BM 3 (8th Grade)
Question #1 . Consider the two functions below.
Part A: What are the rates of change for each function?
Answer: Slope I = 3,
Slope II = 1/3
Part B: What is the difference between the rates of change? 2/3
Part C: How do the intercepts of each function compare to each other?
I: y-intercept ( 0, 3), x-intercept (-1, 0)
II: y-intercept ( 0, 0), x-intercept (0, 0)
Part D: Determine if each function is increasing or decreasing.
Answer: Both are increasing.
Part E: Write an equation for each function. I:
y = 3x + 3 ,
II:
y=
1
3
𝑥
Part F: Based on parts A through E, what relationships exist between the functions?
Answer: Both increasing. Function “I” is faster because bigger slope.
Question #2. Answer A (on your worksheet)
Answer D (on this document)
Question #3
Simplify the following expression.
Answer B.
52
51
 52(1)  53  125
(4).
Answer 135 cw + 35 ccw + 125 cw + 45 cw
= 100 cw + 170 cw = 270 cw = 90 ccw
(5).
In the figure below, lines 1 and 2 are parallel. Lines 3 and 4 are also parallel.
Calculate the measure of the indicated angles.
Note: Figure is not drawn to scale.
The measure of angle A is
The measure of angle E is
The measure of angle B is
The measure of angle F is
122
°.
43
°.
137
°.
43
°.
Question #6
Directions: Type your response in the box.
Brian drew the following quadrilaterals and claimed they were similar.
Describe two sequences of transformations that will transform quadrilateral A into quadrilateral B and prove
Brian is correct.
Answer: Dilate by scale factor =
Reflect over x-axis.
½
Proof: X (-6, -2) → ( -3, -1) → (-3, 1)
Y (-2, -6 ) → ( -1, -3) → (-1, 3)
(#7).
AB = 12,
BC = 5,
CA  (5)2  (12)2  25  144  169  13
CA > AB > BC
Question #8
Directions: Select all the correct answers.
The graph below shows the number of open blossoms in a nursery and the number of hours after dawn.
The equation of the line of best fit is below.
What does the y-intercept represent?

The number of blossoms open at dawn.

There were three blossoms open at dawn.

The number of blossoms open per hour.
There were twenty-three blossoms opening per hour.
Question #9
Ronald worked at his company for many years. Upon retiring, he calculated that he completed 80,022 hours of
work in the time he worked for the company. Which of the following would be a reasonable estimate for the
number of hours he worked at his company?
A.
8 × 10-5 hours
B.
8 × 10-4 hours
C.
8 × 105 hours
D.
8 × 104 hours
Question #10
After 9 p.m., the manager of a local diner records the number of customers in the diner at each hour. At 9
p.m. on Tuesday, there were 38 customers in the diner.
For each hour after 9, the manager noticed that 4 customers entered the diner, while 11 customers left. Use this
information to complete the table.
Each Hour Customers in
After 9
the Restaurant
0
38
1
31
2
24
3
17
4
10
The x-values represent the number of hours after 9 p.m. The y-values represent the number of customers in the
restaurant.
The equation which represents the number of customers in the restaurant is
y=
-7
x+
38
.
Question #11
The slope of the line formed between point B and point E on the graph below is
What is the slope of the line formed between point B and point C?
A.
B.
C.
D.
.
Question #12. Sharon drew the following quadrilaterals and claimed they were congruent.
Describe two sequences of transformations that will transform quadrilateral A into quadrilateral B and prove
Sharon is correct.
Answer Rotate 90°CW → Reflect over y = 5 → Reflect over y-axis → Translate down 1.
Prove: y (-6, -2) → (-2, 6) → (-2,4) → (2,4) → (2,3)
Answer: Part A: Yes, Grayson is correct. It is not a function because x values 4 repeat !!
Replace point (4, 6) with (1, 6).
Question #14
Directions: Drag each tile to the correct box.
Use rational approximations to place the irrational numbers in order from greatest to least.

,
,
Answer:
= 3.14 + 3 = 6.14

2

3.14
 1.57
2
= 6.28 – 3 = 3.28

>
>
Question #15
Directions: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the
fraction bar(s).
Cynthia is making homecoming mums. Her small mums require 6 feet of silk ribbon, and her large mums
require 18 feet of silk ribbon.
After completing all of her orders, she had made 107 mums using a total of 1,230 feet of silk ribbon.
Let l represent the number of large mums and s represent the number of small mums that Cynthia made.
Finish the equations below to represent the system and then solve.
18
6
49
58
Solve by elimination: ( L + s = 107) (-1) ,
3L + s = 205
Question #16
2L = 98,
L = 49
Directions: Select the correct answer.
Look at the scatter plot below.
Which of the following statements is supported by the data shown in the scatter plot?
A.
There is a negative relationship between the length of a CD in minutes and the number of copies sold.
B.
There is a positive relationship between the length of a CD in minutes and the number of copies sold.
C.
There is no relationship between the length of a CD in minutes and the number of copies sold.
D.
There is both a positive and a negative relationship between the length of a CD in minutes and the number of
copies sold.
(17)
Answer Notice the (x,y ) has y values decrease by 4. The x values increase by 2.
Here is the pattern for straight line points:
( -5, 25), (-4, 23), (-3, 21), (-1, 17), (1, 13), (3, 9), (5,5), (7, 1) .
The point ( -2, 17) is not on this line. So replace this point with (1, 13).
Question #18
Directions: Select all the correct answers.
Ramon surveyed 40 men and women to see how many like dancing. The following table represents his results.
Men Women Total
Like Dancing
7
12
19
Do Not Like Dancing 13 8
21
Total
20 20
40
Which associations are suggested by the two-way table?

Most of the people who like dancing are men.

Most men tend to not like dancing.

Most women tend to like dancing.

Most women tend to not like dancing.

Most of the people who like dancing are women.

Most men tend to like dancing.
Question #19
Directions: Type the correct answer in each box. Use numerals instead of words.
In the right triangle shown below,
and all side lengths are integers.
The possible values for a are shown in the answer bank.
Answer Bank for Side a
10 ft 12 ft 24 ft
26 ft 36 ft 48 ft
Determine the values of a, b, and c using the Pythagorean theorem.
For the right triangle, a is
b 
36
feet long, b is
15
1
(36)  3  15 . Then c  (36) 2  (15) 2  1296  225  1521  39
2
Remember the following Pythagorean Triples
3
6
5
9
8
12
7
15
10
15
20
18
16
21
12
15
24
9
27
14
30
24
20
28
33
40
feet long, and c is
4
8
12
12
15
16
24
20
24
36
21
24
30
28
35
36
32
40
36
48
40
45
48
45
44
42
5
10
13
15
17
20
25
25
26
39
29
30
34
35
37
39
40
41
45
50
50
51
52
53
55
58
[3 - 4 - 5]
[3 - 4 - 5]
[3 - 4 - 5]
[3 - 4 - 5]
[5 - 12 - 13]
[5 - 12 - 13]
[3 - 4 - 5]
[8 - 15 - 17]
[3 - 4 - 5]
[5 - 12 - 13]
[3 - 4 - 5]
[3
[7
[3
[8
[5
-
4 - 5]
24 - 25]
4 - 5]
15 - 17]
12 - 13]
[3 - 4 - 5]
[20 - 21 - 29]
39
feet long.
36
48
60
[3 - 4 - 5]
Question #20
Directions: Select the correct answer.
Which graph shows the result of a reflection about the x-axis of this graph?
Answer: A
Question #21
Christina and Stacie each determined the cost of printing posters for their campaigns.
The table below represents the total cost of printing x posters for Christina's campaign.
Quantity Price ($)
3
9
6
9
12
18
27
36
Unit Price
$𝟗
$𝟑
=
𝟑 𝒑𝒐𝒔𝒕𝒆𝒓𝒔
𝟏 𝒑𝒐𝒔𝒕𝒆𝒓
The graph below represents the total cost of printing x posters for Stacie's unit price =
Which of the following is true?
A.
Christina's price per poster is cheaper than Stacie's price per poster .
$𝟓
𝟏 𝒑𝒐𝒔𝒕𝒆𝒓
Question #22
Concrete is being used to construct highways in a city. Jennifer can approximate the area covered by the
concrete using a rectangle with a width of 0.0138 miles and a length of 5.63 × 104 miles.
About how many square miles are covered by the concrete?
Area = (1.38 x 10-2 ) (5.63 x 104 ) = 7.7694 × 102
A.
7.7694 × 102
Question #23
Directions: Select all the correct answers.
Sketch the graph of the equation below.
Based on a sketch of the graph, which of the following statements are true?

The graph of the equation is increasing when 1 < x < 3.

The graph of the equation is increasing when -2 < x < 0.

The equation represents a linear function.

The equation represents a nonlinear function.

The equation represents both a linear and a nonlinear function.

The equation represents neither a linear nor a nonlinear function.
Question #24
Directions: Select all the correct answers.
Identify all correct representations of the solution to the system below.



the intersection of the lines x = -2 and y = 0.

the intersection of the lines x = 1 and y = -3.

the intersection of the lines x = 0 and y = -2.
Question #25
Directions: Use a piece of scratch paper to write equations and calculations to help you write your response.
Then, type your response in the box.
Look at the equation below.
Here
1
y = −2𝑥 + 3
Part A: Create an equation in the form Ax + By = C that passes through the point (1, 1) and creates a system of
equations with the line above that has one solution.
:
Answer point slope form
y- y1 = m ( x – x1)
Y -1 = 2 (x -1) . This gives -2x + y = -1
Part B: Thinking about their graphs of the two equations, how are the two lines similar and how are they
different? They are perpendicular and linear.
Question #26
Directions: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the
fraction bar(s).
Simplify each of the following expressions.
3
5
12
9
Question #27
Hannah was asked to rotate the image in graph A 90° counter-clockwise. However, she did the rotation
incorrectly and ended up with the image in graph B.
What rotation does she need to do in order to correct the image in graph B?
Hannah should rotate the image in graph B
(1, 5) in graph A is at point (
-1
,
180
-5
Question #28
Sal solved the equation as shown below.
WRONG
degrees counter-clockwise, so that the vertex at point
) in graph B.
Part A: Explain what happened between each step and indicate if that step is valid.
Answer Can not combine -2x -1.
Part B: If any steps in solving the equation were invalid, show the correct process of solving the equation.
Answer
3x + 12 = -2x -1
+2x
+2x
(29).
Answer
1
V   r 2h ,
3
60 
1
 r 2h ,
3
180 = r2 h
Test: r = 6 , h= 5. Yes!! 180 = 36 (5).
Diameter = 12.
Question #30
Directions: Type your response in the box.
Cynthia and Ramon bought gifts for their family while on vacation. In one store, Cynthia bought two gifts per
grandchild, one that cost $3 each and one that costs $5 each. She also spent $14 on a keepsake for her daughter.
In another store, Ramon bought one gift per grandchild that cost $8 each. He also spent $12 on a keepsake for
his son and $2 on a key chain for himself. After leaving each store, Cynthia and Ramon compared their receipts
and noticed they spent the same amount of money.
Part A: Letting x represent the number of grandchildren, what equation could be set up in order to determine the
number of grandchildren Cynthia and Ramon have?
ANSWER: 3X + 5X + 14 = 8X + 12 + 2
8X + 14 = 8X + 14
Part B: What is the solution to the algebraic equation found in part A? INFINITE SOLUTIONS
Part C: How many solutions does the equation found in part A have? INFINITE SOLUTIONS