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Algebra 1 Math TAKS-STAAR-STAAR-M Comparison Spacing has been deleted and graphics minimized to fit table. (1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to: (A) describe independent and dependent quantities in functional relationships; (Supporting Standard) TAKS 2009 STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM 11 During a sale at a shoe store, all shoes 1 The sales tax rate at a clothing store is 1 The sales tax rate at a clothing were 25% off the original price. Which 8.75%. Sales tax on an item is a function of store is 8.75%. Sales tax on an item statement best describes the functional its price. Which of the following is the is a function of its price. What is the relationship between the sale price of a pair dependent quantity in this function? dependent quantity in this function? of shoes and the original price? A The sales tax rate on the item A The sales tax rate on the item A The sale price is dependent on the original B The item’s price price. C The amount of sales tax on the item B The item’s price B The original price is dependent on the sale D The item’s size C The amount of sales tax on the item price. C The sale price and the original price are independent of each other. D The sale price is dependent on the number of pairs of shoes purchased. (1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to: (B) gather and record data and use data sets to determine functional relationships between quantities; (Supporting Standard) TAKS 2009 STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM 44 The function table shows the values of 2 Which of the following relations is a 2 Which relation is a function? f(n) for function? A {(0, 0), (0, 1), (0, 2)} given values of n. B {(0, 0), (1, 1), (1, 4)} C {(0, 0), (1, 2), (2, 2)} Which function best represents the relationship between the quantities in the table? J F I, II, and III only G I and II only H II and III only J III and IV only (1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to: (E) interpret and make decisions, predictions, and critical judgments from functional relationships. (READINESS STANDARD) TAKS 2009 31 The function below shows a relationship between x and y. y = 7x + 3 If the value of x increases by 1, what happens to the value of y? A The value of y increases by 3. B The value of y increases by 7. C The value of y increases by 10. D The value of y increases by 21. STAAR RELEASED ITEM 3 Southern Phone Company is promoting a new cell phone service plan: a customer can make up to 500 minutes of calls each month for $39.99. If the number of minutes used in a month exceeds 500, then the function c = 0.40(m – 500) + 39.99 describes the monthly charge, c, in dollars in terms of m, the total number of minutes used. Which of the following statements best describes this function? A If the total number of minutes used is more than 500, then every minute beyond 500 costs 40 cents. B Every minute used costs 40 cents, regardless of the total number of minutes used. C The first 500 minutes used costs 40 cents each, after which there is an additional charge of$39.99. D If the total number of minutes used is more than 500, then every minute used costs 40 cents STAAR MODIFIED RELEASED ITEM 3 Southern Phone Company has a new cell phone service plan. A customer can use up to 500 minutes of service each month for $39.99. If the number of minutes used in a month is more than 500, then the c = 0.40(m – 500) + 39.99 describes the monthly charge, c, in dollars in terms of m, the number of minutes used. Which statement best describes this function? A If more than 500 minutes are used, then every minute over 500 costs 40 cents. B Regardless of the number of minutes used, every minute costs 40 cents. C If more than 500 minutes are used, then every minute costs 40 cents. (2) Foundations for functions. The student uses the properties and attributes of functions. The student is expected to: (B) identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete (READINESS STANDARD) TAKS 2008 STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM 27 The perimeter of an equilateral triangle is 4 What is the domain of the function graphed 4 What is the domain of the function 36 meters or less. below? graphed below? Which set describes the domain for l, the length of one side of the triangle? A {0 < l < 3} B {0 < l < 6} C {0 < l < 12} D {0 < l < 36} F0<x≤5 G2<x≤5 H0<x≤4 J0<x<2 A0<x≤5 B2<x≤5 C0<x≤4 (4) Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to: (A) find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations (READINESS STANDARD) TAKS 2010 STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM 2 18 Look at the polynomial expression 5 In the quadratic equation x – x + c = 0, c 5 In the quadratic equation x2 – 3x + modeled below with algebra tiles. represents an unknown constant. If x = −3 is c = 0, c represents an unknown one of the solutions to this equation, what is constant. If x = 1, what is the value the value of c? -12 of c? 2 Record “A” on the front of your answer Record “A” on the front of your document. Then, fill in the bubbles for your numeric answer on the BACK of the answer document. Then, fill in scantron in section Griddable D on Which of the following expressions is the bubbles for your numeric problem number 1. equivalent to the polynomial expression answer on the BACK of the modeled above? scantron in section Griddable D on 2 F 2x + 7x + 9 G 2x4 + 11x2 + 9 H 2x4 + 30x2 + 20 J 2x2 + 11x + 9 problem number 1. (5) Linear functions. The student understands representations. The student is expected to: (C) use, translate, and make connections (READINESS STANDARD) TAKS 28 Which equation best represents the line graphed below? that linear functions can be represented in different ways and translates among their various among algebraic, tabular, graphical, or verbal descriptions of linear functions. STAAR RELEASED ITEM 6 Which of the following is not a correct description of the graph of the function y = -2x - 7? F The graph of the function contains the point (−2, −3), and when the value of x increases by 1 unit, the value of y decreases by 2 units. G The graph of the function contains the points (−1, −5), (2, −11), and (4, −15). H The graph of the function is a line that passes through the point (0, −7) with a slope of −2. J The graph of the function contains the points (0, −7), (1, −9), and (3, −1). STAAR MODIFIED RELEASED ITEM No STAAR-M Item released for this TEKS. F 7x + 4y = 35 G 4x − 7y = 35 H 4x + 7y = − 35 J 7x − 4y = − 35 (6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to: (A) develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations; (Supporting Standard) TAKS STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM 52 What is the slope of the linear equation 7 If (2k, k) and (3k, 4k) are two points on 6 If (2, 1) and (3, 4) are two points 101x + 53y = 12? H the graph of a line and k is not equal to 0, on the graph of a line, what is the what is the slope of the line? slope of the line? A3 B 3k C D Not here A3 B 11 C (6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to: (F) interpret and predict the effects of changing slope and y-intercept in applied situations (READINESS TEKS) TAKS 2009 STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM 43 Tyler wants to buy a video-game system 8 The amount an appliance repairman 7 A repairman charges a total amount for $375. He can pay for the system in 12 charges for each job is represented by the for each job he completes. months if he pays $75 now and $25 each function • This total amount, t, can be found month. How will the number of monthly t = 50h + 35, where h represents the using the function t = 50h + 35, payments be affected if Tyler pays $75 now number of hours he spent on the job and t where h represents the number of and $30 each month? represents the total amount he charges in A He will make 10 fewer monthly payments. dollars for the job. The repairman plans to hours he spent on the job. change the amount he charges for each job. • The repairman plans to change the B He will make 2 fewer monthly payments. The amount he plans to charge is represented amount he charges for each job. C He will make 3 fewer monthly payments. by the function t = 50h + 45. What will be • The function t = 50h + 45 can be the effect of this change on the amount he D He will make 5 fewer monthly payments. used to find the total amount charged charges for each job? F The total amount he charges for each job for each job after this change. will increase by $10. What will be the effect of this change G The total amount he charges for each job on the amount he charges for each will decrease by $10. job? H The amount he charges per hour will A The total amount he charges for increase by $10. J The amount he charges per hour will each job will increase by $10. decrease by $10. B The total amount he charges for each job will decrease by $10. C The amount he charges per hour will increase by $10. (8) Linear functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: (A) analyze situations and formulate systems of linear equations in two unknowns to solve problems; (Supporting Standard) TAKS STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM 5 A restaurant sold a total of 418 large and 9 The sum of the perimeters of two different 8 Read the information below about small hamburgers during one day. Total squares is 32 centimeters, and the difference two squares. hamburger sales were $1077. Large between their perimeters is 8 centimeters. If • The side length of the larger hamburgers sold for $3, and small x represents the side length of the larger square can be represented by x. hamburgers sold for $1.50. Which system of square and y represents the side length of • The side length of the smaller linear equations can be used to find l, the the smaller square, which of the following number of large hamburgers sold, and s, the systems of equations could be used to find square can be represented by y. number of small hamburgers sold? the dimensions of the squares? • The sum of the perimeters of the A l + s = 1077 A x + y = 32 two squares is 32 centimeters. x−y=8 3l + 1.50s = 418 • The difference between their B l + s = 418 B 4x + 4y = 32 perimeters is 8 centimeters. 3l + 1.50s = 1077 4x − 4y = 8 C 1.50l + 3s = 418 Which system of equations could be l + s = 1077 C 2x + 2y = 32 used to find the side length of each 2y − 2x = 8 D l + s = 418 square? 1.50l + 3s = 1077 D 4x + 2y = 32 A 4x + 4y = 32 4x − 2y = 8 4x − 4y = 8 B 2x + 2y = 32 2y − 2x = 8 C 4x + 2y = 32 4x − 2y = 8 (8) Linear functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: (B) solve systems of linear equations using concrete models, graphs, tables, and algebraic methods (READINESS STANDARD) TAKS STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM 10 Some values for two linear equations are Some values for two linear equations shown in the tables below. are shown in the tables below. No Released Item for this TEKS on TAKS. What is the solution to the system of equations represented by these tables? F (2, 3) G (3, 5) H (−1, 1) J (5, 11) What is the solution to the system of equations represented by these tables? A (3, 5) B (−1, 1) C (5, 11) (9) Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions. The student is expected to: (D) analyze graphs of quadratic functions and draw conclusions. (READINESS STANDARD) TAKS STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM 58 The graph below represents the 11 The graph of a quadratic function is relationship between the density of water and shown below. the temperature of water. Which statement about this graph is not true? A The graph has a y-intercept at (0, 8). B The graph has a maximum point at (-1, 9). C The graph has an x-intercept at (2, 0). D The graph has the y-axis as a line of symmetry According to the graph, which of the following intervals best represents the temperature at which the density of water is greater than 999.9 kilograms per cubic meter? F Less than 1°C G Between 0°C and 4°C H Between 4°C and 8°C J Between 1°C and 7°C No STAAR-M Item released for this TEKS. (10) Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods. The student is expected to: (A) solve quadratic equations using concrete models, tables, graphs, and algebraic methods (READINESS STANDARD) TAKS STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM 43 What is the solution set for the equation 12 The graph of a quadratic function is 10 The graph of a quadratic function 2x 2 − 16x − 96 = 0? shown below. is shown below. A {4, 12} B {−4, 12} C {−4, −12} D {4, −12} What is the best estimate of the positive value of x for which this function equals 8? F2 G4 H 13 What is the best estimate of the positive value of x for which this function equals 8? A2 B4 C7 J7 (11) Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. The student is expected to: (C) analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods. (Supporting Standard) TAKS STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM 13 A population of 1500 deer decreases by 11 A population of 1500 deer 1.5% per year. At the end of 10 years, there decreases by 1.5% per year. At the will be approximately 1290 deer in the end of 10 years, there will be population. Which function can be used to approximately 1290 deer in the determine the number of deer, y, in this population. Which function can be population at the end of t years? A y = 1500(1 – 0.015)t used to determine the number of No Released Item for this TEKS on TAKS. t deer, y, in this population at the end B y = 1500(0.015) C y = 1500(1 + 0.015)t D y = 1500(1.5)t of t years? A y = 1500(1 – 0.015)t B y = 1500(1 + 0.015)t C y = 1500(1.5)t