Review for Calculus Midyear Exam

Please select a Team.

Team 1

Team 2

Team 3

Team 4

Team 5

0% 0% 0%0%0%

1. Rico StaRR

2. The Bushbabies

3. Smoldering Marshmallows

1. From David:Evaluate the limit.

2

4lim

2

0

x

xx

0 -2

Does n

ot exis

t

0% 0%0%

1. 0

2. -2

3. Does not exist

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

2. From Joe. Evaluate.

)(lim7xf

x

2 3 -7 D

NE

0% 0%0%0%

:10

1. 2

2. 3

3. -7

4. DNE

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

3. From Will.Which of the following is not true?

)(lim

1)(lim

)(lim

)(lim

)(lim

0

2

2

0

xf

xf

xf

xf

xf

x

x

x

x

x

A) B) C) D) E)

0% 0% 0%0%0%

1. A)

2. B)

3. C)

4. D)

5. E)

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

4. From Erica.

Why is the function discontinuous at x = -3?

0% 0%0%0%

1. The function doesn’t exist at the same place where it’s defined

2. The function is undefined

3. The limit doesn’t exist

4. The limit doesn’t exist at the same place where the

function is defined

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

5. From Meritt. How would you describe the function

between (-3,3) given the following table?

0% 0%0%0%

1. Increasing, concave up

2. Increasing, concave down

3. Concave down, decreasing

4. Decreasing, concave up

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

6. From Molly. Is the sketch on the right the derivative of the sketch on the left?

0%0%

1. Yes

2. No

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

7. From Nick. Which point(s) on the given function have a tangent line parallel to the line given?

52

2

1

3

1)( 23

yx

xxxf

X=1,2

X=-1,-2

X=1, -2 X=2

0% 0%0%0%

1. X=1,2

2. X=-1,-2

3. X=1, -2

4. X=2

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

8. From Sarah. What is the slope of the function at x=0?

32 8)4cos()( xxxf

0% 0%0%0%

1. 0

2. 1

3. -1

4. 0.5

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

9. From Emily. Looking at the graph of f’(x),

on what intervals is f(x) decreasing?

),7)(5,1(

),10)(5,(

0% 0%0%0%

1. 1. (-5, 10)

2. 2.

3. 3.

4. 4. (-1, 10)

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

10. From Jessica.True or False.

The given function is decreasing on the interval (-1,0).

23

2

1

3

1)( xxxf

0%0%

1. True

2. False

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

11. From Patrick.

Nathaniel is stuck on a train that is moving back and forth. To help save him, you must figure out when the car is stopped before it starts moving

in the other direction because this is the best time to jump aboard. Nathaniel is counting on you. You are his only hope. Between 0 and 10

second, where does the train stop?

2483

1)( 23 tttts

4 2 -4 -8

0% 0%0%0%

1. 4

2. 2

3. -4

4. -8

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

12. From Mo. What is the acceleration equation of this

function? ttttts 625)( 234

4660)(

6415)(

4660)(

64320)(

2

34

23

23

ttta

tttta

ttta

tttta

0% 0%0%0%

1. 1.

2. 2.

3. 3.

4. 4.

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

13. From Sky. The position of a small pony is modeled by the equation below. At 2 seconds, its instantaneous velocity

is 13 mph.True or False.

1052)( 2 xxxs

True

False

0%0%

1. True

2. False

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

14. From Fed.Find the derivative of f(x).

1

2)(

x

xxf

1. 2. 3. 4.

0% 0%0%0%

1. 1.

2. 2.

3. 3.

4. 4.

:10

1

2)('

)1(

2)('

1

24)('

)1(

24)('

2

2

xxf

xxf

x

xxf

x

xxf

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

15. From Bryan. Find the firs derivative.

)63(cos)() 2' xxxfA

)3(sin)( 2xxxf

)sin(cos)(') xxxxfB

)cos1(sin)() 2' xxxfC

)sin2cos(3)(') xxxxxfD

0% 0%0%0%

1. 1.

2. 2.

3. 3.

4. 4.

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

16. From Dan.Find the derivative.

2)cos()('

2)cos()('

2)sin()('

2)sin()('

22

22

22

22

xx

xx

xx

xx

eexf

eexf

eexf

eexf

)sin()( 2xexf

0% 0%0%0%

1. 1.

2. 2.

3. 3.

4. 4.

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

17. Evaluate the limit.

x

xxx

5lim

2

0

0 D

NE 5x 5

0% 0%0%0%

1. 0

2. DNE

3. 5x

4. 5

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

18. Evaluate.

)24)(2(

32lim

2

xx

xxx

Infinity -1 -2 2

0% 0%0%0%

1. Infinity

2. -1

3. -2

4. 2

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

19. At which x-value(s) is the function discontinuous?

232

121

13

)(

xx

x

xx

xf

1 -2

Both 1 and -2

None of t

he above

0% 0%0%0%

1. 1

2. -2

3. Both 1 and -2

4. None of the above

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

20. Consider the following information regarding f(x).What is the best description of f(x) at x=2?

f’(x) > 0 and f’’(x) < 0 for -1 < x < 2f’(2) = 0,

f’(x) < 0 and f’’(x) < 0 for x > 2.

Maxim

um

Inflecti

on point

X-interce

pt

Minim

um

0% 0%0%0%

1. Minimum

2. Inflection point

3. X-intercept

4. Maximum

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

21. Evaluate.

)(lim9

xfx

0% 0%0%0%

1. -2

2. 2

3. -9

4. DNE

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

22. In order, identify f(x), f’(x), f’’(x).

Blue, purp

le, gray

Purple, g

ray,

blue

Gray

, purp

le blue

0% 0%0%1. Blue, purple, gray

2. Purple, gray, blue

3. Gray, purple blue

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

23. To find the slope of a tangent line of f(x) which is parallel to a given line, you must set _____

equal to the ____ of the given line.

f(x);

derivative

f(x);

slope

f’(x);

x-inte

rcept

f’(x);

slope

0% 0%0%0%

1. f(x);derivative

2. f(x);slope

3. f’(x);x-intercept

4. f’(x);slope

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

24. Given the functionbelow, which intervals is it both concave up

and decreasing?

42)( 34 xxxf

)2

3,(

),(

),0)(1,2

3(),

2

3,(

),0)(1,(

0% 0%0%0%

1. 1.

2. 2.

3. 3.

4. 4.

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

25. The position of a cheetah is demonstrated by the function

below. What is the average velocity over the first two seconds?

)1(3)( 2 xxs x

44pmh

33 mph

22mph

0% 0%0%

1. 44pmh

2. 33 mph

3. 22mph

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

26. In a period of 10 seconds, Boris is doing a volleyball suicide. The

following function traces his movement. Which way is he going

at the 1st second?xxxxf 203

3

2)( 23

Left

Right

Stopped

0% 0%0%

1. Left

2. Right

3. Stopped

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

27. Given the function below, write an equation of the tangent

line drawn at x=2.

3

9)(x

xf

)2(16

27

8

9

)8

9(

16

272

)2(16

27

8

9

xy

xy

xy

1. 2. 3.

0% 0%0%

1. 1.

2. 2.

3. 3.

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

28. On what intervals is f(x) concave up?

),5.3)(2,(

)3,1)(2,(

)5.3,2(

)5.3,1)(2,(

1. 2. 3. 4.

0% 0%0%0%

1. 1.

2. 2.

3. 3.

4. 4.

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

29. A particle is moving left and right on a number line following the position of the function below. On

the interval of 1 to 10 seconds, when is the particle slowing down?

86)( 2 xxxs

0% 0%0%

1. Between 1 and 2 seconds

2. Between 1 and 3 seconds

3. Between 3 and 10 seconds

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

30. Find the derivative.

2

2

2

2

2

2

2

2

)3(

)4)(3(ln)2)(3()('

)3(

)4)(3)(3(ln)2)(3()('

)3(

)4)(3)(3(ln)2)(3()('

)3(

)4)(3(ln2)('

x

x

x

xx

x

xx

x

xxxf

xxxf

xxxf

xxxf

x

xxf

3

4)(

2

1. 2. 3. 4.

0% 0%0%0%

1. 1.

2. 2.

3. 3.

4. 4.

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

31. At which x-values does the following function have a horizontal tangent line?

xexxf 2)(

0% 0%0%0%

1. X=1, -2

2. X=0, -2

3. X=1, 0

4. X=-2 only

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

32. Derive.

xxxf 7)( 2

xx

xxf

xx

xxf

xx

xxf

7

7)('

72

72)('

72

2)('

2

2

2

1. 2. 3.

0% 0%0%

1. 1.

2. 2.

3. 3.

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

And now, the real test…

33. In which room is your Midyear exam ?

H4

H1

ME5

ME2

0% 0%0%0%

:10

1. H4

2. H1

3. ME5

4. ME2

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

34. Who is the assigned proctor to your exam?

Mrs.

Lahey

Mrs.

Lehmann

Mr. K

eaney

Mr. C

handler

0% 0%0%0%:10

1. Mrs. Lahey

2. Mrs. Lehmann

3. Mr. Keaney

4. Mr. Chandler

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

35. Are you allowed to use a calculator on your exam?

No

Yes

0%0%

1. No

2. Yes

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5

Last Question…

Derive.

yxyxyx 22 2

2

2

22

221

221

22

yyx

xyx

dx

dy

xyx

yyx

dx

dy

1. 2.

0%0%

1. 1.

2. 2.

:10

Team Scores

0 Team 1

0 Team 2

0 Team 3

0 Team 4

0 Team 5