2019 Algebra 1 Bootcamp 2019 Algebra and Modeling Algebra and Modeling.

2019 Algebra 1 Bootcamp 2019 Algebra and Modeling Algebra and Modeling

MAFS.912.A-APR.1.1 Which expression is equivalent to 2 3𝑔−4 − 8𝑔+3 ?
2019 Algebra 1 Bootcamp 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 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
2019 Algebra 1 Bootcamp MAFS.912.A-APR.1.1 Simplify: 3 3 𝑘 2 −4𝐾+6 − 8 𝑘 2 +𝑘+3 ? 𝑘 2 −13𝑘+15 Group 1 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912.A-APR.1.1 The area of a trapezoid is found using the formula 𝐴= 1 2 ℎ 𝑏 1 + 𝑏 2 , where 𝐴 is the area, ℎ is the height, and 𝑏 1 and 𝑏 2 are the lengths of the bases. What is the area of the above trapezoid? 𝐴 = 4𝑥 + 2 𝐴 = 4𝑥 + 8 𝐴 = 2𝑥² + 4𝑥 – 21 𝐴 = 2𝑥² + 8𝑥 – 42 Groups 1 and 2 B Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912.A-APR.1.1 Which expression is equivalent to (𝑥 + 2)(3𝑥 – 3)? 3 𝑥 2 −6 3 𝑥 2 +3𝑥−6 3 𝑥 2 +6𝑥−6 3 𝑥 2 +9𝑥−6 Groups 1, 2 and 3 𝐵 Algebra and Modeling

MAFS.912.A-APR.1.1 NEW! Subtract 4 𝑥 2 −𝑥+6 from 3 𝑥 2 +5𝑥−8 .
2019 Algebra 1 Bootcamp NEW! MAFS.912.A-APR.1.1 Subtract 4 𝑥 2 −𝑥+6 from 3 𝑥 2 +5𝑥−8 . 7 𝑥 2 +6𝑥−14 − 𝑥 2 +4𝑥+2 7 𝑥 2 +4𝑥−2 − 𝑥 2 +6𝑥−14 Groups 1, 2 and 3 D Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912.A-APR.1.1 Both 𝑓(𝑥) and 𝑔(𝑥) are polynomial functions.
2019 Algebra 1 Bootcamp MAFS.912.A-APR.1.1 Both 𝑓(𝑥) and 𝑔(𝑥) are polynomial functions. Determine whether each expression must be a polynomial. Must Be a Polynomial May Not Be a Polynomial 𝑓 𝑥 +𝑔(𝑥) 𝑔(𝑥) 𝑓 𝑥 −𝑔(𝑥) 𝑓 𝑥 +𝑔(𝑥) 𝑓(𝑥) Groups 2 and 3 Algebra and Modeling

MAFS.912.A-APR.1.1 Consider the polynomial: 2 3 𝑥(2𝑥+3)− 𝑥+7 𝑥−7
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912.A-APR.1.1 The polynomial 2𝑥−1 𝑥 2 −2 −𝑥( 𝑥 2 −𝑥−2) can be written in the form 𝑎 𝑥 3 +𝑏 𝑥 2 +𝑐𝑥+𝑑, where 𝑎, 𝑏, 𝑐, and 𝑑 are constants. What are the values of 𝑎, 𝑏, 𝑐, and 𝑑? 𝑎= 𝑏= 𝑐= 𝑑= 1 Group 3 −2 2 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912.A-CED.1.1 A fence is being built around a rectangular garden. The length of the garden is 35 feet, and the total fencing used to enclose the garden measures 160 feet. Which equation can be used to find the width, , of the garden, in feet? 35𝑤=160 70𝑤=160 35+2𝑤=160 70+2𝑤=160 Groups 1 and 2 D Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912.A-CED.1.1 John has a goal to ride his bike at least 100 miles this summer. John has ridden 12 miles thus far. There are 40 days left in the summer. Part A Write an inequality to represent the average distance, d, in miles, John must ride each day for the rest of the summer to achieve his goal. Enter your inequality in the space provided. 40𝑑 ≥ 100 Part B Determine the average number of miles John must ride each day to reach exactly 100 miles. Enter your answer in the space provided. Groups 1, 2, and 3 2.2 Algebra and Modeling

MAFS.912.A-CED.1.1 A school purchases boxes of candy bars.
2019 Algebra 1 Bootcamp MAFS.912.A-CED.1.1 A school purchases boxes of candy bars. Each box contains 50 candy bars. Each box costs $30. How much does the school have to charge for each candy bar to make a profit of $10 per box? $0.40 $0.50 $0.80 $1.25 Groups 1, 2, and 3 𝐶 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912.A-CED.1.1 Kendrick deposits twice as much money into his account as he did the day before. His initial deposit is $5. Write an equation to model his daily deposit, 𝑦, 𝑥 days after his initial deposit. 𝑦=5 2 𝑥 Groups 2 and 3 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912.A-CED.1.1 A factory has two assembly lines, 𝑀 and 𝑁, that make the same toy. On Monday, only assembly line 𝑀 was functioning, and it made 900 toys. On Tuesday, both assembly lines were functioning for the same amount of time. Line 𝑀 made 300 toys per hour and line 𝑁 made 480 toys per hour. Line 𝑁 made as many toys on Tuesday as line 𝑀 did over both days. Write an equation that can be used to find the number of hours, 𝑡, that the assembly line were functioning on Tuesday. 300𝑡+900=480𝑡 Groups 2 and 3 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912.A-CED.1.1 Two boys, Shawn and Curtis, went for a walk. Shawn began walking 20 seconds earlier than Curtis. Shawn walked at a speed of 5 feet per second. Curtis walked at a speed of 6 feet per second. For how many seconds had Shawn been walking at the moment when the two boys had walked exactly the same distance? Enter your answer in the space provided. Group 3 120 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912.A-REI.2.3 What is the solution of 3 2𝑥−1 ≤4𝑥+7?. 𝑥≤5
2019 Algebra 1 Bootcamp MAFS.912.A-REI.2.3 What is the solution of 3 2𝑥−1 ≤4𝑥+7?. 𝑥≤5 Groups 1, 2, and 3 Algebra and Modeling

MAFS.912.A-REI.2.3 Solve for 𝑥: 3 5 𝑥+2 =𝑥−4 13
2019 Algebra 1 Bootcamp MAFS.912.A-REI.2.3 Solve for 𝑥: 3 5 𝑥+2 =𝑥−4 13 Groups 1, 2, and 3 Algebra and Modeling

MAFS.912.A-REI.2.3 Solve algebraically for 𝑥: 2 𝑥−4 ≥ 1 2 (𝑥−4) 𝑥≥4
2019 Algebra 1 Bootcamp MAFS.912.A-REI.2.3 Solve algebraically for 𝑥: 2 𝑥−4 ≥ 1 2 (𝑥−4) 𝑥≥4 Groups 1, 2, and 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
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912.A-REI.2.3 Consider the inequality 51≤𝑏𝑥+9.
2019 Algebra 1 Bootcamp MAFS.912.A-REI.2.3 Consider the inequality 51≤𝑏𝑥+9. What value of 𝑏 will result in the solution 𝑥≥7? 6 Groups 1, 2, and 3 Algebra and Modeling

MAFS.912.A-REI.2.3 NEW! Solve for 𝑚: (𝑚+2) −4 = −4𝑚+6 2 2
2019 Algebra 1 Bootcamp NEW! MAFS.912.A-REI.2.3 Solve for 𝑚: (𝑚+2) −4 = −4𝑚+6 2 2 Groups 2 and 3 Algebra and Modeling

MAFS.912.A-REI.2.3 NEW! Solve for 𝑣. 5 6 𝑣+25≥20+ 2 3 𝑣 𝑣≥−30 𝑣≤−30
2019 Algebra 1 Bootcamp NEW! MAFS.912.A-REI.2.3 Solve for 𝑣. 5 6 𝑣+25≥ 𝑣 𝑣≥−30 𝑣≤−30 𝑣≥30 𝑣≤30 Groups 2 and 3 𝐴 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912.A-REI.2.3 The value of 𝑥 which makes 𝑥−2 = 𝑥−1 true is: −11. 3 −10 −9. 09 −2 Groups 2 and 3 𝐴 Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912.A-REI.2.3 What is the correct solution to 𝑥+18 =4 2𝑥−6 −9𝑥? 𝒙= −22 Groups 2 and 3 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912.A-CED.1.4 Solve 5𝑏+12𝑐=9 for 𝑏. 𝐷 𝑏=5 12𝑐−9 𝑏=5 9−12𝑐
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912.A-CED.1.4 If 𝑟𝑥−𝑠𝑡=𝑟, which expression represents 𝑥. 𝑟+𝑠𝑡 𝑟
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912.A-CED.1.4 Solve 7𝑥−2𝑧=4−𝑥𝑦 for 𝑥. 𝐷 𝑥=4−𝑥𝑦+ 2𝑧 7 𝑥= 4−𝑥𝑦+2𝑧 7
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912.A-CED.1.4 If 𝑟𝑥−𝑠𝑡=𝑟, which expression represents 𝑟. 𝑠𝑡 (𝑥−𝑟)
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912.A-CED.1.4 Consider the given equation. 4 𝑎 2 + 5𝑏 = 9𝑏 – 7𝑐
2019 Algebra 1 Bootcamp MAFS.912.A-CED.1.4 Consider the given equation. 4 𝑎 𝑏 = 9𝑏 – 7𝑐 Solve the equation for 𝑏. Select all that apply. 𝑏= −7𝑐−4 𝑎 2 5 𝑏= 4𝑎−7𝑐 4 𝑏= 4 𝑎 2 +7𝑐 4 𝑏= 4 𝑎 2 −4𝑐 7 𝑏= 𝑎 2 + 7𝑐 4 Groups 2 and 3 C and E Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912.A-CED.1.4 A company uses the formula 𝑇 = 581𝑠 + 150𝑝 to determine the total cost to purchase 𝑠 computers and 𝑝 printers. Which formula can be used to determine the number of printers purchased, given the total cost, 𝑇, and the number of computers purchased? 𝑝= 𝑇 150 −581𝑠 𝑝=𝑇− 581𝑠 150 𝑝= 𝑇−581𝑠 150 𝑝=𝑇−581𝑠−150 Groups 3 𝐶 Algebra and Modeling

MAFS.912.A-CED.1.4 NEW! A, B, and E ℎ 𝐴 ℎ𝐴 𝑇 𝑠 ℎ𝐴 𝑇 𝑎 𝑇 𝑠 − 𝑇 𝑎
2019 Algebra 1 Bootcamp NEW! MAFS.912.A-CED.1.4 The heat transfer coefficient or convective coefficient (ℎ), is used in thermodynamics to calculate the heat transfer typically occurring by convection. A simple way to calculate ℎ is to define it through the classical formula for convection, 𝑄=ℎ𝐴 𝑇 𝑠 −ℎ𝐴 𝑇 𝑎 Select all the factors of 𝑄. Where 𝑄 𝑖𝑠 𝑡ℎ𝑒 ℎ𝑒𝑎𝑡 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟𝑟𝑒𝑑 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑡𝑖𝑚𝑒 𝐴 𝑖𝑠 𝑡ℎ𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑜𝑏𝑗𝑒𝑐𝑡 ℎ 𝑖𝑠 𝑡ℎ𝑒 ℎ𝑒𝑎𝑡 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑇 𝑠 𝑖𝑠 𝑡ℎ𝑒 𝑜𝑏𝑗𝑒𝑐𝑡′𝑠 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑇 𝑎 𝑖𝑠 𝑡ℎ𝑒 𝑎𝑖𝑟 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 ℎ 𝐴 ℎ𝐴 𝑇 𝑠 ℎ𝐴 𝑇 𝑎 𝑇 𝑠 − 𝑇 𝑎 𝑇 𝑎 − 𝑇 𝑠 Groups 3 A, B, and E Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912.A-CED.1.2 Grace and her brother need $400 to go to band camp. Their parents have agreed to help them earn money by paying them $25 each time they mow the lawn and $10 for each hour they babysit their younger brother. They will have to do a combination of both chores to earn the money. Select the equation that represents the number of lawns they can mow, 𝑚, and hours they can babysit, 𝑏, to earn $400. 10𝑚 + 25𝑏 = 400 10𝑚 − 25𝑏 = 400 25𝑚 + 10𝑏 = 400 25𝑚 − 10𝑏 = 400 Groups 1, 2, and 3 𝐶 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912.A-CED.1.2 Jessie’s bus ride to school is 5 minutes more than the time of Robert’s bus ride. Which graph shows the possible times of Jessie’s and Robert’s bus rides? A. B. C. D. Groups 1, 2, and 3 𝐵 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912.A-CED.1.2 𝑑=(15𝑥)(10𝑥+25)+200 𝑑=15𝑥+(10𝑥+25)+200 𝑑=25𝑥+225
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912.A-CED.1.2 The floor of a rectangular cage has a length 4 feet greater than its width, 𝑤. James will increase both dimensions of the floor by 2 feet. Which equation represents the new area, 𝑁, of the floor of the cage? 𝑁 = 𝑤 2 + 4𝑤 𝑁 = 𝑤 2 + 6𝑤 𝑁 = 𝑤 2 + 6𝑤 + 8 𝑁 = 𝑤 2 + 8𝑤 + 12 Groups 2 and 3 𝐷 Algebra and Modeling

MAFS.912.A-CED.1.2 𝑦= 𝑥 2 −64𝑥 𝑦=− 𝑥 2 +64𝑥 𝑦= 𝑥 2 −32𝑥 𝑦=− 𝑥 2 +32𝑥 𝐷
2019 Algebra 1 Bootcamp MAFS.912.A-CED.1.2 A rectangle has a perimeter of 64. • Let 𝑥 equal the width of the rectangle. • Let 𝑦 equal the area of the rectangle. Which equation can be used to find the area of the rectangle? 𝑦= 𝑥 2 −64𝑥 𝑦=− 𝑥 2 +64𝑥 𝑦= 𝑥 2 −32𝑥 𝑦=− 𝑥 2 +32𝑥 Group 3 𝐷 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912. A-REI.3.5 NEW! 𝐴, 𝐷, 𝑎𝑛𝑑 𝐸 𝐴, 𝑎𝑛𝑑 𝐷
2019 Algebra 1 Bootcamp NEW! MAFS.912. A-REI.3.5 The point (−2,3) is a solution of which of the following systems of equations? Select All that apply. Part A: For which system above is (−2,3) is a unique solution? Select ALL that apply. 6𝑥+3𝑦=−3 1 2 𝑥+9𝑦=26 𝑥−4𝑦=−8 −𝑥+3𝑦=−9 7𝑥+3𝑦=−5 𝑥+𝑦=5 4𝑥+𝑦=−5 −5𝑥+𝑦=13 2𝑥−𝑦=−7 2𝑦=4𝑥+14 𝑥−4𝑦=10 𝑥− 1 3 𝑦=−2 6𝑥+3𝑦=−3 1 2 𝑥+9𝑦=26 𝑥−4𝑦=−8 −𝑥+3𝑦=−9 7𝑥+3𝑦=−5 𝑥+𝑦=5 4𝑥+𝑦=−5 −5𝑥+𝑦=13 2𝑥−𝑦=−7 2𝑦=4𝑥+14 𝑥−4𝑦=10 𝑥− 1 3 𝑦=−2 Group 3 𝐴, 𝐷, 𝑎𝑛𝑑 𝐸 𝐴, 𝑎𝑛𝑑 𝐷 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912. A-REI.3.6 A system of equations is shown below.
2019 Algebra 1 Bootcamp MAFS.912. A-REI.3.6 A system of equations is shown below. Equation 𝑨: 5𝑥 + 9𝑦 = 12 Equation 𝑩: 4𝑥 − 3𝑦 = 8 Which method eliminates one of the variables? Multiply equation 𝐴 by − 1 3 and add the result to equation 𝐵. Multiply equation 𝐵 by 3 and add the result to equation 𝐴. Multiply equation 𝐴 by 2 and equation 𝐵 by −6 and add the results together. Multiply equation 𝐵 by 5 and equation 𝐴 by 4 and add the results together. Groups 1, 2, and 3 𝐵 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912. A-REI.3.6 The math club sells candy bars and drinks during football games. 60 candy bars and 110 drinks will sell for $265. 120 candy bars and 90 drinks will sell for $270. How much does each candy bar sell for? Enter your answer in the space provided. 0.75 Groups 1, 2, and 3 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912. A-REI.3.6 Jackie buys 3 hot dogs and 1 pretzel from a restaurant for $ Sylvia buys 2 hot dogs and 4 pretzels from the same restaurant for $16.50. Part A Which system of equations can be used to determine the price of a hot dog, ℎ, and a pretzel, 𝑝, at the restaurant? Part B What is the price of a hot dog at the restaurant? Enter your answer in the space provided. 3ℎ + 1𝑝 = 12.25 2ℎ + 4𝑝 = 16.50 2ℎ + 1𝑝 = 12.25 3ℎ + 4𝑝 = 16.50 3ℎ + 2ℎ = 12.25 1𝑝 + 4𝑝 = 16.50 2ℎ + 4𝑝 = 12.25 3ℎ + 1𝑝 = 16.50 A. B. C. D. 3.25 Groups 1, 2, and 3 𝐷 Algebra and Modeling

Infinitely Many Solutions
2019 Algebra 1 Bootcamp NEW! MAFS.912. A-REI.3.6 Three systems of equations are shown in the table below. Select the choice that describe the number of solutions of each system. One Solution No Solution Infinitely Many Solutions 2𝑥+2𝑦=16 4𝑥+3𝑦=27 2𝑥+2𝑦=8 4𝑥+4𝑦=16 2𝑥+3𝑦=12 2𝑥+3𝑦=18 Groups 2 and 3 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-REI.3.6 Consider this system of equations 2𝑥+5𝑦=10 6𝑥+𝑛𝑦= What would “𝑛” need to equal for this system to have no solution? 𝒏= 15 Groups 3 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912. A-REI.4.12 Which inequality does this graph represent?
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-REI.4.12 In which graph does the shaded region represent the solution set for the inequality shown below? 2𝑥−𝑦<4 A. B. C. D. Groups 1, 2 and 3 𝐷 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912. A-REI.4.12 What scenario could be modeled by the graph below? The number of pounds of apples, 𝑦, minus two times the number of pounds of oranges, 𝑥, is at most 5. The number of pounds of apples, 𝑦, minus half the number of pounds of oranges, 𝑥, is at most 5. The number of pounds of apples, 𝑦, plus two times the number of pounds of oranges, 𝑥, is at most 5. The number of pounds of apples, 𝑦, plus half the number of pounds of oranges, 𝑥, is at most 5. Groups 1, 2, and 3 𝐶 Algebra and Modeling

MAFS.912. A-REI.4.12 𝑦<−5𝑥−2 𝑦≤−𝑥+2
2019 Algebra 1 Bootcamp MAFS.912. A-REI.4.12 𝑦<−5𝑥−2 𝑦≤−𝑥+2 Graph the system of inequalities: A. B. C. D. Groups 1, 2, and 3 𝐶 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 1, 2, and 3 A , F, and G Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912. A-REI.4.12 Determine the solution to the system of inequalities: 3𝑥+3𝑦≤3 𝑥−3𝑦≥−6 Groups 2 and 3 Algebra and Modeling

MAFS.912. A-REI.4.12 Consider the system of inequalities. 3𝑥+2𝑦<8
2019 Algebra 1 Bootcamp MAFS.912. A-REI.4.12 Consider the system of inequalities. 3𝑥+2𝑦<8 −5𝑥−9𝑦≥2 Select all ordered pairs that are solutions to the system of inequalities. −10, −3 −2, 7 0, 0 1, −1 4, −2 8, 9 Groups 2 and 3 A and D Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-REI.4.12 The graph of a system of inequalities is shown. Create the system of inequalities that is represented by the graph. 𝑦<−3 𝑦≥ 2 3 𝑥−5 Groups 2 and 3 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-CED.1.3 A standard elevator in a medium-rise office building has a maximum capacity of 17 people and can hold a maximum of 2,570 pounds. The average weight of an adult is pounds for men and for women. Select all the inequalities that model the contains for this situation, where 𝑥 represents the number of men and 𝑦 represents the number of women. 𝑥≥0 𝑦≥0 𝑥≤195.5 𝑦≤17 𝑥+𝑦≤17 𝑥+𝑦≤2,570 195.5𝑥+166.2𝑦≤2,570 Groups 1, 2 and 3 A, B, E, and G Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-CED.1.3 Joanna has a total of 50 coins in her purse. • The coins are either nickels or quarters. • The total value of the coins is $7.10. Which system of equations can be used to determine the number of nickels, 𝑛, and quarters, 𝑞, that Joanna has in her purse? 𝑛 + 𝑞 = 50 0.05𝑛 𝑞 = 7.10 𝑛 + 𝑞 = 7.10 50𝑛 + 50𝑞 = 7.10 0.05𝑛 𝑞 = 50 𝑛+𝑞 = 7.10 A. B. C. D. Groups 1, 2 and 3 𝐴 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912. A-CED.1.3 Alicia purchased 𝐻 half-gallons of ice cream for $3.50 each and 𝑃 packages of ice cream cones for $2.50 each. She purchased 14 items and spent $43. Which system of equations could be used to determine how many of each item Alicia purchased? 3.50𝐻 𝑃 = 43 𝐻+𝑃=14 3.50𝑃+ 2.50𝐻 = 43 𝑃+𝐻=14 3.50𝐻+ 2.50𝑃 =14 𝐻+𝑃=43 A. B. C. D. Groups 1, 2, and 3 A Algebra and Modeling

2019 Algebra 1 Bootcamp 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 and 3 Algebra and Modeling

MAFS.912. A-CED.1.3 NEW! 𝐵 Sally works at a store.
2019 Algebra 1 Bootcamp NEW! MAFS.912. A-CED.1.3 Sally works at a store. • 𝑥 represents Sally’s monthly paycheck, and 𝑦 represents her monthly savings. • Sally will save at least $20 more than half of her paycheck each month. • She can save at most $80 more than two-thirds of her paycheck each month. • Her paycheck each month is at least $1,200, but no more than $1,850. Which system of inequalities represents these constraints? 𝑥≤ 1 2 𝑦+20 𝑥≥ 2 3 𝑦+80 𝑦≤1,200 𝑦≥1,850 A. 𝑦≥ 1 2 𝑥+20 𝑦≤ 2 3 𝑥+80 𝑥≥1,200 𝑥≤1,850 B. 𝑦≤ 1 2 𝑥+20 𝑦≥ 2 3 𝑥+80 𝑥≤1,200 𝑥≥1,850 C. 𝑥≥ 1 2 𝑦+20 𝑥≤ 2 3 𝑦+80 𝑦≥1,200 𝑦≤1,850 D. Groups 2 and 3 𝐵 Algebra and Modeling

MAFS.912. A-CED.1.3 NEW! 2x+5y≥500 5𝑥+2𝑦≥500 2+𝑥 5+𝑦 ≥500
2019 Algebra 1 Bootcamp NEW! MAFS.912. A-CED.1.3 Members of a high school sports team are selling boxes of popcorn and boxes of pretzels for a fundraiser. They earn $2 for every box of popcorn they sell and $5 for every box of pretzels. The members want to earn at least $500 from all sales. Let 𝑥 represent the number of boxes of popcorn sold and 𝑦 represent the number of boxes of pretzels sold. Part A: What inequality represents the number of boxes of popcorn and the number of boxes of pretzels that need to be sold to reach the goal of earning at least $500? Part B: A line exists that serves as the boundary for the points making up the solution set of the inequality representing the numbers of boxes of popcorn and boxes of pretzels sold. Consider the line graphed in the 𝑥𝑦-coordinate plane. What would be the interpretation, in context, of its slope? 2x+5y≥500 5𝑥+2𝑦≥500 2+𝑥 5+𝑦 ≥500 (5+𝑥)(2+𝑦)≥500 For every increase of 2 boxes of popcorn sold, 5 more boxes of pretzels need to be sold to earn $500. For every increase of 2 boxes of popcorn sold, 5 fewer boxes of pretzels need to be sold to earn $500. For every increase of 5 boxes of popcorn sold, 2 more boxes of pretzels need to be sold to earn $500. For every increase of 5 boxes of popcorn sold, 2 fewer boxes of pretzels need to be sold to earn $500. Groups 2 and 3 A D Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-CED.1.3 (continued from previous slide) Part C: Members of the team believe they can sell at least 40 boxes of pretzels. Which graph represents the solution in the 𝑥𝑦-coordinate plane of the system of inequalities that represents the number of boxes of popcorn and boxes of pretzels that need to be sold with the constraint that at least 40 boxes of pretzels will be sold? A. B. C. D. Groups 2 and 3 D Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-CED.1.3 (continued from previous slide) Part D: Which combinations of boxes of popcorn and pretzels sold will the team meet the goal of earning at least $500? Select all that apply. 30 boxes of popcorn and 80 boxes of pretzels. 60 boxes of popcorn and 80 boxes of pretzels. 75 boxes of popcorn and 70 boxes of pretzels. 80 boxes of popcorn and 60 boxes of pretzels. 100 boxes of popcorn and 60 boxes of pretzels. Groups 2 and 3 B, C, and E Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-CED.1.3 A store sells two types of toys, A and B. The store owner pays $8 and $14 for each one unit of toy A and B respectively. One unit of toys A yields a profit of $3 while a unit of toys B yields a profit of $2. The store owner estimates that no more than 2000 toys will be sold every month and he does not plan to invest more than $30,000 in inventory of these toys Part A: Select all the inequalities that model the constraints for this situation, where 𝑥 represents the total number of toys A and 𝑦 the number of toys B. 𝑥≥0 𝑦≥0 𝑥+𝑦≤2,000 3𝑥+2𝑦≥2,000 8𝑥+14𝑦≤30,000 Groups 2 and 3 A, B, C, and E Algebra and Modeling

MAFS.912. A-CED.1.3 ________≤𝑥≤________ NEW!
2019 Algebra 1 Bootcamp NEW! MAFS.912. A-CED.1.3 (continued from previous slide) Part B: The uses his estimates to construct the graph shown, where he rounds all the values to the nearest whole number. Based on the store owner’s estimates, select the values for the inequality that would best represent all the possible number of toys A for which his store will yield at least a profit of $4,500 ________≤𝑥≤________ 500 2000 500 1500 2000 2250 500 1500 2000 2250 Groups 2 and 3 Algebra and Modeling

MAFS.912. A-CED.1.3 𝑔+𝑡≤10 𝑔≥1 𝑡≥1 𝑔+𝑡≥10 𝑔≥0 𝑡≥0
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912. A-REI.1.1 Martha solved the equation 5 𝑏+3 =𝑏+39.
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912. A-REI.1.1 When solving the equation 12 𝑥 2 −7𝑥=6−2( 𝑥 2 −1), Evan wrote 𝑥 2 −7𝑥=6−2 𝑥 2 +2, as his first step. Which property justifies this step? subtraction property of equality multiplication property of equality associative property of multiplication distributive property of multiplication over subtraction Groups 1, 2, and 3 𝐷 Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-REI.1.1 Britney is solving a quadratic equation. Her first step is shown below. Problem: 3 𝑥 2 −8−10𝑥=3(2𝑥+3) Step 1: 𝑥 2 −10𝑥−8=6𝑥+9 Which two properties did Britney use to get to step 1? addition property of equality commutative property of addition multiplication property of equality distributive property of multiplication over addition Groups 1, 2 and 3 I and III I and IV II and III II and IV 𝐷 Algebra and Modeling

MAFS.912. A-REI.2.4 NEW! An equation is shown. 16𝑥 2 +10𝑥−27=−6𝑥+5
2019 Algebra 1 Bootcamp NEW! MAFS.912. A-REI.2.4 An equation is shown. 16𝑥 2 +10𝑥−27=−6𝑥+5 What are the solutions to this equation? 1 −2 Groups 1, 2 and 3 Algebra and Modeling

MAFS.912. A-REI.2.4 Which are the solutions to 𝑥 2 +9𝑥=36? 𝑥=−12,𝑥=3
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-REI.2.4 Determine whether the equations shown have real solutions or no real solutions. Real Solution No Real Solution 4 𝑥 2 −2𝑥=−1 3 𝑥 2 +6𝑥=−3 2 𝑥 2 −5𝑥+7=0 Groups 1, 2, 3 Algebra and Modeling

MAFS.912. A-REI.2.4 Consider the equation 𝑥 2 −12𝑥+49=22
2019 Algebra 1 Bootcamp MAFS.912. A-REI.2.4 Consider the equation 𝑥 2 −12𝑥+49=22 Which equation has the same solution(s) as the given equation? (𝑥−6) 2 = 9 (𝑥−7) 2 = 22 (𝑥+7) 2 =4.7 (𝑥−12) 2 = −27 Groups 2 and 3 𝐴 Algebra and Modeling

MAFS.912. A-REI.2.4 Solve by completing the square: 𝑥 2 −6𝑥−4=0 3± 13
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912. A-REI.2.4 Consider the equation. 2 𝑥+4 2 −113=49
2019 Algebra 1 Bootcamp MAFS.912. A-REI.2.4 Consider the equation. 2 𝑥+4 2 −113=49 What value(s) of 𝑥 makes the equation true? Enter one solution in each response box. If there is only one solution, leave one response box blank. Group 3 5 −13 Algebra and Modeling

MAFS.912. A-REI.2.4 Consider the equation. 3 𝑥−5 2 +6=54
2019 Algebra 1 Bootcamp MAFS.912. A-REI.2.4 Consider the equation. 3 𝑥− =54 What value(s) of 𝑥 makes the equation true? Enter one solution in each response box. If there is only one solution, leave one response box blank. Group 3 1 9 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912. A-REI.2.4 Which equations have no real solutions? Select all that apply. 2 𝑥−3 2 =0 2 𝑥 =1 𝑥− =8 𝑥 =2 𝑥 2 +8𝑥=15 Group 3 B and D Algebra and Modeling

MAFS.912. A-REI. 4.11 NEW! 𝑓(𝑥) = 3𝑥 + 7 𝑔(𝑥) = 2𝑥 + 12 -22 -5 5 22 𝐶
2019 Algebra 1 Bootcamp NEW! MAFS.912. A-REI. 4.11 Two functions are shown below. 𝑓(𝑥) = 3𝑥 + 7 𝑔(𝑥) = 2𝑥 + 12 What is the value of 𝑥 where the graphs of 𝑓(𝑥) and 𝑔(𝑥) intersect? -22 -5 5 22 Groups 1, 2 and 3 𝐶 Algebra and Modeling

MAFS.912. A-REI. 4.11 Which system of equations has only one solution?
2019 Algebra 1 Bootcamp MAFS.912. A-REI. 4.11 Which system of equations has only one solution? 𝑦=𝑥+5 and 𝑦=−3𝑥+6 𝑦=𝑥−2and 𝑦=𝑥+4 𝑦=2𝑥+6 and 𝑦=2(𝑥+3) 𝑦= 𝑥 2 −1 and 𝑦=1.5𝑥+1 Groups 1, 2, and 3 𝐴 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912. A-REI. 4.11 The graph of two functions is shown on the coordinate plane. Select all values of 𝑥 for which 𝑓(𝑥) = 𝑔(𝑥). −2 −1 1 3 4 Groups 2 and 3 B and F Algebra and Modeling

MAFS.912. A-REI. 4.11 The graphs of the functions 𝑓 and 𝑔 are shown
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912. A-REI. 4.11 Lucy and Barbara began saving money the same week. The table below shows the models for the amount of money Lucy and Barbara had saved after 𝑥 weeks. After how many weeks will Lucy and Barbara have the same amount of money saved? 1.1 weeks 1.7 weeks 8 weeks 12 weeks Group 3 𝐶 Algebra and Modeling

2019 Algebra 1 Bootcamp 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, 2 and 3 𝐶 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912. A-REI.4.10 When is this statement true? 𝑦 = 𝑥 2 + 4𝑥 − 1
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 1, 2, and 3 Algebra and Modeling

MAFS.912. A-SSE.2.3 Select all the equations with equivalent zeros.
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912. A-SSE.2.3 Nora inherited a savings account that was started by her grandmother 25 years ago. This scenario is modeled by the function 𝐴(𝑡) = 𝑡+25 , where 𝐴(𝑡) represents the value of the account, in dollars, 𝑡 years after the inheritance. Which function below is equivalent to 𝐴(𝑡)? 𝐴 𝑡 = 𝑡 25 𝐴 𝑡 = 𝑡 𝐴 𝑡 = 𝑡 𝑡 𝐴 𝑡 = 𝑡 Groups 2 and 3 𝐵 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912. A-SSE.2.3 A quadratic function is given as 𝑓 𝑥 = 𝑥 2 +8𝑥+6. Rewrite the given function in an equivalent form that would reveal the vertex of the function. Enter your answer in the space provided. 𝑓 𝑥 = 𝑥+4 2 −10 Groups 2 and 3 Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-SSE.2.3 A student studying public policy created a model for the population of Detroit, where the population decreased 25% over a decade. He used the model 𝑃= 𝑑 , where 𝑃 is the population, in thousands, 𝑑 decades after Another student, Suzanne, wants to use a model that would predict the population after 𝑦 years. Suzanne's model is best represented by 𝑃= 𝑦 𝑃= 𝑦 𝑃= 𝑦 𝑃= 𝑦 Groups 2 and 3 𝐶 Algebra and Modeling

2019 Algebra 1 Bootcamp 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. Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912. A-SSE.2.3 Select all expressions equivalent to 16 2 𝑛−3
2019 Algebra 1 Bootcamp MAFS.912. A-SSE.2.3 Select all expressions equivalent to 𝑛−3 2 4𝑛−12 2 4𝑛−3 2 𝑛+1 8 2 𝑛−1 8 2 𝑛−2 Group 3 C and E Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-SSE.2.3 For a given time, 𝑥, in seconds, an electric current, 𝑦, can be represented by 𝑦=2.5 1− 2.7 −0.10𝑥 . Which equation is not equivalent? 𝑦=2.5− −0.10𝑥 𝑦=2.5− −0.05𝑥 𝑦=2.5− 𝑥 𝑦=2.5− − 𝑥 Groups 3 𝐷 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-SSE.1.1 The amount Mike gets paid weekly can be represented by the expression 2.50𝑎+290, where 𝑎 is the number of cell phone accessories he sells that week. What is the constant term in this expression and what does it represent? 2.50𝑎, the amount he is guaranteed to be paid each week 2.50𝑎, the amount he earns when he sells a accessories 290, the amount he is guaranteed to be paid each week 290, the amount he earns when he sells a accessories Groups 1, 2 and 3 C Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-SSE.1.1 Which statement(s) can be interpreted from the equation for an automobile cost, 𝐶(𝑡)=28, 𝑡 where 𝐶(𝑡) represents the cost and 𝑡 represents the time in years? The equation is an exponential growth equation. The equation is an exponential decay equation. The equation is neither exponential decay nor exponential growth. $28,000 represents the initial cost of an automobile that appreciates 27% per year over the course of 𝑡 years. $28,000 represents the initial cost of an automobile that appreciates 73% per year over the course of 𝑡 years. $28,000 represents the initial cost of an automobile that depreciates 27% per year over the course of 𝑡 years. $28,000 represents the initial cost of an automobile that depreciates 73% per year over the course of 𝑡 years. Groups 1, 2 and 3 B and F Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-SSE.1.1 Samantha sells two types of wristbands, rope or beaded. She charges more for beaded wristbands than for rope wristbands. The amount of money, in dollars, that she collects from selling 𝑥 wristbands of one type and 𝑦 wristbands of the other type can be modeled by the expression 5𝑥+8𝑦. What does the variable 𝑦 represent in this situation? The number of rope wristbands sold. The number of beaded wristbands sold. The selling price of one rope wristband. The selling price of one beaded wristband. Groups 1, 2 and 3 𝐵 Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A-SSE.1.1 A T-shirt company bought a new packaging and tracking system for $100,000. The formula 𝑉=100,000 1− 𝑦 models the value of the system 𝑉, in dollars, after depreciating for 𝑦 years. In this formula, what is the meaning of the term 1−0.125 ? The value of the system will be $0 in 12.5 years. The value of the system will decrease by $12.50 each year. The value of the system will decrease by 12.5% each year. The value of the system will continue to decrease for 125 years. Groups 1, 2 and 3 𝐶 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912. A-SSE.1.1 A scientist began a study with a sample of 1,500 bacteria. He noticed that the number of bacteria in the sample after 𝑡 days can be modeled by the equation 𝑃=1,500∙ 5 𝑡 . In this equation, what does 5 𝑡 represent? The number of bacteria increases by 5 bacteria each day. The number of bacteria increases by 𝑡 bacteria after 5 days. The number of bacteria increases by a factor of 5 each day. The number of bacteria increases by a factor of 𝑡 each day for 5 days. Groups 1, 2, and 3 𝐶 Algebra and Modeling

MAFS.912. A-SSE.1.1 𝑓+𝑠 𝑥+𝑦 𝑥𝑓+𝑠𝑦
2019 Algebra 1 Bootcamp 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. Algebra and Modeling

2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912. A.SSE.1.2 Which equation is equivalent to (𝑚 2 −25)?
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912. A.SSE.1.2 Select the expression that is equivalent to 𝑔 2 −144. 𝑔−12 2 𝑔−72 2 𝑔−8 𝑔+18 𝑔−12 𝑔+12 Groups 1, 2, and 3 𝐷 Algebra and Modeling

2019 Algebra 1 Bootcamp NEW! MAFS.912. A.SSE.1.2 David correctly factored the expression 𝑚 2 −12𝑚−64. Which expression did he write? (𝑚−8)(𝑚−8) (𝑚−8)(𝑚+8) 𝑚−16 𝑚+4 (𝑚+16)(𝑚−4) Groups 1, 2 and 3 C Algebra and Modeling

MAFS.912. A.SSE.1.2 Which equation is equivalent to 𝑦 = 3 𝑥 2 +6𝑥 + 5?
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

MAFS.912. A.SSE.1.2 Which equation is equivalent to 121 𝑥 2 −64 𝑦 2 ?
2019 Algebra 1 Bootcamp 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 Algebra and Modeling

2019 Algebra 1 Bootcamp MAFS.912. A.SSE.1.2 Select all expressions that are equivalent to 3 𝑥 5 −6 𝑥 4 +3 𝑥 3 . 3 𝑥 3 𝑥−1 2 3 𝑥 3 𝑥 2 −2𝑥+1 3 𝑥 3 𝑥+1 2 3 𝑥 3 𝑥−1 (𝑥+1) 3 𝑥 3 𝑥−1 𝑥−1 Group 3 A, B, and E Algebra and Modeling

Acknowledgment The assessment items presented in this PowerPoint have been compiled from several free web-based resources like sample items, released items, and practice tests. Regent Exams - PARCC Released Items - NCFE Released Items For High School Subjects ( ) - Ohio Student Practice Resources – Mathematics -

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