Table of Contents. At a Glance. Power Standards. DA Blueprint. Assessed Curriculum. STAAR/EOC Blueprint. Release STAAR/EOC Questions

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2 Table of Contents At a Glance Pacing guide with start/ stop dates, Supporting STAAR Achievement lessons, and recommended power standards for data teams Power Standards List of Power Standards b reporting categor DA Blueprint Blueprint TEKS Assessed Curriculum Eligible TEKS for STAAR/EOC testing STAAR/EOC Blueprint Region XIII blueprint includes TEKS b categor Release STAAR/EOC Questions Sample questions Reference Materials Grade level formula charts Performance Level Descriptors Performance level descriptors identif student understandings b level(i,ii,iii)

3 Department of Curriculum and Instruction Algebra II at a Glance Nine Week Period st Nine Weeks nd Nine Weeks Unit Name Equations and Inequalities Relations and Functions Transformations of Functions Solving Sstems of Equations and Inequalities Solving Sstems of Equations and Inequalities Quadratic Functions, Equations and Inequalities Supporting STAAR Achievement Lessons Domain and Range of Functions Scatterplots Function Transformations Sstems of Equations: Three Unknowns Sstems of Linear Inequalities Determining Reasonableness Quadratic Representations Quadratic Situations Quadratic Formula Standard and Verte Forms Power Standards A.A, A.B A.A, A.B A.A, A.A, A.B, A.C A.B, A.B, A.6A, A.6B, A.7A, A.8A, A.8D Estimated Time Frame das 9 das 8 das das continued das START DATES August 7 September September 6 October 8 October 5 STOP DATES September September 5 October 5 October December rd Nine Weeks th Nine Weeks Quadratic Relations - Conics Radical Functions, Equations and Inequalities Rational Functions, Equations and Inequalities Eponential and Logarithmic Functions, Equations and Inequalities Polnomial Functions, Equations and Inequalities Sstems of Equations: Substitution Square Root Functions Rational Functions Inverse of an Eponential Function Eponential Functions A.B, A.7A A.B, A.9F A.0F A.B, A.A, A.F das 0 das das 9 das das Januar 8 Januar 8 Februar 6 March 5 Ma 0 Januar 5 Februar 5 March Ma 9 Ma 8

4 Department of Curriculum and Instruction Power Standards: Algebra II Categor A.A A.B A.B Categor A.A A.B A.C Categor A.6A A.6B A.8A A.8D Categor A.7A Categor 5 A.9F Categor 6 A.0F Content Standards Properties and Attributes of Functions identif the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations; collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments. etend parent functions with parameters such as a in f () = a/ and describe the effects of the parameter changes on the graph of parent functions; Representational Tools to Solve Problems analze situations and formulate sstems of equations in two or more unknowns or inequalities in two unknowns to solve problems; use algebraic methods, graphs, tables, or matrices, to solve sstems of equations or inequalities; interpret and determine the reasonableness of solutions to sstems of equations or inequalities for given contets. Properties of Quadratic Functions determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities; relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions; analze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems; solve quadratic equations and inequalities using graphs, tables, and algebraic methods. Multiple Representations of Quadratic Relations use characteristics of the quadratic parent function to sketch the related graphs and connect between the = a + b + c and the = a( h) + k smbolic representations of quadratic functions; Properties of Square Root Functions analze situations modeled b square root functions, formulate equations or inequalities, select a method, and solve problems; Properties of Rational Functions analze a situation modeled b a rational function, formulate an equation or inequalit composed of a linear or quadratic function, and solve the problem; Power Standards Algebra II Page of

5 Department of Curriculum and Instruction Categor 7 A.A A.F Properties of Eponential and Logarithmic Functions develop the definition of logarithms b eploring and describing the relationship between eponential functions and their inverses; analze a situation modeled b an eponential function, formulate an equation or inequalit, and solve the problem. Power Standards Algebra II Page of

6 Department of Curriculum and Instruction District Assessment Blueprint Algebra II 0-0 TEKS Grading Period Testing Date: November or November 5, 0 A.A st and determine reasonable domain and range values for identif the mathematical domains and ranges of functions continuous and discrete situations; A.B st, nd, use algebraic methods, graphs, tables, or matrices, to solve rd sstems of equations or inequalities; A.C st nd interpret and determine the reasonableness of solutions to, sstems of equations or inequalities for given contets. A.B st, nd etend parent functions with parameters such as a in f () =, rd a/ and describe the effects of the parameter changes on the graph of parent functions; Number of Items 5 TEKS Grading Period Testing Date: March 6 or March 7, 0 nd relate representations of quadratic functions, such as A.6B algebraic, tabular, graphical, and verbal descriptions use characteristics of the quadratic parent function to sketch A.7A nd, rd the related graphs and connect between the = a + b + c and the = a ( - h) + k smbolic representations of quadratic functions; nd analze situations involving quadratic functions and formulate A.8A quadratic equations or inequalities to solve problems nd solve quadratic equations and inequalities using graphs, A.8D tables, and algebraic methods Number of Items 5

7 Algebra II Assessment Eligible Teas Essential Knowledge and Skills Teas Education Agenc Student Assessment Division Fall 00

8 STAAR Algebra II Assessment Reporting Categor : Properties and Attributes of Functions The student will demonstrate an understanding of the foundational properties and attributes of functions. (A.) Foundations for functions. The student uses properties and attributes of functions and applies functions to problem situations. The student is epected to (A) (B) identif the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations; and Readiness Standard collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments. Readiness Standard (A.) Algebra and geometr. The student connects algebraic and geometric representations of functions. The student is epected to (A) (B) (C) identif and sketch graphs of parent functions, including linear (f () = ), quadratic (f () = ), eponential (f () = a ), and logarithmic (f () = log a ) functions, absolute value of (f () = ), square root of (f () = ), and reciprocal of (f () = /); Supporting Standard etend parent functions with parameters such as a in f () = a/ and describe the effects of the parameter changes on the graph of parent functions; and Readiness Standard describe and analze the relationship between a function and its inverse. Supporting Standard STAAR Algebra II Page of 8 Teas Education Agenc Student Assessment Division Fall 00

9 Reporting Categor : Representational Tools to Solve Problems The student will demonstrate an understanding of the use of representational tools to solve problems. (A.) Foundations for functions. The student understands the importance of the skills required to manipulate smbols in order to solve problems and uses the necessar algebraic skills required to simplif algebraic epressions and solve equations and inequalities in problem situations. The student is epected to (A) (B) use tools including factoring and properties of eponents to simplif epressions and to transform and solve equations; and Supporting Standard use comple numbers to describe the solutions of quadratic equations. Supporting Standard (A.) Foundations for functions. The student formulates sstems of equations and inequalities from problem situations, uses a variet of methods to solve them, and analzes the solutions in terms of the situations. The student is epected to (A) (B) (C) analze situations and formulate sstems of equations in two or more unknowns or inequalities in two unknowns to solve problems; Readiness Standard use algebraic methods, graphs, tables, or matrices, to solve sstems of equations or inequalities; and Readiness Standard interpret and determine the reasonableness of solutions to sstems of equations or inequalities for given contets. Readiness Standard STAAR Algebra II Page of 8 Teas Education Agenc Student Assessment Division Fall 00

10 Reporting Categor : Properties of Quadratic Functions The student will demonstrate an understanding of the properties of quadratic functions. (A.6) Quadratic and square root functions. The student understands that quadratic functions can be represented in different was and translates among their various representations. The student is epected to (A) (B) (C) determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities; Readiness Standard relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions; and Readiness Standard determine a quadratic function from its roots (real and comple) or a graph. Supporting Standard (A.8) Quadratic and square root functions. The student formulates equations and inequalities based on quadratic functions, uses a variet of methods to solve them, and analzes the solutions in terms of the situation. The student is epected to (A) (B) (C) (D) analze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems; Readiness Standard analze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula; Supporting Standard compare and translate between algebraic and graphical solutions of quadratic equations; and Supporting Standard solve quadratic equations and inequalities using graphs, tables, and algebraic methods. Readiness Standard STAAR Algebra II Page of 8 Teas Education Agenc Student Assessment Division Fall 00

11 Reporting Categor : Multiple Representations of Quadratic Relations The student will demonstrate an understanding of the connections between algebraic and geometric representations of quadratic functions and relations. (A.5) Algebra and geometr. The student knows the relationship between the geometric and algebraic descriptions of conic sections. The student is epected to (A) (B) (C) (D) (E) describe a conic section as the intersection of a plane and a cone; Supporting Standard sketch graphs of conic sections to relate simple parameter changes in the equation to corresponding changes in the graph; Supporting Standard identif smmetries from graphs of conic sections; Supporting Standard identif the conic section from a given equation; and Supporting Standard use the method of completing the square. Supporting Standard (A.7) Quadratic and square root functions. The student interprets and describes the effects of changes in the parameters of quadratic functions in applied and mathematical situations. The student is epected to (A) (B) use characteristics of the quadratic parent function to sketch the related graphs and connect between the = a + b + c and the = a( h) + k smbolic representations of quadratic functions; and Readiness Standard use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of = a( h) + k form of a function in applied and purel mathematical situations. Supporting Standard STAAR Algebra II Page 5 of 8 Teas Education Agenc Student Assessment Division Fall 00

12 Reporting Categor 5: Properties of Square Root Functions The student will demonstrate an understanding of the properties of square root functions. (A.9) Quadratic and square root functions. The student formulates equations and inequalities based on square root functions, uses a variet of methods to solve them, and analzes the solutions in terms of the situation. The student is epected to (A) (B) (C) (D) (E) (F) (G) use the parent function to investigate, describe, and predict the effects of parameter changes on the graphs of square root functions and describe limitations on the domains and ranges; Supporting Standard relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions; Supporting Standard determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness of solutions to square root equations and inequalities; Supporting Standard determine solutions of square root equations using graphs, tables, and algebraic methods; Supporting Standard determine solutions of square root inequalities using graphs and tables; Supporting Standard analze situations modeled b square root functions, formulate equations or inequalities, select a method, and solve problems; and Readiness Standard connect inverses of square root functions with quadratic functions. Supporting Standard STAAR Algebra II Page 6 of 8 Teas Education Agenc Student Assessment Division Fall 00

13 Reporting Categor 6: Properties of Rational Functions The student will demonstrate an understanding of the properties of rational functions. (A.0) Rational functions. The student formulates equations and inequalities based on rational functions, uses a variet of methods to solve them, and analzes the solutions in terms of the situation. The student is epected to (A) (B) (C) (D) (E) (F) (G) use quotients of polnomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, and eamine asmptotic behavior; Supporting Standard analze various representations of rational functions with respect to problem situations; Supporting Standard determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational equations and inequalities; Supporting Standard determine the solutions of rational equations using graphs, tables, and algebraic methods; Supporting Standard determine solutions of rational inequalities using graphs and tables; Supporting Standard analze a situation modeled b a rational function, formulate an equation or inequalit composed of a linear or quadratic function, and solve the problem; and Readiness Standard use functions to model and make predictions in problem situations involving direct and inverse variation. Supporting Standard STAAR Algebra II Page 7 of 8 Teas Education Agenc Student Assessment Division Fall 00

14 Reporting Categor 7: Properties of Eponential and Logarithmic Functions The student will demonstrate an understanding of the properties of eponential and logarithmic functions. (A.) Eponential and logarithmic functions. The student formulates equations and inequalities based on eponential and logarithmic functions, uses a variet of methods to solve them, and analzes the solutions in terms of the situation. The student is epected to (A) (B) (C) (D) (E) (F) develop the definition of logarithms b eploring and describing the relationship between eponential functions and their inverses; Readiness Standard use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of eponential and logarithmic functions, describe limitations on the domains and ranges, and eamine asmptotic behavior; Supporting Standard determine the reasonable domain and range values of eponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to eponential and logarithmic equations and inequalities; Supporting Standard determine solutions of eponential and logarithmic equations using graphs, tables, and algebraic methods; Supporting Standard determine solutions of eponential and logarithmic inequalities using graphs and tables; and Supporting Standard analze a situation modeled b an eponential function, formulate an equation or inequalit, and solve the problem. Readiness Standard STAAR Algebra II Page 8 of 8 Teas Education Agenc Student Assessment Division Fall 00

15 STAAR Algebra II Blueprint with TEKS Reporting Categories Number of Standards Number of Questions Readiness Standards A.A, B, B Supporting Standards A.A, C 8 Readiness Standards A.A, B, C Supporting Standards A.A, B 8 Readiness Standards A.6A, 6B, 8A, 8D Supporting Standards A.6C, 8B, 8C Readiness Standards A.7A Supporting Standards A.5A, 5B, 5C, 5D, 5E, 7B 6 6 Readiness Standards A.9F Supporting Standards A.9A, 9B, 9C, 9D, 9E, 9G 6 5 Readiness Standards A.0F Supporting Standards A.0A, 0B, 0C, 0D, 0E, 0G 6 5 Readiness Standards A.A, F Supporting Standards A.B, C, D, E 6 Readiness Standards Total Number of Standards 5 60% 65% 0 Supporting Standards Total Number of Standards 9 5% 0% Multiple Choice Total Number of Questions 5 Griddable on Test 50 Total Reporting Categor : Properties and Attributes of Functions Reporting Categor : Representational Tools Reporting Categor : Properties of Quadratic Functions Reporting Categor : Representations of Quadratic Relations Reporting Categor 5: Square Root Functions Reporting Categor 6: Rational Functions Reporting Categor 7: Eponential and Logarithmic Functions Italicized TEKS were not tested on TAKS. Adapted from TEA STAAR Blueprints and Assessed Curriculum /0/0

16 STAARTM State of Teas Assessments of Academic Readiness Algebra II 0 Released Test Questions These released questions represent selected TEKS student epectations for each reporting categor. These questions are samples onl and do not represent all the student epectations eligible for assessment. Copright 0, Teas Education Agenc. All rights reserved. Reproduction of all or portions of this work is prohibited without epress written permission from the Teas Education Agenc.

17 STAAR Algebra II Released Test Questions 0 Release f 5 g The graph of the function g was obtained from the graph of the function f using a transformation as shown above. Based on the graph, which equation can be used to describe g() in terms of f()? A g() І f() + 6 B g() І f( + 6) C g() І f() Ѝ 6 D g() І f( Ѝ 6) Page

18 STAAR Algebra II Released Test Questions 0 Release The graph of the function f is shown below Which grid shows the graph of f ˉẦ? A C B D Page

19 STAAR Algebra II Released Test Questions 0 Release Given the equation =, which of the following represents in terms of? A = B = C = 6 D = 6 What is the -value of the solution to the matri equation below? = A Ѝ6 B C Ѝ5 D Page

20 STAAR Algebra II Released Test Questions 0 Release 5 Which of the following quadratic functions does not have zeros of Ѝ5 and 6? A f( ) = + 0 B f( ) = C f( ) = D f( ) = The base of a triangle is inches less than twice its height. If the area of the triangle is 6 square inches, which of the following equations can be used to find h, the height of the triangle in inches? A hầ h + 6 І 0 B hầ h 6 І 0 C hầ h + 5 І 0 D hầ h 5 І 0 Page 5

21 STAAR Algebra II Released Test Questions 0 Release 7 The table below shows ordered pairs that satisf the quadratic function f. 0 5 f() 0 5 Based on the table, a solution to the equation f() І 0 is found in which interval? A Ѝ < < Ѝ B Ѝ < < C < < D < < 5 8 Which figure best describes the graph of ầ + 5ầ 0 5 І 0? A Circle B Ellipse C Parabola D Hperbola Page 6

22 STAAR Algebra II Released Test Questions 0 Release 9 The graph of the quadratic function f is shown on the grid below f If the graph of f is translated 5 units to the right and units down to create a new graph, which function best represents this new graph? A g() І Ѝ( + )ầ B g() І Ѝ( )ầ C g() І ( )ầ + D g() І ( )ầ 0 What value of p is a solution to the equation below? 8 p = Record our answer and fill in the bubbles on our answer document. Page 7

23 STAAR Algebra II Released Test Questions 0 Release L The formula P = can be used to approimate the period of a pendulum, where L is the pendulum s length in feet and P is the pendulum s period in seconds. If a pendulum s period is.6 seconds, which of the following is closest to the length of the pendulum? A. ft B. ft C. ft D. ft A chemical compound s concentration in milligrams per liter during a reaction can be modeled b the function below, where t represents the number of seconds that have elapsed during the reaction. f( t) = t 00 + In this situation, what are the domain and range for this function? A Domain: t 0; range: 0 < f(t) 00 B Domain: t 0; range: f(t) 00 C Domain: t 0; range: 0 < f(t) 00 D Domain: t 0; range: f(t) 00 Page 8

24 STAAR Algebra II Released Test Questions 0 Release A monthl cell phone plan charges $5.00 for the first 00 tet messages used and $0.5 for each additional message. On this plan, what is the number of tet messages that must be used in a month in order to make the average cost per message $0.05? A 00 B 50 C 900 D 500 Which function is the inverse of f() = +? A g() І logẃ( ) B g() І logẃ() C g() І logẃ( + ) D g() І logẃ() + 5 A famil spent a total of $96 on fast food this ear. If this famil decreases the amount it spends on fast food b % ever ear, which of the following is closest to the annual amount the famil will spend on fast food after 5 ears? A $888 B $67 C $9 D $65 Page 9

25 STAAR Algebra II Answer Ke 0 Release Item Number Reporting Categor Readiness or Supporting Content Student Epectation Correct Answer Readiness A.(B) D Supporting A.(C) A Supporting A.(A) C Readiness A.(B) A 5 Supporting A.6(C) D 6 Readiness A.8(A) D 7 Readiness A.8(D) C 8 Supporting A.5(D) B 9 Supporting A.7(B) B 0 5 Supporting A.9(D) Readiness A.9(F) C 6 Supporting A.0(C) A 6 Readiness A.0(F) A 7 Readiness A.(A) A 5 7 Readiness A.(F) B For more information about the new STAAR assessments, go to Page 0

26 STAAR ALGEBRA II REFERENCE MATERIALS STAARTM State of Teas Assessments of Academic Readiness GENERAL FORMULAS Slope of a line m = Quadratic formula FACTORING b = b ac a Difference of squares a b = ( a b)( a + b) Difference of cubes a b = ( a b)( a + ab + b ) Sum of cubes a + b = ( a + b)( a ab + b LOGARITHMS ) Product log ( ) = log + log b b b Quotient log b = log log b Power log ( ) = r log CONIC SECTIONS b ( ) r b b General form A + B + C + D + E + F = 0 Circle ( h) + ( k) = r Parabola ( h) = p ( k) ( k) = p ( h) Ellipse ( h) ( k) + a b = ( k) ( h) + a b = Hperbola ( h) ( k) a b = ( k) ( h) a b =

27 STAAR ALGEBRA II REFERENCE MATERIALS CIRCUMFERENCE Circle C = πr or C = πd AREA Triangle A = h b Rectangle or parallelogram A = bh Rhombus A = dd Trapezoid A = (b + b ) h Regular polgon A ap = Circle A = πr SURFACE AREA Lateral Total Prism S = Ph S = Ph +B Pramid S = Pl S = Pl + B Clinder S = πrh S = πrh + πr Cone S = πrl S = πrl + πr Sphere S = πr VOLUME Prism or clinder V = Bh Pramid or cone V = Bh Sphere V = πr

28 State of Teas Assessments of Academic Readiness (STAAR ) Performance Level Descriptors Algebra II Performance Level Descriptors Students achieving Level III: Advanced Academic Performance can Interpret restrictions on the domain and range of a function (linear, quadratic, square root, rational, eponential, and logarithmic) and its inverse Evaluate the effectiveness of the various methods used to solve equations, inequalities, and sstems of equations and/or inequalities Evaluate the strengths and weaknesses of each representation of a function Students achieving Level II: Satisfactor Academic Performance can Determine the domain and range of a function (linear, quadratic, square root, rational, eponential, and logarithmic) and its inverse Determine and consider the reasonableness of numerical solutions to equations, inequalities, and sstems of equations and/or inequalities using a variet of methods Formulate equations, inequalities, and sstems of equations and/or inequalities to solve problems Generate multiple representations of a function and use them to determine attributes of the function Describe and use the relationship between an algebraic and geometric representation of a quadratic function or relation, including conic sections Analze the effects of parameter changes on functional relationships (linear, quadratic, square root, rational, eponential, and logarithmic) Analze situations modeled b linear, quadratic, square root, rational, eponential, and logarithmic functions Students achieving Level I: Unsatisfactor Academic Performance can Determine the domain and range of a function (linear, quadratic, square root, rational, eponential, and logarithmic) represented b a table or a graph Find specific function values using algebraic and graphical methods Generate a graph or a table of a function given in algebraic form Describe the effects of parameter changes on linear, quadratic, and eponential functions Teas Education Agenc Student Assessment Division April 0