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MAFS.912.A-REI.1.1 ***********NO CALCULATOR**************Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. 1. A student solved the equation 7 = 3(t – 1) – 2(t – 3) as shown below. Assume there is a value of t for that satisfies the equation.Provide a justification for each step of the solution process.7 = 3(t – 1) – 2(t – 3)a) 7 = 3t – 3 – 2t + 6 Justification:b) 7 = t + 3 Justification:c) 4 = t Justification:Equation Logic2. Solve the equation 5x+34=7. Explain and justify each step in your solution process.3.MAFS.912.F-IF.2.4 *****************NO CALCULATOR******************* For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Also assesses MAFS.912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. 4. (Old Standard 2: MA.912.A.2.3)The students in Adam's science class measure and graph the speed of a slow-moving snail. A.f(x) = 3xB.f(x) = 2xx2C.f(x) = ?3xD.f(x) = 3x + 2The snail moves at a constant rate, and after the investigation, the students use their data to create the following graph. Based on this graph, what function would best represent the snail's speed if x = time and f(x) = distance?5. (Old Standard 3: MA.912.A.3.9)On a coordinate graph, Celeste places a red marble at the point (2, 2) and a green marble at the point (4, 1). If she draws a line that passes through both of these points, what are the coordinates of the x- and y-intercepts of the line?6. State the x and y intercepts: 3x – y = 37.(Old Standard 7: MA.912.A.7.1)Which of the following is the graph of the function y = x2 ? 4x ? 12? Label any extrema on the graph. Be sure to indicate whether the point represents a relative minimum or absolute minimum, etc. A.B.C.D.8. (Old Standard 7: MA.912.A.7.1)What equation represents the graph shown below? On what interval(s) is the graph decreasing? Increasing? Identify the extrema. 9. State the absolute maximum and/or absolute minimum and list any relative minima or maxima. 10.11. (Old Standard 3: MA.912.A.3.8)Ignacio threw 14 pitches during the first two innings of a baseball game. He threw an average of 8 pitches per inning for the next seven innings. Which graph correctly represents the number of pitches Ignacio threw during the game?ACBDMAFS.912.F-LE.1.1 *******************NO CALCULATOR*******************Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. Also assesses MAFS.912.F-LE.2.5 Interpret the parameters in a linear or exponential function in terms of a context. 12. Name the type of model suggested by the graph to the below.[A] linear [B] quadratic [C] exponential [D] absolute value13. The table gives the number of inner tubes, I, sold in a bike shop between 1985 and 1990. Determine which model best fits the data.[A] quadratic [B] linear [C] absolute value [D] exponential14. A forester has determined that the number of fir trees, N, in a forest can be modeled by the equation N=8000(0.5)t8 where 8000 is the estimated number of trees in 2010 and t is the number of years since 2010. Label and scale the axes appropriately. Then, sketch a graph of this equation for the period 2010-2030. Indicate clearly the coordinates of the points you used to construct the graph.15. A radioactive kind of nitrogen has a half-life of 10 minutes. If you start with 64 grams of the substance, how much will be left after 20 minutes? MAFS.912.F-LE.1.3 **********************NO CALCULATORS********************Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. 16. Let f(x) = x3 and g(x) = 3x + 2. Find solutions of the equation f(x) = g(x) by creating a table of integer values of x for ?2 ≤ ? ≤ 3 and finding the corresponding values of f and g. Be sure to clearly indicate all values from the table that are solutions of f(x) = g(x).17. Two nature parks opened the same year in neighboring towns. Park A’s attendance can be represented by the equation y = 3x2 – 10x + 10, and Park B’s attendance can be represented by the equation y = 1.8x - 1, where x represents the number of years since opening, and y represents the attendance in hundreds. Tables and graphs for both parks are shown below.18B.18A.19a. In which years does Park A have the greater attendance?19b. In which years does Park B have the greater attendance?19c. Describe how the functions are different.19d. If the trends continue, will Park A’s attendance ever surpass Park B’s attendance again? Explain.MAFS.912.A-APR.1.1 ************************NO CALCULATOR****************Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 20. Polynomials are closed under all but which of the following operations?AdditionSubtractionMultiplicationDivision21. (Old Standard 4: MA.912.A.4.2)Which answer choice is equivalent to the sum of the polynomials shown below?(10x2 + 3x ? 6) + (2x2 ? 9x ? 12)A.3(4x2 ? 2x + 6)C.6(2x2 ? x ? 3)B.6(x ? 3)D.18(x3 ? 1) What is the simplified form of each expression?22A. (5m2 – 6m +12) – (5m – 12 – m2) 22B. (3m – 4)(m – 8 ) 22C 4xy2(5x5 – xy + 2y3) 22D. (m – 4)(5m2 + m – 1 ) 23.(Old Standard 4: MA.912.A.4.2)Which of the following expressions is equivalent to (5x ? 3)2?A. 25x2 – 30x + 9 C. 25x2 – 15x + 9B. 25x2 – 15x – 9 D. 25x2 – 9 24. A heart shaped chocolate box is composed of one square and two half circles. The total number of chocolates in the box is calculated by adding the area of a square given by 4?2 and the area of a circle approximated by 3?2. The company plans to add a small additional box for a promotional campaign containing one row (2?) of chocolates. If the total combined heart shape and small box contain 69 chocolates, which of these equations could be utilized to solve for the number of chocolates in the small box (2?)?A. 4?2 + 3?2 + 2? = 69B. 4?2 – 3?2 + 2? = 69C. 4?2 + 3?2 – 2? = 69D. 4?2 – 3?2– 2? = 6925. In the diagram at the right, the dimensions of the large rectangle are (3? ? 1) by (3? + 7) units. Thedimensions of the cut-out rectangle are ? by 2? + 5 units. Which choice expresses the area of the shaded region, in square units? A. ?2 + 23? – 7B. ?2 + 13? – 7C. 7?2 + 23? – 7D. 7?2 + 13? – 7MAFS.912.N-RN.1.2**********************NO CALCULATORS******************** Rewrite expressions involving radicals and rational exponents using the properties of exponents. Also assesses MAFS.912.N-RN.1.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define to be the cube root of 5 because we want ( ) ( ) to hold, so ( ) must equal 5. Also assesses MAFS.912.N-RN.2.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. 26. Which statement is NOT always true?A. The product of two irrational numbers is irrational.B. The product of two rational numbers is rational.C. The sum of two rational numbers is rational.D. The sum of a rational number and an irrational number is irrational.27. Consider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, which statement is true about the other zero?A. The other zero must be rational.B. The other zero must be irrational.C. The other zero can be either rational or irrational.D. The other zero must be non-real.28. What value of x would make the expression below equal to 8? 583x29. (Old Standard 4: MA.912.A.4.1)What is the value of the following expression when x = 3?4x2x?1 30. Simplify for x≠0: x-2x-4x5A. 1x2B. 1x3C. D. 31. 7x2yz6 2xy3z 32. 3xy2z532xyz 33A. (Old Standard 4: MA.912.A.4.1)Simplify the expression below4a2b322a33B. Simplify 12xy3z9x2yz2 34A. (Old Standard 6: MA.912.A.6.2)Which answer choice is equivalent to the expression below?3x-1213x2C. 3x213xD. 3xSimplify:34B. 2yz-1234C. (-3m)-1235. (Old Standard 6: MA.912.A.6.2)What is the value of x in the equation shown below?(8x)[(2x)]?2 = 8A. 18C. 14B. 1D. 436A. (Old Standard 6: MA.912.A.6.2)Simplify the expression below.4 ×255Perform the following operations and simplify, or... just simplify!36B. 54836C. 36D. 8n ?18n 36E. 36F. 36G. 36H. for 36I. 36J. 354MAFS.912.F-IF.1.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Also assesses MAFS.912.F-IF.1.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Also assesses MAFS.912.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. Write a function for the situations in 37A and 37B. Is the graph continuous or discrete?37A.A movie store sells DVDs for $11 each. What is the cost, C, of n DVDs?a.C = 11n; continuousc.C = 11 + n; continuousb.C = 11 + n; discreted.C = 11n; discrete 37B.A produce stand sells roasted peanuts for $1.90 per pound. What is the cost, C, of p pounds of peanuts?a.C = 1.90p; continuousc.C = 1.90 + p; continuousb.C = 1.90p; discreted.C = 1.90 + p; discrete 38. Neil plans to paint sweatshirts. The paint costs $14.75. The sweatshirts cost $7.50 each.Write a function C( x) , for cost of x sweatshirts. Determine the cost of four sweatshirts.39. Elizabeth plans to decorate T-shirts to sell at a fair. The decorations cost a total of $52.50 and the T-shirts cost $6.50 each. Which function expresses the cost, C( x) , of the project in terms of the number of T-shirts decorated, x?A. Cx= 6.50xB. Cx= 6.50x + 52.50C. Cx= 52.50x + 6.50D. Cx= 6.50 + 52.5040. (Old Standard 2: MA.912.A.2.3)Given the function f(x) = 2x + 2, what is the value of x if f(x) = 6?41. Find the range of fx=-2x+6 for the domain {–1, 3, 7, 9}.42. Let fx=23x+9. Find f(-3)andf(6).43. (Old Standard 2: MA.912.A.2.4)What is the range of the following relation? {(5, 0), (6, ?1), (1, 4), (0, 5), (2, 3)} 44. Does the input-output table represent a function? If it does represent a function, list the domain and range. If it does not represent a function, explain why. For items 45A and 45B, state the domain and range. Determine whether the relation is a function.45A 45B MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational, absolute, and exponential functions. Also assesses MAFS.912.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Also assesses MAFS.912.A-CED.1.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law, V = IR, to highlight resistance, R.46. Julie is required to pay a 2% state income tax on all income over $3,000. In addition to the 2% tax, she must pay an extra 2.5% state income tax on all income over $20,000. Julie earned more than $20,000 last year and paid $992.50 in state income taxes. What was her total income for the year?A. $22,056B. $25,056 C. $34,500D. $39,70047 A New York City taxi charges $3 per ride plus as additional $0.50 per mile. Which function below shows how to calculate the total cost of a taxi ride that is x miles long?A. fx=$3x +$0.50B. fx=$3x – $0.50C. fx= $0.50x + $3D. fx= $0.50x – $348A. The ages of three friends are consecutively one year apart. Together, their ages total 48 years. Which equation can be used to find the age of each friend (where ? represents the age of the youngest friend)?A. 3a = 48B. a(a + 1)(a + 2) = 48C. a + (a ? 1) + (a ? 2) = 48D. a + (a + 1) + (a + 2) = 4848B. What are the ages of the friends?A. 16, 17, 18B. 15, 16, 17C. 14, 15, 16D. 17, 18, 1949. (Old Standard 3: MA.912.A.3.1)What is the value of x in the equation below?4(x + 3) = 9x + 16 + 3x50. Solve. Do not use decimals!! NOT MULTIPLE CHOICEA. 10x + (2 + 8x) = 4 -5 (3-9x)B 4x -6x = 9(x+4) – 2C. x+13=xD. 4-x2=851. A ball is kicked from ground level into the air. Its height y, in feet, after x seconds can be represented by the equation y=40x-16x2. What is the total elapsed time, in seconds, from the time the ball is kicked until it reaches ground level again?52.(Old Standard 3: MA.912.A.3.3)What is the equation below correctly solved for b?4ab = 6bc ? 5b + a53.1. Solve the following equation for v. Show all of your work.The next two problems are multiple choice. 545556. (Old Standard 3: MA.912.A.3.4)Which graph represents the solution set for the compound inequality shown below?6x + 4 ≥ 34????or??-35x?? ?1 > 5A.B.C.D.57. (Old Standard 3: MA.912.A.3.4)What is the solution for the inequality shown below??3 < 2x + 11 < 7Solve:58A. 3(5x – 10) < 30x58B. 12x – 10 > 10x – 20 58C. x – 4x < 5x + 16 59. (Old Standard 3: MA.912.A.3.4)Which graph represents the solution set for the inequality shown below?5x + 7 ≤ 23x ? 2A.B.C.D.60. (Old Standard 3: MA.912.A.3.5)The math club needs to raise at least $563 for the national competition this summer. They decide to sell slices of pie on March 14, Pi Day, to earn the amount needed. If they sell each slice of pie for $3 and make 75% profit on each slice, what is the minimum number of slices they need to sell to earn enough money for the national competition? 61. The width of a rectangle is 33 centimeters. The perimeter is at least 776 centimeters. Write and solve an inequality to find the possible lengths of the rectangle.a. 33+l≥776;l≥74b. 233+ 2l≥776;l≥355c. 233+ 2l≤776;l≤355d. 33+l ≤776;l≤743MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Also assesses MAFS.912.A-REI.3.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Also assesses MAFS.912.A-REI.3. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Also assesses MAFS.912.A-REI.4.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.62. Monique owns a catering business. Last weekend, she catered two events in which all attendees were served either a chicken or a steak dinner. The table below shows some pricing information about these two events Before-Tax Prices for Monique’s Catered EventsDay of eventNumber of chickenDinners servedNumber of steakDinners servedTotal before-tax Price of dinnersSaturday2717$809.50Sunday4634$1,495,00 The following system of equations can be used to determine the before-tax prices of c dollars for each chicken dinner and s dollars of each steak dinner Monique served. 27c + 17s = 809.50 46c + 34s = 1,495.00 What is the before-tax price of a chicken dinner?63. (Old Standard 3: MA.912.A.3.14 )In the 1600s, a blacksmith could make a living by hand-forging horseshoes and nails. A diligent blacksmith could make one horseshoe in 12 minutes and a nail in 1 minute. In the 1600s, it would take the blacksmith 210 minutes to complete a particular job. With advances in technology, the blacksmith was able to make a horseshoe in 9 minutes and a nail in 40 seconds, and could complete the same job in 155 minutes. In the equations below, h represents the number of horseshoes in the job, and n represents the number of nails in the job.12h + n = 2109h + 2n3= 155How many nails were in the job the blacksmith completed?64. The solution to the system x+2y=4y= -12x+2 A. all real numbers B. x,y:x+2y=4 C. D. (2, 2)65A. Graph y < 4? – 165B. Graph y≥x+1y<-12xMAFS.912.A-CED.1.3 Represent constraints by equations or inequalities and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. 66. Standard 3: MA.912.A.3.11The table below shows how old Marsha and Tony were in several different years. If T represents Tony's age and M represents Marsha's age, what equation could be used to correctly predict Tony's age when Marsha is M years old?YearMarshaTony20006102002812200410142006121667. The table below shows how many cars were washed and how much money was collected for a fundraiser over a certain amount of time one afternoon. C represents cars washed and m represents the money collected, what equation could be used to correctly predict the amount of money collected (m) after c amount of cars are washed?TimeCars washedMoney collected12:00002:0016$104.004:3036$234.00Write a system of two linear equations. Then solve the system. What are the reasonable domain and range?68A. There are only 35 tickets to be sold for the dance. The number of tickets sold to seniors must be four times the number of tickets sold to juniors.Equations ____________________Solution _________ Domain_______________ Range____________ ____________________68B. A diamond today costs ten dollars more than twice what it cost last year. The sum of the costs (last year and this year) is $2500. What is the cost of last year's diamond? What are the reasonable domain and range?Equations ____________________Solution _________ Domain_______________ Range____________ ____________________69A. Is it possible to prepare a lunch that contains four servings of Food A and three servings of Food B and still satisfy the constraints on cost, amount of sugar, and amount of protein? Explain.69B. Let a represent the number of servings of food A and let b represent the number of servings of food B. Write a set of inequalities that model the constraints on cost, amount of sugar, and amount of protein.MAFS.912.A-REI.4.11 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Also assesses MAFS.912.A-REI.4.10 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately (e.g., using technology to graph the functions, make tables of values, or find successive approximations). Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. 70. Which system has the graph shown?A. B. C. D. The functions (?) = ?2? ? 1 and (?) = ?3 ? 4 are graphed below.71. Identify the x-coordinate of the point where the graphs intersect.72. Show that the x-coordinate of the point of intersection is a solution of the equation ?2? ? 1 = ?3 ? 4.73. Explain, in general, why the x-coordinate of the point of intersection is a solution of the equation f (?) = (?).MAFS.912.A-REI.2.4 Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)? = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x? = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. 74. Jeannie solved the quadratic equation shown below by factoring.x2+2x-8=0 Which of the following shows a step in solving the equation shown?(x + 2)(x + 4) = 0(x + 2)(x – 4) = 0(x – 2)(x + 4) = 0(x – 2)(x – 4) = 075. (Old Standard 7: MA.912.A.7.2)Julianne used a quadratic function to solve a problem. The factored form of the function is shown below.(x ? 3)(x ? 4) = 0What is the sum of the solutions to the problem? 76. Solve by completing the square:x2-8x-6=077. Solve using the Quadratic Formula A. B. C. D. no real solutionSolve using most convenient method78A. 78B. 78C. 79. (Old Standard 7: MA.912.A.7.2: )Marly needs to solve the problem shown below by using the quadratic formula.f(x) = x2 + 7x + 1 = 31Which of the following shows the quadratic formula being used correctly to determine the solutions for this problem? A.C.B.D.MAFS.912.F-IF.2.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Also assesses MAFS.912.S-ID.3.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 80. Standard 3: MA.912.A.3.11The total cost of a taxi for certain distances is shown in the table below. Distance Traveled(in miles)Total Cost(in dollars)041628310The relationship between the values in the table can be expressed as a linear function. What is the slope of this function?81. (Old Standard 3: MA.912.A.3.10)Robert sharpened pencils for the school math contest. He sharpened 8 pencils in 2 minutes and 32 pencils in 8 minutes. If he continues at the same rate, what equation can be used to predict the number of pencils he can sharpen in 30 minutes? Let p represent the number of pencils and t represent the number of minutes. What is the slope of the line this line?82. What is the rate of change for the graph? State the slope of each line83A. x = -283B y = 383C. y = 3x - 183D. 3x – 2y = -683E. Find the slope of the line passing through the points A(5, –1) and B(–8, 3).Find the slope, x-intercept and y-intercept of each line below.84A 84B. MAFS.912.F-IF.3.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as , , , and and classify them as representing exponential growth or decay. y =(1.02)t y =(0.97)t y =(1.01)12t y =(1.2)t 10 Also assesses MAFS.912.A-APR.2.3 Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial. Also assesses MAFS.912.F-IF.3.7a, b, c, and e. Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. c. Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior. d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available and showing end behavior. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude and using phase shift. 85. Which factorization can be used to reveal the zeros of the function fn=-12n2-11n+15?A. fn=-n12n+11+15B. fn=(-4n+3)(3n+5)C. fn=-(4n+3)(3n+5)D. fn=(4n+3)(-3n+5)86. Combined estimates for Etosha National Park and the Northwestern PopulationThe elephant population in northwestern Namibia and Etosha National Park can be predicted by the expression 2,649(1.045)b, where b is the number of years since 1995. What does the value 2,649 represent?A. the predicted increase in the number of elephants in the region each yearB. the predicted number of elephants in the region in 1995C. the year when the elephant population is predicted to stop increasingD. the percentage the elephant population is predicted to increase each year The population of Littleburg has been declining since the year 2000. The function, P = 10000(0.9)t, models the population t years after 2000.87A. Show that the function P = 10000(1 – 0.1)t is equivalent to P = 10000(0.9)t and compare the two functions in terms of what aspect of the population decline each function reveals.87B. Show that the function ? = 10000(.9913)12? is equivalent (within rounding) toP = 10000(0.9)t and compare the two functions in terms of what aspect of the population decline each function reveals.89. For the graph . Give the vertex (minimum point) and the equation of the axis of symmetry .90. The engineers at Rocket Town have designed a toy rocket with an all-new wing design. The cost in dollars, C, for manufacturing x number of parts can be modeled by the following function.? = ?2 – 400? + 4010090A. Rewrite the expression ?2 – 400? + 40100 in vertex form. Show your work below.90B. Is the vertex of the graph of this function a maximum or minimum value? Justify your answer.90C. What is the maximum or minimum value written as an ordered pair?90D. What do the x- and y-coordinates of the vertex represent in the context of this problem? Explain your answer.88. Identify the constant factor for the exponential function y=13x. How can you use the constant factor to tell whether the function represents exponential growth or exponential decay?91. If (?) = 2?2 ? 8? + 9, which statement regarding the vertex form of (?) is true?A. In vertex form, (?) = 2(? ? 2)2 + 1 and therefore has a minimum value of 1.B. In vertex form, (?) = 2(? ? 2)2 + 1 and therefore has a minimum value of -2.C. In vertex form, (?) = 2(? ? 2)2 + 4.5 and therefore has a minimum value of 4.5.D. In vertex form, (?) = 2(? ? 2)2 + 4.5 and therefore has a minimum value of -2.92.MAFS.912.F-BF.2.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. 93.95.94.MAFS.912.F-LE.1.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table). Also assesses MAFS.912.F-BF.1.1 Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. c. Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. Also assesses MAFS.912.F-IF.1.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. 96. Which sequence is represented by ? = 10? ? 29 where x represents the term number and y represents the term? a. 1, -28, -57, -86, … b. -29, -19, -9, 1, … c. -19, -9, -1, 11, … d. 10, -19, -48, -77, … 97. Given the recursive formula find the first 4 terms for each. A. ?? = ???1 ? 3 when ?1 = 5 B. ?? = ???1 + 23 when ?1 = 1 C. ?? = ???1 + 12 when ?1 = ?30 98. Antonio is arranging tiles according to the pattern below. Which represents the explicit formula for the arithmetic sequence that models Antonio’s pattern?a. ?? = 2? + 1 b. ?? = 2? ? 1 c. ?? = 2? + 2 d. ?? = 2? ? 2 99. Sophia started baking cakes at 1:30 PM. By 3:00 Sophia baked 4 cakes and used 12 eggs. By 6:15, Sophia had baked 13 cakes and used a total of 39 eggs. Let e = number of eggs that are used and let c = the number of cakes that are baked. Write an equation to model the number of eggs used (e) after baking c amount of cakes.100. (Old Standard 3: MA.912.A.3.10)Line s passes through the points (2, 7) and (6, 1). Line t passes through the point (5, 2) and is perpendicular to line s. What is the equation for line t?101. What is the equation of the line graphed below?A. y=4x+1B. y=-4x+1C. y=4x- 1D. y=-4x- 1102. Which is an equation of the line through the point (-1, 3) and with slope 12?A y=12x – 3 B. y=12x+72C. y=3x – 1.5 D. y=12x-92103. Which is an equation of the line through the point (4, 5) and which has slope 43?A. 4x+3y=29B. 4x-3y=5 C. 3x+4y=32D. 4x- 3y=1104. Which equation is of a line parallel to the graph of ?A. y=34x -9 B. y=9- 34x C. y=-43x -8D. y=43x -8 Write the standard form of an equation of the line:105A. m=52, through (1, 4)105B m=0, through (1, 3)105C. slope undefined, through (1, 3)Graph each line.106A. x = -2106B. y = 3106C. y = 3x - 1106D. 3x – 2y = -6106E. y + 5 = (x – 4)106F. Graph the equation with x intercept 4 and y intercept -2MAFS.912.A-SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15t can be rewritten as (1.151/12)12 ≈ (1.012)12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. Also assesses MAFS.912.A-SSE.1.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. Also assesses MAFS.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x?)? – (y?)?, thus recognizing it as a difference of squares that can be factored as (x? – y?)(x? + y?). 107. (Old Standard 4: MA.912.A.4.3)Rewrite the expression below factored completely.18x2y2 + 36x3y3 ? 27x3y108. Factor out the greatest common monomial factor. 18u4v5+ 30u5v4 Rewrite each expression below factored completely.109A.x2 ? 2x – 120109B. a2 – 7a + 12 109C. 5x2 – 31x + 6 109D. 2x2 + 7x + 6 109F. 16x2 – 16x + 3110A. (Old Standard 4: MA.912.A.4.3)Rewrite the expression below factored completely.36x ? 100y2x110B. 2x2 – 18 110C. Which is NOT a factor of x4 – 81?A. x + 3 B. x – 3 C. x2 – 3 D. x2 + 9 E. All are factors111. (Old Standard 7: MA.912.A.7.2)Marna wants to find the values of x for which the function below will have a value of 10.f(x) = x2 + x ? 20Which of the following shows the correct factorization of this function for f(x) = 10? A.(x + 5)(x + 4) = 10C.(x ? 5)(x ? 4) = 10B.(x + 6)(x ? 5) = 0D.(x + 5)(x ? 6) = 0112. Last weekend, Cindy purchased two tops, a pair of pants, and a skirt at her favorite store. The equation T = 1.075x can be used to calculate her total cost where x represents the pretax subtotal cost of her purchase.112A. In the equation T = 1.075x, what does the number “1” represent? Explain using the context of Cindy’s situation.112B. In the equation T = 1.075x, what does the number “0.075” represent? Explain using the context of Cindy’s situation.MAFS.912.S-ID.1.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). 113. Construct a box-and-whisker for the data, and use it to determine the shape of the distribution.{98, 97, 101, 100, 88, 76, 51, 39, 93, 91, 92, 85, 72}114. Construct a histogram to determine which best describes the distribution of the following data set.82, 94, 90, 97, 96, 75, 91, 88, 84, 96, 82, 86, 98A symmetric distributionC negatively skewed distributionB positively skewed distribution D simple distribution115. The number of miles that Jonathan drove each week during a 15-week period is shown. Construct a box-and-whisker plot. Describe the center and spread of the data. MAFS.912.S-ID.1.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Also assesses MAFS.912.S-ID.1.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).116. Describe each distribution as negatively skewed, positively skewed or symmetric. NOT MULTIPLE CHOICEA. B. C. 117. Mr. Variability is using a normal curve to assign exam grades for his class. This means students more than 2 standard deviations from the class mean will receive an F. If the class mean is 82% and the standard deviation is 4.5%, what would be the highest F on the exam? 118. For which of the following distributions would you use the mean and standard deviation to describe the data? Justify your answer. NOT MULTIPLE CHOICEB. C. MAFS.912.S-ID.2.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association. Also assesses MAFS.912.S-ID.3.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. Also assesses MAFS.912.S-ID.3.9 Distinguish between correlation and causation. 119. Which equation matches the scatter plot?[A] y=1-4x [B] y=4-4x [C] y=4x+1 [D] y=4x-1120. Determine a possible line of best fit for the scatterplot. a. ? = 8? b. ? = 8? + 100 c. ? = 100? d. ? = 100? + 8 121. Early in the 1900s, an airplane manufacturer was able to increase the time its planes could stay aloft by constantly refining its technologies. They recorded their data in the table below.If x is the number of years after 1910 and y is the time in hours that an airplane stayed aloft, which equation best matches the data points in the table?[A] y=1.07x+0.05 [B] y=0.95x-0.1 [C] ] y=0.87+0.05 [D] ] y=1.06x-0.1 122. List the following correlation coefficients in order from strongest to weakest correlation: 0.58 - 0.991 -0.632 0.122 -0.711 -0.206 0.945123. In which of the following scenarios should a best-fit line be the most appropriate model for the data?A. The scatter plot of the data is fairly disorganized but the sum of the residuals is zero.B. The scatter plot of the data looks linear but the plot of the residuals shows no pattern.C. The scatter plot follows a curved pattern.D. The scatter plot of the data looks linear but the plot of the residuals is curved.124. Which of the following residual plots indicates that a best-fit line was the most appropriate model for the data? 17. Suppose a linear function is fit to a set of data. Which of the following residual plots indicates that this function was an appropriate fit for the data? MAFS.912.A-APR.1.1 *************NO CALCULATOR*********************Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. 125. Determine whether the correlation in each situation below implies causation. Select all that apply.There is a positive correlation between smoking cigarettes and lung cancer.Daily ice cream sales in Florida is positively correlated to the number of shark attacks.The number of miles driven is negatively correlated to the amount of gas left in the gas tank. The number of hours a person spent practicing piano is negatively correlated with the number of mistakes he/she makes during the recital.There is a positive correlation between the number of violent crimes committed in a city and the number of churches in that city.MAFS.912.S-ID.2.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 126.66% of the participants were boys.35% of the participants do not like to surf.80105 of the boys like to surf.1035 of the participants who do not like to surf were girls.The proportion of boys who like to surf is greater than the proportion of girls who like to surf.35127.127A. What numbers represent marginal frequencies?127B. What numbers represent joint frequencies?127C. What is the joint relative frequency of females who did not get promoted? ................
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