Free Printable 11.7 Review (Modeling)

1.

Use the given function or the graph to find the average rate of change

a)

3

b)

-3

c)

3/2

d)

-1/3

2.

Use the given function or the graph to find the average rate of change

a)

5

b)

-1/5

c)

-5

d)

15

3.

Use the given function or the graph to find the average rate of change

a)

-1

b)

1

c)

1/2

d)

2

4.

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

a)

2

b)

1/2

c)

-2

d)

-1/2

5.

Which of the following intervals has the largest average rate of change?

a)

[13,14]

b)

[13, 17]

c)

[16, 17]

d)

[16, 19]

6.

What was the average rate of change in the population from 1900 to 1990?

a)

175 million people/year

b)

1.94 million people/year

c)

2.13 million people/year

d)

-1 million people/year

7.

Find the average rate of change over the given interval.

a)

4

b)

7

c)

7/3

d)

3/7

8.

f(x) = 2x² + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].

a)

2

b)

1/2

c)

-2

d)

-1/2

9.

What is the average rate of change of [1, 5]?

a)

-0.65

b)

-0.75

c)

3.75

d)

4

10.

Find the average rate of change over the given interval.

a)

4

b)

7

c)

7/3

d)

3/7

11.

What is Mrs. Gordon's rate from 0 to 2 seconds?

a)

2.5 feet per second

b)

.4 feet per second

c)

5 feet per second

d)

.2 feet per second

12.

Which company shows a greater rate of change?

a)

Water's Edge Rafts

b)

Ryan's Rafts

13.

Which of the following graphs or equations have an average rate of change of 2 from the x-values 0 to 3? (check all that apply)

a)

f(x)=x²+2x-3

b)

c)

d)

f(x)=x³-7x-1

e)

14.

Which of the following graphs has the largest average rate of change from -1 to 2?

a)

b)

c)

d)

15.

Which of the following graphs has the largest average rate of change from -1 to 2?

a)

b)

c)

d)

16.

Find the average rate of change of f(x)=2x²+3x-1 from 1 to 2.

a)

18

b)

-9

c)

9

d)

3

17.

The table below shows the snowfall in a north-eastern city in inches for the first week in January.

Find the average rate of change in the number of inches of snowfall from January 8 to January 11.

a)

2/3 in.

b)

2 in.

c)

3 in.

d)

6 in.

18.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

19.

Find the slope from the table:

a)

-2/5

b)

5/-2

c)

5/2

d)

2/5

20.

The solution to a system of equations is any ordered pair that makes both equations true.

a)

TRUE

b)

FALSE

21.

^{What is the solution?}

a)

1

b)

-2

c)

(1, 2)

d)

(1, -1)

22.

Steffen graphed two lines in order to find the solution to a given system of equations.
What is the solution?

a)

(-3,-8)

b)

(-8,-3)

c)

(3,-8)

d)

(8,3)

23.

What is the solution to this system?

a)

(-2, -2)

b)

(2, -2)

c)

(-2,2)

d)

(2, 2)

24.

This system has _____ solutions

a)

0

b)

1

c)

2

d)

Infinitely many

25.

Solve using substitution:

y = -6x + 5

-2x + y = 5

a)

(-3, -6)

b)

(-6, 3)

c)

(0, 5)

d)

(-3, 5)

26.

Solve with substitution

x = -3y - 8

x - 2y = -3

a)

(5, -1)

b)

(-5, 1)

c)

(-5,-1)

d)

(1,-5)

27.

Solve with substitution:

y = -2x + 18

y = 8

a)

(5, 8)

b)

(-5, 8)

c)

(2, 8)

d)

(-2, 8)

28.

Solve by elimination
-2x + 6y = 16
-4x - 3y = 2

a)

(2,2)

b)

(-2, -2)

c)

(-2,2)

d)

(2,1)

29.

Solve using elimination.
4x + 8y = 20
-4x + 2y = -30

a)

(-7,1)

b)

(2,-5)

c)

(-2,5)

d)

(7,-1)

30.

You can solve systems using these methods:

a)

graphing, substitution, and elimination

b)

rearranging, thinking, and guessing

c)

only by graphing

31.

Solve by elimination:
7x+y=-9

-3x-y=5

a)

No solution

b)

(1,8)

c)

(-2,-3)

d)

(-1,-2)

32.

Solve for x and y.
y = 2/3x - 2
y = -x + 3

a)

(0,3)

b)

(0,-3)

c)

(3,0)

d)

(-3,0)

33.

Solve for x and y
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

34.

Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3

a)

(0,3)

b)

(3,0)

c)

No solution(parallel lines)

d)

Infinitely many solutions

35.

Solve for y:
5x - y = 16

a)

-y = 5x + 16

b)

y = 5x + 16

c)

x = 5y - 16

d)

y = 5x - 16

36.

Solve for n:
2m - n = 8

a)

n = 2m - 8

b)

n = -2m - 8

c)

n = 2m + 8

d)

n = -2m + 8

37.

ax + c = R
(solve for x)

a)

ax = R + c

b)

ax = R - c

c)

x = a(R-c)

d)

x = (R-c) / a

38.

Solve:
12x - 4y = 20 , for y

a)

y = 3x - 5

b)

y = -3x + 5

c)

y = -3x - 5

d)

y = 3x + 5

39.

Solve the equation for w. ^{x = w / a}

a)

w = a / x

b)

w = x / a

c)

w = ax

d)

x = wa

40.

S = 3F - 24 Solve for F

a)

F = (S + 24)/3

b)

F = S/3 + 24

c)

F = 3S + 24

d)

F = 3(S + 24)

41.

pV = nRT

solve for R

a)

R= p/n + V/T

b)

R= pV - nT

c)

R= (pV-n)/T

d)

R=pV/nT

42.

Solve for x:
ax - b = c+d

a)

x = a(c + d + b)

b)

x = (c + d) / (a-b)

c)

x = a / (c + b + d)

d)

x= (c + b + d)/a

43.

pV = nRT

solve for n

a)

n= pV/RT

b)

n= p/R + V/T

c)

n= pV - RT

d)

n= (pV-R)/T

44.

Solve for x:

a)

x = yb - v

b)

x = by - v

c)

x = by + v

45.

Solve for p
$A\ =\ \frac{1}{2}pa$

a)

$A-\frac{1}{2}a\ =\ p$

b)

$\frac{2A}{a}=p$

c)

$\frac{A}{2a}=p$

d)

$2A-a\ =\ p$

46.

Solve for p
$SA\ =hp\ +\ 2B$

a)

$\frac{SA-2B}{h}=p$

b)

$\frac{SA}{h}-2B=p$

c)

$\frac{SA-h}{2B}=p$

d)

$SA-2B-h=p$

47.

Solve for h
$V\ =\ lwh$

a)

$V\ -l-w\ =\ h$

b)

$V-lw\ =\ h$

c)

$\frac{V}{lw}=\ h$

d)

$V-\frac{l}{w}=h$

48.

Solve for r:
$LA\ =\ 2\pi rh$

a)

$LA-2\pi h\ =\ r$

b)

$\frac{LA}{2\pi h}=\ r$

c)

$\frac{LA}{2}-\pi h\ =\ r$

d)

$\frac{2LA}{\pi h}=\ r$

49.

Solve for h:
$V\ =\ \frac{1}{3}\pi r^2h$

a)

$\frac{3V}{\pi r^2}=h$

b)

$\frac{1}{3}V\ -\pi r^2=h$

c)

$3V\ -\ \pi r^2=h$

d)

$\frac{1}{3}V\pi r^2=h$

50.

Solve for h:
$SA\ =\ 2\pi r^2+2\pi rh$

a)

$\frac{SA}{2\pi r^2+2\pi r}=h$

b)

$\ \frac{SA-2\pi r}{2\pi r^2}=h$

c)

$\frac{SA-2\pi r^2}{2\pi r}=h$

d)

$SA\ -\ \frac{2\pi r^2}{2\pi r}=\ h$

51.

Solve for c:

ax^2+bx+c=0

a)

$c\ =\ -ax^2-bx$

b)

$c\ =\ ax^2+bx$

c)

$c=\frac{ax^2}{bx}$

d)

$c=ax^2-bx$

52.

Solve for p:
$SA\ =\ \frac{1}{2}lp\ +B$

a)

$\frac{2SA-B}{l}=\ p$

b)

$\frac{2SA}{l}-B\ =\ p$

c)

$\frac{SA-B}{2l}=p$

d)

$\frac{2\left(SA-B\right)}{l}=p$

53.

Solve for x:
$m\ =\frac{x+y}{2}$

a)

$\ 2m-y=x$

b)

$\frac{2m}{y}=x$

c)

$\frac{m-y}{2}=x$

d)

$2\left(m-y\right)=x$

54.

When is this function increasing?

a)

-2.5 < x < 2.5

b)

0 < x < 5

c)

0 < x < 55

d)

-5 < x < 0

55.

a)

Decreasing Interval

b)

Increasing Interval

c)

Constant Interval

56.

What is f when x equals 0?

a)

-5

b)

0

c)

1/2

d)

1

57.

What is f when x equals 4?

a)

-5

b)

0

c)

3

d)

6

58.

What is f when x equals 8?

a)

0

b)

5

c)

11

d)

16

59.

Using the pictured graph, what is f(-3)?

a)

-3

b)

-1

c)

1

d)

3

60.

What is the RANGE of the function?

a)

All real numbers

b)

y ≤ 4

c)

y < 4

d)

0 ≤ y ≤ 4

61.

Which piecewise function corresponds to this graph? (Take your time)

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

62.

Find f(-2)

a)

-3

b)

6

c)

8

d)

-6

63.

Find f(0)

a)

-3

b)

18

c)

4

d)

0

64.

Match the graph with the correct equation.

a)

b)

c)

d)

65.

Evaluate f(-5)

a)

0

b)

2

c)

5

d)

-4

66.

Find f(2)

a)

f(2) = 0

b)

f(2) = 1

c)

f(2) = 3

d)

f(2) = 4

67.

A house painter charges $12 per hour for the first 40 hours he works, $18 for the ten hours after that, and $24 for all hours after that.

How much does he earn for a 70 hour week?

a)

$1020

b)

$1140

c)

$840

d)

He works for free!

11.7 Review (Modeling)

Total questions: 67

Worksheet time: 5hrs 56mins

Similar Resources on Wayground