1. Algebra and Modeling Day 1
2017 Algebra 1 Bootcamp

2. MAFS.912.A-APR.1.1 Which expression is equivalent to 2 3𝑔−4 − 8𝑔+3 ?
Algebra and Modeling
MAFS.912.A-APR.1.1
Which expression is equivalent to 2 3𝑔−4 − 8𝑔+3 ?
−2g−1
−2g−5
−2g−7
−2g−11
Group 1 D
2017 Algebra 1 Bootcamp

3. MAFS.912.A-APR.1.1 Simplify: 3 3 𝑘 2 −4𝐾+6 − 8 𝑘 2 +𝑘+3 ? 𝑘 2 −13𝑘+15
Algebra and Modeling
MAFS.912.A-APR.1.1
Simplify: 3 3 𝑘 2 −4𝐾+6 − 8 𝑘 2 +𝑘+3 ?
𝑘 2 −13𝑘+15
Group 1
2017 Algebra 1 Bootcamp

4. Algebra and Modeling
MAFS.912.A-APR.1.1
Write an expression which is equivalent to 𝑤(4𝑤3 + 8𝑤4) – (5𝑤3 – 2𝑤5)
10w5 + 4w4 – 5w3
Group 1 and 2
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5. Algebra and Modeling
MAFS.912.A-APR.1.1
Multiply and combine like terms to determine the product of these polynomials.
2𝑥−3 5𝑥+6
10 𝑥 2 −3𝑥−18
Group 1 and 2
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6. Algebra and Modeling
MAFS.912.A-APR.1.1
Which expression is equivalent to −2𝑛 3𝑚+𝑛 –7 +3 −6𝑚 +2𝑛 +𝑚 𝑛+4𝑚 – 5 ?
A. 4𝑚2 – 5𝑚𝑛 – 23𝑚 + 22𝑛
B. 4𝑚2 + 2𝑛2 – 5𝑚𝑛 – 23𝑚 – 8𝑛
C. 4𝑚2 – 2𝑛2 – 5𝑚𝑛 – 23𝑚 + 20𝑛
D. 4𝑚2 – 2𝑛2 – 6𝑚𝑛 – 23𝑚 + 20𝑛
Group 2 and 3 C
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7. Algebra and Modeling
MAFS.912.A-APR.1.1
Find the area of the shaded region of the square, with side length 2𝑥 – 3, if each of the ovals has an area of 𝑥−5 square inches.
4 𝑥 2 −14𝑥+19
Group 2 and 3
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License
2017 Algebra 1 Bootcamp

8. MAFS.912.A-APR.1.1 Consider the polynomial: 2 3 𝑥(2𝑥+3)− 𝑥+7 𝑥−7
Algebra and Modeling
MAFS.912.A-APR.1.1
Consider the polynomial:
2 3 𝑥(2𝑥+3)− 𝑥+7 𝑥−7
When simplified, what is the coefficient of the quadratic term?
1 3
Group 3
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9. Algebra and Modeling
MAFS.912.A-APR.1.1
Multiply and combine like terms to determine the product of these polynomials.
(−2𝑥−3)(2 𝑥 2 −𝑥+1)(𝑥−2)
−4 𝑥 4 +4 𝑥 3 +9 𝑥 2 −5𝑥+6
Group 3
2017 Algebra 1 Bootcamp

10. Algebra and Modeling
MAFS.912.A-APR.1.1
Kiera claimed that the sum of two linear polynomials with rational coefficients is always a linear polynomial with rational coefficients.
Drag the six statements into a logical sequence to outline an argument that proves this claim.
Group 3
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11. Algebra and Modeling
MAFS.912.A-CED.1.1
A parking garage charges a base rate of $3.50 for up to 2 hours, and an hourly rate for each additional hour. The sign below gives the prices for up to 5 hours of parking.
Which linear equation can be used to find x, the additional hourly parking rate?
Group 1 and 2
9.00+3𝑥=20.00
𝑥=20.00
2𝑥+3.50=14.50
2𝑥+9.00=14.50 C
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12. Algebra and Modeling
MAFS.912.A-CED.1.1
Kyran was given a check for $100 by his grandmother for his birthday, but had to promise her that he would invest the money in a bank until it had at least doubled in value. Kyran agreed, reluctantly, and found a bank where he could invest the $100 in a simple interest account that would gain 5% interest per year. If 𝑦 represents the number of years that Kyran will invest his money, which inequality could be used to find when he would have at least $200 in his account?
200< 𝑦
200≤100(1+0.05𝑦)
200> 𝑦
200≥100(1+0.05𝑦)
Group 1 and 2 B
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13. Algebra and Modeling
MAFS.912.A-CED.1.1
A sales clerk’s daily earnings include $125 per day plus commission equal to 𝑥 percent of his daily sales.
Enter an equation that can be used to find the commission percentage (𝑥), if the clerk’s daily sales are $1375 and his total earnings for that day are $180.
125+ 𝑥 100 ∙1375=180
Groups 1, 2, and 3
2017 Algebra 1 Bootcamp

14. Algebra and Modeling
MAFS.912.A-CED.1.1
Carmella just planted seeds for her vegetable garden. Anxious to view the progress of her plants, she checks her garden one afternoon, but sees that 4 weeds she has never seen before are growing in her vegetable garden. After a few weeks, she notices that the number of weeds appears to be tripling each week. If she doesn’t do something, she calculates that there could soon be 972 weeds in her garden. If 𝑤 represents the number of weeks, which equation could be used to determine what week Carmella would expect to find 972 weeds in her garden:
3𝑤+4=972
3 (4) 𝑤 =972
4 (3) 𝑤 =972
4 (𝑤) 3 =972
Group 1 and 2 C
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15. Algebra and Modeling
MAFS.912.A-CED.1.1
Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is Which equation could be used to find Jeremy’s age, 𝑗, if he is the younger man?
𝑗 2 +2=783
𝑗 2 −2=783
𝑗 2 +2𝑗=783
𝑗 2 −2𝑗=783
Group 2 and 3 C
2017 Algebra 1 Bootcamp

16. Algebra and Modeling
MAFS.912.A-CED.1.1
A rectangular garden measures 13 meters by 17 meters and has cement walkway around its perimeter, as shown. The width of the walkway remains constant on all four sides. The garden and walkway have a combined area of 396 square meters.
Part A: Enter an equation that can be used to help determine the width, 𝑤, of the walkway in the first response box.
Part B: Determine the width, in meters, of the walkway. Enter your answer in the second response box.
(17+2𝑤)(13+2𝑤)=396
Group 2 and 3
5 2
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17. Algebra and Modeling
MAFS.912.A-CED.1.1
The length of a rectangle is 2 inches more than a number. The width is 1 inch less than twice the same number. If the area of the rectangle is 42 𝑖𝑛 2 , find the dimensions of the rectangle.
Width: 4 in
Length: 4 in
Width: 6 in
Length: 6 in
Width: 7 in
Length: 7 in
Group 3
Length: 6 in, Width: 7 in
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18. Algebra and Modeling
MAFS.912.A-REI.2.3
Enter the value for 𝑥 that makes the given equation true.
20𝑥−5 6𝑥+4 =4𝑥−6 −1
Groups 1, 2, and 3
2017 Algebra 1 Bootcamp

19. MAFS.912.A-REI.2.3 What is the solution of 3 2𝑥−1 ≤4𝑥+7?. 𝑥≤5
Algebra and Modeling
MAFS.912.A-REI.2.3
What is the solution of 3 2𝑥−1 ≤4𝑥+7?.
𝑥≤5
Groups 1, 2, and 3
2017 Algebra 1 Bootcamp

20. MAFS.912.A-REI.2.3 Solve for 𝑥: 3 5 𝑥+2 =𝑥−4 13 Algebra and Modeling
3 5 𝑥+2 =𝑥−4 13
Groups 1, 2, and 3
2017 Algebra 1 Bootcamp

21. MAFS.912.A-REI.2.3 Solve algebraically for 𝑥: 2 𝑥−4 ≥ 1 2 (𝑥−4) 𝑥≥4
Algebra and Modeling
MAFS.912.A-REI.2.3
Solve algebraically for 𝑥:
2 𝑥−4 ≥ 1 2 (𝑥−4)
𝑥≥4
Groups 1, 2, and 3
2017 Algebra 1 Bootcamp

22. MAFS.912.A-REI.2.3 Solve for 𝑥: (𝑥+4) 2 =4𝑥−6 𝑥= 16 7 𝑥= 8 3 𝑥= 10 3
Algebra and Modeling
MAFS.912.A-REI.2.3
Solve for 𝑥:
(𝑥+4) 2 =4𝑥−6
𝑥= 16 7
𝑥= 8 3
𝑥= 10 3
𝑥=7
Groups 1, 2, and 3 𝐴
2017 Algebra 1 Bootcamp

23. Algebra and Modeling
MAFS.912.A-REI.2.3
Equivalent equations have exactly the same solution set. Select Yes or No to indicate whether each equation is equivalent to this equation: 4𝑥+3= 5 2 𝑥−7
Equation
Yes No
4𝑥= 5 2 𝑥−4
8𝑥+3=5𝑥−7
4𝑥= 5 2 𝑥−10
Groups 2 and 3
2017 Algebra 1 Bootcamp

24. MAFS.912.A-CED.1.4 Solve 5𝑏+12𝑐=9 for 𝑏. 𝐷 𝑏=5 12𝑐−9 𝑏=5 9−12𝑐
Algebra and Modeling
MAFS.912.A-CED.1.4
Solve 5𝑏+12𝑐=9 for 𝑏.
𝑏=5 12𝑐−9
𝑏=5 9−12𝑐
𝑏= 12𝑐−9 5
𝑏= 9−12𝑐 5
Group 1 and 2 𝐷
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25. MAFS.912.A-CED.1.4 Solve 7𝑥−2𝑧=4−𝑥𝑦 for 𝑥. 𝐷 𝑥=4−𝑥𝑦+ 2𝑧 7 𝑥= 4−𝑥𝑦+2𝑧 7
Algebra and Modeling
MAFS.912.A-CED.1.4
Solve 7𝑥−2𝑧=4−𝑥𝑦 for 𝑥.
𝑥=4−𝑥𝑦+ 2𝑧 7
𝑥= 4−𝑥𝑦+2𝑧 7
𝑥=4+2𝑧−(7+𝑦)
𝑥= 4+2𝑧 (7+𝑦)
Groups 2 and 3 𝐷
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26. MAFS.912.A-CED.1.4 If 𝑟𝑥−𝑠𝑡=𝑟, which expression represents 𝑥. 𝑟+𝑠𝑡 𝑟
Algebra and Modeling
MAFS.912.A-CED.1.4
If 𝑟𝑥−𝑠𝑡=𝑟, which expression represents 𝑥.
𝑟+𝑠𝑡 𝑟
𝑟 𝑟+𝑠𝑡
𝑟 𝑟−𝑠𝑡
𝑟−𝑠𝑡 𝑟
Groups 1, 2 and 3 𝐴
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27. MAFS.912.A-CED.1.4 If 𝑟𝑥−𝑠𝑡=𝑟, which expression represents 𝑟. 𝑠𝑡 (𝑥−𝑟)
Algebra and Modeling
MAFS.912.A-CED.1.4
If 𝑟𝑥−𝑠𝑡=𝑟, which expression represents 𝑟.
𝑠𝑡 (𝑥−𝑟)
𝑟+𝑠𝑡 𝑥
𝑠𝑡 𝑥
𝑠𝑡−(𝑥+𝑟)
Groups 2 and 3 𝐴
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28. Algebra and Modeling
MAFS.912.A-CED.1.2
An elementary school is having sand delivered for the playground. Sadie’s Sand charges $5.00 per ton of sand plus a delivery fee of $200. Greg’s Sand Pit charges $12.00 per ton of sand plus a delivery fee of $50.
Use the graph below to represent functions that show the cost C of buying T tons of sand from each company.
Groups 1, 2 and 3
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29. Algebra and Modeling
MAFS.912.A-CED.1.2
Emily has a gift certificate for $10 to use at an online store. She can purchase songs for $1 each or episodes of TV shows for $3 each. She wants to spend exactly $10.
Create an equation to show the relationship between the number of songs, 𝑥, Emily can purchase and the number of episodes of TV shows, 𝑦, she can purchase.
𝑥+3𝑦=10
Groups 1 and 2
2017 Algebra 1 Bootcamp

30. MAFS.912.A-CED.1.2 𝑑=(15𝑥)(10𝑥+25)+200 𝑑=15𝑥+(10𝑥+25)+200 𝑑=25𝑥+225
Algebra and Modeling
MAFS.912.A-CED.1.2
A local coffee company, Netherlanders Sisters, is trying to determine how much it costs to run a coffee stand for one day. The daily cost to pay employees can be represented by 15𝑥, the daily cost for ingredients/supplies can be represented by 10𝑥+25, and the daily cost to rent the coffee stand is $200. It has been determined that the product of the daily cost of employees and the daily cost of ingredients/supplies, plus the daily cost to rent the coffee stand represents the total cost to run the coffee stand for one day.
Select all of the equations, which could be used to find the daily cost, 𝑑, to run the coffee stand:
𝑑=(15𝑥)(10𝑥+25)+200
𝑑=15𝑥+(10𝑥+25)+200
𝑑=25𝑥+225
𝑑=150 𝑥 𝑥+200
𝑑=(15𝑥)(10𝑥+25)(200)
Groups 2 and 3
A and D
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31. Algebra and Modeling
MAFS.912.A-CED.1.2
Meredith is purchasing a new toilet for her home. Toilet A costs $149 and uses approximately 380 gallons of water per month. Toilet B costs $169 and uses approximately 300 gallons of water per month. Water costs $2.75 per 1000 gallons. Part A: Write a system of equations that models this situation. A.
A= ∙300∙t
B= ∙380∙t C.
A= ∙0.3∙t
B= ∙0.38∙t B.
A= ∙380∙t
B= ∙300∙t D.
A= ∙0.38∙t
B= ∙0.3∙t 𝐷
Part B: How many months will it take for Toilet B to be more cost effective?
Groups 2 and 3 91
2017 Algebra 1 Bootcamp

32. Algebra and Modeling
MAFS.912.A-CED.1.2
Malik and Nora are playing a video game.
• Malik starts with m points and Nora starts n points.
• Then Malik gets 150 more points, while Nora loses 50 points.
• Finally, Nora gets a bonus and her score is doubled.
• Nora now has 50 more points than Malik.
Write an equation that represents the relationship between 𝑚 and 𝑛 given the information above.
2 𝑛−50 = 𝑚
Groups 2 and 3
2017 Algebra 1 Bootcamp

33. Algebra and Modeling
MAFS.912.A-CED.1.2
Maia deposited $5,500 in a bank account. The money earns interest annually, and the interest is deposited back into her account.
Maia uses an online calculator to determine the amount of money she will have in the account at the end of each year. The amount of money that Maia will have in her account at the end of the selected year, up to 6 years, is shown in the table below.
Enter an equation that models the amount of money, y, Maia will have in the account at the end of 𝑡 years.
Years
Money in Bank 1
5,665.00 2
5,834.95 3
6,009.99 4
6,190.30 5
6,376.01 6
6,567.29
𝑦=5, 𝑡
Group 3
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34. Algebra and Modeling
MAFS.912. A-REI.3.5
Which system of equations has the same solution as the system below?
𝑥+3𝑦=6
4𝑥−8𝑦=4
−5𝑥+15𝑦=30
5𝑥−5𝑦=10
5𝑥+15𝑦=30
−5𝑥−15𝑦=−30
5𝑥+𝑦=10 A. B.
Groups 2 and 3 C. D. 𝐵
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35. Algebra and Modeling
MAFS.912. A-REI.3.5
Mr. Xavier is solving the system of equations 4𝑥 – 3𝑦 = 9 and 2𝑥 + 6𝑦 = 5. Which system of equations has the same solution as the system that Mr. Xavier is solving? A.
4𝑥 – 3𝑦 = 9
−19𝑦=−1
4𝑥−3𝑦=9
9𝑦=19
2𝑥+6𝑦=5
6𝑥=23
10𝑥=23 B.
Group 3 C. D. 𝐷
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36. Algebra and Modeling
MAFS.912. A-REI.3.6
The equations 5𝑥+2𝑦=48 and 3𝑥+2𝑦=32 represent the money collected from school concert ticket sales during two class periods. If 𝑥 represents the cost for each adult ticket and 𝑦 represents the cost for each student ticket, what is the cost for each adult ticket?
𝑥=8
Groups 1 and 2
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37. Algebra and Modeling
MAFS.912. A-REI.3.6
A restaurant serves a vegetarian and a chicken lunch special each day. Each vegetarian special is the same price. Each chicken special is the same price. However, the price of the vegetarian special is different from the price of the chicken special.
On Thursday, the restaurant collected $467 selling 21 vegetarian specials and 40 chicken specials.
On Friday, the restaurant collected $484 selling 28 vegetarian specials and 36 chicken specials.
What is the cost, in dollars, of each lunch special? 7
Group 3 8
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38. Algebra and Modeling
MAFS.912. A-REI.3.6
The basketball team sold t-shirts and hats as a fund-raiser. They sold a total of 23 items and made a profit of $246. They made a profit of $10 for every t-shirt they sold and $12 for every hat they sold.
Determine the number of t-shirts and the number of hats the basketball team sold.
Enter the number of t-shirts in the first response box.
Enter the number of hats in the second response box. 15 8
Group 3
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39. Algebra and Modeling
MAFS.912. A-REI.4.12
Which is a graph of the solution set of the inequality 3𝑦 – 𝑥 > 6? A. B. C. D.
Group 1 𝐶
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40. MAFS.912. A-REI.4.12 Which inequality does this graph represent?
Algebra and Modeling
MAFS.912. A-REI.4.12
Which inequality does this graph represent?
A. 𝑦 > 3𝑥 + 2
B. 𝑦 > −3𝑥 – 2
C. 𝑦 < 3𝑥 – 2
D. 𝑦 < −3𝑥 – 2
Group 1 and 2 𝐷
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41. MAFS.912. A-REI.4.12 𝑦<−5𝑥−2 𝑦≤−𝑥+2
Algebra and Modeling
MAFS.912. A-REI.4.12
𝑦<−5𝑥−2
𝑦≤−𝑥+2
Graph the system of inequalities: A. B. C. D.
Group 3 𝐶
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42. Algebra and Modeling
MAFS.912. A-REI.4.12
Determine the solution to the system of inequalities:
3𝑥+3𝑦≤3
𝑥−3𝑦≥−6
Groups 2 and 3
2017 Algebra 1 Bootcamp

43. Algebra and Modeling
MAFS.912. A-REI.4.12
The coordinate grid below shows points A through J.
Given the system of inequalities shown below, select all the points that are solutions to this system of inequalities.
𝑥+𝑦<3
2𝑥−𝑦>−6 A B C D E F G
Groups 2 and 3
A , F, and G
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44. Algebra and Modeling
MAFS.912. A-CED.1.3
The number of medals won by an Olympic Team is modeled by 𝑦 = 3𝑥 + 5, where 𝑥 is the number of athletes. The number of medals for another team is modeled by 𝑦 =5𝑥 – 8, where 𝑥 is the number of athletes.
Part A: For what number of athletes would both teams have the same number of Olympic medals?
Part B: Is this a viable answer? Explain.
𝑥= or 𝑥=6.5
This answer is not a viable solution because you cannot have part of an athlete. 6.5 athletes implies half an athlete, which is not possible in the context of the problem.
Groups 1 and 2
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45. Algebra and Modeling
MAFS.912. A-CED.1.3
David has two jobs. He earns $8 per hour babysitting his neighbor’s children and he earns $11 per hour working at the coffee shop.
Part A: Write an inequality to represent the number of hours, 𝑥, babysitting and the number of hours, 𝑦, working at the coffee shop that David will need to work to earn a minimum of $200.
Part B: David worked 15 hours at the coffee shop. Use the inequality to find the number of full hours he must babysit to reach his goal of $200.
8𝑥+11𝑦≥200 5
Group 2
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46. MAFS.912. A-CED.1.3 𝑔+𝑡≤10 𝑔≥1 𝑡≥1 𝑔+𝑡≥10 𝑔≥0 𝑡≥0
Algebra and Modeling
MAFS.912. A-CED.1.3
In a community service program, students earn points for painting over graffiti and picking up trash. The following restrictions are imposed on the program:
A student may not serve more than 10 total hours per week; and
A student must serve at least 1 hour per week at each task.
Let 𝑔= the number of hours a student spends in a week painting over graffiti.
Let 𝑡= the number of hours a student spends in a week picking up trash.
Part A: Which system represents the imposed constraints?
Part B: Which numbers of hours spent painting over graffiti and hours spent picking up trash could fit the community service requirements? Select all that apply. A. C.
𝑔+𝑡≤10 𝑔≥1 𝑡≥1
𝑔+𝑡≥10 𝑔≥0 𝑡≥0
Group 3
3 graffiti hours and 4 trash hours
6 graffiti hours and 7 trash hours
8 graffiti hours and 3 trash hours
9 graffiti hours and 1 trash hours
0 graffiti hours and 10 trash hours
5 graffiti hours and 5 trash hours B. D.
𝑔+𝑡≤10 𝑔≥0 𝑡≥0
𝑔+𝑡<10 𝑔=𝑡 A
A, D, and F
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47. Algebra and Modeling
MAFS.912. A-REI.1.1
When solving for the value of 𝑥 in the equation 4(𝑥−1)+3=18 , Aaron wrote the following lines on the board.
Step 1
4 𝑥−1 +3=18
Step 2
4 𝑥−1 =15
Step 3
4𝑥−1=15
Step 4
4𝑥=16
Step 5
𝑥=4
Which property was used incorrectly when going from Step 2 to Step 3?
Addition Property
Distributive Property
Substitution Property
Transitive Property
Groups 1, 2, and 3 𝐵
2017 Algebra 1 Bootcamp

48. MAFS.912. A-REI.1.1 Martha solved the equation 5 𝑏+3 =𝑏+39.
Algebra and Modeling
MAFS.912. A-REI.1.1
Martha solved the equation 5 𝑏+3 =𝑏+39.
Which step is the first incorrect step in Martha’s solution shown above?
Step 1
5(𝑏+3)=𝑏+39
Step 2
5𝑏+15=𝑏+39
Step 3
6𝑏+15=39
Step 4
6𝑏=24
Step 5
𝑏=4
Step 2
Step 3
Step 4
Step 5
Groups 1, 2, and 3 𝐵
2017 Algebra 1 Bootcamp

49. MAFS.912. A-REI.2.4 Which are the solutions to 𝑥 2 +9𝑥=36? 𝑥=−12,𝑥=3
Algebra and Modeling
MAFS.912. A-REI.2.4
Which are the solutions to 𝑥 2 +9𝑥=36?
𝑥=−12,𝑥=3
𝑥=4,𝑥=9
𝑥=12,𝑥=−3
𝑥=−4,𝑥=9
Groups 1, 2, and 3 𝐴
2017 Algebra 1 Bootcamp

50. MAFS.912. A-REI.2.4 Solve by completing the square: 𝑥 2 −6𝑥−4=0 3± 13
Algebra and Modeling
MAFS.912. A-REI.2.4
Solve by completing the square:
𝑥 2 −6𝑥−4=0
3± 13
−3±2 13
3±2 13
−3± 13
Group 3 𝐴
2017 Algebra 1 Bootcamp

51. MAFS.912. A-REI. 4.11 The graphs of the functions 𝑓 and 𝑔 are shown
Algebra and Modeling
MAFS.912. A-REI. 4.11
The graphs of the functions 𝑓 and 𝑔 are shown
Use the graphs to approximate the solution(s) to the equation f(𝑥) = 𝑔(𝑥).
- 0.8 2
Group 3
2017 Algebra 1 Bootcamp

52. Algebra and Modeling
MAFS.912. A-REI.3.6
Based on the tables, at what point do the lines 𝑦 = –𝑥 + 5 and 𝑦 = 2𝑥 – 1
intersect?
(1, 1)
(3, 5)
(2, 3)
(3, 2)
Group 1 𝐶
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53. Algebra and Modeling
MAFS.912. A-REI.3.6
Look at the tables of values for two linear functions, 𝑓(𝑥) and 𝑔(𝑥).
What is the solution to 𝑓(𝑥) = 𝑔(𝑥)?
𝑥=3
Groups 1, 2, and 3
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54. Algebra and Modeling
MAFS.912. A-REI.4.10
Choose the ordered pair that is a solution to the equation represented by the graph.
(0, −3)
(2, 0)
(2, 2)
(−3, 0)
Group 1 𝐷
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55. Algebra and Modeling
MAFS.912. A-REI.4.10
Which points are on the graph of the equation 3 − 6𝑥 + 2𝑦 = −5? Select all that apply.
(-2, -10)
(-1, 1)
(0, 4)
(4, 8)
(6, 14)
Groups 1 and 2
A, D, and E
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56. MAFS.912. A-REI.4.10 When is this statement true? 𝑦 = 𝑥 2 + 4𝑥 − 1
Algebra and Modeling
MAFS.912. A-REI.4.10
When is this statement true?
𝑦 = 𝑥 𝑥 − 1
A. This statement is true for all positive values of 𝑥 only.
B. This statement is true for all negative values of 𝑥 only.
C. This statement is true for the point (1,4).
D. This statement is true for the point (0,0).
Groups 2 and 3 𝐶
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57. Algebra and Modeling
MAFS.912. A-REI.4.10
For the function 𝑓 𝑥 = 2 𝑥 . Is (5, 32) a solution to 𝑓(𝑥)? Explain.
Yes, it is a solution. Two raised to the power of 5 is equal 32.
Groups 1, 2, and 3
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58. Algebra and Modeling
MAFS.912. A-REI. 4.10
Which point is NOT on the graph represented by 𝑦= 𝑥 2 +3𝑥−6?
(−6, 12)
(−4, −2)
(2, 4)
(3, −6)
Group 3 𝐷
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59. Algebra and Modeling
MAFS.912. A-SSE.2.3
Arturo made an error when finding the minimum value of the function
𝑔(𝑥) = 𝑥 2 – 6𝑥 His work is shown below.
𝑔(𝑥) = 𝑥 2 – 6𝑥 + 10
𝑔(𝑥) = ( 𝑥 2 – 6𝑥 – 9)
𝑔(𝑥) = (𝑥 – 3)
The vertex is (3, 19), so the minimum value is 19.
Describe the error that Arturo made. Then give the correct minimum value of the function. Write your answer on the lines provided.
Group 3
To complete the square, Arturo should have added 9 inside the parenthesis instead of subtracting 9. To keep the equation balanced he should have subtracted 9 instead of adding it. The correct minimum value of the function is 1.
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60. Algebra and Modeling
MAFS.912. A-SSE.2.3
Consider the function f x = 𝑥 2 – 6𝑥 + 8.Rewrite the equation to reveal the zeros of the function.
𝑦=(𝑥−4)(𝑥−2)
Group 1 and 2
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61. MAFS.912. A-SSE.2.3 Select all the equations with equivalent zeros.
Algebra and Modeling
MAFS.912. A-SSE.2.3
Select all the equations with equivalent zeros.
𝑦= 𝑥 2 +14
𝑦= 𝑥 2 +9𝑥+14
𝑦= 𝑥− − 25 4
𝑦=(𝑥+7)(𝑥+2)
Groups 2 and 3
𝑦= 1 2 𝑥+7 2𝑥+2
B and D
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62. Algebra and Modeling
MAFS.912. A-SSE.2.3
Consider the function f x = 𝑥 2 –2𝑥 −3.Rewrite the equation to reveal the zeros of the function.
𝑦 =(𝑥+1)(𝑥−3)
Groups 2 and 3
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63. Algebra and Modeling
MAFS.912. A-SSE.2.3
Given (𝑥+4) is a factor of 2 𝑥 2 +11𝑥+2𝑚, determine the value of 𝑚.
Since (𝑥+4) is a factor, 𝑚 must be 4.
Since (𝑥+4) is a factor, 𝑥=−4. Substitute −4 into 2 𝑥 2 +11𝑥+2𝑚=0 and solve for 𝑚 to get 𝑚=6.
Since (𝑥+4) is a factor, 2𝑚=−4, therefore 𝑚=−2.
Since (𝑥+4) is a factor, 𝑥=4. Substitute 4 into 2 𝑥 2 +11𝑥+2𝑚=0 and solve for 𝑚 to get 𝑚=−38.
Group 3 B
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64. Algebra and Modeling
MAFS.912. A-SSE.1.1
In the equation 𝑦 = 𝑥 , what value does the 35 represent?
𝑥-intercept
Starting value
Growth rate
Decay rate
Groups 1 and 2 𝐵
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65. Algebra and Modeling
MAFS.912. A-SSE.1.1
Is the equation 𝐴=21000 (1−0.12) 𝑡 a model of exponential growth or exponential decay, and what is the rate (percent) of change per time period?
exponential growth and 12%
exponential growth and 88%
exponential decay and 12%
exponential decay and 88%
Groups 1 and 2 𝐷
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66. MAFS.912. A-SSE.1.1 𝑓+𝑠 𝑥+𝑦 𝑥𝑓+𝑠𝑦
Algebra and Modeling
MAFS.912. A-SSE.1.1
A company uses two different-sized trucks to deliver cement. The first truck can deliver 𝑥 cubic yards at a time and the second 𝑦 cubic yards. The first truck makes 𝑓 trips to a job site, while the second truck makes 𝑠 trips. What do the following expressions represent in this context?
𝑓+𝑠
The total number of trips both trucks make to the job site.
The total number of cubic yards that the two trucks deliver in one trip.
𝑥+𝑦
Group 3
𝑥𝑓+𝑠𝑦
The total number of cubic yards delivered to the job site.
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67. Algebra and Modeling
MAFS.912. A-SSE.1.1
Amy owns a graphic design store. She purchases a new printer to use in her store. The printer depreciates by a constant rate of 14% per year. The function V=2,400 (1−0.14) 𝑡 can be used to model the value of the printer in dollars after 𝑡 years.
Part A: Explain what the parameter 2,400 represents in the equation of the function.
The parameter 2,400 represents the initial cost of the printer.
Part B: What is the factor by which the printer depreciates each year?
The factor is 0.86.
Group 3
Part C: Amy also considered purchasing a printer that costs $4,000 and depreciates by 25% each year. Which printer will have more value in 5 years?
The printer that cost $2,400 will have a better value by $179.80
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68. MAFS.912. A.SSE.1.2 Which equation is equivalent to 𝑦 = 3 𝑥 2 +6𝑥 + 5?
Algebra and Modeling
MAFS.912. A.SSE.1.2
Which equation is equivalent to 𝑦 = 3 𝑥 2 +6𝑥 + 5?
𝑦 = 3 (𝑥+3) 2 – 9
𝑦 = 3 (𝑥+3) 2 – 4
𝑦 = 3 (𝑥+1) 2 + 4
𝑦 = 3 (𝑥+1) 2 + 2
Groups 2 and 3 𝐷
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69. MAFS.912. A.SSE.1.2 Which equation is equivalent to (𝑚 2 −25)?
Algebra and Modeling
MAFS.912. A.SSE.1.2
Which equation is equivalent to (𝑚 2 −25)?
( 𝑚 2 −10𝑚+25)
( 𝑚 2 +10𝑚+25)
𝑚−5 𝑚+5
(𝑚−5) 2
Group 1 and 2 𝐶
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70. MAFS.912. A.SSE.1.2 Which equation is equivalent to 121 𝑥 2 −64 𝑦 2 ?
Algebra and Modeling
MAFS.912. A.SSE.1.2
Which equation is equivalent to 121 𝑥 2 −64 𝑦 2 ?
(11𝑥−16𝑦)(11𝑥+16𝑦)
(11𝑥−16𝑦)(11𝑥−16𝑦)
11𝑥+8𝑦 11𝑥+8𝑦
(11𝑥+8𝑦)(11𝑥−8𝑦)
Groups 2 and 3 𝐷
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