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Algebra 1 Teachers
Weekly Assessment Package
Unit 2
Created by:
Jeanette Stein
©2015 Algebra 1 Teachers
1
Semester 1 Skills | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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SEMESTER 1 SKILLS
3
UNIT 2
5
WEEK #5
WEEK #6
WEEK #7
6
8
10
UNIT 2 - KEYS
12
WEEK #5 - KEY
WEEK #6 - KEY
WEEK #7 - KEY
13
15
17
2
Semester 1 Skills | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Algebra 1 Common Core
Semester 1 Skills
Number
Unit
CCSS
Skill
1
1
A.REI.3
Solve two step equations (including proportions)
2
1
Order of Operations
3
1
Create a table from a situation
4
1
A.REI.10
Create a graph from a situation
5
1
F.BF.1
Create an equation from a situation
6
1
F.IF.1
Identify a function
7
1
F.IF.2
Evaluate a function
8
1
A.REI.6
Basic Systems with a table and graph
9
1
F.LE.1
Identify linear, exponential, quadratic, and absolute value
functions
10
2
F.BF.3
Translate a graph in function notation
11
2
F.IF.6
Calculate Slope
12
2
S.ID.7
Interpret meaning of the slope and intercepts
13
2
F.BF.2
Construct an arithmetic sequence
14
2
F.BF.4
Find the inverse of a function
3
Semester 1 Skills | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Number
Unit
CCSS
Skill
15
3
S.ID.6
Find the line of best fit
16
3
S.ID.6
Predict future events given data
17
3
S.ID.8
Calculate Correlation Coefficient with technology
18
3
S.ID.9
Understand the difference between Causation and Correlation
19
4
S.ID.1
Create box plots
20
4
S.ID.2
Calculate and compare measures of central tendencies
21
4
S.ID.3
Understand the effects of outliers
22
4
S.ID.5
Use two way frequency tables to make predictions
23
4
N.QA.1
Convert Units
24
4
N.QA.3
Understand Accuracy
25
5
A.REI.3
Solve advanced linear equations
26
5
A.REI.1 A.CED.4
Solve literal equations and justify the steps
27
5
A.REI.3
Solve inequalities
28
5
A.REI.12
Graph inequalities
29
6
A.REI.6
Solve a system of equations by graphing
30
6
A.REI.6
Solve a system of equations by substitution
31
6
A.REI.5
Solve a system of equations by elimination
4
Semester 1 Skills | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Unit 2
Weekly Assessments
5
Unit 2 | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Week #5
1. Given 𝑓(𝑥) = 𝑥 2 − 2𝑥 + 9, find:
a. 𝑓(2) =
2. Find the slope of the graph between the two
points.
a. (4, 3), (8, -5)
b. 𝑓(−3) =
b. (3/4, 5/2), (2/3, -1/4)
c. 𝑓(1/2) =
c. (5, 8), (5, 10)
3. You have $22.50 in your piggy bank. You choose to buy two cookies every day at lunch for
yourself and your sweetheart. They cost $0.75 for both cookies. Create an equation, table, and
graph for this situation.
Equation: _________________________
Table:
Graph:
6
Unit 2 | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Week #5 Continued
4. The below table provides some U.S. Population data from 1982 to 1988:
Population
Change in Population
(thousands)
(thousands)
1982
231,664
--1983
233,792
2128
1984
235,825
2033
1985
237,924
2099
1986
240,133
2209
1987
242,289
2156
1987
244,499
2210
If we were to model the relationship between the U.S. population and the year, would a linear function be
appropriate? Explain why or why not.
Year
Mike decides to use a linear function to model the relationship. He chooses 2139, the average of the
values in the 3rd column, for the slope. What meaning does this value have in the context of this
model?
Use Mike's model to predict the U.S. population in 1992.
5. As I fill the following beaker with water at a
constant rate, graph the height of the water in
relation to time.
6. Suppose 𝑓 is a function. If 12 = 𝑓(−9),
give the coordinates of a point on the
graph of f.
If 16 is a solution of the equation
𝑓(𝑤) = 6, give a point on the graph of f.
7
Unit 2 | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Week #6
1. Emma understands that the function, 𝑓(𝑥) =
3.5𝑥 + 10 gives her the price for the bands tshirts given the $10 set up fee and the price of
$3.50 per shirt.
2. Lauren keeps records of the distances she
travels in a taxi and what she pays:
Distance, d
(in miles)
Fare, F
(in dollars)
3
5
8.25
12.75
11
26.25
She also knows that there are 88 band members.
a. If you graph the ordered pairs
(𝑑, 𝐹) from the table, they lie on a line.
How can you tell this without graphing
them?
What is the total cost for the shirts?
b. Show that the linear function in part (a)
has equation 𝐹 = 2.25𝑑 + 1.5.
c. What do the 2.25 and the 1.5 in the
equation represent in terms of taxi
rides?
3. Solve the following equations and justify the steps.
1
(4𝑥
3
a.
8
+ 1) = 9
b. 10 =
5𝑥−3
4
Unit 2 | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Week #6 Continued
4. If you have $10, you can buy 4 cookies and no
brownies or you can buy 5 brownies and no
cookies. There are several other options as well.
Graph the situation.
If you have $10 and you buy 1 cookie a day you
will run out of money after 5 days. Graph the
situation.
5. Let F assign to each student in your math
class his/her locker number. Explain
why F is a function.
Describe conditions on the class that
would have to be true in order for F to
have an inverse.
Which situation has the cheaper cookie? (Circle one)
1st
2nd
Not enough information
6. Candy bars cost $1.50 each. What is the total bill?
What is the domain? _____________________
What is the range? _____________________
9
Unit 2 | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Week #7
1. A souvenir shop in Niagara Falls sells picture postcards priced as follows:
Postcards
15 cents each
Six for $1
a. Graph the price of buying postcards as a function of
the number of cards purchased.
b. Is there something wrong with this pricing scheme?
Explain.
2. Suppose P1= (0,5) and P2= (3, −3). Sketch P1 and P2.
a. For which real numbers m and b does the graph of a
linear function described by the equation
𝑓(𝑥) = 𝑚𝑥 + 𝑏 contain P1 and P2? Explain.
Do any of these graphs also contain P2? Explain.
b. Suppose P1= (0,5) and P2= (0,7). Sketch P1 and P2.
Are there real numbers m and b for which the graph of
a linear function described by the equation
𝑓(𝑥) = 𝑚𝑥 + 𝑏 contains P1 and P2? Explain.
c. Suppose P1= (𝑐, 𝑑) and P2= (𝑔, ℎ) and c is not equal to g. Show that there is only one real
number m and only one real number b for which the graph of 𝑓(𝑥) = 𝑚𝑥 + 𝑏 contains the
points P1 and P2.
10
Unit 2 | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Week #7 Continued
𝑥
1
3. Given 𝑓(𝑥) = 2𝑥 + 1 and 𝑔(𝑥) = 2 − 2.
4. Graph 𝑓(𝑥) = 2𝑥 + 4 and the inverse of 𝑓(𝑥).
Show that the two functions are inverses.
Where do they intersect? _____________________
5. Translate the functions so that they
intersect at (3,4). (Feel free to use the
graph if you like.)
1
𝑓(𝑥) = 𝑥 + 1
3
1
𝑔(𝑥) = − 𝑥 + 7
2
6. The three graphs show the functions
𝑓(𝑥) = 2𝑥
𝑔(𝑥) = 2(𝑥 + 1)
Label the three graphs below.
𝑓(𝑥) =____________________________________
𝑔(𝑥) =____________________________________
11
Unit 2 | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
ℎ(𝑥) = 2𝑥 + 1
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Unit 2 - KEYS
Weekly Assessments
12
Unit 2 - KEYS | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Week #5 - KEY
1. Given 𝑓(𝑥) = 𝑥 2 − 2𝑥 + 9, find:
2. Find the slope of the graph between the two
points.
a. 𝑓(2) = 9
a. (4, 3), (8, -5) -1/2
b. 𝑓(−3) = 24
b. (3/4, 5/2), (1/2, -1/4) 11
c. 𝑓(1/2) = 8.25
c. (5, 8), (5, 10) undefined
3. You have $22.50 in your piggy bank. You choose to buy two cookies every day at lunch for yourself and
your sweetheart. They cost $.75 for both cookies. Create an equation, table, and graph for this situation.
Equation:
y = 22.5 - 0.75x
13
Table:
x
y
0
5
10
15
22.50 18.75 15.00 11.25
Unit 2 - KEYS | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Week #5 Key Continued
4. The below table provides some U.S. Population data from 1982 to 1988:
Population
Change in Population
(thousands)
(thousands)
1982
231,664
--1983
233,792
2128
1984
235,825
2033
1985
237,924
2099
1986
240,133
2209
1987
242,289
2156
1987
244,499
2210
If we were to model the relationship between the U.S. population and the year, would a linear function be
appropriate? Explain why or why not.
Year
Yes the function is linear, because the change of population stays relatively the same each year.
Mike decides to use a linear function to model the relationship. He chooses 2139, the average of the
values in the 3rd column, for the slope. What meaning does this value have in the context of this
model?
The number 2139 tells us the amount that the population increases each year.
Use Mike's model to predict the U.S. population in 1992.
5*2139 + 244,499 = 255,194
http://illustrativemathematics.org/illustrations/353
5. As I fill the following beaker with water at a
6. Suppose 𝑓 is a function.
constant rate, graph the height of the water in
relation to time.
a. If 12 = 𝑓(−9), give the coordinates of a point
on the graph of f.
(-9, 12)
b. If 16 is a solution of the equation𝑓(𝑤) = 6,
give a point on the graph of f.
(16, 6)
14
Unit 2 - KEYS | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Week #6 - KEY
1. mma understands that the function, 𝑓(𝑥) =
3.5𝑥 + 10 gives her the price for the bands tshirts given the $10 set up fee and the price
of $3.50 per shirt.
2. Lauren keeps records of the distances she travels
in a taxi and what she pays:
Distance, d
(in miles)
Fare, F
(in dollars)
She also knows that there are 88 band members.
3
8.25
What is the total cost for the shirts?
5
12.75
11
26.25
𝒇(𝟖𝟖) = 𝟑𝟏𝟖
$318
a. If you graph the ordered pairs (𝑑, 𝐹) from
the table, they lie on a line. How can you
tell this without graphing them? Yes,
finding the slopes tells us that they are the
same for both intervals.
b. Show that the linear function in part (a)
has equation 𝐹 = 2.25𝑑 + 1.5. There is
only one possible line in part (a) since two
points determine a line. The graph of F= 2.25d + 1.5 is a line, so if we show that each
ordered pair satisfies it then we will know
that it is the same line as in part (a).
(3, 8.25)(5, 12.75)(11, 26.25)
2.25(3) + 1.5 = 8.25
2.25(5) + 1.5 = 12.75
2.25(11) + 1.5 = 26.25
c. What do the 2.25 and the 1.5 in the
equation represent in terms of taxi rides?
The 2.25 represents the cost per mile for
the ride. The 1.5 represents a fixed cost for
every ride; it does not depend on the
distance traveled.
http://illustrativemathematics.org/illustrations/243
3. Solve the following equations and justify the steps.
1
a. 3 (4𝑥 + 1) = 9
4x + 1 = 27 (Mult prop of equality)
4x = 26 (Add prop of equality)
X = 6.5 (Div prop of equality)
15
b. 10 =
5𝑥−3
4
40 = 5x – 3 (Mult prop of equality)
43 = 5x (Add prop of equality)
8.6 = x (Division prop of equality)
Unit 2 - KEYS | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Week #6 Continued
br
o
w
ni
es
4. If you have $10, you can buy 4 cookies and no
brownies or you can buy 5 brownies and no
cookies. There are several other options as well.
Graph the situation.
5.
a. Let F assign to each student in your math
class his/her locker number. Explain
why F is a function.
F is a function because it assigns to each student
in the class exactly one element, his/her locker
number.
b. Describe conditions on the class that would
have to be true in order for F to have an
inverse.
cookies
If you have $10 and you buy 1 cookie a day you will
run out of money after 5 days. Graph the situation.
Students would not share lockers.
$
cookies
Which situation has the cheaper cookie? (Circle one)
1st
2nd
Not enough information
6. Candy bars cost $1.50 each. What is the total bill?
What is the domain? Number of Candy Bars
What is the range? Cost
16
Unit 2 - KEYS | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Name _________________________
Week #7 - KEY
1. A souvenir shop in Niagara Falls sells
picture postcards priced as follows:
2.
a. Suppose P1= (0,5) and P2= (3, −3). Sketch P1
and P2 .
Postcards
15 cents each
Six for $1
a. Graph the price of buying postcards as a
function of the number of cards purchased.
Price
(Doll
ars)
For which real numbers m and b does the graph of
a linear function described by the equation 𝑓(𝑥) =
𝑚𝑥 + 𝑏 contain P1 and P2? Explain.
m = -8/3
b=5
b. Suppose P1= (0,5) and P2= (0,7).
Sketch P1 and P2.
Number of Postcards
b. Is there something wrong with this pricing
scheme? Explain.
Are there real numbers m and b for which the
graph of a linear function described by the
equation 𝑓(𝑥) = 𝑚𝑥 + 𝑏 contains P1 and P2?
Explain.
No, because this is not a function.
Six for $1 cost approximately $0.17 each which is
higher than the initial $0.15 per postcard.
c. Extension: Now suppose P1= (𝑐, 𝑑) and P2=
(𝑔, ℎ) and c is not equal to g. Show that there is
only one real number m and only one real
number b for which the graph of 𝑓(𝑥) = 𝑚𝑥 +
𝑏 contains the points P1 and P2.
See website for full explanation
http://illustrativemathematics.org/illustrations/377
17
Unit 2 - KEYS | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers
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Week #7 Continued
𝑥
1
3. Given 𝑓(𝑥) = 2𝑥 + 1 and 𝑔(𝑥) = 2 − 2. Show
4. Graph 𝑓(𝑥) = 2𝑥 + 4 and the inverse of 𝑓(𝑥).
that the two functions are inverses.
𝒙
𝟏
F(g(x)) = 2(𝟐 − 𝟐) +1 = x
G(f(x)) =
𝟐𝒙+𝟏
𝟏
− =x
𝟐
𝟐
Where do they intersect? (-4, -4)
5. Translate the functions so that they intersect at
(3,4). (Feel free to use the graph if you like.)
6. The three graphs show the functions
𝑓(𝑥) = 2𝑥 (Blue)
1
𝑓(𝑥) = 𝑥 + 1
3
1
𝑔(𝑥) = − 𝑥 + 7
2
𝑔(𝑥) = 2(𝑥 + 1) (Red)
ℎ(𝑥) = 2𝑥 + 1 (Green)
Label the three graphs below.
𝒇(𝒙) =
𝟏
(𝒙 + 𝟒) + 𝟏
𝟑
𝟏
𝒈(𝒙) = − (𝒙 + 𝟒) + 𝟕
𝟐
18
http://map.mathshell.org/materials/tasks.php?tas
kid=295&subpage=novice
Unit 2 - KEYS | Algebra 1 Weekly Assessments | ©2015 Algebra 1 Teachers