Math | Extended Problems | SequencesName:

Date:

Extended Problems

Sequences

Solve the problems. When you have finished, submit this assignment to your teacher by the due date for full

credit.

Total score: ____ of 20 points

An employer provides two payment options for employees.

Option A: Receive $200 the first week. Receive an additional $50 for each of the following weeks.

Option B: Receive $200 the first week. Receive an additional 10% for each of the following weeks.

(Score for Question 1: ___ of 2 points)

1. Complete the tables to show how much money would be received for both payment options, each week, for 6

weeks.

Option A:

Week

1

2

3

4

5

6

1

2

3

4

5

6

Amount Paid

Option B:

Week

Amount Paid

Answer:

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Page 1 of 4

Math | Extended Problems | Sequences

(Score for Question 2: ___ of 8 points)

2. Suppose you are a new employee. You notice that each payment option describes a sequence and decide to

use rules to help determine which option to take.

(a) Determine the iterative rule for each sequence. Show your work.

(b) Your friend trusts your tables in Problem 1, but wonders if you wrote the iterative rules correctly. Show

two calculations to convince your friend that both your rules work.

Answer:

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Math | Extended Problems | Sequences

(Score for Question 3: ___ of 5 points)

3. Consider the iterative rules you wrote in Problem 2.

(a) Explain why the rules are functions.

(b) Your friend says that because the rules are functions, they can be graphed and must have yintercepts. How would you respond to your friend’s comment?

(c) Your friend uses your rules to determine the outputs when the inputs are 18.5. Explain why her

outputs are meaningless in this situation. What would you tell her about the inputs she can use?

Answer:

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Math | Extended Problems | Sequences

(Score for Question 4: ___ of 5 points)

4. The longest amount of time employees can work under Option A or Option B is 20 weeks. After employees

work 20 weeks, they can either quit or keep making the same amount they made during Week 20. If an

employee plans on quitting after 20 weeks, which payment option gives the greatest total income? Explain.

Answer:

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Page 4 of 4

Math | Graded Assignment | Unit Test, Part 2 | Working with Functions

Name:

Date:

Graded Assignment

Unit Test, Part 2: Working with Functions

Answer the questions below. When you are finished, submit this test to your teacher for full credit.

Total score: ____ of 15 points

(Score for Question 1: ___ of 6 points)

1. Judy took $30 with her to spend on popcorn and drinks for herself and her friends at the movie theater. The

price for each bag of popcorn was $5. The price of each drink was half the price of a bag of popcorn.

(a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the

number of bags of popcorn and the other axis to represent the number of drinks.

(b) Explain your graph.

Answer:

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Page 1 of 3

Math | Graded Assignment | Unit Test, Part 2 | Working with Functions

(Score for Question 2: ___ of 5 points)

2. Graph the piecewise function.

⎧3x − 5 if x ≤ −1

⎪

f ( x ) = ⎨−2 x + 3 if − 1 < x < 4
⎪2 if x ≥ 4
⎩
Answer:
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Page 2 of 3
Math | Graded Assignment | Unit Test, Part 2 | Working with Functions
(Score for Question 3: ___ of 4 points)
3. Graph the step function over the interval −2 ≤ x ≤ 2 .
f (x ) = ⎡⎢ x + 3 ⎤⎥
Answer:
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Page 3 of 3
Math | Graded Assignment | Unit Test, Part 2 | Quadratic Equations
Name:
Date:
Graded Assignment
Unit Test, Part 2: Quadratic Equations
Answer the questions below. When you are finished, submit this test to your teacher for full credit.
Total score: ____ of 15 points
(Score for Question 1: ___ of 6 points)
1. Explain why the equation
Show your work.
(x − 4 )2
− 28 = 8
has two solutions. Then solve the equation to find the solutions.
Answer:
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Math | Graded Assignment | Unit Test, Part 2 | Quadratic Equations
(Score for Question 2: ___ of 3 points)
2
2. This is Josh’s solution for the equation x − 6 x − 7 = 0 :
x 2 − 6x − 7 = 0
x 2 − 6x = 7
x 2 − 6x + 9 = 7 + 9
(x − 3 )2
= 16
x − 3 = 16
x = 19
x − 3 = −16
x = −13
Is Josh’s solution correct? Explain.
Answer:
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Page 2 of 3
Math | Graded Assignment | Unit Test, Part 2 | Quadratic Equations
(Score for Question 3: ___ of 6 points)
2
3. Use the quadratic formula to solve x − 4 x + 3 . Show your work. Then describe the solution.
Answer:
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Page 3 of 3
Math | Graded Assignment | Unit Test, Part 2 | Bivariate Data
Name:
Date:
Graded Assignment
Unit Test, Part 2: Bivariate Data
Answer the questions below. When you are finished, submit this test to your teacher for full credit.
Total score: ____ of 15 points
(Score for Question 1: ___ of 5 points)
1.
The table shows the minimum wage rates for the United States during different years.
Year
1978
1979
1980
1990
1991
1996
1997
2007
2008
2009
Minimum hourly wage ($)
2.65
2.90
3.35
3.80
4.25
4.75
5.15
5.85
6.55
7.25
(a) Write the least squares regression equation that models the data. Let x = time in years since
1900 and let y = minimum hourly wage.
(b) Use the equation to estimate the minimum hourly wage of a U.S. worker in 2025. Show your
work.
Answer:
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Page 1 of 3
Math | Graded Assignment | Unit Test, Part 2 | Bivariate Data
(Score for Question 2: ___ of 5 points)
2. The table shows the soil density of several soil samples at different depths.
Depth (m)
Soil density (
mg/cm3 )
1
5
6
8
10
12
14
21
23
24
28
1045
1063
1102
1140
1191
1232
1249
1254
1265
1268
1273
(a) Write the quadratic regression equation that models the data. Let x = depth below the surface
and let y = soil density.
(b) Use the equation to estimate the soil density of a sample at a depth of 20 m. Show your work.
Answer:
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Page 2 of 3
Math | Graded Assignment | Unit Test, Part 2 | Bivariate Data
(Score for Question 3: ___ of 5 points)
3. Jackson relies on his customers to tell their friends about his business. His business grows as each customer
continues to tell others about his or her experience and they in turn tell others as well.
The table shows the number of people who have recommended Jackson’s business for different days after it
first opens.
Time (days), x
3
4
7
10
12
13
17
18
21
27
30
Number of personal recommendations, y
12
14
18
23
28
31
46
50
67
118
157
(a) Write the exponential regression equation that models the data.
(b) Use the equation to estimate the number of personal recommendations 60 days after Jackson
opens his business. Show your work.
Answer:
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Page 3 of 3
Math | Graded Assignment | Unit Test, Part 2 | Polynomials
Name:
Date:
Graded Assignment
Unit Test, Part 2: Polynomials
Answer the questions below. When you are finished, submit this test to your teacher for full credit.
Total score: ____ of 15 points
(Score for Question 1: ___ of 5 points)
1x − 1
2
4 and 5 x 2 − 2 x + 6 ? Write your answer in standard form.
1. What is the product of
(a) Show your work.
1x − 1
1x − 1
2
5
x
−
2
x
+
6
2
4
4
2 and 5 x 2 − 2 x + 6 ?
(b) Is the product of
and
equal to the product of
Explain your answer.
Answer:
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Page 1 of 3
Math | Graded Assignment | Unit Test, Part 2 | Polynomials
(Score for Question 2: ___ of 5 points)
3
3
2. What is the product of −2 x + x − 5 and x − 3 x − 4 ?
(a) Show your work.
3
3
3
(b) Is the product of −2 x + x − 5 and x − 3 x − 4 equal to the product of x − 3 x − 4 and
−2 x 3 + x − 5 ? Explain your answer.
Answer:
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Page 2 of 3
Math | Graded Assignment | Unit Test, Part 2 | Polynomials
(Score for Question 3: ___ of 5 points)
2
3. Write an equation in which the quadratic expression 2 x − 2 x − 12 equals 0. Show the expression in factored
form and explain what your solutions mean for the equation. Show your work.
Answer:
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