Algebra 2 Name______________________

Semester 1 Final Review ALT 2 I can represent functions in multiple forms and find key features of functions.

Tell  whether  the  relation  is  a  function.    1.         2.     3.              

Consider the relation given by the ordered pair. Identify the domain and range. Then tell whether the relation is a function. 12. (-2, -2), (-1, 0), (2, 6), (3, 8) 13. (-1, -5), (1, 2), (2, 4), (1, -7)

   Use  the  vertical  line  test  to  tell  whether  the  relation  is  a  function.      6.     7.                    Function:        Yes        No     Function:        Yes        No    Determine  the  domain  and  range  of  each  relation.  You  can  use  either  set  builder  or  interval  notation.      8.       9.                           Domain:       Domain:       Range:       Range:  

Directions:  For  each  absolute  value  function  give  the  coordinates  of  the  vertex,  whether  it  opens  up  or  down,  and  if  it  is  narrower,  wider,  or  the  same  width  as   y = x .  Then  graph  each  function.  

14.   y = x − 4 +1     15.   y = − 23x − 2  

vertex:       vertex:    opens:          up        down     opens:      up        down    narrower        wider        same  width     narrower        wider        same  width                      

Algebra 2 Name______________________

Semester 1 Final Review ALT 3 and ALT 4 I can write and sketch a quadratic function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

I can find real or complex solutions to quadratic equations.

Directions: Find the axis of symmetry, vertex, x-intercept(s), and y-intercept. If x-intercepts are complex, write “None”. If x-intercepts are irrational, write as decimal rounded to the nearest tenth. Then graph the function. (ALT 3 & 4) 1. y = −2x2 − 4x +3 axis of symmetry: vertex: y-intercept: x-intercept: min or max? increasing interval: decreasing interval: 2. y = (x − 4)2 + 5 axis of symmetry: vertex: y-intercept: x-intercept: min or max? increasing interval: decreasing interval:

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(0.5x� 0.3y = 1.3

�1.4x+ 1.2y = �2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(0.5x� 0.3y = 1.3

�1.4x+ 1.2y = �2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

3. y = (x + 4)(x − 2) axis of symmetry: vertex: y-intercept: x-intercept: min or max? increasing interval: decreasing interval: 4. y = x2 − 6x + 7 axis of symmetry: vertex: y-intercept: x-intercept: min or max? increasing interval: decreasing interval:  

 

Change  into  Standard  Form.  (ALT  3)  

5)   𝒚 = 𝟑(𝒙 − 𝟐)𝟐 + 𝟔                                                                                6)            𝒚 = −𝟑(𝒙 − 𝟐)(𝒙 + 𝟔)  

 

 

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(0.5x� 0.3y = 1.3

�1.4x+ 1.2y = �2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

Algebra 2 Name:

Chapter 3 Review – Systems of Equations and Matrices

For exercises 1-3, graph the system of equations and determine the solution.

1.

(x+ 2y = 7

3x+ y = 62.

(x� 5y = �5

3x� 15y = 93.

(y = 2|x� 3|� 4

y = x� 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

x

y

�10 10

�10

10

For exercises 4-7, use substitution to solve the system of equations.

4.

(6x� 3y = 12

�2x+ y = �45.

(x+ 2y = 11

4x+ 3y = 9

6.

(15x+ 2y = 4

3

x+ 23y = 2

7.

(0.5x� 0.3y = 1.3

�1.4x+ 1.2y = �2.2

For exercises 8-11, use elimination (also known as linear combination) to solve the system of equations.

8.

(6x+ 12y = �7

x+ 2y = 29.

(5x+ 4y = �3

3x� 7y = 17

10.

(43x+ 6y = �1

4x� 4y = 133

11.

(0.3x� 0.2y = 1.4

0.12x� 0.8y = 0.56

12. Write a system of equations that has no solutions.

13. Write a system of equations that has infinitely many solutions.

14. Write a system of equations that has exactly one solution.

15. A 100 point math test needs to be created. It needs to have 20 exercises in total, with the multiple choice

exercises worth 4 points each and the free response exercises worth 6 points each.

(a) Let m represent the number of multiple choice exercises and f represent the number of free response

exercises. Write a system of two equations to represent the situation.

(b) Solve your system of equations to part (a).

1 of 3

 

 

Change  into  Intercept  (Factored)  Form.  (ALT  3)  

7)   𝒚 = −𝒙𝟐 − 𝟏𝟔𝒙 − 𝟐𝟖       8)   𝒚 = 𝟑𝒙𝟐 − 𝟏𝟓𝒙 − 𝟏𝟖  

Change into Vertex Form.  (ALT  3) 9) 𝒚 = 𝒙𝟐 + 𝟏𝟎𝒙 + 𝟐𝟑 10) 𝒚 = 𝒙𝟐 − 𝟒𝒙 + 𝟗

Solving Quadratic Equations (ALT 4)

Solve the equation. Use factoring, completing the square, or the quadratic formula:    !𝒃± 𝒃𝟐!𝟒𝒂𝒄𝟐𝒂

. 11. 2x2 +3x − 2 = 0 12. 4x2 −8x +3= 0 13. 2x2 −3x − 9 = 0 14. 5x2 − 20x + 20 = 35 15. x2 + 4x − 2 = 0 16. −6x2 +3x + 2 = 3 17. 5x2 − 2x − 6 = −3x2 + 6x 18. 18x2 + 48x = −32 19. 2(x + 2)2 = 72 20. (3x + 2)2 − 49 = 0

21. 3(x −3)2 + 2 = 26 22. −2(x −1)2 = 36 .

Complex Number Operations (ALT 4)

Write the expression as a complex number in standard form.

13. 73+ i

14. 6− 4i2− i

15. 2+3i4+ 5i

16. −4i8− 2i

Algebra 2 Name______________________

Semester 1 Final Review ALT 11

I can solve systems of equations and inequalities.

Use substitution to solve the system of equations. Remember to write the answer as an ordered pair (x, y).

1. 8x + 4y = −4x − 2y = 6"#$

2. 5x + 2y = −33x + y = −1"#$

Use elimination to solve the system of equations. Remember to write the answer as an ordered pair (x, y).

3. 4x + 2y = −1−2x −3y = −4"#$

4. 6x − 4y = 4−2x +3y = −4"#$

Solve the system using any algebraic method. Remember to write the answer as an ordered pair (x, y).

5. x − 2y = 52x − 4y =10"#$

6. 5x + y =16−3x + y = 0"#$

7. 16x + 5y = −48x − 2y = 7"#$

8. 9x + 4y = −73x − 5y = −34"#$

Graph the system of inequalities and shade the solution.

9.

x ≥ 4y ≥ 05x + 4y ≤ 40

#

$%

&%

10. x + y ≤ 3−4x + 2y >1#$%

Graph the system of inequalities.

11. 12.

€

2x − 3y > 62x − y ≤ 8

€

4x + y <1−x + 2y ≤ 5

For exercises 16-19, graph the system of inequalities and shade the solution.

16. 17.

(x� y > �1

2x+ y < �1

(2x+ y 3

y � |x|+ 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

18. 19.

8><

>:

3x+ 6y > 4

3x� 4y > 4

x� y < 5

8>>><

>>>:

�2x+ 4y < 8

2x+ 4y > �8

�4x+ y � 0

x � �2

x

y

�10 10

�10

10

x

y

�10 10

�10

10

2 of 3

For exercises 16-19, graph the system of inequalities and shade the solution.

16. 17.

(x� y > �1

2x+ y < �1

(2x+ y 3

y � |x|+ 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

18. 19.

8><

>:

3x+ 6y > 4

3x� 4y > 4

x� y < 5

8>>><

>>>:

�2x+ 4y < 8

2x+ 4y > �8

�4x+ y � 0

x � �2

x

y

�10 10

�10

10

x

y

�10 10

�10

10

2 of 3

For exercises 16-19, graph the system of inequalities and shade the solution.

16. 17.

(x� y > �1

2x+ y < �1

(2x+ y 3

y � |x|+ 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

18. 19.

8><

>:

3x+ 6y > 4

3x� 4y > 4

x� y < 5

8>>><

>>>:

�2x+ 4y < 8

2x+ 4y > �8

�4x+ y � 0

x � �2

x

y

�10 10

�10

10

x

y

�10 10

�10

10

2 of 3

For exercises 16-19, graph the system of inequalities and shade the solution.

16. 17.

(x� y > �1

2x+ y < �1

(2x+ y 3

y � |x|+ 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

18. 19.

8><

>:

3x+ 6y > 4

3x� 4y > 4

x� y < 5

8>>><

>>>:

�2x+ 4y < 8

2x+ 4y > �8

�4x+ y � 0

x � �2

x

y

�10 10

�10

10

x

y

�10 10

�10

10

2 of 3

13.) y ≤ 5y > x2 − 6x +8

#$%

14.)  

y ≤ x2 − 2x −3y < 2x +1

#$%

       

 

 

 

 

 

 

 

 

 

For exercises 16-19, graph the system of inequalities and shade the solution.

16. 17.

(x� y > �1

2x+ y < �1

(2x+ y 3

y � |x|+ 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

18. 19.

8><

>:

3x+ 6y > 4

3x� 4y > 4

x� y < 5

8>>><

>>>:

�2x+ 4y < 8

2x+ 4y > �8

�4x+ y � 0

x � �2

x

y

�10 10

�10

10

x

y

�10 10

�10

10

2 of 3

For exercises 16-19, graph the system of inequalities and shade the solution.

16. 17.

(x� y > �1

2x+ y < �1

(2x+ y 3

y � |x|+ 1

x

y

�10 10

�10

10

x

y

�10 10

�10

10

18. 19.

8><

>:

3x+ 6y > 4

3x� 4y > 4

x� y < 5

8>>><

>>>:

�2x+ 4y < 8

2x+ 4y > �8

�4x+ y � 0

x � �2

x

y

�10 10

�10

10

x

y

�10 10

�10

10

2 of 3