Algebra 1
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FINAL EXAM REVIEW
Name______________
DO NOT FALL BEHIND. Do the problems that are assigned every night and come to class prepared to
ask questions about the things you could not do.
START YOUR NOTECARD NOW. As you do these problems, you will come across things that you
would like to have on your notecard. Keep it in a safe place.
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.
TENTATIVE ASSIGNMENT SCHEDULE
Due Monday –
Due Tuesday –
Due Wednesday –
Due Thursday –
Due Friday –
Exam Review 2014
Page 1 of 34
Chapter 6 – Absolute Values
Solve the equations.
1.
x 9
2.
x  1  13
1._____________
2._____________
3.
x  9  12
4.
2x  8  3  5
3._____________
4._____________
Solve then graph inequalities. Graph your answer.
5.
x 3
6.
x  4 1
5._____________
6._____________
7.
x 1  3  2
8.
x2 46
7._____________
8._____________
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Page 2 of 34
Chapter 7 – Linear Systems
Solve by Graphing.
1.
y  3x
y  x  4
2.
x y  2
y  2 x  4
3.
y  3x  5
y  1  3x
4.
3x  3 y  6
x y  2
5. Graph the following:
a.
a system with one real solution
Exam Review 2014
b.
a system with no real solutions
Page 3 of 34
Solve by Elimination.
6.
2 x  4 y  10
3x  3 y  6
6. _____________
7.
4x  6 y  8
8 x  12 y  16
7. _____________
8.
3x  4 y  6
2 x  5 y  19
8. _____________
Solve by Substitution.
9.
x  y4
2 x  3 y  28
9. _____________
10.
x  y  14
2x  y  7
10. ____________
11.
y  x  3
y  x 1
Exam Review 2014
11. ____________
Page 4 of 34
Graphing the following Linear Inequalities. List two possible solutions and circle them.
12. y  x  2
13. y  2 x  2
14. 2 x  2 y  6
Graphing the System of Linear Inequalities. List two possible solutions and circle them.
15.
y  3
y  x  2
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16.
Page 5 of 34
y  x4
y  x2
Chapter 8 – Exponents
Simplify.
1.
93 97
2.
3b   b
3 4
2
1. _____________
2. _____________
3.
x  x 
3 0
7
4.
2 x 2 y 3
3. _____________
4. _____________
5.
 3x y   5x y 
3 2
4 6
6.
(2 y 2 z 3 ) 4
5. _____________
6. _____________
7.
a3  a6
8.
 5a b 3a 
2
4
7. _____________
8. _____________
9.
 2ab c 
2 3
4
10.
10a10b5
2a11b 2
9. _____________
10. ____________
11.
 x 4 
 
3
12.
x x 
4
3
11. ____________
12. ____________
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Page 6 of 34
13. y 3  y 3
14.
x5
x3
13.____________
14.____________
15.
 3x 2 5 x 


 5x 


0
16.
4
x2
15.____________
16.____________
64 x 4 y 3 z 1
17.
16 x  2 y z 3
4 x 2 y 5 z 1
18.
30 x  2 y 1 z  4
17.____________
18.____________
19. Label each graph as exponential growth or decay
20. Graph the exponential function: y  0.4(2 x ) ---- Is this exponential growth or decay?
x
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y
Page 7 of 34
21. You deposit $500 into your bank account. The account grows at 10% per year.
How much money would you have in 4 years?
22. Your car is worth $15,000 when you bought. It decays at a rate of 7.5% per year.
How much money is the car worth is 6 years?
Exam Review 2014
Page 8 of 34
Chapter 9 – Quadratic
Equations and Functions
Simplify.
1.
196
2.
 256
1. _____________
2._____________
3.
 36
4.
0
3. _____________
4. _____________
5.
121
49
6.
1
25
5. _____________
6._____________
7.
75
8.
4 72
7._____________
8._____________
9.
1
10.
5
2
9._____________
3
10.____________
11.
5
7
12.
10
20
11.____________
12.____________
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Page 9 of 34
Solve each equation for x.
13. x 2  64
14. x 2  100
13.____________
14.____________
15. x 2  81
16. 2 x 2  72
15.____________
16.____________
17. x 2  15  40
18. 3 x 2  10  38
17.____________
18.____________
19. x 2  0
20.  2 x 2  800
19.____________
20.____________
For each of the quadratic equations below, fill out all necessary information and graph accordingly.
21. y  x 2  2 x  8
a=
b=
c=
Axis of Symmetry:
_______________
Vertex:
_______________
Opens Up or Down
_______________
Max or Min AND Value
_______________
y-Intercept
_______________
Solutions/roots/zeros/x-intercepts
_______________
x
Exam Review 2014
y
Page 10 of 34
22.
y  x 2  2x  3
a=
b=
c=
Axis of Symmetry:
_______________
Vertex:
_______________
Opens Up or Down
_______________
Max or Min AND Value
_______________
y-Intercept
_______________
Solutions/roots/zeros/x-intercepts
_______________
x
y
Use the Quadratic Formula to solve each of the following.
23.
24.
x2  7 x  2  0
23. ____________
3x 2  2 x  1
24. ____________
Find the Discriminant. Then use the discriminant to determine the number and types of solutions.
25.
x 2  9 x  14  0
25.____________
_______________
26.
x 2  4x  4  0
26.____________
_______________
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Page 11 of 34
27. Give an example of a graph of a parabola which has:
a) No real roots
b) One real root
28.
y  2 x 2  4 x  3
b=
c=
Axis of Symmetry:
_______________
Vertex:
_______________
Opens Up or Down
_______________
y-Intercept
_______________
Dashed or Solid Line and Shade Above or Below
_______________
Identify TWO solutions
_______________
x
29.
a=
c) Two real roots
y
y  x 2  2x  1
a=
b=
c=
Axis of Symmetry:
_______________
Vertex:
_______________
Opens Up or Down
_______________
y-Intercept
_______________
Dashed or Solid Line and Shade Above or Below
_______________
Identify TWO solutions
_______________
x
Exam Review 2014
y
Page 12 of 34
Chapter 10 – Polynomials
AND Factoring
1.
Find the degree of this polynomial and arrange it so that the powers of x are in descending order.
3xy3  2  5x4 y3  4 x3 y  x5
1.____________________________________________ degree = ______
Simplify the following.
2.
(h2  4h  4)  (5h2  8h  2)
3.
z 2 (4 z 4  z 3  11z 2  6)
2._____________
3. _____________
4.
5x
2
 
 x  7  2 x 2  3x  4

5.
 10 pq(3 pq  4 p  5q 2 )
4._____________
5._____________
6.
(16 x  9)  (4 x  1)
7.
(9b3  13b2  b)  (13b3  5b  14)
6._____________
7._____________
8.
x  2( x  3)
9.
a  6
2
8._____________
9._____________
10.
2 x  y  2 x  y 
11.
7 y  4 2 y  5
10.____________
11.____________
Exam Review 2014
Page 13 of 34
12.
2x  4 x  2
13.
3 y  52
12.____________
13.____________
14.
 x  4 2
15.
3k  14k  9
14.____________
15.____________
2x + 3
16.
a. Find the perimeter of the rectangle
16a.___________
5x – 1
b. Find the area of the rectangle
b.___________
Solve the following equations. They range from simple solving all the way to Solving by Factoring.
17. 2x  8  12
18.
7x  2  7
17.____________
18.____________
19. 2a  5  4  a  9
20.
bb  8  bb  7  5
19.____________
20.____________
Factor Completely. That means START by taking out the GCF then keep going if you can!!!
21. 8a 2b3  10ab2
2 2
22. 20xy  100x y
21.____________
22.____________
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Page 14 of 34
23. y 2  64
24.
2 x 2  200
23.____________
24.____________
25. x 2  5 x  6
26. 9 x 2  30 x  25
25.____________
26.____________
27. 16 x 2  8 x  1
28. m 2  m  42
27.____________
28.____________
29. 2 x 2  4 x  18
30. 6a 2  10a  4
29.____________
30.____________
31. a 2  12a  27
32.  2h 2  5h  3
31.___________
32.____________
Solve by factoring.
33. x  4x  4  0
34. (3 x  2)( x  5)  0
33.____________
34.____________
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Page 15 of 34
35. 14 x  x 2  0
36. x 2  10 x  21  0
35.____________
36.____________
37. x 2  5 x  14
38. a 2  5a  50
37.____________
38.____________
39. 3a 2  4a
40. m 2  22m  23m
39.____________
40.____________
41. s ( s  1)  72
42. 3 x 3  18 x 2  24 x
41.____________
42.____________
43. The area of a rectangular living room is 40 square feet. The length of the
room is 3 ft longer than the width. Find the dimensions of the room.
43.
L = __________
W = _________
Find the value of c that makes the trinomial a perfect square and then factor accordingly.
x2  4x  c
x 2  12 x  c
44.
45.
44.____________
45.____________
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Page 16 of 34
Solve by completing the square..
x2  2x  3
46.
47.
x 2  14 x  15
46.____________
47.____________
Identify the type of graph as:
System of equations
48.
Linear
Quadratic
49.
Exponential
48.____________
49.____________
50.
51.
50.____________
51.____________
52.
53.
52.____________
53.____________
54.
55.
54.____________
55.____________
Exam Review 2014
Page 17 of 34
Chapter 11 – Solving
Proportions
Solve for the indicated variable.
1.
5
n

8 64
2.
r
5

11 22
1._____________
2. _____________
3.
3
4

t 3 t 2
4.
x5 3

x3 4
3. _____________
4. _____________
5.
7
6

z3 z7
6.
6 x2

5
x
5. _____________
6. _____________
7.
3 x 1

x
4
8.
x x 1

4
x
7. _____________
8. _____________
Exam Review 2014
Page 18 of 34
Chapter 12 – Pythagorean,
Distance, and Midpoint
Find the missing side of the right triangle.
1.
a=6
1. c =__________
c=?
b=8
2.
2. b =__________
b=?
c = 13
a = 12
3.
3. c = _________
c=?
a=4
b=8
Determine if the 3 lengths can form a right triangle.
4. 24, 10, 26
5. 9, 16, 25
4._____________
5._____________
Find the distance and midpoint between the two points. Round your solution to the nearest
hundredth if necessary.
6. (5, 8) and (-2, 3)
7. (-1, 9) and (0, 7)
6._____________
_______________
7._____________
_______________
8.
(4, -3) and (10, 9)
9.
(0, 0) and (3, 4)
8._____________
_______________
9._____________
_______________
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Page 19 of 34
CHAPTER 6 ANSWERS
1. -9, 9
2. No solution
4.
0, 8
5. 𝑥 ≤ 3 𝐴𝑁𝐷 𝑥 ≥ −3
7.
𝑥 ≤ −6 or 𝑥 ≥ 4
8.
CHAPTER 7 ANSWERS
1. (1, 3)
2.
(2, 0)
Infinitely many – same line
6.
(-1, 3)
7.
Infinitely Many
8.
(-2, 3)
9.
(8, 4)
15.
Exam Review 2014
6. 𝑥 < −5 or 𝑥 > −3
𝑥 < 4 𝐴𝑁𝐷 𝑥 > 0
4.
12.
3. -3, 21
3.
5a.
5b.
10. (7, 7)
13.
11. (1, 2)
14.
16.
Page 20 of 34
No solution because parallel
CHAPTER 8 ANSWERS
1.
910
81b14
2.
3. x7
4.
2
x y3
2
5. -15x7y8
6. 16y z
7. a
8. -15a b
9. 16a b c
5b 3
10.
a
11. x12
12. x7
13. 1
14. x2
15. 1
16. 4x2
17.
8 12
9
6
4x 6
y4z4
20. Exponential Growth
4 8 12
2x 4 z 3
15 y 4
18.
21. $732.05
19. Growth, Decay, Growth, Decay
22.
$9,395.97
CHAPTER 9 ANSWERS
1.
14
2.
±16
3.
-6
4.
0
5.
11
7
6.
1
5
7.
5 3
8.
24 2
9.
5
5
10.
2 3
3
12.
2
2
11.
35
7
16. x = ±6
17. x = ±5
13. x = ±8
14. x = ±10
15. No Solution
18. x = ±4
19. x = 0
20. No Solution
21a. Aos: x = 1 Vertex: (1, -9) Opens Up
Min @ -9
y-Intercept: (0, -8) Solutions: (-2, 0) and (4, 0)
22a. Aos: x = -1 Vertex: (-1, 4) Opens Down
Max @ 4
y-Intercept: (0, 3) Solutions: (-3, 0) and (1, 0)
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Page 21 of 34
23. x 
 7  41
  0.3,  6.7
2
27a.
24. x 1, 
1
3
25. 25, 2 solutions
b.
26. 0, 1 solution
c.
28a. Aos: x = 1 Vertex: (1, 5) Opens Down
y-Intercept: (0, 3) Dashed Line Shaded Above
Solutions: (5, 0) and (6, 2)
29a. Aos: x = 1 Vertex: (1, 0) Opens Down
y-Intercept: (0, -1) Solid Line Shaded Below
Solutions: (1, -1) and (2, -5)
CHAPTER 10 ANSWERS
1. x5 – 5x4y3 + 4x3y + 3xy3 + 2;
Degree = 5
2.
6h2 – 4h – 2
3.
4z6 + z5 – 11z4 – 6z2
4. 7x2 + 2x – 3
5. -30p2q2 – 40p2q + 50pq3
6. 20x – 10
7. 22b3 – 13b2 + 6b – 14
8. x2 – x – 6
9. a2 – 12a + 36
10. 4x2 – y2
11. 14y2 + 27y – 20
12. 2x2 – 8
13. 9y2 – 30y + 25
14. x2 + 8x + 16
15. 12k2 + 23k – 9
16a. 14𝑥 + 4
19. a = 15
20. b = 5
21. 2ab2(4ab + 5)
22. 20xy(1 – 5xy)
23. (y – 8)(y + 8)
24. 2(x – 10)(x + 10)
25. (x – 2)(x – 3)
26. (3x – 5)(3x - 5)
27. (4x + 1)(4x + 1)
28. (m – 7)(m + 6)
29. 2(x2 – 2x + 9)
30. 2(3a + 1)(a – 2)
31. (a – 9)(a – 3)
32. –(h – 3)(2h + 1)
33. x = 4, -4
34. x 
35. x = 0, 14
36. x = 7, 3
37. x = -2, 7
38. a = 10, -5
Exam Review 2014
b. 10𝑥 2 + 13𝑥 − 3
Page 22 of 34
17. x = 2
18. x = 1
2
, 5
3
39. a  0,
4
3
40. m = 0, -45
41. s = 9, -8
42. x = 0, -4, -2
43. L = 8 ft, W = 5 ft
44. c = 4; (x – 2)2
45. c = 36; (x + 6)2
47. c = 15, -1
48. Quadratic
49. Linear
51. Exponential
52. Exponential
53. System of Equations
54. Quadratic
55. Linear
46. x = 1, -3
50. System of Equations
CHAPTER 11 ANSWERS
r
5
2
1.
n = 40
2.
5.
z = 67
6. x = 10
CHAPTER 12 ANSWERS
1. c = 10
2.
b=5
5.
No
8.
D = 180 = 13.42; MP = (7, 3)
Exam Review 2014
6. D =
3. t = 18
4. x = 11
7. x = -4, 3
8. x = 2
3.
c4 5
 3 11 
74 = 8.60; MP =  , 
2 2 
9.
4. Yes
7. D =
3 
D = 5; MP =  , 2 
2 
Page 23 of 34
5 = 2.23; MP = (-1/2, 8)
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