K12 Online School Algebra Math Worksheets

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:
© 2016 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
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:
© 2016 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 2 of 4
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:
© 2016 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
Page 3 of 4
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:
© 2016 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
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:
© 2016 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.
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: © 2016 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. 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: © 2016 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. 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: © 2016 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 1 of 3 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: © 2016 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. 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: © 2016 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. 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: © 2016 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. 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: © 2016 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. 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: © 2016 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. 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: © 2016 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. 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: © 2016 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. 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: © 2016 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 3 of 3