17

Name_______________________________ Rockswold College Algebra Chapter 2 Test–Form A

1. Write a formula for f. 1. _____

(A) = −2( ) 4

3f x x

(B) = − −3( ) 4

2f x x

(C) = −3( ) 4

2f x x

(D) = − −2( ) 4

3f x x

2. To receive an A in the course a student must earn at least 90% of the total points 2. _____ possible on a series of exams. There are three 100-point unit exams and a 200-point final exam. Mark’s scores on the first three exams are 85, 91, and 88. What is the lowest score he can earn on the final exam to earn an A in the course? (A) 93 (B) 186 (C) He cannot earn enough points. (D) 96

3. Solve the linear equation + − = − −6 6(12 ) 4( 1) 1.x x 3. _____

(A) 9.3125 (B) −41.5

(C) −36.5 (D) 8.3

4. Find the slope-intercept form of the equation of the line parallel to = −4 1,y x 4. _____ passing through (5, –3).

(A) = − −13

4y x (B) = −4 3y x

(C) = − −1 7

4 4y x (D) = −4 23y x

5. The graphs of two linear functions f and g are shown in the figure. Solve the 5. _____ inequality ( ) ( ).g x f x>

(A) < 2x

(B) > 2x

(C) > 3x

(D) < 3x

Chapter 2 Test–Form A Rockswold College Algebra

18

6. Solve the linear inequality + ≤ −3 9 5 2.x x Write the solution set in interval 6. _____ notation.

(A) ⎡ ⎞− ∞ ⎟⎢⎣ ⎠

11,

2 (B)

⎛ ⎤−∞ −⎜ ⎥⎝ ⎦

11,

2

(C) ⎛ ⎤−∞⎜ ⎥⎝ ⎦

11,

2 (D)

⎡ ⎞∞ ⎟⎢⎣ ⎠

11,

2

7. Solve the absolute value inequality 7 3 5.x− ≥ 7. _____

(A) ≤ ≤24

3x (B) ≤ 2

3x or ≥ 4x

(C) − ≤ ≤ − 24

3x (D) ≤ −4x or ≥ − 2

3x

8. Find = +( )f x ax b so that f models the data exactly. 8. _____

X −6 –2 1 5 9

f(x) −0.64 −0.48 −0.36 −0.20 −0.04

(A) = +( ) 6.06 0.36f x x (B) = −( ) 0.165 0.625f x x

(C) = −( ) 0.04 0.4f x x (D) = −( ) 25 124.8f x x

9. Graph the linear function3

( ) 3.5

f x x= − 9. _____

Test Page 2

Chapter 2 Test–Form A Rockswold College Algebra

19

10. The Old Campaign Warhouse can prepare a political mailing in 8 hours 10. _____ if working alone. It would take the Enthusiastic Volunteer, working on her first campaign, 12 hours. How long will it take them to prepare the mailing if they work together? (A) 20 hours (B) 4.8 hours (C) 10 hours (D) 2 hours

11. Solve the absolute value equation 5 2 2 5.x + − = 11. _____

(A) No solutions (B) − 91,

5

(C) −1,1 (D) − 51,

9

12. Sketch the graph of the function ( ) 4f x x= − 12. _____

13. The inequality 78 18T− ≤ describes the range of monthly average 13. _____ temperatures T in degrees Fahrenheit for Austin, Texas. Find the high and low monthly average temperatures for Austin.

(A) = ° = °High 96 F; Low 0 F (B) = ° = °High 60 F; Low 0 F

(C) = ° = °High 96 F; Low 60 F (D) = ° = °High 78 F; Low 18 F

Test Page 3

Chapter 2 Test–Form A Rockswold College Algebra

20

14. The table lists data that are exactly linear. Predict the value of y 14. _____ when = −2.1.x

x −3 −2 −1 0 1

Y 8.8 5.6 2.4 −0.8 −4

(A) = 7.52y (B) = −5.92y

(C) = −7.52y (D) = 5.92y

15. The graph depicts the distance y that a person driving a car on a straight road 15. _____ is from home after x hours. Between what hours was the person driving slowest?

(A) 0 and 2 (B) 2 and 4 (C) 4 and 5 (D) 5 and 6

16. Determine how much pure water should be mixed with 18 liters of a 15% solution 16. _____ of hydrochloric acid to make a 12% solution of hydrochloric acid. (A) 27 liters (B) 0.8 liters (C) 4.5 liters (D) 22.5 liters

17. A driver of a car is initially 315 miles from home, traveling away from home on a 17. _____ straight freeway at 60 miles per hour. Write a formula for a linear function f that models the distance between the driver and home after x hours. (A) = +( ) 315 60f x x (B) = +( ) 60 315f x x

(C) = −( ) 315 60f x x (D) = −( ) 60 315f x x

18. Find an equation of the line parallel to the x-axis, passing through (4, –3). 18. _____

(A) = 4x (B) = −3x

(C) = 4y (D) = −3y

Test Page 4

Chapter 2 Test–Form A Rockswold College Algebra

21

19. Sketch the graph of the function 19. _____

⎧ + − ≤ < −⎪⎪⎨= − ≤ <⎪⎪− + ≤ ≤⎩

46 if 6 3

3( ) 2 if 3 2

4 if 2 6.

x x

f x x

x x

20. The graphs of three linear functions f, g, and h with domains = ≤ ≤{ }0 7D x x 20. _____ are shown in the figure. Solve the inequality < <( ) ( ) ( ).f x g x h x

(A) < <2 4x

(B) < <2 3x

(C) < <3 6x

(D) < <0 3x

Test Page 5

22

Name_______________________________ Rockswold College Algebra Chapter 2 Test–Form B

1. Write a formula for f. 1. _____

(A) = − −5( ) 2

2f x x

(B) = −2( ) 2

5f x x

(C) = − −2( ) 2

5f x x

(D) = −5( ) 2

2f x x

2. To receive an A in the course a student must earn at least 90% of the total points 2. _____ possible on a series of exams. There are three 100-point unit exams and a 200-point final exam. Mark’s scores on the first three exams are 78, 96, and 87. What is the lowest score he can earn on the final exam to earn an A in the course? (A) He cannot earn enough points (B) 154 (C) 189 (D) 94

3. Solve the linear equation − + = + −5 (3 ) 5( 4).x x x x 3. _____

(A) No solutions (B) −2.3

(C) 8.5 (D) −8.5

4. Find the slope-intercept form of the equation of the line parallel to = − +2 3,y x 4. _____ passing through (3, −7).

(A) = − −17

2y x (B) = −1 17

2 2y x

(C) = − −2 1y x (D) = −2 7y x

5. The graphs of two linear functions f and g are shown in the figure. Solve the 5. _____ inequality >( ) ( ).f x g x

(A) < −4x

(B) > −4x

(C) > −2x

(D) < −2x

Chapter 2 Test–Form B Rockswold College Algebra

23

6. Solve the linear inequality − ≥ +2 7 9 2.x x Write the solution set in interval 6. _____ notation.

(A) ⎡ ⎞− ∞ ⎟⎢⎣ ⎠

9,

7 (B)

⎛ ⎤−∞ −⎜ ⎥⎝ ⎦

9,

7

(C) ⎛ ⎤−∞ −⎜ ⎥⎝ ⎦

9,

7 (D)

⎡ ⎞∞ ⎟⎢⎣ ⎠

9,

7

7. Solve the absolute value inequality 7 3 4.x − ≥ 7. _____

(A) ≤ − 1

7x or ≥ 1x (B) − ≤ ≤1

17

x

(C) − ≤ ≤ 11

7x (D) ≤ −1x or ≥ 1

7x

8. Find = +( )f x ax b so that f models the data exactly. 8. _____

x −6 −2 1 5 9

f(x) 2.86 1.58 0.62 −0.66 −1.94

(A) = − +( ) 2.2 1.58f x x (B) = − +( ) 3.125 2.505f x x

(C) = − −( ) 2.2 2.82f x x (D) = − +( ) 0.32 0.94f x x

9. Graph the linear function ( ) 4 5.f x x= − 9. _____

Test Page 2

Chapter 2 Test–Form B Rockswold College Algebra

24

10. An upgraded version of a computer chip can process a standard data set in 10. _____ 6 μ sec. The earlier version of the chip takes 9 μ sec to process the same data set. How long would it take both chips working together to process the data set?

(A) 15 μ sec (B) 3 μ sec

(C) 7.5 μ sec (D) 3.6 μ sec

11. Solve the absolute value equation − + =| 3 5 | 2 9.x 11. _____

(A) No solutions (B) −4, 4

(C) 2

, 43

(D) − 2, 4

3

12. Sketch the graph of the function ( ) | 4 | .f x x= − 12. _____

13. The inequality − ≤| 49 | 22T describes the range of monthly average 13. _____ temperatures T in degrees Fahrenheit for Holland, Michigan. Find the high and low monthly average temperatures for Holland. (A) = ° = °High 71 F; Low 0 F (B) = ° = °High 71 F; Low 27 F

(C) = ° = °High 27 F; Low 60 F (D) = ° = °High 49 F; Low 22 F

14. The table lists data that are exactly linear. Predict the value of y 14. _____ when = −1.7.x

X −3 −2 −1 0 1

Y 0.4 1.3 2.2 3.1 4

(A) = 1.57y (B) = 4.63y

(C) = −4.83y (D) = −1.57y

Test Page 3

Chapter 2 Test–Form B Rockswold College Algebra

25

15. The graph depicts the distance y that a person driving a car on a straight road is 15. _____ from home after x hours. Between what hours was the person driving fastest?

(A) 0 and 1 (B) 1 and 2 (C) 2 and 4 (D) 4 and 6

16. Determine how much pure water should be mixed with 12 liters of a 18% 16. _____ solution of sodium chloride to make a 10% solution of sodium chloride. (A) 0.56 liters (B) 9.6 liters (C) 28 liters (D) 21.6 liters

17. A driver of a car is initially 245 miles from home, traveling away from home 17. _____ on a straight freeway at 70 miles per hour. Write a formula for a linear function f that models the distance between the driver and home after x hours. (A) = +( ) 245 70f x x (B) = +( ) 60 245f x x

(C) = −( ) 245 70f x x (D) = −( ) 70 245f x x

18. Find an equation of the line parallel to the y-axis, passing through (4, –3). 18. _____ (A) = 4x (B) = −3x (C) = 4y (D) = −3y

19. Sketch the graph of the function 19. _____

⎧− − ≤ < −⎪⎪⎪= − ≤ <⎨⎪⎪− + ≤ ≤⎪⎩

2if 6 3

3( ) 2 if 3 2

3 7if 2 6.

4 2

x x

f x x

x x

Test Page 4

Chapter 2 Test–Form B Rockswold College Algebra

26

20. The graphs of three linear functions f, g, and h with domains = ≤ ≤{ | 0 7}D x x 20. _____ are shown in the figure. Solve the inequality < <( ) ( ) ( ).f x g x h x

(A) 2 5x< <

(B) < <2 6x

(C) 0 5x< <

(D) < <0 4x

Test Page 5

27

Name_______________________________ Rockswold College Algebra Chapter 2 Test–Form C

1. Write a formula for f. 1. ____________

2. To receive an A in a course a student must earn at least 90% of the total points 2. ____________ possible on a series of exams. There are three 100-point unit exams and a 200-point final exam. Mark’s scores on the first three exams are 65, 91, and 89. What is the lowest score he can earn on the final exam to earn an A in the course?

3. Solve the linear equation − − = −7 8( 4) 3 7.x x 3. ____________

4. Find the slope-intercept form of the equation of the line parallel to = +14,

3y x 4. ____________

passing through (6, −1).

5. The graphs of two linear functions f and g are shown in the figure. Solve the 5. ____________ inequality ( ) ( ).f x g x<

6. Solve the linear inequality + > +5 7 8 2.x x Write the solution set in interval 6. ____________ notation.

7. Solve the absolute value inequality | 5 2 | 2.x − < 7. ____________

8. Find = +( )f x ax b so that f models the data exactly. 8. ____________

x −6 −2 1 5 9

f(x) 1.50 0.78 0.24 −0.48 −1.20

Chapter 2 Test–Form C Rockswold College Algebra

28

9. Graph the linear function = −( ) 7 4 .f x x 9. ____________

10. An upgraded version of a computer chip can process a standard data set in 10. ____________ 12 μ sec. The earlier version of the chip takes 18 μ sec to process the same data set. How long would it take both chips working together to process the data set?

11. Solve the absolute value equation | 7 3 | 7 11.x − − = 11. ____________

12. Sketch the graph of the function = +( ) | 5 | .f x x 12. ____________

13. The inequality − ≤| 48 | 28T describes the range of monthly average 13. ____________ temperatures T in degrees Fahrenheit for Des Moines, Iowa. Find the high and low monthly average temperatures for Des Moines.

14. The table lists data that are exactly linear. Predict the value of y when 14. ____________ x = −2.7.

x −3 −2 −1 0 1

y −12.7 −11.5 −10.3 −9.1 −7.9

Test Page 2

Chapter 2 Test–Form C Rockswold College Algebra

29

15. The graph depicts the distance y that a person driving a car on a straight road 15. ____________ is from home after x hours. Between what hours was the person driving slowest?

16. Determine how much pure water should be mixed with 25 liters of a 70% 16. ____________ solution of naphthalene to make a 20% solution of naphthalene.

17. A driver of a car is initially 455 miles from home, traveling away from home 17. ____________ on a straight freeway at 65 miles per hour. Write a formula for a linear function f that models the distance between the driver and home after x hours.

18. Find an equation of the line parallel to the y-axis, passing through (−2, 7). 18. ____________

19. Sketch the graph of the function 19. ____________

⎧ + − ≤ < −⎪⎪⎪= − ≤ <⎨⎪⎪ + ≤ ≤⎪⎩

710 if 6 3

3( ) 3 if 3 2

1 5if 2 6.

4 2

x x

f x x

x x

20. The graphs of three linear functions f, g, and h with domains 20. ____________ D = ≤ ≤{ | 0 7}x x are shown in the figure. Solve the inequality

< <( ) ( ) ( ).f x g x h x

Test Page 3

30

Name_______________________________ Rockswold College Algebra Chapter 2 Test–Form D

1. Write a formula for f. 1. ____________

2. To receive an A in the course a student must earn 92% of the total points 2. ____________ possible on a series of exams. There are three 100-point unit exams and a 200-point final exam. Mark’s scores on the first three exams are 90, 94, and 86. What is the lowest score he can earn on the final exam to earn an A in the course?

3. Solve the linear equation − − = − −8 3(3 2 ) 4( 3).x x x 3. ____________

4. Find the slope-intercept form of the equation of the line parallel to = − −3 1,y x 4. ____________

passing through (1, 9).

5. The graphs of two linear functions f and g are shown in the figure. Solve the 5. ____________ inequality ( ) ( ).f x g x<

6. Solve the linear inequality − > −9 8 6.x x Write the solution set in interval 6. ____________ notation.

7. Solve the absolute value inequality + <| 4 7 | 3.x 7. ____________

8. Find = +( )f x ax b so that f models the data exactly. 8. ____________

x −6 −2 1 5 9

f(x) 8.90 3.62 −0.34 −5.62 −10.9

Chapter 2 Test–Form D Rockswold College Algebra

31

9. Graph the linear function = −( ) 5 2.f x x 9. ____________

10. The Old Campaign Warhorse can prepare a political mailing in 12 hours if 10. ____________ working alone. It would take the Enthusiastic Volunteer, working on her first campaign, 20 hours. How long will it take them to prepare the mailing if they work together?

11. Solve the absolute value equation | 2 9 | 7 3.x − + = 11. ____________

12. Sketch the graph of the function = −( ) | 5 | .f x x 12. ____________

13. The inequality − ≤| 44 | 25T describes the range of monthly average 13. ____________ temperatures T in degrees Fahrenheit for Idaho Falls, Idaho. Find the high and low monthly average temperatures for Idaho Falls.

14. The table lists data that are exactly linear. Predict the value of y when 14. ____________ x = 3.7.

X −3 −2 −1 0 1

Y 19.4 14.5 9.6 4.7 −0.2

15. The graph depicts the distance y that a person driving a car on a straight road 15. ____________ is from home after x hours. Between what hours was the person driving fastest?

Test Page 2

Chapter 2 Test–Form D Rockswold College Algebra

32

16. Determine how much pure water should be mixed with 18 liters of a 35% 16. ____________ solution of antifreeze to make a 20% solution of antifreeze.

17. A driver of a car is initially 435 miles from home, traveling away from home 17. ____________ on a straight freeway at 60 miles per hour. Write a formula for a linear function f that models the distance between the driver and home after x hours.

18. Find an equation of the line parallel to the x-axis, passing through (−2, 7). 18. ____________

19. Sketch the graph of the function 19. ____________

− ≤ < −⎧⎪⎪= + − ≤ <⎨⎪⎪− + ≤ ≤⎩

5 if 6 3

1 28( ) if 3 2

5 53 12 if 2 6.

x

f x x x

x x

20. The graphs of three linear functions f, g, and h with domains 20. ____________ = ≤ ≤{ | 0 7}D x x are shown in the figure. Solve the inequality

< <( ) ( ) ( ).f x g x h x

Test Page 3

Rockswold College Algebra Test 2 Answers

33

Test 2 Answers

Form A Form B Form C Form D

1. A

2. B

3. D

4. D

5. B

6. D

7. B

8. C

9. D

10. B

11. B

12. D

13. C

14. D

15. B

16. C

17. A

18. D

19. C

20. C

1. A

2. C

3. C

4. C

5. C

6. B

7. A

8. D

9. C

10. D

11. D

12. A

13. B

14. A

15. B

16. B

17. A

18. A

19. A

20. A

1. = − +2( ) 1

5f x x

2. Not enough points

3. ≈464.18

11

4. = −13

3y x

5. 1x < −

6. ⎛ ⎞−∞⎜ ⎟⎝ ⎠

5,

3

7. 4

05

x< <

8. = − −( ) 0.18 0.42f x x

9.

10. 7.2 μ sec

11. 15

3,7

−

12.

13. = ° = °High 76 F; Low 20 F

14. = −12.34y

15. 2 and 4

16. 62.5 liters

17. ( ) 455 65f x x= +

18. 2x = −

19.

20. < <1 6x

1. = −7( ) 3

3f x x

2. 190

3. ≈131.44

9

4. = − +3 12y x

5. 2x <

6. ⎛ ⎞−∞ −⎜ ⎟⎝ ⎠

3,

7

7. − < < −51

2x

8. = − +( ) 1.32 0.98f x x

9.

10. 7.5 hours

11. No Solution

12.

13. = ° = °High 69 F; Low 19 F

14. = −13.43y

15. 4 and 5

16. 13.5 liters

17. ( ) 435 60f x x= +

18. 7y =

19.

20. < <1 5x