ap sets 2014-2015

Name: Due:

AP FRQ 1A Partner(s):

1) (Non-Calculator)

Draw a function 𝑓(𝑥) such that:

𝑓(2) = 3

lim𝑥→2+

𝑓(𝑥) 𝑑𝑛𝑒

lim𝑥→2−

𝑓(𝑥) = −1

2) (Non-Calculator)

Write a function 𝑓(𝑥) such that:

𝑓(𝑥) has a hole at 𝑥 = 2 and a vertical asymptote at 𝑥 = −1. (Answers will vary)

3) 2008 MC #77 (Calculator)

The figure above shows the graph of a function f with domain 0 4 x . Write the limit, or state that it does not

exist. If the limit does not exist, explain why.

I) lim𝑥→2−

𝑓(𝑥)

II) lim𝑥→2+

𝑓(𝑥)

III) lim𝑥→2

𝑓(𝑥)

1 2 3 4

x

y

9

152)(

2

2

x

xxxf

Name: Due:

AP FRQ 1B Partner(s):

1) (Non-Calculator)

(a) Find all discontinuities of 𝑓(𝑥).

(b) Identify each discontinuity as removable or non-removable.

(c) If removable, give the coordinates of the hole.

(d) If the graph has any vertical asymptotes, use one-sided limit notation to describe the behavior on each side of

the asymptote.

2) 2014 AB 4 (Non-Calculator)

b) Do the data in the table support the conclusion that train A’s velocity is -100 meters per minute at some time 𝑡

with 5 < 𝑡 < 8? Give a reason for your answer.

Name: Due:

AP FRQ 1C Partner(s):

1)

535

301)(

xforx

xforxxf

(a) Graph the function.

(b) Is f continuous at x = 3? Using the definition of continuity, explain why or why not.

(c) Is f differentiable at x = 3?

Use the definition of differentiability at a point and one sided limits to justify your answer.

(d) Are we guaranteed that f(c) = 1 for some c in the interval [3, 5] ? Justify your answer.

2) 2007 AB3 (Calculator)

𝑥 𝑓(𝑥) 𝑔(𝑥) 1 6 2 2 9 3 3 10 4 4 -1 6

The table above gives selected values of the functions 𝑓 and 𝑔 at selected values of 𝑥. Both functions are

continuous. The function ℎ is given by ℎ(𝑥) = 𝑓(𝑔(𝑥)) − 6. Explain why there must be a value 𝑟 for 1 < 𝑟 < 3,

such that ℎ(𝑟) = −5.

-4 -2 2 4

-4

-2

2

4

x

y

Name:

AP Set #2A Partner(s):

2008 MC #6 – without graphing calculator

2if1

2if)( 2

42

x

xxf x

x

Let f be the function defined above. Which of the following statements about f are true?

I. f has a limit at x = 2.

II. f is continuous at x = 2.

III. f is differentiable at x = 2.

(A) I only (B) II only (C) III only (D) I and II only (E) I, II, and III


2for x

2for )(

2 xcx

xdcxxf

Let f be the function defined above, where c and d are constants.

If f is differentiable at x = 2, what is the value of c + d ?

Name:

AP Set #2B Partner(s):


If y = 23

32

x

x, then

dx

dy

(A) 2

23

1312

x

x (B)

223

1312

x

x (C)

223

5

x (D)

223

5

x (E)

3

2

2013 FR #6 (modified) – without graphing calculator

The function 𝑦 = 𝑓(𝑥) passes through the point (1,0) and has the derivative 𝑑𝑦

𝑑𝑥= 𝑒𝑥(3𝑥2 − 6𝑥). Write an equation

for the tangent to the graph of 𝑓 at the point (1,0).

Name:

AP Set #2C Partner(s):

2008 MC #86 – with graphing calculator

t 0 1 2 3 4

)(tv –1 2 3 0 –4

The table gives selected values of the velocity, ),(tv of a particle moving along the x-axis. At time t = 0, the particle

is at the origin. Which of the following could be the graph of the position, ),(tx of the particle for ?40 t

2013 FR #2 – with graphing calculator

A particle moves along a straight line. For 0 ≤ 𝑡 ≤ 5, the velocity of the particle is given by

𝑣(𝑡) = −2 + (𝑡2 + 3𝑡)6

5 − 𝑡3, and the position of the particle is given by 𝑠(𝑡).

(a) Find all values of 𝑡 in the interval 2 ≤ 𝑡 ≤ 4 for which the speed of the particle is 2.

(b) Find all times 𝑡 in the interval 0 ≤ 𝑡 ≤ 5 at which the particle is at rest. Justify your answer.

(c) Find all times 𝑡 in the interval 0 ≤ 𝑡 ≤ 5 at which the particle changes direction. Justify your answer.

(d) Is the speed of the particle increasing or decreasing at time 𝑡 = 4? Give a reason for your answer.

Name:

AP Set #2D Partner(s):


If y = 2 3 1x , then dx

dy

(A) 2 23x (B) 12 3 x (C) 132 2 x (D) 13 32 xx (E) 16 32 xx


If ,)2)(1()( 32 xxxf then )(xf

(A) 22 )2(6 xx (B) 22 )2)(1(6 xxx (C) )13()2( 222 xxx

(D) )267()2( 222 xxx (E) 22 )2)(1(3 xx

FRQ – without graphing calculator

Using the function 𝑔(𝑡) = −16𝑡2 + 8𝑡, answer the following questions.

(a) What is the equation of the tangent line to g(t) at the point (0.5, 0) ?

(b) At what t value does the function have a horizontal tangent line?

(c) If g(t) represents a position function, what is the average velocity for the interval [0, 0.5]?

(d) If g(t) represents a position function, what is the velocity at t = 2?

(e) If g(t) represents a position function, what is the average acceleration for the interval [0, 0.5]?

(f) If g(t) represents a position function, what is the acceleration at t=2?

Name:


2012 FRQ #4 (No Calculator)

Name: Due:


2008 (Form B) FRQ #6 (No Calculator)

Name: Due:


(Calculator Allowed)

Sand is falling from a rectangular box container whose base measures 40 inches by 20 inches at a constant rate of 300

cubic inches per minute. (V = LWH.)

(a) At what rate is the height, H, of the sand in the box changing?

(b) The sand is forming a conical pile (V = 1

3𝜋 𝑟2 ℎ). At a particular moment, the pile is 23 inches high and the radius of

the base is 8 inches. The radius of the base at this moment is increasing at 0.75 inches per minute.

At this moment,

(i) how fast is the area of the circular base of the cone increasing?

(ii) how fast is the height of the pile increasing?

Name: Due:


2009 (Form B) FR #3 – with graphing calculator

Name: Due:


2014 FR #3 – without graphing calculator

Let 𝑔′(𝑥) = 𝑓(𝑥). The graph of 𝑓(𝑥) is shown to the right. Let 𝑔(3) = 9.

(a) On what open intervals contained in −5 < 𝑥 < 4 is the graph of g

increasing? Justify your answer.

(b) On what open intervals contained in −5 < 𝑥 < 4 is the graph of g

concave down? Give a reason for your answer.

(c) The function ℎ is defined by ℎ(𝑥) =𝑔(𝑥)

5𝑥. Find ℎ′(3).

(d) The function 𝑝 is defined by 𝑝(𝑥) = 𝑓(𝑥2 − 𝑥). Find the slope of the line tangent to the graph of 𝑝 at the

point where 𝑥 = −1.

Name: Due:


2014 FR #5—without graphing calculator

Name: Due:


2010 FR #6 (modified) – without graphing calculator

The function 𝑦 = 𝑓(𝑥) passes through the point (1,2) and has first derivative 𝑑𝑦

𝑑𝑥= 𝑥𝑦3 and second derivative

𝑑2𝑦

𝑑𝑥2 =

𝑦3(1 + 3𝑥2𝑦2).

(a) Write an equation for the tangent to the graph of 𝑓 at 𝑥 = 1.

(b) Use the tangent line from part (a) to approximate 𝑓(1.1). Given that 𝑓(𝑥) > 0 for 1 < 𝑥 < 1.1, is the

approximation for 𝑓(1.1) greater than or less than 𝑓(1.1)? Explain your reasoning.

Name: Due:


2011 (Form B) FR #5 – without graphing calculator

Name: Due:


2012 AB3 – without graphing calculator

Name: Due:


2013 AB1 – with graphing calculator

Name: Due:


2012 AB1—with calculator

Name: Due:


2014 FR #1 – with graphing calculator

Name: Due:



Name: Due:


2014 FR#1 – with graphing calculator

ap sets 2014-2015

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