This Activity Reviews the Following Calculus Topics

Calculus Review – Don’t Be Clueless

This activity reviews the following calculus topics:

Functions and Derivative Graphs Matching
Analyzing Limits
Definite Integrals from graphs
1st and 2nd Fundamental Theorems of Calculus
Evaluating derivatives at a given point
Slope Field and Differential Equation Matching
Position, Velocity, and Acceleration graph analysis

It was a long night in the library and a large group of students were gathering to study for the upcoming AP Calculus test. As the hours dragged on, the group became restless and the Calculus teacher stopped by to check on them. And then it happened! The lights went out and one student snapped. There was a scream and when the lights came back on, the teacher was lying dead on the floor. Who did it? Which student is the killer? To find the guilty person, solve the following groups of questions to reveal 6 clues. --- The guilty is among you. Was it you?

The Suspects

Number / Name / Sex / Right/Left / Hat / Hair / Driver? / Shirt
1 / F / Right / Yes / Dark / No / Purple
2 / F / Right / Yes / Fair / No / Green
3 / M / Right / Yes / Dark / No / Blue
4 / M / Left / No / Dark / Yes / Blue
5 / F / Right / No / Dark / Yes / Green
6 / F / Left / No / Fair / No / Purple
7 / M / Left / Yes / Red / Yes / Purple
8 / F / Left / Yes / Red / Yes / Purple
9 / F / Right / No / Red / Yes / Green
10 / M / Right / No / Red / Yes / Green
11 / F / Left / Yes / Dark / Yes / Blue
12 / M / Right / Yes / Dark / Yes / Blue
13 / F / Left / Yes / Dark / No / Purple
14 / F / Left / No / Dark / No / Purple
15 / M / Right / No / Dark / Yes / Purple
16 / F / Left / Yes / Fair / No / Blue
17 / F / Right / Yes / Dark / Yes / Green
18 / M / Left / Yes / Fair / No / Green
19 / F / Right / No / Fair / No / Blue
20 / M / Left / Yes / Dark / Yes / Blue
21 / F / Right / No / Dark / No / Blue
22 / M / Right / No / Fair / No / Green
23 / M / Right / No / Dark / No / Green
24 / M / Left / No / Red / Yes / Purple
25 / F / Left / No / Dark / Yes / Purple
26 / M / Right / Yes / Red / Yes / Purple
27 / M / Right / Yes / Fair / No / Blue
28 / M / Left / No / Fair / No / Blue
29 / M / Left / Yes / Dark / No / Green
30 / F / Left / No / Red / Yes / Green
31 / M / Left / No / Dark / No / Blue
32 / F / Right / Yes / Red / Yes / Green
33 / F / Right / Yes / Dark / No / Purple
34 / F / Right / Yes / Fair / No / Purple
35 / M / Right / Yes / Dark / No / Purple
36 / M / Left / No / Dark / Yes / Green
37 / F / Right / No / Dark / Yes / Blue
38 / F / Left / No / Fair / No / Blue
39 / M / Left / Yes / Red / Yes / Blue
40 / F / Left / Yes / Red / Yes / Green
41 / F / Right / No / Red / Yes / Purple
42 / M / Right / No / Red / Yes / Purple
43 / F / Left / Yes / Dark / Yes / Green
44 / M / Right / Yes / Dark / Yes / Green
45 / F / Left / Yes / Dark / No / Blue
46 / F / Left / No / Dark / No / Green
47 / M / Right / No / Dark / Yes / Blue
48 / F / Left / Yes / Fair / No / Blue
49 / M / Left / Yes / Fair / No / Green
50 / F / Right / No / Fair / No / Purple

Clue #1: Make a match in this line up.

Match each graph (#1-16) with the correct derivative graph to spell out a clue.

2. 3.

5. 6.

8. 9.

11. 12.

13. 14. 15.

16.

Derivative Graphs

L W S

T I K

R I O

E A R

L K R

Clue #2: Crime is a slippery slope.

Find the derivative of each function and evaluate at the given point. Then use the code to uncover the clue.

;

A / 4
B / -4
C / -1/5
D / 1
E / -1/4
F / -5
G / -1
H / 3
I / 24
J / -11
K / 15
L / 1/12
M / -1/3
N / -2
O / 2
P / -1/7
Q / 7
R / 0
S / 3/5
T / 5
U / -3
V / -21/4
W / 2/5
X / 6
Y / 10
Z / -6

;
;
;
;
;
;
;
;
;
;
;
;
; (0, 0)
;
;
;
; (1, 1)
;
;
; (1, -5)
; Find
; Find
;
;

Clue #3: There is no limit to what this criminal will do!

Place the letter next to the correct answer in the blank to spell out a clue.

___ 1. H) 5 T) 0 S) M) 1 G)

___ 2. = H) -3 O) ∞ A) DNE I) 1 E) 0

___ 3. = N) DNE D) 0 L) -1 R) E)

___ 4. What is

T) 0 W) 1 M) DNE K) -2 C)-1

___ 5. = I) U) A) -1 Y) W) ∞

___ 6. D) -1 N) E) P) L) None of these

___ 7. = D) L) T) S) P) -∞

___8. What is

A) 0E) 1I) DNE O) -3Y)5

___ 9. = S) R) N) 0 T) 14 F)

___ 10. = H) 7 I) 11 W) -11 F) 4 D) -7

___ 11. = R) 75 U) 10 I) DNE E) 25 N) 0

___ 12. = A) 1 N) O) 4 L) ∞ G) 0

____13. What is

N) 3 P) -3 T) ∞ C) 0 S) DNE

___ 14. = P) E) ∞ A) 5 L) -4 N) 1

___ 15. = I) 1 G) -1 M) DNE R) -6 E) 0

___ 16. = D) E) 1 O) -1 C) 0 A) -2

___ 17. = R) 0 S) T) ∞ O) A) None of these

___18. What is

R) 3 L) -3 H) ∞ C) -∞ D) -1

___ 19. E) -2 O) I) A) Y) None of these

___ 20. = M) 0 S) G) T) D) None of these

Clue #4: The murderer is hiding in the fields!

Match the differential equation with the correct slope field to reveal a clue.

_____ 1.

_____ 2.

_____ 3.

_____ 4.

_____ 5.

_____ 6.

_____ 7.

_____ 8.

_____ 9.

_____ 10.

_____ 11.

_____ 12.

_____ 13.

_____ 14.

_____ 15.

_____ 16.

Clue #5: The suspect is on the move.

Use the following 3 graphs to answer position, velocity, and acceleration questions.

Then swap your letters in for new letters to uncover the clue.

The figure to the right shows a graph of the velocity

of a moving object (along the x-axis) as a

function of time.

_____ 1. At which of the marked points

is the speed the greatest?

T) b H) c U) d X)f F) both choice T and H

_____2. At which of the marked points is

the object changing direction?

J) f F) a S)d A) b M) E

_____3. Which choice best describes the

object’s movement between points bandc?

G) The object is not moving.

W) The object is not accelerating, yet the object is moving forward.

J) The object is moving backwards.

Y) The object is accelerating.

N) The object is moving forward and accelerating.

_____ 4. Which choice best describes the object’s movement between points c and f?

G) The object is moving backward at a constant rate.

S) The object is moving backward at an increasing rate.

A) The object is not moving.

W) The object is slowing down and moving in a negative direction.

U) The object is slowing down while moving in a positive direction.

_____ 5. Which choice best describes the object’s movement between points d and e?

J) The object is slowing down while moving in a negative direction.

R) The object is speeding up.

M) The object has stopped moving.

Y) The object is moving faster in a negative direction.

S) The object has constant speed during this interval, but not constant velocity.

_____ 6. What is the object’s acceleration from points a to b?

W) -2 S) 4 T) 0 Y) 2 M) 1/2

____ 7. What is the distance traveled by the object between point a and f?

W) 18 J) 20 H) 6 Y) 16 L) 7

------

A biker starts at Park A at time (sec) and travels along a straight path to Park B. For , the biker’s velocity (ft/sec) is modeled by the piecewise-linear function defined by the graph shown.

______8. What is the biker’s position at t= 18 ?

S) 115 J) 10 A) 225 N) 25 M) 95

______9. What is the total distance traveled by the biker from t =0 to t = 18?

T) 95 ft S)115 ft Y) 215 ft B) 10 ft X) 25 ft

______10. When does the biker change direction?

J) t= 9 sec D) t = 15 sec G) t = 2 sec L) t = 7 sec N) t= 9 and 15 sec

______11. At what time is the biker furthest from Park A?

G) t = 7 sec W) t = 9 sec K) t = 15 sec N) t = 16 sec A) t = 18 sec

______12. What is the biker’s acceleration at t = 8?

A) -10 ft/sec2 W) 10 ft/sec2 J) 130 ft/sec2 Y) 0 ft/sec2 N) -1/10 ft/sec2

______13. How many times is the biker 100 feet from Park A between ?

Y) Never L) 1 H) 2 X) 3 C) 4 R) 5

______14. What is the biker’s velocity at t = 4?

G) 0 ft/sec I) 20 ft/sec R) 60 ft/sec K) 5 ft/sec W) 1/5 ft/sec

------

The velocity of a remote control car is recorded for the first 20 seconds and plotted on the graph above. The car’s initial position at t = 0 was 13m. Use the velocity graph to answer the questions below.

______15. Approximately, at what moment(s) in time does the car change direction?

J)5 sec S) 6 sec A) 12 sec T) 12.5 sec P) Both J and A N) Both S and T

______16. At which of the following moments is the velocity of the car the greatest?

W)5 sec Y) 10 sec O) 13 sec C) 14 sec L) 15 sec R) 20 sec

______17. At which of the following moments is the acceleration of the car the greatest?

J)4 sec B) 5 sec S) 6 sec A) 10 sec M) 14 sec P) 15 sec

______18. What is the greatest speed (m/sec) of the car during this 20 second interval?

G)6 Y) 3 B) 5 K) 14 M) 10 W) 2

______19. At what moment(s) in time is the car not moving?

G)1 sec S) 10 sec N) 17 sec T) 19.5 sec B) All G, S N, and T J) Both G and T

______20. Approximately what is the total distance traveled by the car from ?

I)-12m U) -1m G) 48 m D) 35 m X) 24 m

______21. Approximately what was the car’s position at t = 10?

Y) 14 J) 2 X) 1 L) -6 I) 26

______22. What is the car’s final position at t = 20?

J) 48 Y) -12 X) 35 F) 12 P)1

Top row is YOUR answer. Swap it out for the letter below in the second row.

S / M / L / K / J / D / C / B / A / E / F / G / H / I / N / U / V / W / X / Y / T / Z / R / Q / P / O
A / B / C / D / E / F / G / H / I / J / K / L / M / N / O / P / Q / R / S / T / U / V / W / X / Y / Z

Clue #6:There is definitely a problem here.

Solve the definite integral problem and then use the code to spell out your clue.

Let g be the function given by .

_____ 1. Find the value of

_____ 2. Find the value, if possible, of

_____ 3. Find the value, if possible, of

A / 3
B / -4
C / -7.5
D / 2
E / 9
F / -3
G / 6.5
H / 1/3
I / 0
J / 7.5
K / 1/2
L / -1/3
M / Not Possible
N / 1
O / -1/2
P / 4
Q / 8
R / -2
S / 5
T / -1
U / 7
V / -5
W / -9
X / -3.5
Y / 6
Z / -2.5

_____ 4. Find the value, if possible, of

Let h be the function given by

_____ 5. Find the value of

_____ 6. For which of the values of x,on the interval (0, 3), is

_____ 7. Find the value, if possible, of

_____ 8. Find the value, if possible, of

_____ 9. Find the value of

Use the graph of w(x) to find the values of the definite integrals.

_____ 10.

_____ 11.

_____ 12.

_____ 13.

_____ 14.

_____ 15.

_____ 16.

_____ 17.

_____ 18.

Team Name ______

Team Members

______

Clue #1: ______

Clue #2: ______

Clue #3: ______

Clue #4: ______

Clue #5: ______

Clue #6: ______

The Killer is: ______