Algebra 2 CP and Algebra 2 A/B Curriculum Pacing Guide First Nine Weeks

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1 Algebra CP and Algebra A/B Curriculum Pacing Guide First Nine Weeks Unit Functions A.APR. 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. A.APR.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. A.REI.8 (+) Represent a system of linear equations as a single matrix equation in a vector variable. A.REI. 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. F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. F.IF.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. F.IF.7b F.BF.3 F.BF.4 F.BF.4a F.LE. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(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. Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = x 3 or f(x) = (x+)/(x-) for x. Distinguish between situations that can be modeled with linear functions and with exponential functions. Unit - Functions (A.APR.) Perform operations with functions by evaluating. Worksheet Operations with Functions (F.BF.3) Find the composition of two functions by evaluating. Worksheet Compositions of Functions (A.APR.3, A.REI.8, F.BF.3, F.BF.4, F.BF.4a) Graph parent functions and perform transformations. PowerPoint Day 3 Transformations Find domain and range (using interval notation) from graphs. Find inverse functions graphically (exponential, linear, quadratic). Anderson School District Five Page Copyright July, 03

2 Algebra CP and Algebra A/B Curriculum Pacing Guide First Nine Weeks Unit - Functions (F.IF.5, F.IF.7b) Define and graph a step function. Identify the domain and range (in interval notation) of step functions. (F.IF.5, F.IF.7b) Define and graph piecewise functions. Worksheet Graphing Piecewise Functions Identify the domain and range (in interval notation) of piecewise functions. (F.IF.6, F.LE.) 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 (A.REI.) Represent and solve absolute value equations and inequalities. Review Chapter Study Guide Review for Test on Unit Linear Functions Study Guide Unit Test Test A Test B Anderson School District Five Page Copyright July, 03

3 Unit - Systems of Equations and Inequalities A.CED. A.CED.3 Algebra CP and Algebra A/B Curriculum Pacing Guide First Nine Weeks Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. A.REI. 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. Unit - Systems of Equations and Inequalities (A.CED.3) Identify a system as consistent, inconsistent, dependent, or independent. Worksheet Solve by Graphing Solve a system of linear equations by graphing. (A.CED.3) Solve a system of 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 Systems of Three Equations Elimination Systems of Three Equations Substitution (A.CED., A.CED.3, A.REI.) Create equations in two or more variables and use them to solve problems (including systems). Systems of Equations Word Problems Solve systems of equations using technology (linear, polynomial, rational, absolute value, exponential, and logarithmic functions). (A.CED.3) Graph a system of linear inequalities. Worksheet Systems of Inequalities Systems of Inequalities Anderson School District Five Page 3 Copyright July, 03

4 Algebra CP and Algebra A/B Curriculum Pacing Guide First Nine Weeks Unit - Systems of Equations and Inequalities (A.CED.3) Write and graph a set of constraints for a linear programming problem. Worksheet Linear Programming (a) Worksheet Linear Programming (b) Worksheet Linear Programming (c) 3 Use linear programming to find the maximum or minimum value of an objective function. Review Project Rescue the Princess Review for the Test Unit Test Anderson School District Five Page 4 Copyright July, 03

5 Unit 3 Radical Functions Algebra CP and Algebra A/B Curriculum Pacing Guide First Nine Weeks A.REI. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Unit 3 Radical Functions (A.REI.) Simplify a radical. More on Simplifying Radicals Simplify Radical Expression (A.REI.) Add, Subtract, and multiply radicals. More on Operations with Radicals Divide radicals and rationalize the denominator. Unit 3 will continue in the nd Nine Weeks. Anderson School District Five Page 5 Copyright July, 03

6 Algebra CP and Algebra A/B Curriculum Pacing Guide First Nine Weeks Anderson School District Five Page 6 Copyright July, 03

7 Unit 3 Radical Functions Continued Algebra CP and Algebra A/B Curriculum Pacing Guide Second Nine Weeks A.APR.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. A.APR.7(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. A.REI. F.BF.3 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Identify the effect on the graph of replacing f(x) + k, k f(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. Unit 3 Radical Functions Continued (A.REI.) Create and/or solve radical equations, verify solutions, and determine the domain restrictions. Worksheet Solving Radical Equations Create and/or solve literal radical equations. (A.APR.3, A.APR.7, F.BF.3) Graph radical functions using transformations. Worksheet Graphing Radical Transformations Determine the domain and range (using interval notation) of a radical function given the graph. Review Jeopardy Review Review Chapter 7 Study Guide Review for Test Unit Test Anderson School District Five Page 7 Copyright July, 03

8 Unit 4 Quadratic Functions Algebra CP and Algebra A/B Curriculum Pacing Guide Second Nine Weeks N.CN. N.CN. N.CN.7 A.SSE.a A.CED. A.CED. A.CED.3 A.CED.4 F.IF.6 F.IF.8 F.IF.9 F.BF. F.BF.3 F.BF.4 F.BF.4a Know there is a complex number i such that i = -, and every complex number has the form a + bi with a and b real. Use the relation i = - and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Solve quadratic equations with real coefficients that have complex solutions. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. 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. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Write a function that describes a relationship between two quantities. Identify the effect on the graph of replacing f(x) + k, k f(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. Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = x 3 or f(x) = (x+)/(x-) for x. Unit 4 Quadratic Functions Define quadratic functions. (A.CED., A.CED.3, A.CED.4, F.IF.9, F.BF.) 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 Anderson School District Five Page 8 Copyright July, 03

9 Algebra CP and Algebra A/B Curriculum Pacing Guide Second Nine Weeks Unit 4 Quadratic Functions (A.CED., A.CED.3, A.CED.4, F.IF.9, F.BF.) Determine the domain and range (using interval notation) for quadratic functions. (A.CED., A.SSE.a) Factor quadratic expressions. Factoring Quadratic Form Factoring Quadratic Expressions Factoring by Grouping Factoring a Sum & Difference of Cubes Factoring All Techniques Worksheet Mixed Factoring Practice Worksheet Perfect Squares and Cubes and Graphing Worksheet Factoring Trinomials (A.CED., A.SSE.a) Solve quadratic functions by factoring. Worksheet Solve by Factoring Worksheet Factoring and Solve by Factoring Quadratic Equations by Factoring (F.IF.6, F.BF.4, F.BF.4a) Calculate and interpret average rate of change of quadratic functions over a specific interval. Find inverses of quadratic functions algebraically. (F.IF.8, F.IF.9, F.BF.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 (N.CN.) Define and simplify complex numbers. Anderson School District Five Page 9 Copyright July, 03

10 Algebra CP and Algebra A/B Curriculum Pacing Guide Second Nine Weeks Unit 4 Quadratic Functions (N.CN.) Perform operations using complex numbers. Worksheet Complex Numbers Operations with Complex Numbers Properties of Complex Numbers Rationalizing Imaginary Denominators (N.CN.7) Solve quadratic functions using the quadratic formula. Worksheet Solve Using Quadratic Formula Quadratic Formula (A.CED.3) Use the discriminant to determine the nature of the solutions. Activity Lab for Nature of Roots The Discriminant (F.IF.8) Write the equation of a quadratic function when given its roots. Worksheet Finding Eq from Roots Factors and Zeros Review Chutes and Ladders Review for Quadratics Jeopardy Review Review Part B Unit Test Review for Midterm Exam Second Nine Weeks Study Guide Second Nine Weeks Exam Review Midterm Exam Anderson School District Five Page 0 Copyright July, 03

11 Unit 5 Polynomial Functions Algebra CP and Algebra A/B Curriculum Pacing Guide Second Nine Weeks A.APR. A.APR.3 A.APR.6 F.IF.4 F.IF.7c F.IF.9 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. 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. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. 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. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Unit 5 Polynomial Functions (A.APR., A.APR.6) Add, subtract, and multiply polynomial functions. Divide polynomial functions using long division. (A.APR.3, F.IF.7c) Graph and describe the shape of polynomial functions (by hand in simple cases, with technology in complex situations). (F.IF.4, F.IF.9 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 Unit 5 will continue in the 3 rd Nine Weeks Anderson School District Five Page Copyright July, 03

12 Algebra CP and Algebra A/B Curriculum Pacing Guide Second Nine Weeks Anderson School District Five Page Copyright July, 03

13 Unit 5 Polynomial Functions Continued Algebra CP and Algebra A/B Curriculum Pacing Guide Third Nine Weeks A.SSE. A.SSE.a A.SSE.b A.SSE. A.APR. A.APR. A.APR.3 A.APR.4 A.APR.6 F.IF.4 F.IF.7c F.IF.9 Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity. Use the structure of an expression to identify ways to rewrite it. 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. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x a is p(a), so p(a) = 0 if and only if (x a) is a factor of p(x). 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. Prove polynomial identities and use them to describe numerical relationships. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. 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. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Unit 5 Polynomial Functions (A.SSE., A.SSE.a, A.SSE.b, A.SSE., A.APR.4) Factor and solve polynomial functions, including special products like (x + y) 3, (x y) 3, etc. Review 7. to 7.3 Prove polynomial identities. Anderson School District Five Page 3 Copyright July, 03

14 Algebra CP and Algebra A/B Curriculum Pacing Guide Third Nine Weeks Unit 5 Polynomial Functions (A.APR.) Use the rational root theorem and the complex conjugate root theorem to find the zeros of a polynomial function. The Remainder Theorem Rational Room 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 Review Review Chapter 6 Study Guide Review for Test Unit Test Anderson School District Five Page 4 Copyright July, 03

15 Unit 6 Rational Functions Algebra CP and Algebra A/B Curriculum Pacing Guide Third Nine Weeks A.APR.6 A.REI. F.IF.7 F.BF.4 F.BF.4a Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. Unit 6 Rational Functions Identify and evaluate rational functions. (A.APR.6) Multiply and divide rational expressions including complex fractions. Worksheet Multiply and Divide Rational Exp (A.APR.6) Add and subtract rational expressions. Worksheet Review of Operations Worksheet More on Adding and Subtracting Worksheet Add and Subtract with Like Denominators Worksheet - Mixed Review of Operations (F.BF.4, F.BF.4a) Find the inverse of simple rational functions. (F.IF.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) (A.REI.) Solve rational equations. Worksheet More on Solving Rational Exp Worksheet Solving Rational Exp Anderson School District Five Page 5 Copyright July, 03

16 Algebra CP and Algebra A/B Curriculum Pacing Guide Third Nine Weeks Unit 6 Rational Functions Review Review Chapter 9 Study Guide Review Graphing and Operations Review Operations & Solving Rational Equations Review Unit Test Anderson School District Five Page 6 Copyright July, 03

17 Algebra CP and Algebra A/B Curriculum Pacing Guide Third Nine Weeks Unit 7 Exponential Functions & Logarithmic Functions A.SSE.a Interpret parts of an expression, such as terms, factors, and coefficients. A.SSE.b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(+r) n as the product of P and a factor not depending on P. A.CED. Create equations and inequalities in one variable and use them to solve problems. F.IF.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. F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. F.BF.b Combine standard function types using arithmetic operations. F.BF.4 Find inverse functions. F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = x 3 or f(x) = (x+)/(x-) for x. F.LE.4 For exponential models, express as a logarithm the solution to ab ct =d where a, c, and d are numbers and the base b. Unit 7 Exponential Functions & Logarithmic Functions (F.IF.6) Calculate and interpret the average rate of change of exponential functions over a specific interval. (F.IF.7e) Graph exponential functions using transformations. Worksheet Exponential Graphs Worksheet Exponential Eq with Like Bases Find the domain and range (in interval notation), intercepts, end behavior, and the equation of the horizontal asymptote for an exponential function. (F.IF.7e) Graph the inverse of the exponential function and define the logarithmic function. (F.LE.4) Find the domain and range (in interval notation), intercepts, end behavior, and the equation of the vertical asymptote for a logarithmic function. Worksheet Intro to Logs Anderson School District Five Page 7 Copyright July, 03

18 Algebra CP and Algebra A/B Curriculum Pacing Guide Third Nine Weeks Unit 7 Exponential Functions & Logarithmic Functions (F.LE.4) 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 (A.CED.) Use the definitions of exponential and logarithmic functions to solve equations. Classify an exponential function as representing a growth or a decay. Review st Half Through Log Properties Worksheet Basic Log Equations with No Calculator Worksheet Logs Worksheet Worksheet More on Logs (F.BF.4, F.BF.4a) Solve equations involving logarithms algebraically and graphically. (F.BF.4, F.BF.4a) Solve exponential equations using common logs algebraically and graphically. Review Log Equations and Exponential Equations using Logs Worksheet Exponential Eq with Unlike Bases (A.SSE.a, A.SSE.b, F.BF.b) Calculate the growth of investments under various conditions using exponential and natural exponential functions. Worksheet Compound Interest and Exp. Functions Worksheet Growth & Decay Solve for New Variable (A.SSE.a, A.SSE.b, F.BF.b) Write and evaluate exponential expressions to model growth and decay situations. Activity Shedding Light on the Subject Activity Spreading Rumors Worksheet More Word Problems Worksheet Word Problems Finding Other Variables Unit 7 will continue in the 4 th Nine Weeks Anderson School District Five Page 8 Copyright July, 03

19 Algebra CP and Algebra A/B Curriculum Pacing Guide Fourth Nine Weeks Unit 7 Exponential Functions & Logarithmic Functions Continued A.SSE.a Interpret parts of an expression, such as terms, factors, and coefficients. A.SSE.b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(+r) n as the product of P and a factor not depending on P. A.SSE.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not ), and use the formula to solve problems. For example, calculate mortgage payments. A.CED. Create equations and inequalities in one variable and use them to solve problems. F.IF.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. F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. F.BF.b Combine standard function types using arithmetic operations. F.BF.4 Find inverse functions. F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = x 3 or f(x) = (x+)/(x-) for x. F.LE.4 For exponential models, express as a logarithm the solution to ab ct =d where a, c, and d are numbers and the base b. Unit 7 Exponential Functions & Logarithmic Functions Continued (A.SSE.4) Calculate the sum of a finite geometric series. Use it to solve word problems (for example, calculate mortgage payments). Review Unit Test Quiz on Logs Jeopardy Review Station Rotation Quiz on Logarithms Anderson School District Five Page 9 Copyright July, 03

20 Unit 8 Trigonometric Functions Algebra CP and Algebra A/B Curriculum Pacing Guide Fourth Nine Weeks F.IF.7e F.BF.3 F.TF. F.TF. F.TF.5 F.TF.8 Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(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. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. Prove the Pythagorean identity sin (θ) + cos (θ) = and use it find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant. Unit 8 Trigonometric Functions (F.TF.) Define and understand radians. Convert between degrees and radians. (F.TF.) Draw and measure positive angles between 0 and in standard position using radian measure. (F.TF.) Define the unit circle and use it to find sine, cosine, and tangent function values. (F.TF.8) Prove and apply the Pythagorean identify (sin + cos = ) given one trig function value and the quadrant of the angle. (F.IF.7e, F.BF.3) Graph sine and cosine functions and identify the period, midline, and amplitude. (F.TF.5) Model periodical phenomena with sine and cosine functions. 3 Review Unit Test Anderson School District Five Page 0 Copyright July, 03

21 Unit 9 Inferences and Conclusions from Data Algebra CP and Algebra A/B Curriculum Pacing Guide Fourth Nine Weeks S.ID.4 S.IC. S.IC. S.IC.3 S.IC.4 S.IC.5 S.IC.6 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. Understand statistics as a process for making inferences to be made about population parameters based on a random sample from that population. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. Evaluate reports based on data. Unit 9 Inferences and Conclusions from Data (S.ID.4) Define and describe normal distributions and their properties See for great statistics lessons. Define a standard score and apply its formula to compare outcomes from different distributions. (S.ID.4) Define the standard normal distribution and use it to find areas under the standard normal curve (using calculator & table). (S.ID.4) Use the standard normal distribution to find probabilities for any normal distribution scenario. (S.IC.) Explain in context the difference between values describing a population and a sample. (S.IC.) Define and compare the different sampling methods (simple random, stratified, cluster, and systematic). Explain how well and why a sample represents the variable of interest from a population. Anderson School District Five Page Copyright July, 03

22 Algebra CP and Algebra A/B Curriculum Pacing Guide Fourth Nine Weeks Unit 9 Inferences and Conclusions from Data (S.IC.) Design simulations of random sampling (assign digits in appropriate proportions and use calculator or table to generate random numbers). Explain the outcomes in context of the population and the known proportions (S.IC.3) Describe and compare different data collection methods (surveys, observational studies, and experiments). Explain the necessity of randomization in each. (S.IC.6) Define the characteristics of experimental design (control, randomization, and replication). (S.IC.4) Use sample means and sample proportions to estimate population values. Conduct simulations of random sampling to gather sample means and sample proportions. Explain what the results mean about variability in a population and use results to calculate margins of error for these estimates. (S.IC.6) Given statistical reports, evaluate the experimental study design, how the data was gathered, what analysis (numerical or graphical) was used (ex: use of randomization, control, replication). (S.IC.5) Evaluate effectiveness and differences in two treatments based on data from randomized experiments. Explain in context. (S.IC.5) Use simulations to generate data simulating application of two treatments. Use results to evaluate significance of differences. See for great statistics lessons. Review and Unit Test Review for End of Course Exam End of Course Review End of Course Exam Anderson School District Five Page Copyright July, 03