Educational Service Center North – Secondary Mathematics
Common Core Math 8 Interim Assessment (Fall)
College Preparatory Math (CPM Chapters 1 - 4)
Directions: Answer all questions within the assessment packet. All answers may be written directly on this assessment in
spaces or boxes provided. When you are finished with the page, go on to the next page. Answer all constructed response
items in the test booklet, using the answer spaces given within each item. Use additional paper as needed.
1. For each linear equation in the table, select
whether the equation has no solution, one
solution, or infinitely many solutions.
Equation
No
Solutions
One
Solution
3. Three students solved the equation 3(5x-14) =18
in different ways, but each student arrived at the
correct answer. Select all of the solutions that
show a correct method for solving the equation.
Infinitely
Many
Solutions
36x + 24 = 12 (x + 2 + 2x)
x=x+1
-12(x + 2) = -14x + 2
2. Consider the equation 3(2x+5) = ax + b
Part A
Find one value for a and one value for b so that
there is exactly one value of x that makes the
equation true. Explain your reasoning.
a=
b=
4. Consider this equation:
C = ax – bx
Part B
Find one value for a and one value for b so that
there are infinitely many values of x that make
the equation true. Explain your reasoning.
a=
b=
Joseph claims that if a, b, c are non-negative
integers, then the equation has exactly one
solution for x.
Circle all cases that show Joseph’s claim is
incorrect.
o
o
o
o
o
a – b = 1, c = 0
a = b, c ≠0
a = b, c = 0
a – b = 1, c ≠ 1
a ≠ b, c = 0
1
Educational Service Center North – Secondary Mathematics
Common Core Math 8 Interim Assessment (Fall)
College Preparatory Math (CPM Chapters 1 - 4)
Directions: Answer all questions within the assessment packet. All answers may be written directly on this assessment in
spaces or boxes provided. When you are finished with the page, go on to the next page. Answer all constructed response
items in the test booklet, using the answer spaces given within each item. Use additional paper as needed.
5. a.
7. John and Kim wrote down two different
functions that have the same rates of change.
John’s function is represented by the table
shown.
b. Point A is plotted on xy-coordinate plane
below. You must determine the location of
point C given the following criteria:
 Point C has integer coordinates.
 The graph of line AC is not a function.
Graph a function that could be Kim’s function.
Place a point that could represent point C on the
coordinate axis below.
6. This graph shows the amount of money (s) in
Jack’s account after w weeks.
Write an equation to represent the amount of
money (s) in Jack’s account after w weeks.
8. Amy was assigned to write an example of a
linear functional relationship. She wrote this
example for the assignment. The relationship
between the year and population of a county
when the population increases by 10% each
year.
Part A
Complete the table on next page to create an
example of the population of a certain county
that is increasing by 10% each year.
Complete table on
next page.
2
Educational Service Center North – Secondary Mathematics
Common Core Math 8 Interim Assessment (Fall)
College Preparatory Math (CPM Chapters 1 - 4)
Directions: Answer all questions within the assessment packet. All answers may be written directly on this assessment in
spaces or boxes provided. When you are finished with the page, go on to the next page. Answer all constructed response
items in the test booklet, using the answer spaces given within each item. Use additional paper as needed.
10. The total cost of an order of shirts from a
company consists of the cost of each shirt plus a
one-time design fee. The cost of each shirt is the
same regardless of how many shirts are ordered.
The company provides the following examples
to customers to help them estimate the total cost
of an order of shirts.
 50 shirts cost $349.50
 500 shirts cost $2,370
Part A
Part B
State whether Amy’s example represents a linear
functional relationship. Explain your reasoning.
Based on the examples, what is the cost of each
shirt, not including the one-time design fee?
_____________________________. Explain
how you found your answer.
Part B
What is the cost of the one-time design fee?
_____________________________. Explain
how you found your answer.
11. A swimming pool containing 1600 gallons of
water is emptied at a rate of 300 gallons every 2
hours.
9. This table shows a linear relationship of water
level in a tank and time.
Determine whether each statement about the
amount of water in the pool is true. Select true
or false for each statement.
Statement
Write the rate of change of the water level, in
feet per hour.
True
False
The initial amount of water in the
pool is 1600 gallons.
The amount of water in the pool
decreases by 150 gallons every 1
hour.
The amount of water in the pool at 3
hours is 450 gallons.
3
Educational Service Center North – Secondary Mathematics
Common Core Math 8 Interim Assessment (Fall)
College Preparatory Math (CPM Chapters 1 - 4)
Directions: Answer all questions within the assessment packet. All answers may be written directly on this assessment in
spaces or boxes provided. When you are finished with the page, go on to the next page. Answer all constructed response
items in the test booklet, using the answer spaces given within each item. Use additional paper as needed.
12. This graph represents a linear function.
14. Which table of values can be represented by the
function, y = 3x + 2?
Write an equation in the form y = mx + b that
represents the function described by the graph.
13. The table and equation shown each represent a
different linear function.
Write the difference between the rates of change
for these two functions.
4