Pre-Test - Hialeah High

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Chapter 2 Assessments 815

2

Pre-Test

Name Date

1. An elevator in a high-rise building moves upward at a constant rate. The table shows the height of the elevator above the ground floor after various times.

Time Height

Units Seconds Feet

0 0

1 12

2 24

3

4.5

5

Expression t

a. What are the dependent and independent quantities in this problem situation? Explain your reasoning.

b. Determine the unit rate of change for the problem situation.

c. Complete the table. Write an expression that represents the height for an arbitrary time t seconds in the last row.

d. Use function notation to determine the height of the elevator at a time of 14 seconds.

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816 Chapter 2 Assessments

2

2. Solve the equation and justify your reasoning.

5(x 1 4) 2 8 5 x 1 32

3. Suppose an elevator starts at the top floor of a high-rise building at a height of 372 feet above the ground floor and descends without stopping at a constant rate of 15 feet per second.

a. Write a function that describes the height, h, of the elevator after t seconds.

b. Graph the function that you wrote in part (a).

Pre-Test page 2

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Pre-Test page 3

Name Date

c. Estimate when the elevator is at a height of 200 feet.

d. Determine the exact time that the elevator is at a height of 200 feet.

4. Evaluate the function f(x) 5 31.572x 2 17.741 at each of these values.

a. f(6.2)

b. f(227.018)

5. Solve the inequality and graph the solution on the number line.

24(x 1 1) $ 12

6. Graph the compound inequality on the number line.

x , 4 and x $ 21

25 24 23 22 21 0 1 32 4 5

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Pre-Test page 4

7. Evaluate each expression. Show your work.

a. |4 – 12| b. |28(7)|

8. Solve the absolute value equation.

|2x 2 5| 5 7

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2 1. Elena works a part-time job after school to earn money for a summer vacation. She is paid a constant

rate for each hour she works. The table shows the amounts of money that Elena earned for various amounts of time that she worked.

Time Worked Amount Earned

Units Hours Dollars

2.5 22.50

3 27.00

3.5 31.50

4.5

5

6

Expression t

a. What are the dependent and independent quantities in this problem situation? Explain your reasoning.

b. Determine the unit rate of change for the problem situation.

c. Complete the table. Write an expression that represents the amount of money Elena earns for an arbitrary time worked of t hours.

d. Use function notation to determine the amount of money that Elena earns for working 7.5 hours.

Post-Test

Name Date

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Post-Test page 2

2. Solve the equation and justify your reasoning.

24(x 1 1) 2 9 5 212x 1 11

3. Malik received a $300 gift card from his grandparents and is using it only to pay for his karate lessons, which cost $28 per month.

a. Write a function that describes the dollar amount of money d, on the card after t months.

b. Graph the function that you wrote in part (a).

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Post-Test page 3

Name Date

c. Malik decides he wants to use the last of the gift card to buy some karate equipment that will cost $75. Estimate when there will be $75 remaining on the card.

d. Determine exactly when there will be $75 remaining on the card.


a. f(12.605)

b. f(21.0092)

5. Solve the inequality and graph the solution on the number line.

23(x 2 3) , 24

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6. Graph the compound inequality on the number line.

x . 23 and x # 2

25 24 23 22 21 0 1 32 4 5


a. |27 2 6| b. | 36 ___ 24

|

8. Solve the absolute value equation.

|22x 1 7| 5 11

Post-Test page 4

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Mid-Chapter Test

Name Date

1. A helicopter takes off from the ground and moves upward at a constant rate of 22 feet per second.

a. What are the dependent and independent quantities in this problem situation? Include the units for each quantity. Explain your reasoning.

b. Write the independent and dependent quantities and their units in the table. Then calculate the height of the helicopter at each of the given times. In the last row, write an expression that represents the dependent quantity in terms of the independent quantity.

Independent Quantity Dependent Quantity

Quantity

Units

0

1

2.5

5

10.5

15

20

Expression t

c. Use function notation to express the height of the helicopter as a function of time. What type of function is this?

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Mid-Chapter Test page 2

d. Create a graph to represent the height of the helicopter over time. Be sure to label the axes and the function.

e. Identify the slope and y-intercept of the graph. Describe what each means in terms of this problem situation.

f. Estimate when the helicopter is at a height of 250 feet. Explain your answer.

g. Determine exactly when the helicopter is at a height of 250 feet. Explain your answer.

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2 2. Solve each equation. Show your work.

a. 3x 1 9 5 6(x 2 2) b. x 1 3 _____ 12

5 2 __ 7

3. While on a trip to Japan, Patricia has 642.75 Japanese yen (symbol ¥) and needs to exchange more of her U.S. dollars for Japanese yen. The exchange rate from U.S. dollars to Japanese yen is ¥77.962 to every dollar.

a. Write a function that represents the amount of Japanese yen that Patricia will have after converting U.S. dollars to yen. Define your variables.

b. Classify the function your wrote in part (a). Explain your reasoning.

c. Determine the amount of money in Japanese yen Patricia will have if she exchanges an additional $250. Show your work.


Name Date

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d. Determine how much Japanese yen Patricia will have after exchanging different amounts of U.S. dollars. Round to the nearest yen if necessary.

U.S. Dollars Japanese Yen

$100

$150

$200

¥24,031

¥30,736


a. f(21.041)

b. f(2.885)

5. Determine the independent value which results in the given function value.

a. f(x) 5 227.083x 2 16.819 when f(x) 5 211.246

b. f(x) 5 0.313x 2 7.281 when f(x) 5 28.836

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End of Chapter Test

Name Date

1. A faucet leaks water at a constant rate. Tara places a measuring cup under the leak to catch the water. The table shows the number of milliliters of water in the cup at different times.

Time Amount of Water

Units Hours Milliliters

3.5 14

4 16

4.5 18

5

5.5

6.5

Expression t

a. Complete the table. In the last row, write an expression that represents the amount of water in the cup for an arbitrary time t hours.

b. Use function notation to determine the amount of water in the cup after the faucet leaks at a constant rate for 12 hours.

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2. Solve the equation.

27(x 1 1) 2 6 5 241x 1 55

3. Gina has saved $420. She plans to spend $35 each month for music lessons. The function s(t) 5 235t 1 420 describes her savings s in dollars as a function of the time t in months.

a. Graph the function that describes Gina’s savings s as a function of the time she works, t.

b. Estimate how much Gina will have left of her savings after 10 months.

End of Chapter Test page 2

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Name Date

4. Evaluate the function f(x) 5 7.45x 1 33.7 at x 5 24.3.

5. Riley buys pairs of socks for $4 a pair and a sweater for $35. She has $50. Write an inequality that shows the number of pairs of socks s she can buy without spending more than $50.

6. Solve each inequality, and graph the solution on the number line.

a. 2 3 __ 7 x # 2

b. 81 . 69 2 x

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7. The graph represents the temperature range in a city over 20 hours. Luke hates extreme cold and decides he will only go outside when the temperature is 30° or greater. Draw a circle on the graph to represent when Luke will go outside.

0

40

45

30

20

10

35

25

15

5

4 8 12 16 182 6 10 14x

y

Time (hours)

Tem

per

atur

e (d

egre

es F

ahre

nhei

t)

8. A number is less than 24 or greater than 35. Write a compound inequality that represents the possible values of the number. Then graph the compound inequality on the number line.

9. Represent the solution to each compound inequality on the number line shown. Then, write the final solution that represents the graph.

a. x , 21 or x , 3

25 24 23 22 21 0 1 32 4 5

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Name Date

b. x , 1 and x . 22

25 24 23 22 21 0 1 32 4 5


a. |8| 2 |22| b. | 281 _____ 9 |

11. Evaluate each linear absolute value equation. Show your work.

a. 41 5 |x 2 6| 1 18

b. 52 5 7|x 2 2| 2 4

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12. Solve the linear absolute value inequality. Then graph the solution on the number line.

8 # |3x 2 2|

25 24 23 22 21 0 1 32 4 5

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2 1. Jasmin is practicing her juggling act. She tosses one ball straight up in the air to a maximum height

of 16 feet. She knows she can then toss the second ball any time the first ball is at a height greater than 10 feet. Which graph correctly represents this problem situation using an oval to represent the time when she can toss the second ball?

a.

0

16

18

12

8

4

14

10

6

2

4 8 12 16 182 6 10 14x

y

Time (seconds)

Hei

ght

(feet

)

b.

0

16

18

12

8

4

14

10

6

2

4 8 12 16 182 6 10 14x

y

Time (seconds)

Hei

ght

(feet

)

c.

0

16

18

12

8

4

14

10

6

2

4 8 12 16 182 6 10 14x

y

Time (seconds)

Hei

ght

(feet

)

d.

0

16

18

12

8

4

14

10

6

2

4 8 12 16 182 6 10 14x

y

Time (seconds)

Hei

ght

(feet

)

Standardized Test Practice

Name Date

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Standardized Test Practice page 2

2. What is the solution to the compound inequality 85 # 17m # 136?

a. 5 # m or m # 8

b. 5 # m and m # 8

c. 5 $ m or m $ 8

d. 5 $ m and m $ 8

3. What is the solution to the equation 4(x 2 3) 2 8 5 16?

a. 1

b. 3

c. 7

d. 9

4. Alex saved $65. He has already spent $25. He plans to spend $8 on a movie ticket each month. Which inequality represents the number of movie tickets he can buy?

a. 8t 1 25 # 65

b. 8t 2 25 # 65

c. 28t 1 25 # 65

d. 28t 2 25 # 65

5. Which graph represents the compound inequality x , 232 or x . 24?

a.

250 240 230 220 210 0 10 3020 40 50

b.

250 240 230 220 210 0 10 3020 40 50

c.

250 240 230 220 210 0 10 3020 40 50

d. 250 240 230 220 210 0 10 3020 40 50

6. Determine the unit rate of change of the ordered pairs (1140, 1) and (1450, 4).

a. 21240

b. 0.010

c. 0.788

d. 103.33

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Name Date

7. What is the value of the linear absolute value expression |215| 2 |8 2 14|?

a. 221

b. 29

c. 9

d. 21

8. What is the solution to the inequality 8(7 2 x) , 64?

a. x , 21

b. x , 1

c. x . 21

d. x . 1

9. Thomas is training for a marathon. He runs the first 3 miles of his practice run at a constant speed. Which function could be used to represent the distance Thomas runs, d, in terms of his speed, s?

a. d(s) 5 3s

b. d(s) 5 3 __ s

c. s(d) 5 3d

d. s(d) 5 3s

10. What is the value of the linear absolute value expression | 217 1 8 ________ 4 | ?

a. 29 ___ 4

b. 9 __ 4

c. 225 _____ 4

d. 25 ___ 4

11. Which compound inequality has no solution?

a. x , 5 and x , 22

b. x . 5 and x , 24

c. x . 5 or x , 24

d. x , 5 or x , 22

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12. The graph shows which intersection?

240 230 220 210 0 10

10

210

220

230

240

20

30

40

20 30 40x

y

a. f(x) 5 22x 1 10 when f(x) 5 26 1 __ 2

b. f(x) 5 22x 2 10 when f(x) 5 26 1 __ 2

c. f(x) 5 22x 1 10 when f(x) 5 226 1 __ 2

d. f(x) 5 22x 2 10 when f(x) 5 226 1 __ 2

13. What is the solution to the linear absolute value equation |2x 1 18| 5 7?

a. x 5 211 or x 5 25

b. x 5 211 or x 5 225

c. x 5 11 or x 5 211

d. x 5 11 or x 5 25

14. What is the solution to the linear absolute value equation 102 5 211|x 1 16| 2 19?

a. x 5 25 or x 5 227

b. x 5 25 or x 5 27

c. x 5 5 or x 5 227

d. No solution

15. What is the value of f(x) 5 23.25x 1 22.41 at x 5 24.2?

a. 28.76

b. 2.70

c. 11.10

d. 36.06

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Name Date

16. Which graph shows the solution to the inequality 2 7 ___ 12 x . 3?

a.

212 210 28 26 24 22 0 42 6 8

b.

212 210 28 26 24 22 0 42 6 8

c.

212 210 28 26 24 22 0 42 6 8

d. 212 210 28 26 24 22 0 42 6 8

17. What is the solution to the linear absolute value equation 4|2x 2 6| 1 3 5 19?

a. x 5 21 or x 5 25

b. x 5 21 or x 5 5

c. x 5 1 or x 5 5

d. x 5 1 or x 5 25

18. The graph shows the solution to which linear absolute value equation?

225 220 215 210 25 0 5 1510 20 25

a. 35 # |2x 2 5|

b. 35 # |2x 1 5|

c. 25 # |2x 2 5|

d. 25 # |2x 1 5|

19. Which compound inequality does the graph represent?

212 210 28 26 24 22 0 42 6 8

a. 3 __ 5

x 2 7 , 10 or 2x , 5

b. 3 __ 5

x 1 7 . 10 or 2x , 5

c. 3 __ 5

x 1 7 . 10 or x , 5

d. 3 __ 5

x 2 7 . 10 or x , 5

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20. Gasoline costs $3.95 per gallon. Which graph correctly shows the number of gallons bought for $7.90?

a.

0 2 4 6 8 10 12 14 16 18

45.00

40.00

35.00

30.00

25.00

20.00

15.00

10.00

5.00

x

y

Amount of Gasoline (gallons)

Cos

t (d

olla

rs)

b.

0 5 10 15 20 25 30 35 40 45

18

16

14

12

10

8

6

4

2

x

y

Cost (dollars)

Am

ount

of G

asol

ine

(gal

lons

)c.

0 2 4 6 8 10 12 14 16 18

45.00

40.00

35.00

30.00

25.00

20.00

15.00

10.00

5.00

x

y


Cos

t (d

olla

rs)

d.

0 2 4 6 8 10 12 14 16 18

45.00

40.00

35.00

30.00

25.00

20.00

15.00

10.00

5.00

x

y


Cos

t (d

olla

rs)

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Pre-Test - Hialeah High