8th Grade Honors
Summer Review Packet
Name _____________
Solve each of the following equations.
3d
 5  11
4
2.
5 2x  3  15
  4  2x   3x  16
4.
3a  2  5a  14
5.
10  3x  2  2x  12
6.
2  6x  7   3  4x  5 
7.
Create an equation that has infinitely many solutions.
1.

3.
8. West Middle School’s enrollment has been decreasing at a rate of 75 students per year, whereas
East Middle School’s enrollment has been increasing at a rate of 60 students per year. West Middle has
3150 students and East Middle has 2475. If the enrollments continue to change at the same rates, in
how many years will the two schools have the same number of students?
Solve each of the following inequalities. Then graph the solution.
9.
x  8  12
11.

6
y  6  42
7
10.
2x  7  45
Decide whether the given ordered pair is a solution of the equation.
12. -3x + 6y = 12, (-4, 0)
13. x + 5y = 11, (2, 1)
14. y = 1, (3, 1)
15. 3y – 5x = 4, (-2, 2)
Use the function to create a table and a graph.
16. y = 3x – 4
x
17. y = -3(x – 1)
y
x
y
18. Miguel reads 20 pages every hour. Fill in the table to represent the function. Let the x-coordinate
represent the number of hours and the y-coordinate represents the number of pages read. Graph the
function.
x
y
Graph the equation.
19. y = 0
20. x = -4
21. x = 2
Calculate the rate of change.
22.
Time (min)
1
2
3
4
Distance (m)
40
80
120
160
23.
Number of
Erasers
Cost ($)
5
10
15
20
$0.30
$0.60
$0.90
$1.20
Calculate the slope of the line that passes through the two points.
24.
(1, 3), (5, 5)
25.
(-2, 1) and (7, 1)
26.
Determine the slope of the line.
27.
28.
29.
(2, -3), (5, -4)
30. The speeds of a coyote and giraffe are shown in the graph and table below.
Land Speed of a Coyote
Land Speed of a Giraffe
Number of Distance Ran
Hours
(mi)
0.5
16
1
32
1.5
48
a. Compare the functions by comparing the rates of change.
b. How much farther does a coyote run than a giraffe after 3 hours?
Graph each line.
1
x 3
2
31.
y 
33.
y   x 7
3
4
32.
y  4x  2
34.
y  3x  5
35. Mrs. Allison charges $15 for a basic cake that serves 12 people. A larger cake costs an additional
$2.50 per additional slice. The total cost can be given by y = 2.50x + 15, where x represents the number
of additional slices.
a. Graph the equation.
b. Interpret what the slope and the y-intercept
represent in this situation.
36. You are in charge of planning a barbeque. Hamburger costs $2 per pound and chicken costs $3 per
pound. You have $30 to spend. The graph below shows this situation. Interpret the x- and y-intercepts
from the graph.
37. The table shows the growth of a plant… Construct a function to model the relationship between the
number of days and the height of the plant.
Day
0
2
4
6
Height (cm)
5
10
15
20
38. The girls hockey team is going to put in an order for new jerseys. The total cost will include a onetime design fee plus the cost per jersey. If they order 30 jerseys the total cost will be $800. If they
order 40 jerseys the total cost will be $1050.
A. Use this information to determine the one-time design fee and the cost per jersey for the order.
B. Construct a function using the one-time design fee and the cost per jersey that would determine the
total cost for any number of jerseys ordered.
Solve the linear system graphically. Check the solution algebraically.
39.
y  x  5
y  x 1
40.
y  2x  2
y x 4
Use the substitution method to solve each linear system.
41.
x 4
x  3y  16
42.
x  2y  5
4x  3y  2
43.
3x  3y  7
y  x  5
44. Jose has $20 more than Sarah. Their combined money totals $90. Write and solve an algebraic
model to determine the amount of money each person has.
45. Last year you mowed grass and shoveled snow for 10 households. You earned $200 per household
mowing for the entire season and $180 per household shoveling for the entire season. You earn a total of
$1880 last year. Write and solve an algebraic model to determine the number of households you mow and
shovel for.
Perform the indicated operation and simplify each expression.
46. x 3 • x 6
49.
x8
x2
52. (-3cd) 3 (-d 2 )
47. (2x 4 )(3x 6 )
50.
53.
15x 3
5x
10x 3y 6
5x 5 y
48. (x 2 )4
51. (-x) 0
54.
x2
x5