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$: ExamView - Algebra 2 - Unit 2 Test - PC\|MACimages.pcmac.org/.../Documents/ExamView_-_Algebra_2_-_Unit_2_Test.pdfAlgebra 2 - Unit 2 Test 1. ... 35 50 70 95 125 160 200 245 295$
Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Algebra 2 - Unit 2 Test

1. Factor 15x3

− 6x2

− 25x + 10 by grouping.

2. Factor the trinomial a2

+ 14a + 48.

3. Factor 2x2

+ 7x + 6.

4. Factor the trinomial 42n2

− n − 30.

5. The latus rectum of a parabola is the line segment perpendicular to the axis of symmetry through the focus,

with endpoints on the parabola. Find the length of the latus rectum of the parabola y =1

12x

2.

____ 6. Identify the axis of symmetry for the graph of f(x) = x2

+ 2x − 3.

F. x = −1 H. y = −1

G. y = −4 J. x = −4

7. Find the zeros of the function h x( ) = x2

+ 23x + 60 by factoring.

8. A quadratic equation has the following coefficients: a = 2, b = –2, and c = 1. Write the solution(s) of the equation.

9. Solve the equation 2x2

+ 18 = 0.

Name: ________________________ ID: A

2

10. Write a quadratic function in standard form with zeros 6 and –8.

11. Solve the equation x2

= 3 − 2x by completing the square.

12. Write the equation in standard form for the parabola with vertex (0,0) and directrix y = −7.

13. Solve x2

= −4 using square roots.

____ 14. Solve 3x2 – 6x + 1 = 0 using the Quadratic Formula. If necessary, round to the nearest hundredth.

F. There are no solutions. H. x ≈ 6.82 or x ≈ 5.18

G. x ≈ 10.90 or x ≈ 1.10 J. x ≈ 1.82 or x ≈ 0.18

____ 15. Find the discriminant of −3x2

− 4x + 6 = 0.

A. 72 C. 89

B. 88 D. 90

16. Write a quadratic function that fits the points (0, 6), (2, 4), and (3, 6).

Name: ________________________ ID: A

3

17. For the equation x2

− 6x − 8y − 23 = 0 find the coordinates of the vertex and focus, and the equations of the

directrix and the axis of symmetry. Then graph the equation.

____ 18. Write the equation of the parabola y = x2

− 4x − 29 in standard form.

F. y + 33 = x − 2( )2

H. y + 4 = x − 2( )2

G. y + 29 = x − 2( )2

J. y − 2 = x − 2( )2

19. Express 8 −84 in terms of i.

20. Find the values of x and y that make the equation −9x + 8i = −54 + (16y)i true.

21. Find the complex conjugate of 3i + 4.

22. Find the absolute value −7 − 9i| |.

23. Subtract. Write the result in the form a + bi.

(5 – 2i) – (6 + 8i)

Name: ________________________ ID: A

4

24. Multiply 6i 4 − 6i( ). Write the result in the form a + bi.

25. Simplify −8i20

.

26. Simplify −2 + 2i

5 + 3i.

27. Simplify the expression 50

98.

28. Simplify 7

5 by rationalizing the denominator.

29. Graph y ≤ −x2

− 5x + 4.

Name: ________________________ ID: A

5

30. Solve −8x + 4y = 48

y + 3 = (x + 6)2

Ï

Ì

Ó

ÔÔÔÔÔÔÔÔÔÔÔÔÔÔ

.

____ 31. Graph the system.

x2

+ y2

≤ 49

y ≤ 3 − x2

A. C.

B. D.

Name: ________________________ ID: A

6

32. The table below gives the stopping distance y (in 100 meters) for a train traveling on a track at various speeds

x (miles per hour).

Speed, x

(mi/h)

50 55 60 65 70 75 80 85 90

Distance, y

(100 m)

20 25 35 50 70 95 125 160 200

Find an equation of the quadratic function that models the data, and predict the stopping distance for the train

traveling at 95 miles per hour.

33. What quadratic function does the graph represent?

ID: A

1

Algebra 2 - Unit 2 TestAnswer Section

1. ANS:

(5x − 2)(3x2

− 5)

DIF: Average

2. ANS: a + 6( ) a + 8( )

DIF: Basic

3. ANS: x + 2( ) 2x + 3( )

DIF: Basic

4. ANS: (6n + 5)(7n − 6)

DIF: Advanced

5. ANS: 12

DIF: Advanced

6. ANS: F DIF: Average

7. ANS: x = −20 or x = −3

DIF: Basic

8. ANS: 0.5, 0.5

9. ANS: x = ±3i

DIF: Average

10. ANS:

f(x) = x2

+ 2x − 48

DIF: Average

11. ANS: x = 1 or x = –3

DIF: Basic

12. ANS:

y =1

28x

2

DIF: Average

ID: A

2

13. ANS: There is no solution.

DIF: Basic

14. ANS: J DIF: Average

15. ANS: B

16. ANS:

f x( ) = x2

− 3x + 6

DIF: Average

17. ANS:

Vertex: 3, − 4ÊËÁÁ ˆ

¯˜̃ ; focus: 3, − 2Ê

ËÁÁ ˆ

¯˜̃; directrix:y = − 6; axis of symmetry:x = 3

18. ANS: F

19. ANS:

16i 21

DIF: Average

20. ANS:

x = 6, y =1

2

DIF: Average

21. ANS: 4 − 3i

DIF: Basic

22. ANS:

130

DIF: Basic

23. ANS: –1 – 10i

DIF: Average

ID: A

3

24. ANS: 36 + 24i

DIF: Basic

25. ANS: –8

DIF: Average

26. ANS:

−2

17 +

8

17i

DIF: Average

27. ANS: 5

7

DIF: Basic

28. ANS:

35

5

DIF: Average

29. ANS:

DIF: Average

30. ANS: (−7, − 2) and (−3, 6)

DIF: Average

31. ANS: D

ID: A

4

32. ANS:

y = 0.1x2

− 9.5x + 245

about 245 hundred meters

DIF: Advanced

33. ANS:

f(x) = −x2

+ 8x − 14

DIF: Advanced

ID: A Algebra 2 - Unit 2 Test [Answer Strip]

_____ 6.F

_____14.J

_____15.B

_____18.F

_____31.D

Name: ________________________ Class: ___________________ Date: __________ ID: B

1


1. Factor 15x3

− 6x2


2. Factor the trinomial m2

+ 10m + 16.

3. Factor 2x2

+ 7x + 6.

4. Factor the trinomial 63x2

− 43x − 30.



24x

2.

____ 6. Identify the axis of symmetry for the graph of f(x) = −x2

+ 4x + 5.

F. x = 9 H. y = 2

G. y = 9 J. x = 2



8. A quadratic equation has the following coefficients: a = –1, b = 3, and c = –3. Write the solution(s) of the equation.


+ 45 = 0.

Name: ________________________ ID: B

2





13. Solve x2

= −25 using square roots.

____ 14. Solve 3x2 – x – 1 = 0 using the Quadratic Formula. If necessary, round to the nearest hundredth.

F. x ≈ 1.60 or x ≈ 0.40 H. x ≈ 0.77 or x ≈ –0.43

G. x ≈ 4.61 or x ≈ –2.61 J. There are no solutions.

____ 15. Find the discriminant of 2x2

+ 2x − 3 = 0.

A. 28 C. 29

B. 30 D. 24


Name: ________________________ ID: B

3


− 6x − 8y − 23 = 0 find the coordinates of the vertex and focus, and the equations of the




F. y + 16 = x − 4( )2

H. y + 69 = x − 4( )2

G. y + 85 = x − 4( )2

J. y − 4 = x − 4( )2


20. Find the values of x and y that make the equation −2x + 9i = 8 + (45y)i true.

21. Find the complex conjugate of −7i − 17.

22. Find the absolute value −9 + 7i| |.

23. Add. Write the result in the form a + bi.

(–7 – i) + (6 + 5i)

Name: ________________________ ID: B

4


25. Simplify 9i16

.

26. Simplify 2 + 5i

3 − 2i.


192.

28. Simplify 14


29. Graph y ≤ −5x2

+ 2x − 4.

Name: ________________________ ID: B

5

30. Solve −8x + 4y = 20

y + 8 = (x + 5)2

Ï

Ì

Ó


.


x2

+ y2

≤ 16

y ≤ 3 − x2

A. C.

B. D.

Name: ________________________ ID: B

6


x (miles per hour).

Speed, x

(mi/h)

60 65 70 75 80 85 90 95 100

Distance, y

(100 m)

35 50 70 95 125 160 200 245 295




ID: B

1


1. ANS:

(5x − 2)(3x2

− 5)

DIF: Average

2. ANS: m + 8( ) m + 2( )

DIF: Basic

3. ANS: x + 2( ) 2x + 3( )

DIF: Basic

4. ANS: (7x + 3)(9x − 10)

DIF: Advanced

5. ANS: 24

DIF: Advanced


7. ANS: x = −10 or x = −9

DIF: Basic

8. ANS: 1.5, 1.5

9. ANS: x = ±3i

DIF: Average

10. ANS:

f(x) = x2

− 6x − 16

DIF: Average

11. ANS: x = 5 or x = –13

DIF: Basic

12. ANS:

y =1

16x

2

DIF: Average

ID: B

2

13. ANS: There is no solution.

DIF: Basic

14. ANS: H DIF: Average

15. ANS: A

16. ANS:

f x( ) = x2

− 3x + 4

DIF: Average

17. ANS:

Vertex: 3, − 4ÊËÁÁ ˆ

¯˜̃ ; focus: 3, − 2Ê

ËÁÁ ˆ

¯˜̃; directrix:y = − 6; axis of symmetry:x = 3

18. ANS: G

19. ANS:

21i 11

DIF: Average

20. ANS:

x = −4, y =1

5

DIF: Average

21. ANS: −17 + 7i

DIF: Basic

22. ANS:

130

DIF: Basic

23. ANS: –1 + 4i

DIF: Average

ID: B

3

24. ANS: 10 + 20i

DIF: Basic

25. ANS: 9

DIF: Average

26. ANS:

−4

13 +

19

13i

DIF: Average

27. ANS: 7

8

DIF: Basic

28. ANS:

42

3

DIF: Average

29. ANS:

DIF: Average

30. ANS: (−6, − 7) and (−2, 1)

DIF: Average

31. ANS: B

ID: B

4

32. ANS:

y = 0.1x2

− 9.5x + 245


DIF: Advanced

33. ANS:

f(x) = −x2

+ 10x − 21

DIF: Advanced

ID: B Algebra 2 - Unit 2 Test [Answer Strip]

_____ 6.J

_____14.H

_____15.A

_____18.G

_____31.B

Name: ________________________ Class: ___________________ Date: __________ ID: C

1


1. Factor 15x3

− 6x2


2. Factor the trinomial m2

+ 10m + 16.

3. Factor 3x2

− 17x + 10.

4. Factor the trinomial 9y2

− 17y − 30.



16x

2.

____ 6. Identify the axis of symmetry for the graph of f(x) = 2x2

+ 4x + 2.

F. y = 0 H. x = −1

G. x = 0 J. y = −1



8. A quadratic equation has the following coefficients: a = 1, b = 9, and c = 9. Write the solution(s) of the equation.


+ 63 = 0.

Name: ________________________ ID: C

2





13. Solve x2

= 16 using square roots.

____ 14. Solve 2x2 + 3x – 4 = 0 using the Quadratic Formula. If necessary, round to the nearest hundredth.

F. x ≈ 0.85 or x ≈ –2.35 H. x ≈ 3.40 or x ≈ –9.40

G. x ≈ –1.40 or x ≈ –4.60 J. There are no solutions.


− 5x + 6 = 0.

A. 169 C. 171

B. 170 D. 144


Name: ________________________ ID: C

3


− 4x − 8y + 28 = 0 find the coordinates of the vertex and focus, and the equations of the



+ 10x − 55 in standard form.

F. y + 25 = x + 5( )2

H. y + 80 = x + 5( )2

G. y + 55 = x + 5( )2

J. y + 5 = x + 5( )2



21. Find the complex conjugate of −20i + 10.

22. Find the absolute value 3 + 9i| |.

23. Subtract. Write the result in the form a + bi.

(–8 – 5i) – (–2 – i)

Name: ________________________ ID: C

4



.

26. Simplify −5 + 4i

2 + 5i.


147.

28. Simplify 5


29. Graph y ≥ 3x2

− x + 2.

Name: ________________________ ID: C

5

30. Solve −8x + 4y = 8

y + 5 = (x + 2)2

Ï

Ì

Ó


.


x2

+ y2

≤ 4

y ≤ 6 − x2

A. C.

B. D.

Name: ________________________ ID: C

6


x (miles per hour).

Speed, x

(mi/h)

55 60 65 70 75 80 85 90 95

Distance, y

(100 m)

25 35 50 70 95 125 160 200 245




ID: C

1


1. ANS:

(5x − 2)(3x2

− 5)

DIF: Average

2. ANS: m + 8( ) m + 2( )

DIF: Basic

3. ANS: x − 5( ) 3x − 2( )

DIF: Basic

4. ANS: (y − 3)(9y + 10)

DIF: Advanced

5. ANS: 16

DIF: Advanced


7. ANS: x = −10 or x = −5

DIF: Basic

8. ANS: –1.15, –7.85

9. ANS: x = ±3i

DIF: Average

10. ANS:

f(x) = x2

− 2x − 24

DIF: Average

11. ANS: x = 3 or x = –13

DIF: Basic

12. ANS:

y =1

40x

2

DIF: Average

ID: C

2

13. ANS: The solutions are 4 and –4.

DIF: Basic

14. ANS: F DIF: Average

15. ANS: A

16. ANS:

f x( ) = x2

− 3x + 4

DIF: Average

17. ANS:

Vertex: 2, 3ÊËÁÁ ˆ

¯˜̃; focus: 2, 5Ê

ËÁÁ ˆ

¯˜̃ ; directrix:y = 1; axis of symmetry:x = 2

18. ANS: H

19. ANS:

12i 6

DIF: Average

20. ANS:

x = −2, y =1

5

DIF: Average

21. ANS: 10 + 20i

DIF: Basic

22. ANS:

3 10

DIF: Basic

23. ANS: –6 – 4i

DIF: Average

ID: C

3

24. ANS: 9 + 18i

DIF: Basic

25. ANS: –9

DIF: Average

26. ANS: 10

29 +

33

29i

DIF: Average

27. ANS: 6

7

DIF: Basic

28. ANS:

35

7

DIF: Average

29. ANS:

DIF: Average

30. ANS: (−3, − 4) and (1, 4)

DIF: Average

31. ANS: D

ID: C

4

32. ANS:

y = 0.1x2

− 9.5x + 245


DIF: Advanced

33. ANS:

f(x) = −x2

+ 4x − 2

DIF: Advanced

ID: C Algebra 2 - Unit 2 Test [Answer Strip]

_____ 6.H

_____14.F

_____15.A

_____18.H

_____31.D

Name: ________________________ Class: ___________________ Date: __________ ID: D

1


1. Factor 15x3

− 6x2


2. Factor the trinomial z2

+ 14z + 45.

3. Factor 2x2

− 11x + 15.

4. Factor the trinomial 20y2

− 7y − 40.



8x

2.


− 8x + 6.

F. y = 2 H. x = −2

G. y = −2 J. x = 2


− 27x − 90 by factoring.

8. A quadratic equation has the following coefficients: a = 1, b = 4, and c = 9. Write the solution(s) of the equation.


+ 63 = 0.

Name: ________________________ ID: D

2





13. Solve x2


____ 14. Solve 3x2 + x – 5 = 0 using the Quadratic Formula. If necessary, round to the nearest hundredth.

F. x ≈ 0.30 or x ≈ –2.30 H. There are no solutions.

G. x ≈ 6.81 or x ≈ –8.81 J. x ≈ 1.14 or x ≈ –1.47


+ 5x + 5 = 0.

A. 100 C. 127

B. 126 D. 125


Name: ________________________ ID: D

3


+ 8x + 4y + 8 = 0 find the coordinates of the vertex and focus, and the equations of the



+ 4x − 46 in standard form.

F. y + 46 = x + 2( )2

H. y + 50 = x + 2( )2

G. y + 4 = x + 2( )2

J. y + 2 = x + 2( )2


20. Find the values of x and y that make the equation 2x + 10i = 14 + (40y)i true.

21. Find the complex conjugate of 5i − 19.

22. Find the absolute value 4 − 5i| |.


(4 – 8i) + (–1 – 7i)

Name: ________________________ ID: D

4



.

26. Simplify 4 + 3i

−4 − 4i.


75.

28. Simplify 5


29. Graph y ≥ x2

− 5x + 4.

Name: ________________________ ID: D

5

30. Solve −8x + 4y = 0

y + 7 = (x + 2)2

Ï

Ì

Ó


.


x2

+ y2

≤ 9

y ≤ 5 − x2

A. C.

B. D.

Name: ________________________ ID: D

6


x (miles per hour).

Speed, x

(mi/h)

60 65 70 75 80 85 90 95 100

Distance, y

(100 m)

35 50 70 95 125 160 200 245 295




ID: D

1


1. ANS:

(5x − 2)(3x2

− 5)

DIF: Average

2. ANS: z + 5( ) z + 9( )

DIF: Basic

3. ANS: x − 3( ) 2x − 5( )

DIF: Basic

4. ANS: (4y + 5)(5y − 8)

DIF: Advanced

5. ANS: 8

DIF: Advanced


7. ANS: x = 30 or x = −3

DIF: Basic

8. ANS: –2, –2

9. ANS: x = ±3i

DIF: Average

10. ANS:

f(x) = x2

− 2x − 24

DIF: Average

11. ANS: x = 2 or x = –14

DIF: Basic

12. ANS:

y =1

60x

2

DIF: Average

ID: D

2


DIF: Basic


15. ANS: D

16. ANS:

f x( ) = x2

− 4x + 7

DIF: Average

17. ANS:

Vertex: −4, 2ÊËÁÁ ˆ

¯˜̃ ; focus: −4, 1Ê

ËÁÁ ˆ

¯˜̃; directrix:y = 3; axis of symmetry: x = − 4

18. ANS: H

19. ANS:

12i 17

DIF: Average

20. ANS:

x = 7, y =1

4

DIF: Average

21. ANS: −19 − 5i

DIF: Basic

22. ANS:

41

DIF: Basic

23. ANS: 3 – 15i

DIF: Average

ID: D

3

24. ANS: 24 + 8i

DIF: Basic

25. ANS: 4

DIF: Average

26. ANS:

−7

8 +

1

8i

DIF: Average

27. ANS: 4

5

DIF: Basic

28. ANS:

30

6

DIF: Average

29. ANS:

DIF: Average

30. ANS: (−3, − 6) and (1, 2)

DIF: Average

31. ANS: C

ID: D

4

32. ANS:

y = 0.1x2

− 9.5x + 245


DIF: Advanced

33. ANS:

f(x) = −x2

+ 8x − 14

DIF: Advanced

ID: D Algebra 2 - Unit 2 Test [Answer Strip]

_____ 6.J

_____14.J

_____15.D

_____18.H

_____31.C

Name: ________________________ Class: ___________________ Date: __________ ID: E

1


1. Factor 15x3

− 6x2


2. Factor the trinomial x2

+ 14x + 45.

3. Factor 2x2

− 13x + 15.

4. Factor the trinomial 6n2

− 11n − 10.



28x

2.


+ 4x + 2.

F. y = 0 H. x = −1

G. y = −1 J. x = 0



8. A quadratic equation has the following coefficients: a = 2, b = –1, and c = –2. Write the solution(s) of the equation.


+ 75 = 0.

Name: ________________________ ID: E

2





13. Solve x2


____ 14. Solve 3x2 + 4x – 2 = 0 using the Quadratic Formula. If necessary, round to the nearest hundredth.

F. x ≈ 2.32 or x ≈ –10.32 H. x ≈ 0.39 or x ≈ –1.72

G. x ≈ –2.95 or x ≈ –5.05 J. There are no solutions.

____ 15. Find the discriminant of 2x2

+ x − 6 = 0.

A. 48 C. 50

B. 49 D. 51


Name: ________________________ ID: E

3


− 6x + 8y − 31 = 0 find the coordinates of the vertex and focus, and the equations of the




F. y − 3 = x − 3( )2

H. y + 9 = x − 3( )2

G. y + 68 = x − 3( )2

J. y + 77 = x − 3( )2



21. Find the complex conjugate of 20i + 12.

22. Find the absolute value −7 + 6i| |.


(–8 – 8i) + (–6 – 4i)

Name: ________________________ ID: E

4


25. Simplify 11i15

.

26. Simplify 1 − 4i

−1 − 5i.


98.

28. Simplify 3


29. Graph y ≤ −2x2

+ x − 3.

Name: ________________________ ID: E

5

30. Solve −8x + 4y = 12

y + 8 = (x + 4)2

Ï

Ì

Ó


.


x2

+ y2

≤ 9

y ≤ 8 − x2

A. C.

B. D.

Name: ________________________ ID: E

6


x (miles per hour).

Speed, x

(mi/h)

60 65 70 75 80 85 90 95 100

Distance, y

(100 m)

35 50 70 95 125 160 200 245 295




ID: E

1


1. ANS:

(5x − 2)(3x2

− 5)

DIF: Average

2. ANS: x + 5( ) x + 9( )

DIF: Basic

3. ANS: x − 5( ) 2x − 3( )

DIF: Basic

4. ANS: (2n − 5)(3n + 2)

DIF: Advanced

5. ANS: 28

DIF: Advanced


7. ANS: x = −30 or x = −3

DIF: Basic

8. ANS: 1.28, –0.78

9. ANS: x = ±5i

DIF: Average

10. ANS:

f(x) = x2

− 3x − 40

DIF: Average

11. ANS: x = 3 or x = –15

DIF: Basic

12. ANS:

y =1

64x

2

DIF: Average

ID: E

2


DIF: Basic


15. ANS: B

16. ANS:

f x( ) = x2

− 2x + 5

DIF: Average

17. ANS:

Vertex: 3, 5ÊËÁÁ ˆ

¯˜̃; focus: 3, 3Ê

ËÁÁ ˆ

¯˜̃ ; directrix:y = 7; axis of symmetry:x = 3

18. ANS: J

19. ANS:

3i 70

DIF: Average

20. ANS:

x = −7, y =1

3

DIF: Average

21. ANS: 12 − 20i

DIF: Basic

22. ANS:

85

DIF: Basic

23. ANS: –14 – 12i

DIF: Average

ID: E

3

24. ANS: 4 + 12i

DIF: Basic

25. ANS: –11i

DIF: Average

26. ANS: 19

26 +

9

26i

DIF: Average

27. ANS: 5

7

DIF: Basic

28. ANS:

6

2

DIF: Average

29. ANS:

DIF: Average

30. ANS: (−5, − 7) and (−1, 1)

DIF: Average

31. ANS: C

ID: E

4

32. ANS:

y = 0.1x2

− 9.5x + 245


DIF: Advanced

33. ANS:

f(x) = −x2

+ 10x − 24

DIF: Advanced

ID: E Algebra 2 - Unit 2 Test [Answer Strip]

_____ 6.H

_____14.H

_____15.B

_____18.J

_____31.C