Algebra 2 Year-at-a-Glance Leander ISD st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks

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1 Algebra 2 Year-at-a-Glance Leander ISD st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks Essential Unit of Study 6 weeks 3 weeks 3 weeks 6 weeks 3 weeks 3 weeks 6 weeks 4 weeks Polynomials & Inverses & 07 Quadratic Functions & Rational Exponential & Log Linear Functions Polynomial Square Root Conics Factoring Functions Functions Functions Functions Content Topics TEKS Solve linear equations, model data using linear functions, scatterplots/regressi on. Graph/write abs value functions w/ transformations, solve abs value equations/inequaliti es. Solve 2 & 3 variable system of linear equations. Graph system of linear inequalities. 2A.1AB, 2A.2A, 2A.3ABC, 2A.4AB Support A.1D, A.6D, A.7A Use properties of exponents to simplify expressions. Add, subtract, multiply polynomials. Factor and solve polynomial equations. Evaluate nth roots and use rational exponents. Apply properties of rational 2A.2A Support a.1, a.2, 2A.1A t Graph quadratics functions in standard, vertex, or intercept form. Solve quadratic equations by factoring, finding square roots, completing the square, and the quadratic formula. Use imaginary and complex numbers. Graph and solve quadratic inequalities. Write quadratic functions and models. 2A.2AB, 2A.6ABC, 2A.7AB, 2A.8BD Support 2A.4AB Explore the relationship between a function and its inverse. Find the inverse of a linear, quadratic, cubic, and power function. Graph square root functions. Solve square root and other simple radical equation by a variety of methods. 2A.4AC, 2A.9ABCDEFG Write and graph direct variation equations. Model inverse and joint variation. Graph rational functions. Multiply, divide, add, and subtract rational expressions. Solve rational equations. 2A.10ABCDEFG Graph exponential growth and decay functions. Use functions involving e. Evaluate logarithms and graph logarithmic functions. Apply properties of logarithms. Solve exponential and logarithmic equations. Use the graphing calculator to model exponential and power functions. 2A.11ABCDEF Support Support a.5, 2A.1B, 2A.2A 2A.4AC Graph and write the equations of circles ellipses, hyperbolas, and parabolas. Identify the important characteristics of conics. Use completing the square to write conics in (h,k) form. 2A.5ABCDE Support a.5 McDougal Text Resources Alg 2 Resources McDougal 1.1, 1.2, 1.3, 2.1, 2.2, 2.3, 2.4, 2.6, 2.7, 1.7, 2.8, 3.1, 3.2, 3.3, 3.4 McDougal 5.1, 5.3, 5.4, 6.1,.6.2 McDougal 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7 McDougal 6.4, 6.5, 6.6 McDougal 2.5, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6 McDougal 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7 McDougal 9.1, 9.2, 9.3, 9.4, 9.5, Aug 2007

2 (2A.1) Foundations for functions: uses properties and attributes of functions and applies functions to problem situations. The student is expected to: (A) identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations. (B) 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. (2A.2) Foundations for functions: 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) use tools including factoring and properties of exponents to simplify expressions and transform and solve equations. 01 EUS - Linear Functions (6 Weeks) Use properties of real numbers. 1.1 Evaluate and simplify expressions involving real numbers. 1.2 Solve linear equations. 1.3 Represent relations and graph linear functions. 2.1 Find slopes of lines and rates of change. 2.2 Graph linear equations in slope-intercept form. Discuss domain/range. 2.3 Write linear equations in standard, slope-intercept, & point-slope form. 2.4 Fit lines to data in scatter plots using linear regression. 2.6 Graph and write absolute value functions with simple transformations. 2.7 Solve absolute value equations and inequalities. 1.7 Graph linear inequalities in two variables. 2.8 Solve systems of linear equations by graphing. 3.1 Solve systems of linear equations by algebraically. 3.2 Graph system of linear inequalities. 3.3 Solve system of equations in three variables 3.4 (2A.3) Foundations for functions: formulates systems of equations and inequalities from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situations. The student is expected to: (A) analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems. (B) use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities for given contexts. (C) interpret and determine the reasonableness of solutions to systems of equations or inequalities. (2A.4) Algebra and geometry: connects algebraic and geometric representations of functions. The student is expected to: (A) identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x2), exponential (f(x) = ax), and logarithmic (f(x) = logax) functions, absolute value of x (f(x) = x ), square root of x (f(x) = x), and reciprocal of x (f(x) = 1/x) (B) parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions. A.1D Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. (TAKS 1) A.6D Graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept. (TAKS 3) A.7A Analyze situations involving linear functions and formulate linear equations or inequalities to solve problems. (TAKS 4) - Equivalent equations - Absolute value - Extraneous solutions - Domain, range - Parent function - Slope-intercept form - Point-slope form - Correlation coefficient - Best-fitting line - Absolute value function - Transformation - Linear inequality in two variables - Substitution method - Elimination method - System of linear inequalities - System of three linear equations - Ordered triple

3 (2A.2) Foundations for functions: 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) use tools including factoring and properties of exponents to simplify expressions and transform and solve equations. 02 EUS - Polynomials and Polynomial Functions (3 Weeks) Simplify expressions involving properties of exponents such as product of 5.1 powers, power of a power, power of a product, negative exponent, zero exponent, quotient of powers, and power of a quotient. Add, subtract, and multiply polynomials. Become familiar with the product of conjugates, square of a binomial, and cube of a binomial. Factor (including a common monomial factor, difference of two squares and factoring by grouping) and solve polynomial equations. Evaluate expressions with nth roots and rational exponents with and without a calculator. Us properties of rational exponents to simplify expressions a.1 Foundations for high school mathematics. As presented in Grades K-8, the basic understandings of number, operation, quantitative reasoning,; patterns, relationships, and algebraic thinking; geometry; measurement; and probability and statistics are essential foundations for all work I high school mathematics. Students continue to build on this foundation as they expand their understanding through other mathematical experiences. a.2 Algebraic thinking and symbolic reasoning. Symbolic reasoning plays a critical role in algebra; symbols provide powerful ways to represent mathematical situations and to express generalizations. Students study algebraic concepts and the relationship among them to better understand the structure of algebra. (2A.1) Foundations for functions: uses properties and attributes of functions and applies functions to problem situations. The student is expected to: (A) identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations. - polynomial - polynomial function - end behavior - factored completely - factor by grouping - quadratic form - nth root of a - index of a radical - simplest form of a radical - like radicals - power function - inverse relation - inverse function - radical function - radical equation

4 (2A.2) Foundations for functions: 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) use tools including factoring and properties of exponents to simplify expressions and transform and solve equations. (B) Use complex numbers to describe the solutions of quadratic equations. 03 EUS - Quadratic Functions and Factoring (9 Weeks) Graph quadratic functions in standard form. 4.1 Graph quadratic functions in vertex form and intercept form. 4.2 Use factoring to solve a quadratic with a leading coefficient of Use factoring to solve a quadratic with a leading coefficient of 'a'. 4.4 Solve quadratic equations by finding square roots. Solutions may be 4.5 comple n mbers b t no operations or plotting of comple n mbers Solve quadratic equations with complex number solutions. No complex numbers operations or plotting. 4.6 (2A.6) Quadratic and square root functions: understands that quadratic functions can be represented in different ways and translates among their various representations. The student is expected to: (A) 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. (B) relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions. (C) determine a quadratic function from its roots or a graph. Solve quadratic equations by completing the square. 4.7 Solve quadratic equations using the quadratic formula. 4.8 Graph and solve quadratic inequalities. 4.9 Write quadratic functions and models given a graph or description (2A.7) Quadratic and square root functions: interprets and describes the effects of changes in the parameters of quadratic functions in applied and mathematical situations. The student is expected to: (A) use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax^2 + bx + c and the y = a(x - h)^2 + k symbolic representations of quadratic functions. (B) use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x - h)2 + k form of a function in applied and purely mathematical situations. (2A.8) Quadratic and square root functions: formulates equations and inequalities based on quadratic functions, 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 involving quadratic functions and formulate quadratic equations or inequalities to solve problems. (B) Analyze and interprets the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula. - standard form of a quadratic function - parabola - vertex form - intercept form - root of an equation - zero of a function - square root - imaginary number - complex number - completing the square - quadratic formula - discriminant (2A.4) Algebra and geometry: connects algebraic and geometric representations of functions. The student is expected to: (A) identify and sketch graphs of parent functions, including linear, quadratic, exponential, and logarithmic functions, absolute value of x, square root of x, and reciprocal of x. (B) parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions

5 04 EUS - Inverses and Square Root Functions (3 Weeks) Explore the relationship between a function and its inverse. 6.4 activity (p. 437) (2A.4) Algebra and geometry: connects algebraic and geometric representations of functions. The student is expected to: (A) identify and sketch graphs of parent functions, including square root of x. (C) describe and analyze the relationship between a function and its inverse. (2A.9) Quadratic and square root functions: formulates equations and inequalities based on square root functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: Find the inverse of a linear, quadratic, cubic, and power function of the form y = a x^n + c Graphs of square root functions including parameter change and domain/range. Solve and determine the reasonableness of solutions for square root and 6.6 other simple radical equations using algebraic, tabular, graphical, and verbal representation 6.6 extension (p. 460) (A) 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. (B) Relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions. (C) 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. (D) Determine solutions of square root equations using graphs, tables, and algebraic methods. (E) Determine solutions of square root inequalities using graphs and tables. (F) Analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems. -inverse relation - inverse function - radical function - radical equation - extraneous solution

6 05 EUS - Rational Functions (3 Weeks) (2A.10) Rational functions: formulates equations and Write and graph direct variation equations from verbal descriptions. Apply 2.5 inequalities based on rational functions, uses a variety of a model for direct variation from verbal description. methods to solve them, and analyzes the solutions in terms of the situation. Use inverse variation and joint variation models. 8.1 (A) use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, and examine asymptotic behavior. (B) analyze various representations of rational functions with respect to problem situations. (C) 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. (D) determine the solutions of rational equations using graphs, tables, and algebraic methods. (E) determine solutions of rational inequalities using graphs and tables. (F) analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem. (G) use functions to model to and make predictions in problem situations involving direct and inverse variation. Graph simple rational functions and be able to describe vertical/horizontal asymptotes and domain/range of those functions. Graph rational functions with higher-degree polynomials. Include endbehavior in description. Multiply and divide rational expressions and then simplify. 8.4 Add, subtract and then simplify rational expressions. 8.5 Solve rational equations by multiplying by the LCD. Check for extraneous solutions. a.5 Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools and technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to model mathematical situations to solve meaningful problems. (2A.1) Foundations for functions: uses properties and attributes of functions and applies functions to problem situations. The student is expected to: (B) 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. (2A.2) Foundations for functions: 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) use tools including factoring and properties of exponents to simplify expressions and transform and solve equations direct variation - constant of variation - inverse variation - joint variation - rational function - horizontal asymptote - vertical asymptote - simplified form of a rational expression - complex fraction - cross multiplying - least common denominator - extraneous solutions

7 06 EUS - Exponential and Log Functions (6 Weeks) (2A.11) Exponential and logarithmic functions: formulates Graph and use exponential growth functions with base b > 1. equations and inequalities based on exponential and 7.1 logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: Graph and use exponential decay functions with base 0 > b > (A) Develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses. (B) Use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior. (C) Determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities. (D) Determine the solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods. Study functions involving the natural base "e". 7.3 Evaluate logarithms and graph logarithmic functions of base "b". 7.4 Apply properties of logarithms (product property, quotient property, and power property) to rewrite logarithmic expressions. Solve exponential and logarithmic equations. 7.6 Use the regression feature on the graphing calculator to model exponential and power functions. (E) Determine solutions of exponential and logarithmic inequalities using graphs and tables. (F) Analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem Vocabulary - exponential function - exponential growth - growth factor - exponential decay - decay factor - logarithm of y with base b (2A.4) Algebra and geometry: connects algebraic and geometric representations of functions. The student is expected to: - natural base e (A) identify and sketch graphs of parent functions, including linear, quadratic, exponential, and logarithmic functions, absolute value - common logarithm of x, square root of x, and reciprocal of x. - natural logarithm (C) describe and analyze the relationship between a function and its inverse. - exponential equation - logarithmic equation

8 07 EUS - Conics (4 Weeks) Explore the intersections of planes and cones. 9.6 Activity (p. 649) (2A.5) Algebra and geometry: knows the relationship between the geometric and algebraic descriptions of conic sections. (A) Describe a conic section as the intersection of a plane and a cone. (B) Sketch graphs of conic sections to relate simple paramerter changes in the equation to corresponding changes in the graph. (C) Identify symmetries from graphs of conic sections. (D) Identify the conic section from a given equation. (E) Use the method of completing the square. Graph and write the equations of circles centered at the origin. Determine the equation of a circle given its center and a point on the circle. Graph and write the equation of an ellipse in standard form. Identify the vertices, foci, major, and minor axes. Graph and write equations of hyperbolas. Identify vertices, foci, and asymptotes. Graph and write the equations of parabolas that open up/down or left/right Graph and write equations of translated conics and identify the important characteristics of the graphs. Complete the square to write conics in (h,k) form. 9.6 a.5 Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools and technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to model mathematical situations to solve meaningful problems. - conic sections - ellipse - focus, foci - directrix - vertices - major axis - minor axis - hyperbola - transverse axis - circle equation - general second degree equation

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