Interactive video lesson plan for: AP Calculus AB 2010 #6 FRQ Free Response calc differential equation seperation of variables particul

Activity overview:

AP® CALCULUS AB
2010 SCORING GUIDELINES
Question 1
© 2010 The College Board.
Visit the College Board on the Web: www.collegeboard.com.
There is no snow on Janet’s driveway when snow begins to fall at midnight. From midnight to 9 A.M., snow
accumulates on the driveway at a rate modeled by f (t ) = 7tecos t cubic feet per hour, where t is measured in
hours since midnight. Janet starts removing snow at 6 A.M. (t = 6). The rate g(t ), in cubic feet per hour, at
which Janet removes snow from the driveway at time t hours after midnight is modeled by
( )
0 for0 6
125 for 6 7

(a) How many cubic feet of snow have accumulated on the driveway by 6 A.M.?
(b) Find the rate of change of the volume of snow on the driveway at 8 A.M.
(c) Let h(t ) represent the total amount of snow, in cubic feet, that Janet has removed from the driveway at time
t hours after midnight. Express h as a piecewise-defined function with domain 0 t 9.
(d) How many cubic feet of snow are on the driveway at 9 A.M.?
(a) ( ) 6
0
∫ f t dt = 142.274 or 142.275 cubic feet 2 : { 1 : integral
1
Question 2
© 2010 The College Board.
Visit the College Board on the Web: www.collegeboard.com.
A zoo sponsored a one-day contest to name a new baby elephant. Zoo visitors deposited entries in a special box
between noon (t = 0) and 8 P.M. (t = 8). The number of entries in the box t hours after noon is modeled by a
differentiable function E for 0 t 8. Values of E(t ), in hundreds of entries, at various times t are shown in
the table above.
(a) Use the data in the table to approximate the rate, in hundreds of entries per hour, at which entries were being
deposited at time t = 6. Show the computations that lead to your answer.
(b) Use a trapezoidal sum with the four subintervals given by the table to approximate the value of ( ) 8
0
1 . 8 ∫ E t dt
Using correct units, explain the meaning of ( ) 8
0
18
∫ E t dt in terms of the number of entries.
(c) At 8 P.M., volunteers began to process the entries. They processed the entries at a rate modeled by the function
P, where P(t ) = t3 − 30t2 + 298t − 976 hundreds of entries per hour for 8 t 12. According to the model,
how many entries had not yet been processed by midnight (t = 12) ?
(d) According to the model from part (c), at what time were the entries being processed most quickly? Justify

Entries are being processed most quickly at time t = 12.
3 :
1 : considers ( ) 0
1 : identifies candidates
1 : answer with justification
There are 700 people in line for a popular amusement-park ride
when the ride begins operation in the morning. Once it begins
operation, the ride accepts passengers until the park closes 8 hours
later. While there is a line, people move onto the ride at a rate of
800 people per hour. The graph above shows the rate, r(t ), at
which people arrive at the ride throughout the day. Time t is
measured in hours from the time the ride begins operation.
(a) How many people arrive at the ride between t = 0 and t = 3 ?
(b) Is the number of people waiting in line to get on the ride
increasing or decreasing between t = 2 and t = 3 ? Justify
(c) At what time t is the line for the ride the longest? How many people are in line at that time? Justify your
(d) Write, but do not solve, an equation involving an integral expression of r whose solution gives the earliest
Let R be the region in the first quadrant bounded by the graph of y = 2 x, the horizontal line y = 6, and the
y-axis, as shown in the figure above.
(a) Find the area of R.
(b) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is
rotated about the horizontal line y = 7.
(c) Region R is the base of a solid. For each y, where 0 ≤ y ≤ 6, the cross section of the solid taken
perpendicular to the y-axis is a rectangle whose height is 3 times the length of its base in region R. Write,
but do not evaluate, an integral expression that gives the volume of the solid.
The function g is defined and differentiable on the closed interval [−7, 5] and satisfies g(0) = 5. The graph of
y = g′( x), the derivative of g, consists of a semicircle and three line segments, as shown in the figure above.
(a) Find g(3) and g(−2).
(b) Find the x-coordinate of each point of inflection of the graph of y = g( x) on the interval −7 x 5.
(c) The function h is defined by h( x) = g( x) − 12 x2. Find the x-coordinate of each critical point of h, where
−7 x 5, and classify each critical point as the location of a relative minimum, relative maximum, or
neither a minimum nor a maximum. Explain your reasoning
Solutions to the differential equation ddyx xy3 = also satisfy ( ) 2
3 2 2
2 d y y 1 3x y .
dx
= + Let y = f ( x) be a
particular solution to the differential equation ddyx xy3 = with f (1) = 2.

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

Play this activity 1. Students enter a simple code 2. You play the video 3. The students comment 4. You review and reflect

* Whiteboard required for teacher-paced activities

Ready to see what else can do?

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.

Quickfire

Carry out a quickfire formative assessment to see what the whole class is thinking

Discuss

Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices

Clip

Turn any public video into a live chat with questions and quizzes

Spiral Reviews by Teachers and Digital Learning Coaches @kklaster

Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech @ordmiss

Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral @strykerstennis

Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks!

Get the Clip Chrome Extension & Create Video Lessons in Seconds

Add Clip to Chrome