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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
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