STUDY GUIDE—Math 8
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5 x  2 y  8
1. Solve:
x  y  3
a. (-5,-1)
c. (-2,-1)
b. (5,1)
d. (-2,1)
x  2 y  2
2. Solve :
3x  2 y  6
a. (3,-4)
c. (4,-3)
b. (-3,-4)
d. (4,3)
3. Solve:
2 x  7 y  6
2 x  7 y  9
a. (-5, 4)
c. No solution
b. Infinitely many
d. (5,-3)
4. Solve:
Name___________________
y  2 x  7
3 y  6 x  21
a. (0,0)
c. Infinitely many
b. No solution
5. Solve:
d. (8,0)
x  4 y  16
3x  2 y  6
a. (4,-3)
c. (-4,-2)
b. (-4,3)
d. (-4,-3)
6. What are the different types of solutions to a system of equations and what type
of lines produce those solutions?
Types of solutions
Types of lines
7. Mrs. Stoltz and Miss Bobb are selling fruit for a school fundraiser. Customers
can buy small boxes of grapefruit and larges boxes of grapefruit. Mrs. Stoltz sold
5 small boxes and 12 large boxes for a total of $188. Miss Bobb sold 7 small and
2 large boxes for $56. What was the cost of one small and one large box of
grapefruit?
a. Small box $5, large box $16
c. Small box $14, large box $4
b. Small box $4, large box $14
d. Small box $5, large box $7
8. Mrs. Conte has a farm. She has 20 animals consisting of ducks and cows. There
are 70 total legs. How many ducks does she have?
a. 5 ducks
c. 7 ducks
b. 10 ducks
d. 15 ducks
3(6 x  3)  40
9. Solve:
a. x  12
b. x 
49
18
49
18
d. x  12
4x  30  9x  9
10. Solve:
a. x  
b. x 
c. x  
21
5
21
5
c. x  
d. x 
5
21
5
21
11. Solve 6( x  4)  3(2 x  8)
a. x  30
c. Infinitely many
b. No solution
d. x  0
12. Solve:
4
x  9  26
7
a. x  20
b. x 
245
4
c. x  20
d. x  
245
4
13. Solve: 6(2 x  1)  4  2(2 x  5)
a. No solution
c. x  0
b. x  10
d. x  10
14. Solve: 3(6 x  5)  2(9 x  10)
a. No solution
c. x 
5
36
b. Infinitely many
d. x 
35
36
7
15. Solve: 54  9  x
8
a. x  72
b. x 
441
8
c. x  
441
8
d. x  72
Simplify the following.
16. -7√200
a. 48√6
b. -80
c. -18√7
d. -70√2
17. 2√12 ∙ -3√6
a. -72
b. -6√2
18.
c. 3√2
d. -36√2
7√3
5√36
a.
b.
7√3
30
7√12
5
c. .
d.
2
√12
7
30
19. -3√45 + 2√20
a. -10√5
b. -5√5
c. -6√5
d. -√5
20. 3√2 - 3√18 + 3√24
a. -6√2 + 6√6
b. -15√2 + 6√6
c. -12√2 + 6√6
d. -21√2 + 6√6
21. Is the following graph a function?_______ Why or why not?__________________
_____________________________________________________________________
22. Which of the following is NOT a function?
a. {(-1,0), (0,0), (-1,1), (1,3)}
c. {(9,3), (6,2), (4,4), (3,3)}
b. {(0,0), (-1,0), (-2,0), (-3,0)}
d. {(2,4), (4,6), (6,8), (8,10)}
23. Which equation is linear?
a. y = 2x – 3
c. y = 𝑥 4 + 7
b. y = xy + 2
d. y = 𝑥
5
24. Which equation is linear?
a. 𝑥 2 + 𝑦 2 = 16
2
b. y = 3x – 2
c. y = 𝑥 3 – 1
d. y = xy
25 – 27. Write the correct equations for the following graphs. Your final answer
should be in slope intercept form. (y = mx + b)
25.___________________________________
26.___________________________________
27._____________________________________
28. What is the equation of the line graphed below?
29. What is the slope of each triangle?
30. What is the slope of the line that passes through the points A(2, -4) and B(1, -4)?
31. What is the equation of the line graphed?
32.
What is the equation of the line graphed?
33. What is the slope of the line for the following points: (5, 7) (-5, 4)?
3
x  1 , and
4
function 2 is represented by the graph to the right.
34. Function 1 is defined by the equation y 
Which statement about the functions is true?
a. Function 1 has the greater rate of change and the
greater y-intercept.
b. Function 2 has the greater rate of change and the
greater y-intercept.
c. Function 1 has the greater rate of change and function
2 has the greater y-intercept.
d. Function 2 has the greater rate of change and function 1 has the greater yintercept.
35. Order the boys from winner to loser: __________
____________ ___________
36. What is the slope of the line?
37. What is the equation of the line that passes through the point (4,12) and has a yintercept of (0,-2)?
a. y 
5
x2
2
c. y  2 x  2
b. y 
7
x2
2
d. y  6 x  2
38. A line contains the points (4,2) and (0,-1). What is the equation of the line?
a. y  2 x  6
c. y 
1
x 1
4
3
x 1
4
d. y 
4
10
x
3
3
b. y 
39. What is the equation of the line given the two points?
(0, 4) and (2, -2)
Directions: Use the following table to answer questions 40 – 42.
Taking PE
Not taking PE
Totals
Band
25
45
Chorus
35
72
Orchestra
50
8
58
Total
40. What is the marginal frequency of students who are not taking PE?
a. 53 students
c. 100 students
b. 90 students
d. 37 students
41. Given that a student is in Band, what is the joint relative frequency that they are not
taking PE?
a. 25%
c. 64.29%
b. 22.5%
d. 35%
42. What is the relative frequency of kids in Orchestra to the total number of students?
a. 29%
c. 50%
b. 8%
d. 58%
43. Make a scatter plot of the
following data. Please title and
label your display. Use the plot
to answer questions 44 and 45.
Number Oz. of
of Bees Honey
20
46
50
110
30
60
40
85
100
200
80
170
44. Draw in a Line of Best Fit. Which equation is closest to your Line of Best Fit?
a. y = -2x
c. y = 3x
b. y = 2x + 10
d. y = -3x + 30
45. Use the equation that you selected to predict how many bees are need to produce
450 oz of honey.
a. -225 bees
c. 150 bees
b. 220 bees
d. -140 bees
Directions: Use the follow qualitative graph to answer questions 46 - 50.
Distnace form Home
Mary's Daily Travels
10
C
8
D
6
4
E
B
2
F
G
A
0
0
2
4
6
8
10
12
14
Time in Hours
46. How many hours was Mary at work?
a. 8 hours
c. 7 hours
b. 1 hour
d. 6 hours
47. When did Mary drive the fastest?
a. section B
c. section E
b. section F
d. section G
48. What scenario makes the most sense for section F?
a. Mary is at work.
c. Mary is driving home.
b. Mary is at a stop light. d. Mary goes to the grocery store.
49. How far from home is Mary’s place of work?
a. 4 miles
c. 6 miles
b. 8 miles
d. 5 miles
50. Which description match section E?
a. Mary is moving towards home at a rapid pace
b. Mary is not moving at all.
c. Mary is moving away from home at a moderate pace.
d. Mary is moving slowly toward home.