Download A.CED.A.4 (multiple choice) - Howard County Public School System

Algebra I Items to Support Formative Assessment
Unit 2: Linear and Exponential Relationships
Part I: Representing Linear and Exponential Relationships
F.IF.C Analyze linear and exponential functions using different representations.
F.IF.C.7 Graph functions expressed symbolically and show key features of the graph, by
hand in simple cases and using technology for more complicated cases.
a.
Graph linear and exponential functions and show intercepts, maxima, and minima.
e.
Graph exponential functions, showing intercepts and end behavior.
F.IF.C.7a,e Short-item
Use the function below to complete the problem.
f(x) = -0.5x + 5
a. Complete the table and graph the function.
x
f(x)
b. Identify the intercepts, and rate of change.
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F.IF.C.7a,e Short item
Calvin is traveling from South Carolina and is 510 miles away from his home. He knows that
every half hour, he travels about 30 miles.
a.
b.
c.
d.
Create a graph to represent the relationship between the number of hours (x) and the
distance (y) Calvin is from home.
Find the x- and y-intercepts and explain what they represent in the situation.
What is the rate of change?
What is a reasonable domain and range for this situation?
Solution:
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a.
b. The y-intercept (510) represents the starting distance Calvin is from home. The x-intercept
(8.5) represents how long it takes Calvin to get home.
c. Every hour Calvin travels 60 miles.
d. Domain: 0 < x < 8.5
Range: 0 < y < 510
F.IF.C.7a,e
Complete the following table for the exponential function 𝑦 = 𝑎𝑏 𝑥 .
a value
b value
Equation
y-intercept
Coordinate on
Graph
2
3
𝑦 = 2(3)𝑥
2
(1, 6)
5
2
𝑦 = 10(3)𝑥
5
7
9
5
6
(1, 36)
(1, 20)
(2, 24)
Solution:
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a value
b value
Equation
y-intercept
Coordinate on
Graph
2
3
𝑦 = 2(3)𝑥
2
(1, 6)
5
2
𝑦 = 5(2)𝑥
5
(1, 10)
10
3
𝑦 = 10(3)𝑥
10
(1, 30)
7
5
𝑦 = 7(5)𝑥
7
(1, 35)
9
4
𝑦 = 9(4)𝑥
9
(1, 36)
4
5
𝑦 = 4(5)𝑥
4
(1, 20)
6
2
𝑦 = 6(2)𝑥
6
(2, 24)
F.IF.C.7a,e Short item
Match each item with the correct graph.
1.
y = 0.25x -6
2.
x
0
2
4
6
8
y
5
11.25
25.313
56.95
128.14
3.
m = 2/3 and b = -5
4.
y = 20 (0.15)x
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Solution:
1. F
2. E
3. C
4. A
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F.IF.C.7a,e Short task
Determine the equation for the graph below and write a scenario that could be represented by the
graph. Be sure to include the domain and range.
Solution:
y = 50(0.90)^x
Scenarios will vary. Sample: The value of a piece of jewelry was originally $50 and decreases
by 10% each year.
Domain: x > 0
Range: 50 > y > 0
A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with
coefficients represented by letters. Note: Students have solved multi-step linear equations
in Pre-Algebra. Pretest this standard and review as needed. This standard is here to
support the work of linear and exponential relationships.
A.REI.B.3
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John has a baseball card collection that is worth $280.00. He has 64 baseball cards from 1988.
Each of the 1988 cards is worth $2.30. He also has a set of 30 baseball cards from 1983. Each of
the 1983 cards are worth the same amount.
a. Write an equation to model this situation. Be sure to define your variables.
b. What is the value of each baseball card from 1983?
Solution:
a. 30x + 64(2.30) = 280, where x represents the cost of each 1983 baseball card.
OR
30x + 64y = 280, where x represents the cost of each 1983 card and y represents the cost
of each 1988
b. 30x + 64(2.30) = 280
30x + 147.20 = 280
30x = 132.8
x = 4.43
Each baseball card from 1983 is worth $4.43.
A.REI.B.3 Task
Josh went to the Orioles game and bought 3 hot dogs and 2 sodas for a total of $20.25. Each hot
dog is $0.50 more than a soda.
a. Write an equation to model this situation. Be sure to define your variables.
b. Find the cost of each hot dog and each soda.
c. What is the cost of 5 hot dogs and 3 sodas?
Solution:
a. 3h + 2(h – 0.50) = 20.25 OR
3(s + 0.50) + 2s = 20.25
b. 3h + 2(h – 0.50) = 20.25
5h = 21.25
h = 4.25
Each hot dog costs $4.25 and each soda costs $3.75.
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c. 5(4.25) + 3(3.75) = 32.25
5 hot dogs and 3 sodas would cost $32.25.
A.REI.B.3
Write a real world scenario that could be represented symbolically by each of the equations or
inequalities
Equation/Inequality
Scenario
15x +10x + 10 = 430
500 - 10m £ 300
13h + 50 ³ 20h
Possible Solutions:
Equation/Inequality
Scenario
15x +10x + 10 = 430
Purchase $15 shirts and $10 shorts for new uniforms for a team of
x people. There is a $10 shipping charge and the total expense for
the uniforms is $430.
500 - 10m £ 300
A plane is 500 miles away from the airport and is approaching at a
rate of 10 miles per minute. In order to be in range of the airport
tower the plane must be within 300 miles of the airport.
13h + 50 ³ 20h
Matt makes $13 per hour plus $50 in tips. John makes $20 an
hour. How many hours does Matt have to work in order to make
more money than John?
A.REI.B.3
You have a cell phone plan that allows for unlimited calling and 1000 text messages for $21.25.
Every text message over 1000 text messages will cost $0.10 per text. Your parents will only pay
up to $60 for you phone bill.
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a. Write an inequality to model this situation. Be sure to define your variable.
b. How many text messages could you send each month?
Solution
a. 21.25 + 0.10𝑥 ≤ 60, where x represents number of text messages over 1000.
b.
21.25 + 0.10x £ 60
0.10x £ 38.75
x £ 387.5
I can send 387 extra text messages per month. In total I can send 1, 387 text messages
per month.
A.REI.B.3
Write a real world scenario that represents this equation, then solve.
5x + 3 = 2x + 6
Possible real world solution:
Taxi service A charges $3 for a pick up plus an additional $5 per mile driven. Taxi service B
charges $6 for a pick up plus an additional $2 per mile. At how many miles would you pay the
same amount for each taxi service.
Possible Solution: The taxi services will charge the same amount at 1 mile.
Solution
5x + 3 = 2x + 6
3x + 3 = 6
3x = 3
x=1
A.REI.B.3/A.CED.A.4 Perimeter Formula
You’ve been hired as the technology consultant for a fencing company. Pricing is calculated by
the length used in feet. Technicians giving estimates to customers need an efficient way to
calculate possible dimensions based on the customer’s budget. They have a program that will do
the calculations (similar to a graphing calculator), but they need to be able to input formulas in
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the correct formatting. For example, if a customer can afford 86 feet of fencing, the technician
needs to be able to give the customer different combinations of dimensions.
Your job is to develop a formula that the technicians can use to efficiently determine one
dimension given the other.
a. If the customer needs 86 feet, write the formula for the technician.
b. Can you generalize this so that the technician is prepared for any length of fence?
Solution:
a. 2𝑙 + 2𝑤 = 86, where l represents length and w represents width.
b. 2𝑙 = 86 − 2𝑤
𝑙 = 43 − 𝑤
Teacher Note: If students are struggling with developing the formula, an intermediate step may
be to determine values for the width given specified lengths so that students can generalize the
process.
A.CED.A.4 Rearrange linear formulas to highlight a quantity of interest, using the same
reasoning as in solving equations.
A.CED.A.4 (short answer)
Circle the formulas below that are equivalent to d = rt , where d = distance, r = rate, t = time.
r = dt
r=
t
d
r=
d
t
d = tr
t=
r
d
t=
d
r
t = dr
r=
t
d
r=
d
t
d = tr
t=
r
d
t=
d
r
t = dr
Solutions:
r = dt
A.CED.A.4 (multiple choice)
Carla rewrote the equation 12x - 4y = 52 in slope-intercept form so that she could easily graph it.
Which choice correctly represents 12x - 4y = 52 when solved for y?
a. y =13 - 3x
b. 3x -13 = y
1
3
c. y = x 3
13
1
d. - x +13 = y
3
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correct answer b. 3x -13 = y
A.CED.A.4 (short answer)
Write the equation below in slope-intercept form.
2x + 5y = 30
correct answer
2
y = - x +6
5
A.CED.A.4 (open response)
Braden showed the work he used to change an equation in standard from to slope-intercept form.
Identify and explain the error that he made. Show the work Braden should have completed to
change this equation correctly.
Braden’s work
Corrected work
3𝑥 − 2𝑦 = 12
3𝑥 − 2𝑦 = 12
2𝑦 = 12 − 3𝑥
2𝑦
2
=
12−3𝑥
2
3
𝑦 = 6 −2𝑥
Braden forgot to bring down the negative sign after he subtracted the 3x.
3𝑥 − 2𝑦 = 12
−2𝑦 = 12 − 3𝑥
−2𝑦
−2
=
12 − 3𝑥
−2
3
𝑦 = −6 + 2 𝑥
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