Algebra 1-2
Name: _______________________________________
Hour: _________
(2014 Algebra 1 CP Final Exam Review(
Things to keep in mind while you review:
• GET ORGANIZED. Successful studying begins with being organized. Get out all of your NOTES and REVIEWS from each chapter while you review and look back at them for help.
• DO NOT FALL BEHIND. Do all of the problems that are assigned each night and come to class prepared to ask questions about the things you could not do.
• KEEP YOUR NOTECARD IN MIND. As you do these problems, you will come across things that you would like to have on your note card. Keep notes of these in your packet. Organize your note card so you know where to find information that you need (e.g. use highlighters to highlight key terms or different colored pens for different topics).
• GET SERIOUS. The grade you earn on this final is worth 20% of your final grade.
• It is YOUR RESPONSIBILITY to successfully demonstrate your algebra skills to the best of your ability.
Homework Schedule
|Chapter |Due Date |( |
|12 |Monday, June 2nd | |
|8 |Tuesday, June 3rd | |
|9 |Wednesday, June 4th | |
|10 |Thursday, June 5th | |
|11 |Friday, June 6th | |
2nd Hour Exam: MONDAY, JUNE 9th (9:45 – 11:15 a.m.)
5th Hour Exam: WEDNESDAY, JUNE 11th (8:00 – 9:30 a.m.)
BE READY! (
Chapter 8: Exponents
1. Write [pic] in rational exponent notation.
2. Write [pic] in radical notation.
Simplify the expression.
3. [pic] 4. [pic] 5. [pic]
6. [pic] 7. [pic] 8. [pic]
Simplify.
9. [pic] 10. [pic] 11. [pic]
12. [pic] 13. [pic] 14. [pic]
15. [pic] 16. [pic] 17. [pic]
18. [pic] 19. [pic] 20. [pic]
21. [pic] 22. [pic] 23. [pic]
24. [pic] 25. [pic] 26. [pic]
27. [pic]
28. Identify each picture as growth or decay. Then identify the graph of exponential growth [pic]
__________________ __________________ __________________ __________________
Write a rule for the following functions.
29. 30.
Circle whether the function represents exponential growth and decay. Graph the function. Identify its domain and range.
31. [pic] Growth/Decay 32. [pic] Growth/Decay
|x |-2 |-1 |0 |1 |2 |
|y | | | | | |
|x |-2 |-1 |0 |1 |2 |
|y | | | | | |
D: _________ D: _________
R: _________ R: _________
CHAPTER 8 ANSWERS
1. [pic] 2. [pic]or [pic] 3. [pic]=1000 4. [pic] 5. [pic]= 36 6. [pic]= 3
7. [pic] 8. [pic] 9. [pic] 10. [pic] 11. [pic] 12. [pic]
13. [pic] 14. [pic] 15. [pic] 16. [pic] 17. [pic] 18. [pic]
19. 1 20. [pic] 21. [pic] 22. [pic] 23. 1 24. [pic]
25. [pic] 26. [pic] 27. [pic] 28. G, D, G, G 29. [pic] 30. [pic]
31. Decay, D: all reals, R: y > 0 32. Growth, D: all reals, R: y < 0
|x |-2 |-1 |0 |1 |2 |
|y |50 |10 |2 |0.4 |.08 |
|x |-2 |-1 |0 |1 |2 |
|y | - | -.5 | |- -18|- -108|
| |.083 | |-3 | | |
Chapter 9: Factoring
Use this polynomial to answer #1: [pic]
1. (a) Is the polynomial in order? If not, put it in order.
(b) What is the leading coefficient of the polynomial?
(c) What is the degree of the polynomial?
Simplify.
2. [pic] 3. [pic] 4. [pic]
5. [pic] 6. [pic] 7. [pic]
8. [pic] 9. [pic] 10. [pic]
11. [pic] 12. [pic][pic] 13. [pic]
14. [pic] 15. [pic] 16.[pic]
Factor completely.
17. [pic] 18. [pic] 19. [pic]
20. [pic] 21. [pic] 22. [pic]
23. [pic] 24. [pic] 25. [pic]
26. [pic] 27. [pic] 28. [pic]
29. [pic]
Solve the equation by factoring.
30. [pic] 31. [pic] 32. [pic]
33. [pic] 34. [pic] 35. [pic]
36. Find the zeros of the function: [pic]
37. Find a polynomial that represents the PERIMETER of the figure.
38. Find a polynomial that represents the AREA of the figure.
CHAPTER 9 ANSWERS
1. [pic] 2. [pic] 3. [pic] 4. [pic]
LC: -4, Deg: 5
5. [pic] 6. [pic] 7. [pic] 8. [pic]
9. [pic] 10. [pic] 11. [pic] 12. [pic] 13. [pic]
14. [pic] 15. [pic] 16. [pic] 17. [pic]
18. [pic] 19. [pic] 20. [pic] 21. [pic]
22. [pic] 23. [pic] 24. [pic] 25. [pic]
26. [pic] 27. [pic] 28. [pic] 29. [pic]
30. [pic] 31. x = 7, 3 32. x = 7, -2. 33. [pic]
34. m = 0, -45 35. s = -8, 9 36. x = 0, -4, -2 37. 10x + 2 38. [pic]
Chapter 10: Quadratics
Graph and compare to the parent function:[pic]
1. [pic] 2. [pic] 3. [pic]
Fill in the following missing information and graph!
4. [pic] 5. [pic]
Opens:_________ Opens:_________
Axis of Symmetry:_____________ Axis of Symmetry:_____________
Vertex: (____, ____) Vertex: (____, ____)
Max or Min Value:____________ Max or Min Value:____________
Y-Intercept:__________ Y-Intercept:__________
|x | | | | | |
|y | | | | | |
|x | | | | | |
|y | | | | | |
Solution(s): _______________ Solution(s): _______________
Solve the following equations using square roots. Leave your answers in radical form when necessary!
6. [pic] 7. [pic] 8. [pic]
Given the following equations, find the solutions/roots/zeros by completing the square.
9. [pic] 10. [pic] 11. [pic]
Convert the quadratic to vertex form: y = a(x – h)[pic]+ k. Identify the vertex and axis of symmetry.
12. [pic] 13. [pic] 14. [pic]
Axis of Symmetry: _________ Axis of Symmetry: _________ Axis of Symmetry: _________
Vertex: (____, ____) Vertex: (____, ____) Vertex: (____, ____)
Given the following equations: a) Find the value of the Discriminant; b) Tell whether the equation has two real solutions, one real solution, or no real solutions.
15. [pic] 16. [pic] 17. [pic]
A)____________________________ A)____________________________ A)____________________________
B)____________________________ B)____________________________ B)____________________________
Solve the following equations by using the quadratic formula.
18. [pic] 19. [pic] 20. [pic]
Tell if the each table is linear, exponential or quadratic.
|x |-2 |-1 |0 |1 |2 |
|y |1 |2 |4 |8 |16 |
21. 22.
23. Give an example of a graph of a parabola which has:
a) No real roots b) One real root c) Two real roots
Solve the quadratic using any method.
24. [pic][pic] 25. [pic] 26. [pic]
27. The length of Rachel’s rectangular garden is 6 yards more than its width.
The area of the garden is 91 square yards. What are the dimensions of the garden?
Tell whether the table represents a linear, exponential, or quadratic function.
| x | 0 | 1 | 2 | 3 | 4 |
| y | -3 | -1 | 1 | 3 | 5 |
| x | -2 | -1 | 0 | 1 | 2 |
| y | 80 | 40 | 20 | 10 | 5 |
28. 29.
Tell whether the graph represents a linear, exponential, or quadratic function.
30. 31. 32.
CHAPTER 10 ANSWERS
1. reflection and 2. vertical shrink 3. translated down 5
|x |-1 |0 |1 |2 |3 |
|y |6 |3 |2 |3 |6 |
vertical stretch
4. opens: up, Axis: x = 1, vertex: (1, 2), min value: 2, y-int: (0, 3), solutions: none
|x |-5 |-4 |-3 |-2 |-1 |
|y |3 |0 |-1 |0 |3 |
5. opens: up, Axis: x = -3 ,vertex:(-3, -1) , min value: -1, y-int: (0,8) solutions: -2, -4
6. [pic] 7. no solution 8. x = [pic] 9. x = 1, -3
10. c = 15, -1 11. x = 9, -1 12. [pic] 13. [pic] 14. [pic]
a.o.s: x = -4 a.o.s: x = 6 a.o.s: x = 1
vertex: (-4, -1) vertex: (6, 0) vertex: (1, -4)
15. 12, 2 real 16. 0, 1 real 17. -31, no real 18. x = -1, 3/5 19. no solution 20. x = [pic]
21. quadratic – table is symmetric, 22. exponential – y’s multiplied by 2 23a
second differences the same
23b. 23c. 24. x = 0, 14 25. no solution 26. x = [pic] 27. L = 13 yd; W = 7 yd.
28. Linear 29. Exponential 30. Exponential 31. Quadratic 32. Linear
Chapter 11: Radicals
For problems #1-2, complete the tables, then graph.
1. [pic] 2. [pic]
|x |-1 |0 |1 |2 |
|y | | | | |
|x |0 |1 |2 |3 |
|y | | | | |
Compare to y =[pic]: Compare to y =[pic]:
______________________ ______________________
______________________ ______________________
______________________ ______________________
Simplify the following.
3. [pic] 4. [pic] 5. [pic]
6. [pic] 7. [pic] 8. [pic]
9. [pic] 10. [pic] 11. [pic]
12. [pic] 13. [pic] 14. [pic]
Simplify the expression by rationalizing the denominator.
15. [pic] 16. [pic] 17. [pic]
18. [pic] 19. [pic] 20. [pic]
Simplify the following expressions.
21. [pic] 22. [pic] 23. [pic]
24. [pic] 25. [pic] 26. [pic]
Solve the equation. Check for extraneous solutions.
27. [pic] 28. [pic] 29. [pic]
30. [pic]
Find the unknown lengths using the Pythagorean Theorem.
31. a = 2, b = 8 32. b = 7, c = 11 33.
34. Tell whether the triangle with the given side lengths is a right triangle: 3, 4, 5
Find the distance between the two points.
35. (-5, 3) and (1, 2) 36. (8, -7) and (4, -3)
Find the midpoint of the line segment with the given endpoints.
37. (2, 5) and (4, 12) 38. (-9, -5) and (7, -14)
CHAPTER 11 ANSWERS
|x |0 |1 |2 |3 |
|y |-1 |1 |1.8 |2.5 |
|x |-1 |0 |1 |2 |
|y |0 |-2 |-2.8 |-3.5 |
1. reflection, v. stretch, left 1 2. v. stretch, down 1
3. [pic] 4. [pic] 5. [pic] 6. [pic] 7. [pic] 8. [pic] 9. [pic]
10. [pic] 11. [pic] 12. [pic] 13. [pic] 14. [pic] 15. [pic] 16. [pic]
17. [pic] 18. [pic] 19. [pic] 20. [pic] 21. [pic] 22. [pic] 23. [pic]
24. [pic] 25. [pic] 26. [pic] 27. x = 80 28. x = -2 29. x = 4 30. x = 2,3
31. [pic] 32. [pic] 33. x = 8 34. yes 35. [pic] 36. [pic] 37. (3, 8.5) 38. (-1, -9.5)
Chapter 12: Rational Functions
State the values excluded from the domain, then simplify the expression if possible.
1. [pic] 2. [pic] 3. [pic]
4. [pic] 5. [pic] 6. [pic]
Simplify the expression.
7. [pic] 8. [pic] 9. [pic]
10. [pic] 11. [pic] 12. [pic]
Simplify the expression.
13. [pic] 14. [pic] 15. [pic]
Find the LCD for:
16. [pic] and [pic] 17. [pic] and [pic] 18. [pic] and [pic]
Find the sum or difference.
19. [pic] 20. [pic] 21. [pic]
22. [pic] 23. [pic] 24. [pic]
►CHAPTER 12 ANSWERS
1. [pic],[pic] 2. [pic], [pic] 3. [pic], [pic] 4. [pic], [pic]
5. [pic] 6. [pic] 7. 2x 8. [pic] 9. 3(x+5) 10. [pic]
11. [pic] 12. [pic] 13. [pic] 14. [pic] 15. [pic] 16. 5x
17. [pic] 18. [pic] 19. [pic] 20. [pic] 21. [pic] 22. [pic]
23. [pic] 24. [pic]
-----------------------
3x + 5
2x - 7
|x |-3 |-2 |-1 |0 |1 |
|y |13.5 |6 |1.5 |0 |1.5 |
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