. Beezer in room 138!!
BC Calculus: Summer Assignment NAME ______
Ch. 1, 2, & 3 DATE ______PER _____
#1-12 Multiple Choice: Write the letter of the BEST answer.
Show your process! NO calculator!
_____ 1) Given , find .
a) 16 b) 5 c) 4 d) 1 e) The limit does not exist.
_____ 2) Use the accompanying graph to determine which of the following statements are true.
I. is continuous at .
II. exists.
III.
IV.
a) I and II b) II and III c) III and IV d) I and IV e) I, III, and IV
_____ 3) Let .
If is continuous on the entire real line, what must be the value of a?
a) b) c) 4 d) 15 e) none of these
_____ 4) Find .
a) 0 b) c) d) e) none of these
_____ 5) Find the instantaneous rate of change at of the function f given by .
a) b) c) d) 2 e) 4
_____ 6) If , , and , what is ?
a) b) c)
d) e) 2
_____ 7) A circular conical tank, vertex down, has depth 4 feet and radius of the top 6 feet.
If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of
change of depth of water when the water is 2 feet deep. Draw and label a diagram!
[HINT: ]
a) b) c) d)
_____ 8) Let f be a function such that .
Which of the following must be true?
I. The derivative of f is continuous at .
II. f is continuous at .
III. f is differentiable at .
a) I only b) II only c) I and II only
d) I and III only e) II and III only
_____ 9) The derivative of is given by . In which of the
following open intervals is f is decreasing?
a) b) c)
d) only e)
_____ 10) A bug begins to crawl up a vertical wire at time . The velocity v of the bug at
time t, , is given by the function whose graph is shown above. At what
value of t does the bug change direction?
a) 2 b) 4 c) 6 d) 7 e) 8
_____ 11) For , what is the ordered pair (a, b) if the point is an extrema of f ?
a) b) c) d) e)
_____ 12) Find if .
a) b)
c) d)
#13-16 Completion. Show all work.
13) Suppose that . What is and WHY??
14) Determine the continuity of
15) Show that has a value c in the interval [1,2]
such that .
16) Find each limit.
a) b)
BC Calculus: Summer Assignment NAME ______
Ch. 1, 2, & 3 DATE ______PER _____
#17-21 Multiple Choice: Write the letter of the BEST answer.
Show your work! You may use a calculator.
_____ 17) The curve passes through the point . Use the equation of the
tangent line to the curve at the point to approximate .
a) 0.45 b) 0.475 c) 0.5 d) 0.525 e) 0.55
_____ 18) Use TI-83. For what value of x does the graph of the function
change concavity?
a) -1.58 b) -1.63 c) -1.67 d) -1.89 e) -2.33
_____ 19) What is the area of the largest rectangle with lower base on the x-axis and upper vertices on
the curve ?
a) 8
b) 12
c) 16
d) 32
e) 48
_____ 20) Which value of x best approximates the value which satisfies the Mean Value Theorem for
the function on the interval .
a) 0.265
b) 1.158
c) 1.555
d) 3.657
e) 3.764
_____ 21) At what point on the curve is the tangent line vertical?
a) only
b) only
c) only
d) and
e) The tangent line is never vertical.
22) The function has a zero between 1 and 2. Use with
three iterations of Newton’s Method to approximate this zero to 4 decimal places.
Show work to earn credit.
23) The function for describes the motion of a particle moving along a
line.
a) Find the velocity function of the particle at any time t.
b) Identify the time(s) when the particle is changing its direction.
c) Identify the time intervals when the particle is moving in a negative direction.
d) What is the value of the velocity when the acceleration is 0?
e) Describe the particle’s speed.