2019 Algebra 1 boot camp Algebra and Modeling

MAFS. 912. A-APR. 1. 1

MAFS. 912. A-APR. 1. 1 What is the area of the above trapezoid?

MAFS. 912. A-APR. 1. 1

MAFS. 912. A-APR. 1. 1 Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-Non. Commercial-No. Derivs 3. 0 Unported License

MAFS. 912. A-APR. 1. 1 Must Be a Polynomial May Not Be a Polynomial

MAFS. 912. A-APR. 1. 1

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.

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?

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?

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 �� 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?

MAFS. 912. A-CED. 1. 1

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. 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.

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? A. $0. 40 B. $0. 50 C. $0. 80 D. $1. 25

MAFS. 912. A-CED. 1. 1

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.

MAFS. 912. A-CED. 1. 1 q Width: 4 in q Length: 4 in q Width: 6 in q Length: 6 in q Width: 7 in q Length: 7 in

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.

MAFS. 912. A-REI. 2. 3

MAFS. 912. A-REI. 2. 3 Equation Yes No

MAFS. 912. A-CED. 1. 4

MAFS. 912. A-CED. 1. 4 Consider the given equation.

MAFS. 912. A-CED. 1. 4

MAFS. 912. A-CED. 1. 2

MAFS. 912. A-CED. 1. 2 A. B. C. D.

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.

MAFS. 912. A-CED. 1. 2

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. C. B. D. Part B: How many months will it take for Toilet B to be more cost effective?

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.

MAFS. 912. A-CED. 1. 2

MAFS. 912. A-CED. 1. 2 A rectangle has a perimeter of 64. Which equation can be used to find the area of the rectangle?

MAFS. 912. A-CED. 1. 2 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

MAFS. 912. A-REI. 3. 5 Which system of equations has the same solution as the system below? A. B. C. D.

MAFS. 912. A-REI. 3. 5 A. B. C. D.

MAFS. 912. A-REI. 3. 5

MAFS. 912. A-REI. 3. 6

MAFS. 912. A-REI. 3. 6 A system of equations is shown below. Which method eliminates one of the variables?

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.

MAFS. 912. A-REI. 3. 6 Jackie buys 3 hot dogs and 1 pretzel from a restaurant for $12. 25. Sylvia buys 2 hot dogs and 4 pretzels from the same restaurant for $16. 50. Part B What is the price of a hot dog at the restaurant? Enter your answer in the space provided. A. B. C. D.

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

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?

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.

MAFS. 912. A-REI. 3. 6

MAFS. 912. A-REI. 4. 12 A. B. C. D.

MAFS. 912. A-REI. 4. 12 Which inequality does this graph represent?

MAFS. 912. A-REI. 4. 12 A. B. C. D.

MAFS. 912. A-REI. 4. 12 What scenario could be modeled by the graph below?

MAFS. 912. A-REI. 4. 12 Graph the system of inequalities: A. B. C. D.

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. q. A q. B q. C q. D q. E q. F q. G

MAFS. 912. A-REI. 4. 12 Determine the solution to the system of inequalities:

MAFS. 912. A-REI. 4. 12 Consider the system of inequalities. Select all ordered pairs that are solutions to the system of inequalities.

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.

MAFS. 912. A-CED. 1. 3 Part A: For what number of athletes would Part B: Is this a viable answer? Explain. both teams have the same number of Olympic medals?

MAFS. 912. A-CED. 1. 3

MAFS. 912. A-CED. 1. 3 Joanna has a total of 50 coins in her purse. • • A. B. C. D. The coins are either nickels or quarters. The total value of the coins is $7. 10.

MAFS. 912. A-CED. 1. 3 A. B. C. D.

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 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.

MAFS. 912. A-CED. 1. 3 Sally works at a store. Which system of inequalities represents these constraints? A. B. C. D.

MAFS. 912. A-CED. 1. 3 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? A. For every increase of 2 boxes of popcorn sold, 5 more boxes of pretzels need to be sold to earn $500. B. For every increase of 2 boxes of popcorn sold, 5 fewer boxes of pretzels need to be sold to earn $500. C. For every increase of 5 boxes of popcorn sold, 2 more boxes of pretzels need to be sold to earn $500. D. For every increase of 5 boxes of popcorn sold, 2 fewer boxes of pretzels need to be sold to earn $500.

(continued from previous slide) MAFS. 912. A-CED. 1. 3 A. B. C. D.

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. q 30 boxes of popcorn and 80 boxes of pretzels. q 60 boxes of popcorn and 80 boxes of pretzels. q 75 boxes of popcorn and 70 boxes of pretzels. q 80 boxes of popcorn and 60 boxes of pretzels. q 100 boxes of popcorn and 60 boxes of pretzels.

MAFS. 912. A-CED. 1. 3

(continued from previous slide) MAFS. 912. A-CED. 1. 3 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 0 500 1500 2000 2250

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. Part A: Which system represents the imposed Part B: Which numbers of hours spent painting constraints? over graffiti and hours spent picking up trash could fit the community service requirements? Select all A. C. that apply. q 3 graffiti hours and 4 trash hours q 6 graffiti hours and 7 trash hours q 8 graffiti hours and 3 trash hours B. D. q 9 graffiti hours and 1 trash hours q 0 graffiti hours and 10 trash hours q 5 graffiti hours and 5 trash hours

MAFS. 912. A-REI. 1. 1 Step 1 Step 2 Step 3 Step 4 Step 5 Which property was used incorrectly when going from Step 2 to Step 3? A. B. C. D. Addition Property Distributive Property Substitution Property Transitive Property

MAFS. 912. A-REI. 1. 1 Step 1 Step 2 Step 3 Step 4 Step 5 Which step is the first incorrect step in Martha’s solution shown above? A. B. C. D. Step 2 Step 3 Step 4 Step 5

MAFS. 912. A-REI. 1. 1 A. subtraction property of equality B. multiplication property of equality C. associative property of multiplication D. distributive property of multiplication over subtraction

MAFS. 912. A-REI. 1. 1 Britney is solving a quadratic equation. Her first step is shown below. Which two properties did Britney use to get to step 1? I. III. IV. A. I and III B. I and IV C. II and III D. II and IV addition property of equality commutative property of addition multiplication property of equality distributive property of multiplication over addition

MAFS. 912. A-REI. 2. 4

MAFS. 912. A-REI. 2. 4 Determine whether the equations shown have real solutions or no real solutions. Real Solution No Real Solution

MAFS. 912. A-REI. 2. 4 Consider the equation Which equation has the same solution(s) as the given equation?

MAFS. 912. A-REI. 2. 4

MAFS. 912. A-REI. 2. 4 Consider the equation. Enter one solution in each response box. If there is only one solution, leave one response box blank.

MAFS. 912. A-REI. 2. 4 Which equations have no real solutions? Select all that apply.

MAFS. 912. A-REI. 4. 11 Two functions are shown below. A. -22 B. -5 C. 5 D. 22

MAFS. 912. A-REI. 4. 11 Which system of equations has only one solution?

MAFS. 912. A-REI. 4. 11 The graph of two functions is shown on the coordinate plane. q − 2 q − 1 q 0 q 1 q 3 q 4

MAFS. 912. A-REI. 4. 11 The graphs of the functions �� and �� are shown

MAFS. 912. A-REI. 4. 11 After how many weeks will Lucy and Barbara have the same amount of money saved? A. 1. 1 weeks B. 1. 7 weeks C. 8 weeks D. 12 weeks

MAFS. 912. A-REI. 3. 6 A. B. C. D. (1, 1) (3, 5) (2, 3) (3, 2)

MAFS. 912. A-REI. 3. 6

MAFS. 912. A-REI. 4. 10 Choose the ordered pair that is a solution to the equation represented by the graph.

MAFS. 912. A-REI. 4. 10 q (-2, -10) q (-1, 1) q (0, 4) q (4, 8) q (6, 14)

MAFS. 912. A-REI. 4. 10

MAFS. 912. A-REI. 4. 10 When is this statement true?

MAFS. 912. A-REI. 4. 10

MAFS. 912. A-SSE. 2. 3

MAFS. 912. A-SSE. 2. 3 Select all the equations with equivalent zeros.

MAFS. 912. A-SSE. 2. 3

MAFS. 912. A-SSE. 2. 3 Rewrite the given function in an equivalent form that would reveal the vertex of the function. Enter your answer in the space provided.

MAFS. 912. A-SSE. 2. 3

MAFS. 912. A-SSE. 1. 1

MAFS. 912. A-SSE. 1. 1 A. The number of rope wristbands sold. B. The number of beaded wristbands sold. C. The selling price of one rope wristband. D. The selling price of one beaded wristband.

MAFS. 912. A-SSE. 1. 1 A. The value of the system will be $0 in 12. 5 years. B. The value of the system will decrease by $12. 50 each year. C. The value of the system will decrease by 12. 5% each year. D. The value of the system will continue to decrease for 125 years.

MAFS. 912. A-SSE. 1. 1

MAFS. 912. A-SSE. 1. 1 Part A: Explain what the parameter 2, 400 represents in the equation of the function. Part B: What is the factor by which the printer depreciates each year? 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?

MAFS. 912. A. SSE. 1. 2

Acknowledgment The assessment items presented in this Power. Point have been compiled from several free web-based resources like sample items, released items, and practice tests. • Regent Exams - http: //www. jmap. org/JMAP_REGENTS_EXAMS. htm • PARCC Released Items - https: //parcc-assessment. org/released-items/ • NCFE Released Items For High School Subjects (2017 -18) http: //www. ncpublicschools. org/accountability/testing/common-exams/releaseditems/highschoolitems • Ohio Student Practice Resources – Mathematics https: //oh. portal. airast. org/resources/mathematics-spr/