Download Problems 1-3, solve and graph

Name_____________________________________Date________________Period_____
Algebra 1 ~ Review for Final Exam ~ FALL 2012
Problems 1-3, solve and graph.
1. 5x − 7(x+ 1) > −9
answer:______
2. −p + 6p ≤ 4 + 6p
answer:______
3. x x 









answer:______
4. Latisha is on page 30 of her book and reads 3 pages every night. Sal is on page 40 of the same book
and reads 2 pages every night. How long will it take Latisha to be further in the book than Sal? Write
and solve an inequality. Write your answer in a sentence.
5. Jasmine and her sister are saving to buy MP3 players. Jasmine has $50 and plans to save $10 per
week. Her sister has $80 and plans to save $7 per week. In how many weeks will Jasmine have more
money saved than her sister? Write and solve an inequality. Write your answer in a sentence.
6. A principal is choosing between two fieldtrips. The first costs $600. The second costs $240 plus $40
per student. For what number of students is the first trip less expensive? Write and solve an
inequality. Write your answer in a sentence.
7. Give the domain and range of the relation. Tell whether the relation is a function.
x
3
3
4
5
y
2
–2
7
9
D:_______________
R:_______________
Function?_______
8. Give the domain and range of the relation. Tell whether the relation is a function.
D:_______________
R:_______________
Function?_______
9. Express the relationship {(-5, 7), (-1, 4), (3, -2), (4, -6)} as a table, a mapping, and as a graph.
x
y
Problems 10-14, determine a relationship between the x- and y-values.
Write an equation in y = mx + b.
10.
x
y
0
5
1
10
2
15
3
20
1
15
2
12
Equation: ____________________
11.
x
y
-1
21
0
18
Equation: ____________________
12.
x
y
2
14
4
18
6
22
8
26
Equation: ____________________
13.
y-intercept:_______
slope:______
equation: ____________
14.
Write an equation that shows the relationship between x and y in (1, -3 ) and ( 2, -1 )
slope:______
y-intercept:_______
equation: ____________
15. This table shows the number of people at a festival at
certain times during the day.
Independent (x):___________
Dependent (y):___________
During which time interval did the number of people increase at the greatest rate?___________
What was the rate of change for that interval?__________
Solve the following equations for the given variables.
16. 48 = 14 + 2(z – 1)
17. A truck company charges $300 plus $15 per hour. Another company charges
$120 plus $35 per hour. How long would a job take for the cost to be the same at
both companies?
Name_____________________________________Date________________Period_____
Part 2 Review for Final
18. 74a + 28 = 72a – 12
19. Write equation to represent “23 less than a number is 8.” Then solve.
20. Write an equation to represent “the quotient of 55 and a number is 5.”
21. Write an equation to represent the relationship “the product of a number
and 12 is 60.” Then solve the equation.
22. A fitness company charges $500 plus $30 per hour. Another company
charges $320 plus $40 per hour. How many hours would it take for the cost
to be the same at both companies?
23. The triangles shown have the same perimeter. What is value of the x?
X+8
2X+5
X+2
3X - 2
X+4
X
24. Given the equation 3x+4y=-8, solve for y.
25. Given the function h(x) = ½ x – 3, what is h (12)?
26. Given the function F(x) = 3x + 2, what is F(–4)?
27. Given the function For f(x)= 5x, find f(x) when f(x) = 30.
28. F(x) = 6x – 1, find f(x)= –5
29. Use the graph below to answer the following questions.
a. f(3)=______
b. f(-2)=______
9
8
7
6
5
4
3
2
1
c. f(x)=0 ______
d. f(x)=-7_____
-9
-8 -7 -6
-5 -4 -3 -2
-1 -1
-2
-3
-4
-5
-6
-7
-8
-9
30. –4+(–3)= _____
31. 5 – 8 = _____
32. Simplify using order of operations
.
________
y
f(x)=-abs(x-3)+4
x
1
2
3
4
5
6
7
8
9
33. Simplify using order of operations
3 1  62
6  3 5
34. Simplify the following expression:
________
2  x 2  3  x   4  x  x 2  2 
2 x 2  6 x  14
2
b. x  5 x  1
a.
c. 2 x  12 x  1
2
d. 2 x  2 x  2
2
35. Which expression is equal to :
a.)
b.)
c.)
d.)
-(3x - 2) + 3(-2 + 4x)
15x - 4
9x - 4
9x - 8
15x + 8
36. Which simplified equation represents the algebra tile model below?
2x  4  x  2  x
A.
B.
C.
D.
3x 2  2 x  2
2 x2  2
2x  2
2x2  2x  2
37. Which simplified equation represents the algebra tile model below?
x 2  2 x  4  3x  2
A.
B.
C.
D.
x2  2  x
2  x  x 2
x2  2  x
x  3x  4
Solve the following equations, grid your answer below.
38. 3x  27
39.
1
x7
7
40. 2( y  3)  34
Name_____________________________________Date________________Period_____
Part 3 Review for Final
41. 12  x  15
44.
45.
46.
47.
42. 3x  5  7 x  3
43. 5 y  9  2 y  30
48. Is the function
a linear function? ________ If so, graph the function.
49. Use intercepts to graph the line described by the equation
.
50. Define rate of change. Write down all the different ways that we described rate of change.
__________________________________________________________________________________
__________________________________________________________________________________
51. Find the slope of the line that contains
and
.
52. Find the slope of the line.
m = _________
y
10
8
6
4
(8, 2)
2
–10 –8
m = __________
–6
–4
–2
–2
–4
–6
–8
–10
2
4
6
8
10
(8, –6)
x
53. The graph shows a linear relationship. Find the slope.
m = __________
y
10
8
6
4
(–7, 3)
–10 –8
–6
–4
2
–2
–2
2
4
6
8
10
x
–4
(–8, –5)
–6
–8
–10
54. Find the slope of the line that contains (–3, –2) and (4, –2)
m = __________
55. Tara creates a budget for her weekly expenses. The graph shows how much money is in the account at
different times. Find the slope of the line. Then tell what rate the slope represents.
2750
2500
(4, 2400)
Amount ($)
2250
(12, 2000)
2000
m = __________
1750
The slope represents:
1500
1250
1000
_______________________________
750
500
________________________________
250
2
4
6
8 10 12 14 16 18 20 22
Time (weeks)
________________________________
Name_____________________________________Date________________Period_____
Part 4 Review for Final
56. Graph the line with the slope  and y-intercept –3.
2
3
57. Graph the line with a slope of  3 that contains the point (–3, –4).
5
58. Fill in the second step of the solution process and the justification
Step 1: 10x - 2 (x - 3) = 22
Step 2: ____________________
Step 3:
8x +6
= 22
A.
10x - 2x - 6 = 22; combine like term
B.
10x - 2x + 6 = 22; distributive property
C.
8x - (x - 3) =22; subtract 2 from 5x
D.
10x - 2x - 6 = 22; distributive property
59. For his cellular phone services, Joseph pays $45 a month, plus $ 0.45 for each minute over the
allowed minutes in his plan. Joseph received a bill of $55.35 last month. How many minutes did he
use over the allowed minutes?
a.
b.
c.
d.
108
23
43
17.25
60. A movie rental store charges a membership fee of $10 and $1.35 per movie for the first month.
Kim paid $19.45, how many movies did she rent that month?
a.
b.
c.
d.
7
6
14
5
61. A catering company charges a fixed fee of $110 and $6.25 a person attending the party. If an
event cost $303.75, how many people attended that event?
a.
b.
c.
c.
31
49
17
3
62. Marco and his friend want to go the movies together and have a total of $47. The
ticket are sold $7.5 each how many tickets can they buy?
a. 0 tickets
b. 6 tickets
c. 8 tickets
d. 10 tickets
63. Solve the inequality
and graph the solutions.
64. Solve the inequality
Find the x and y intercepts and then graph. Find the slope.
65. 2y – 6x = 12
66. 9x +18y = -36
67. 2y = -12 + 4x