Algebra 2 CP Curriculum Pacing Guide 207-208 Unit Functions A2.AAPR.* A2.ACE.2* A2.FBF.3* A2.FIF.6* Add, subtract, and multiply polyomials and understand that polynomials are closed under these operations. Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. Describe the effect of the transformations k f (x), f (x) + k, f (x + k), and combinations of such transformations on the graph of y = f (x) for any real number k. Find the value of k given the graphs and write the equation of a transformed parent function given its graph. Given a function in graphical, symbolic, or tabular form, determine the average rate of change of the function over a specified interval. Interpret the meaning of the average rate of change in a given context. Unit - Functions (A2.AAPR.) Perform operations with functions graphically and algebraically. Worksheet Introduction to Functions Worksheet Operations with Functions (A2.FBF.3) Find the composition of two functions graphically and algebraically. Worksheet Compositions of Functions (A2.FIF.6) Identify linear functions as having a constant rate of change with tables, and groups using real world data. Find and analyze the slope of a linear function. Worksheet Modeling Linear Equations Operations with Linear Functions Function Operations Composition & Inverses Function Inverses Sect 2.3 (A2.ACE.2) Represent and solve absolute value equations and inequalities. Review Unit Test Chapter Study Guide Review for Test on Unit Linear Functions Study Guide Test A Test B Sect.4 &.6 2 Anderson School District Five Page 207-208
Unit 2 - Systems of Equations and Inequalities Algebra 2 CP Curriculum Pacing Guide 207-208 A2.ACE.2* A2.ACE.3 A2.AREI.7 A2.AREI.* A2.FLQE.5* Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. Use systems of equations and inequalities to represent constraints arising in real-world situations. Solve such systems using graphical and analytical methods, including linear programming. Interpret the solution within the context of the situation. (Limit to linear programming.) Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Understand that such systems may have zero, one, two, or infinitely many solutions. (Limit to linear equations and quadratic functions.) Solve an equation of the form f (x) = g (x) graphically by identifying the x-coordinate(s) of the point(s) of intersection of the graphs of y = f (x) and y = g (x). Interpret the parameters in a linear or exponential function in terms of the context. Unit 2 - Systems of Equations and Inequalities (A2.ACE.3) Identify a system as consistent, inconsistent, dependent, or independent. Worksheet Solve by Graphing Sect. 3. Solve a system of linear equations by graphing. (A2.ACE.3) Solve a system of two linear equations algebraically (substitution and elimination). Solve systems of equations using technology (linear, polynomial, rational, absolute value, exponential, and logarithmic functions). Systems of Two Equations Worksheet Mixed Practice on Solving Systems Worksheet Elimination and Substitution Sect. 3. 2 (A2.ACE.2, A2.ACE.3, A2.AREI.7, A2.AREI., A2.FLQE.5) Create equations in two or more variables and use them to solve problems (including systems). Solve systems of equations using technology (linear, polynomial, rational, absolute value, exponential, and logarithmic functions). Systems of Equations Word Problems Sect. 3. (A2.ACE.3) Graph a system of linear inequalities. Worksheet Systems of Inequalities Systems of Inequalities Sect. 3.2 Anderson School District Five Page 2 207-208
Algebra 2 CP Curriculum Pacing Guide 207-208 Unit 2 - Systems of Equations and Inequalities (A2.ACE.3, A2.FLQE.5) Graph a set of given constraints for a linear programming problem. Use linear programming to find the maximum or minimum value given the objective function. Worksheet Linear Programming (a) Worksheet Linear Programming (b) Worksheet Linear Programming (c) Sect. 3.3 2 Review Project Rescue the Princess (2 files) Review for the Test Unit Test Anderson School District Five Page 3 207-208
Algebra 2 CP Curriculum Pacing Guide 207-208 Unit 3 Quadratic Functions A2.AREI.2* A2.ASE.3c A2.NCNS.* Solve simple rational and radical equations in one variable and understand how extraneous solutions may arise. Use the properties of exponents to transform expressions for exponential functions. Know there is a complex number i such that 2 i =, and every complex number has the form a + bi with a and b real. Unit 3 Exponents and Radical Functions A2.ASE.3c Law of Exponents (include rational exponents) Worksheet Properties of Exponents Worksheet Simplifying Rational Exponents Exponent Jeopardy Game http://www.math- play.com/exponents-jeopardy/exponents- Jeopardy.html Laws of Exponents Game http://www.superteachertools.com/jeopardy/usergam es/nov20044/game288705963.php Exponent Asteroid Game http://www.mathdork.com/games/asteroidsexp3/aster oidsexp3.html Sect 5. & Sect 6.6 2 (A2.AREI.2) Simplify a radical. Multiply radicals. Simplify Radical Expression More on Simplifying Radicals Sect. 6.4 (A2.AREI.2) Add and subtract radicals Divide radicals and rationalize the denominator. (A2.AREI.2) Create and/or solve radical equations, verify solutions, and determine the domain restrictions. More on Operations with Radicals Sect. 6.5 2 Worksheet Solving Radical Equations Sect. 6.7 Create and/or solve literal radical equations. (A2.NCNS.) Define and simplify complex numbers. Sect. 4.4 Anderson School District Five Page 4 207-208
Algebra 2 CP Curriculum Pacing Guide 207-208 Unit 3 Exponents and Radical Functions (A2.NCNS.) Perform operations using complex numbers. Worksheet Complex Numbers Operations with Complex Numbers Properties of Complex Numbers Rationalizing Imaginary Denominators Sect. 4.4 2 Review Unit Test Anderson School District Five Page 5 207-208
Unit 4A Quadratic Functions with Factoring Algebra 2 CP Curriculum Pacing Guide 207-208 A2.ACE.2* A2.ACE.3 A2.ACE.4* A2.AREI.4* A2.AREI.4b A.ASE.2* A2.FBF.* A2.FIF.8* A2.FIF.9* Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. Use systems of equations and inequalities to represent constraints arising in real-world situations. Solve such systems using graphical and analytical methods, including linear programming. Interpret the solution within the context of the situation. (Limit to linear programming.) Solve literal equations and formulas for a specified variable including equations and formulas that arise in a variety of disciplines. Solve mathematical and real-world problems involving quadratic equations in one variable. Solve quadratic equations by inspection, 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. Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions. Write a function that describes a relationship between two quantities. Translate between different but equivalent forms of a function equation to reveal and explain different properties of the function. Compare properties of two function given in different representations such as algebraic, graphical, tabular, or verbal. Unit 4 A Quadratic Functions with factoring (A2.ACE.2, A2.ACE.3, A2.ACE.4, A2.FBF., A2.FIF.8, A2.FIF.9) Create and/or graph quadratic functions using a graphing calculator and identify important features including the maximum/ minimum, the zeros, and the intervals where the function is increasing/decreasing. Compare different forms of quadratic functions. Worksheet Introduction to Quadratics Properties of Parabolas Worksheet Word Problems and Solving with the Calculator Sect. 4. & 4.5 2 Determine the domain and range (using interval notation) for quadratic functions. (A2.AREI.4b, A2.ASE.2) Factor quadratic expressions. Factoring Quadratic Form Factoring Quadratic Expressions Factoring by Grouping Factoring All Techniques Worksheet Mixed Factoring Practice Worksheet Perfect Squares Worksheet Factoring Trinomials Sect. 4.3 3 Anderson School District Five Page 6 207-208
Algebra 2 CP Curriculum Pacing Guide 207-208 Unit 4 A Quadratic Functions with factoring (A2.AREI.4, A2.AREI.4b, A2.ASE.2) Solve quadratic functions by factoring. Worksheet Solve by Factoring Worksheet Factoring and Solve by Factoring Quadratic Equations by Factoring Sect. 4.3 Review Unit Test Anderson School District Five Page 7 207-208
Algebra 2 CP Curriculum Pacing Guide 207-208 Unit 4 B Quadratics continued A2.ACE.3 A2.ASE.3* A2.ASE.3b A2.FBF.3* A2.FIF.6* A2.FIF.8* A2.FIF.9* A2.NCNS.7* Use systems of equations and inequalities to represent constraints arising in real-world situations. Solve such systems using graphical and analytical methods, including linear programming. Interpret the solution within the context of the situation. (Limit to linear programming.) Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Determine the maximum and minimum value of a quadratic function by completing the square. Describe the effect of the transformations k f (x), f (x) + k, f (x + k), and combinations of such transformations on the graph of y = f (x) for any real number k. Find the value of k given the graphs and write the equation of a transformed parent function given its graph. Given a function in graphical, symbolic, or tabular form, determine the average rate of change of the function over a specified interval. Interpret the meaning of the average rate of change in a given context. Translate between different but equivalent forms of a function equation to reveal and explain different properties of the function. Compare properties of two function given in different representations such as algebraic, graphical, tabular, or verbal. Solve quadratic equations in one variable that have complex solutions. Unit 4 B Quadratics continued (A2.FIF.6) Calculate and interpret average rate of change of quadratic functions over a specific interval. P. 28 (lab) (A2.FIF.8, A2.FIF.9, A2.FBF.3, A2.ASE.3b, A2.ASE.3) Complete the square to write a quadratic function in vertex form. Graph quadratic functions using vertex form. Determine the domain and range (using interval notation) for quadratic functions (with graphs). Completing the Square Worksheet Write in Vertex Form and Graph Worksheet Complete the Square to Find the Vertex Worksheet More on Completing the Square to Find the Vertex Sect. 4.5 2 (A2.NCNS.7) Solve quadratic functions using the quadratic formula. (A2.ACE.3) Use the discriminant to determine the nature of the solutions. Worksheet Solve Using Quadratic Formula Quadratic Formula Activity Lab for Nature of Roots The Discriminant Sect. 4.6 Sect. 4.6 2 Anderson School District Five Page 8 207-208
Algebra 2 CP Curriculum Pacing Guide 207-208 Unit 4 B Quadratics continued (A2.FIF.8) Write the equation of a quadratic function when given its roots. Worksheet Finding Eq from Roots Factors and Zeros Sect. 4.3 Review Chutes and Ladders Review for Quadratics Jeopardy Review Review Part B Unit Test MIDTERM EXAM Anderson School District Five Page 9 207-208
Algebra 2 CP Curriculum Pacing Guide 207-208 Second Half of Semester Unit 5 Polynomial Functions A2.AAPR.* A2.AAPR.3 A2.ASE.* A2.ASE.2* A2.FBF.b A2.FIF.4* A2.FIF.7* A2.FIF.9* Add, subtract, and multiply polyomials and understand that polynomials are closed under these operations. Graph polynomials identifying zeros when suitable factorizations are available and indicating end behavior. Write a polynomial function of least degree corresponding to a given graph. (Limit to polynomials with degrees 3 or less.) Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions. Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite equivalent expressions. Combine functions using the operations addition, subtraction, multiplication, and division to build new functions that describe the relationship between two quantities in mathematical and real-world situations. Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases. Compare properties of two function given in different representations such as algebraic, graphical, tabular, or verbal. Unit 5 Polynomial Functions (A2.AAPR.3, A2.FIF.4, A2.FIF.7, A2.FIF.9) Graph and describe the shape of polynomial functions Identify and describe important features of the graph of a polynomial function including absolute and relative maximum/ minimum points, intervals where the function is increasing/decreasing, zeros (including the multiplicity of each), domain and range (in interval notation), and end behavior. Graphing Polynomial Functions Basic Shape Graphing Polynomial Functions Sect. 5.3 & 5.4 2 (A2.AAPR., A2.FBF.b) Add, subtract, and multiply polynomial functions. Divide polynomial functions using long division and synthetic. Sect. 5. & 5.2 3 (A2.ASE., A2.ASE.2,) Factor and solve polynomial functions, including special products like (x + y) 3, (x y) 3, etc. Review 7. to 7.3 Sect. 5.5 & 5.6 Anderson School District Five Page 0 207-208
Algebra 2 CP Curriculum Pacing Guide 207-208 Second Half of Semester Unit 5 Polynomial Functions (A2.AAPR.3) Use the rational root theorem and the remainder theorem to find the zeros of a polynomial function. The Remainder Theorem Rational Root Theorem More on Factors, Zeros, and Dividing Irrational and Imaginary Root Theorems Descartes Rule of Signs Analyzing and Solving Polynomial Equations Worksheet Rational Root Theorem (A) to Solve Worksheet Rational Root Theorem (B) to Solve Worksheet Last Practice Rational Root Theorem to Find All Roots Sect. 5.7 & 5.8 2 Review Review Chapter 6 Study Guide Review for Test Unit Test Anderson School District Five Page 207-208
Algebra 2 CP Curriculum Pacing Guide 207-208 Second Half of Semester Unit 6 Rational Functions A2.AREI.2 A2.FIF.7 Solve simple rational and radical equations in one variable and understand how extraneous solutions may arise. Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases. Unit 6 Rational Functions days Identify and evaluate rational functions. Sect 8. (A2.AREI.2) Multiply and divide rational expressions including complex fractions. (A2.AREI.2) Add and subtract rational expressions. Worksheet Multiply and Divide Rational Expressions Worksheet Review of Operations Worksheet Add and Subtract with Like Denominators Worksheet More on Adding and Subtracting Worksheet - Mixed Review of Operations Sect 8.2 2 (A2.FIF.7) Graph a rational function and find its domain and range (in interval notation), write equations for its asymptotes, and identify any holes in its graph. Worksheet Graphing Rationals (a) Worksheet Graphing Rationals (b) Worksheet Graphing Rationals (c) Sect 8.3 & 8.4 2 (A2.AREI.2) Solve rational equations. Worksheet Solving Rational Expressions Worksheet More on Solving Rational Expressions Sect 8.6 Review Review Chapter 9 Study Guide Review Graphing and Operations Review Operations & Solving Rational Equations Review Unit Test Anderson School District Five Page 2 207-208
Unit 7 Exponential & Logarithmic Functions Algebra 2 CP Curriculum Pacing Guide 207-208 Second Half of Semester A2.ACE.* A2.ACE.2* A2.ASE.* A2.ASE.3c A2.FBF.b A2.FIF.4* A2.FIF.5* A2.FIF.6* A2.FIF.7* A2.FIF.8b A2.FLQE.* A2.FLQE.b A2.FLQE.5* Create and solve equations and inequalities in one variable that model real-world problems involving linear, quadratic, simple rational, and exponential relationships. Interpret the solutions and determine whether they are reasonable. Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret complicated expressions as being composed of simpler expressions. Use the properties of exponents to transform expressions for exponential functions. Combine functions using the operations addition, subtraction, multiplication, and division to build new functions that describe the relationship between two quantities in mathematical and real-world situations. Interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes. Given a function in graphical, symbolic, or tabular form, determine the average rate of change of the function over a specified interval. Interpret the meaning of the average rate of change in a given context. Graph functions from their symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated cases. Interpret expressions for exponential functions by using the properties of exponents. Distinguish between situations that can be modeled with linear functions or exponential functions by recognizing situations in which one quantity changes at a constant rate per unit interval as opposed to those in which a quantity changes by constant percent rate per unit interval. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. Interpret the parameters in a linear or exponential function in terms of the context. Anderson School District Five Page 3 207-208
Algebra 2 CP Curriculum Pacing Guide 207-208 Second Half of Semester Unit 7 Exponential Functions & Logarithmic Functions days (A2.ASE., A2.FBF.b, A2.FIF.8b, A2.FLQE.b, A2.FLQE.5) Write and evaluate exponential expressions to model growth and decay situations. Classify an exponential function as representing a growth or a decay. Calculate the growth of investments under various conditions using exponential and natural exponential functions. Activity Shedding Light on the Subject Activity Spreading Rumors Worksheet Word Problems Finding Other Variables Using Logs Worksheet More Word Problems Worksheet Compound Interest and Exp. Functions Worksheet Growth & Decay Solve for New Variable (A2.FIF.6) Calculate and interpret the average rate of change of exponential functions over a specific interval. (A2.FIF.7) Graph exponential functions using transformations. Find the domain and range (in interval notation), intercepts, end behavior, and the equation of the horizontal asymptote for an exponential function. Worksheet Exponential Graphs Worksheet Exponential Equations with Like Bases (A2.ACE.2) Rewrite exponential equations as logarithmic equations and vice versa. Simplify and evaluate expressions involving logarithms using the properties of logarithms. Worksheet Practice with Log Properties and Solving Log Equations Anderson School District Five Page 4 207-208
Algebra 2 CP Curriculum Pacing Guide 207-208 Second Half of Semester Unit 7 Exponential Functions & Logarithmic Functions days (A2.F.IF.7) Graph the inverse of the exponential function and define the logarithmic function. Worksheet Intro to Logs (A2.FIF.5, A2.FIF.4) Find the domain and range (in interval notation), intercepts, end behavior, and the equation of the vertical asymptote for a logarithmic function. (A2.ACE., A2.ASE.3c, A2.FLQE., A2.FLQE.b) Use the definitions of exponential and logarithmic functions to solve equations. Solve equations involving logarithms algebraically and graphically. Solve exponential equations using common logs algebraically and graphically. Review st Half Through Log Properties Worksheet Basic Log Equations with No Calculator Worksheet Logs Worksheet More on Logs Review Log Equations and Exponential Equations using Logs Worksheet Exponential Equations with Unlike Bases 2 Review Jeopardy Review Station Rotation Quiz on Logarithms Unit Test Anderson School District Five Page 5 207-208
Algebra 2 CP Curriculum Pacing Guide 207-208 Second Half of Semester Unit 8 Sequences and Series A2.ACE.2* A2.FBF.a A2.FBF.2* A2.FIF.3* A2.FLQE.* A2.FLQE.2* Create equations in two or more variables to represent relationships between quantities. Graph the equations on coordinate axes using appropriate labels, units, and scales. Write a function that models a relationship between two quantities using both explicit expressions and a recursive process by combining standard forms using addition, subtraction, multiplication and division to build new functions. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Define functions recursively and recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Distinguish between situations that can be modeled with linear functions or exponential functions by recognizing situations in which one quantity changes at a constant rate per unit interval as opposed to those in which a quantity changes by constant percent rate per unit interval. Create symbolic representations of linear and exponential functions, including arithmetic and geometric sequences, given graphs, verbal descriptions, and tables. Unit 8 Sequences and Series (A2.ACE.2, A2.FBF.a, A2.FLQE.2) Recognize, write, and find the nth term of arithmetic sequences. Find the partial sum of an arithmetic series. (A2.FBF.a, A2.FBF.2, A2.FIF.3) Recognize, write, and find the nth term of geometric sequences. Find partial sums of geometric sequences. (A2.FLQE.) Use sigma notation to represent arithmetic and geometric series. Introduction to Sequences Arithmetic Sequences Sequences and Series Reality Project Sequences and Series Art Project Arithmetic Series Worksheet Arithmetic Sequences and Series Review of Arithmetic and Geometric Arithmetic and Geometric Means Geometric Sequences Finite Geometric Series Infinite Geometric Series days Sect 0.2 Sect 0.2 Sect 0.3 Sect 0.3 Review Unit Test Anderson School District Five Page 6 207-208