Helpful Links

Khan Academy

Old AP Questions

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Calculus: The Musical!

Calculus Cheat Sheet

Calculus in Case You Forgot

Online Graphing Calculator

How to Succeed in AP Calc

Keep a calculus handbook full of useful information to be memorized

Memorize calculus handbook

Really memorize the fundamental theorem of calculus

Be prepared for class by printing out notes ahead of time and doing assigned homework

Don’t just copy the answer key for homework to get the credit; you aren’t helping anyone

Don’t be afraid to ask the teacher questions during class, during a free, or after school

Form a study group to work on homework with and to get help on difficult topics

At home, use textbook and various online tools such as Khan Academy when you are stuck

Take advantage of class time given to you to do homework – you can alleviate your homework load for that night and get help from the teacher

Teaching is the best way to learn, so help your classmates when they need it

Practice makes perfect, so do as many practice AP questions as possible

Take advantage of extra credit opportunities and test upgrades if offered

Information to Be Memorized

s(t) or x(t) means position at time t

v(t) means velocity at time t

a(t) means acceleration at time t

s’(t)=v(t)

s’’(t)=v’(t)=a(t)

s(t)=∫v(t) dt

v(t)=∫a(t) dt

Fundamental Theorem for Motion

s(a)=s(b)+∫_a^b v(t) dt

v(a)=v(b)+∫_a^b a(t) dt

displacement=∫v(t) dt

distance=∫|v(t)| dt

speed=|velocity|

speed is increasing when velocity and acceleration have same sign

speed is decreasing when velocity and acceleration have different sign

acceleration due to gravity is -32 ft/sec²

Answers

1. a) Matt is running at 150.653 m/sec when he crosses the finish line.

b) Matt is accelerating at 47.622 m/sec² when he crosses the finish line.

2. C

3. B

4. a) t=9 and t=15 because that’s where velocity changes sign

b) The particle has traveled 205 feet after 18 minutes.

c) The particle is 105 feet from its original location after 18 minutes.

5. B

6. a) The particle’s velocity at time t=10 is -9.041.

b) The particle’s acceleration at time t=10 is -357.706.

c) The particle is speeding up at time t=10 because v(10) and a(10) both have the same sign.

7. D

8. The distance between John and Thomas is growing at a rate of 3.259 mph after 15 minutes of driving.

9. A

10. C

10. (no calculator) Jimmy left New York at 8 AM to drive to San Francisco, 3000 miles away. His velocity for the trip is modeled by the function v(t)=4t. How far is Jimmy from San Francisco at 8 PM the first day?

a) 360 miles
b) 2640 miles
c) 2712 miles
d) 288 miles

Question 9

9. (no calculator) Winnie is running the 3200 meter race at the German Olympics Trials. He is confused as to which direction to run and accidentally runs the whole race backwards. His velocity is modeled by the function v(t)=-t² where distance is measured in meters and time in minutes. What is his speed 10 minutes into the race?

a) 100 m/min
b) -100 m/min
c) 20 m/min
d) -20 m/min

Question 8 (FRQ)

8. John and Thomas are in separate cars at an intersection. They both leave the intersection at the same time. John is travelling due north and is accelerating from 0 mph at 10 miles/hour^2. Thomas is travelling due east and accelerating at 15 miles/hour². How fast is the distance between John and Thomas growing 15 minutes after they leave?

Question 7

s(t)

7. Olivia is walking her dog, Piggy, up and down the street. The graph above represents her position, s(t), from her house for the first three hours of her walk. At what times t does Olivia change direction?

a) t=1.8 and t=2.5
b) t=1.25 and t=2.8
c) t=0, t=1.8, t=2.5, and t=3
d) t=1.25, t=2.1, and t=2.8

Question 6 (FRQ)

6. A particle is moving along the x-axis. Its position is modeled by the function x(t)=cos(t²+1).

(a) Find the particle’s velocity at time t=10.

(b) Find the particle’s acceleration at time t=10.

(c) Is the particle speeding up or slowing down at time t=10? Justify your answer.

Question 5

5. Sam is skiing down the mountain. His acceleration is modeled by the function
a(t)=2t²-10t-37. 5 minutes after leaving the summit, he is traveling at 30 mph. What is Sam’s velocity 10 minutes after leaving the summit?

a) 23.333 mph
b) 53.333 mph
c) 63 mph
d) 30 mph

Question 4 (FRQ)

4. A particle is moving along the x-axis. Its velocity is shown in the graph above in feet per minute.

a) At what times t does the particle change direction? Justify your answer.

b) How far has the particle traveled after 18 minutes?

c) How far is the particle from its original position at 18 minutes?

Question 3

3. (no calculator) Taylor drops her camera off the Golden Gate Bridge when sightseeing in California. If the bridge is 400 feet above the water, what is the camera's velocity when it hits the water?

a) 160 ft/sec
b) -160 ft/sec
c) 12800 ft/sec
d) -12800 ft/sec

Question 2

2. Caleigh is driving her car from home to school. Her velocity is modeled by the function v(t)=sin(t)+2 in miles per minute. How far is Caleigh from her house 5 minutes from when she left?

a) 1.041 miles

b) 0.284 miles

c) 10.716 miles

d) 13.487 miles

Question 1 (FRQ)

1. Matt is running in the 100 meter dash at Loucks Games. His position from the start line is modeled by the function s(t)=t³-10t²-5t-5. t represents time in seconds.

a) How fast is Matt running when he crosses the finish line?

b) How fast is Matt accelerating when he crosses the finish line?

Tuesday, June 4, 2013