Randolph County Curriculum Frameworks 2016 2017 Algebra II with Trigonometry First 9 weeks Chapter 2, Chapter 3, Chapter 12, 4.1 4.3 Standards I Can Statements Resources Recom mendati on / 21.) Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A CED2] 30. a. Graph square root, cube root, and piecewise defined functions, including step functions and absolute value functions. [F IF7b] 31.) Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F IF8] 32.) Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F IF9] 34.) 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. [F BF3] 1. I can write linear equations in standard form and slope intercept form when given two points, a point and the slope, or the graph of the equation 2. I can graph linear equations 3. I can graph piecewise defined functions, including step functions and absolute value functions 4. I can analyze transformations of functions 5. I can graph absolute value functions 6. I can graph 2 variable inequalities Book: Chapter 1 and Chapter 2 (suggested: 2.3, 2.4, CB 2.4, 2.6, 2.7, 2.8) 12 days Linear Systems: Chapter 3 Algebra II with Trigonometry 1
Standard I Can Statements Resource s Recom mendati on / 27. 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. [A REI11] 21. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.[a CED2] 22. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A CED3] 1) I can create equations in two or more variables to represent relationships between quantities. 2) I can write and use a system of inequalities to solve a real world problem. 3) I can recognize that the equations or inequalities represent the constraints of the problem. 4) I can solve a system of equations by using substitution or elimination 5) I can solve a system of inequalities by graphing. 6) I can create simple rational inequalities in one variable and use them to solve problems. 7) I can explain why the intersection of y = f(x) and y = g(x) is the solution of f(x) = g(x). 8) I can approximate solutions to linear equations by using technology to graph the equation, creating a table of values, or finding successive approximations. 9) I can interpret solutions as viable or nonviable options for modeling a problem. (Honors) 10) I can use Linear Programming to find the maximum and/or minimum to a real world problem. 11) I can solve systems of equations which have 3 variables, and can determine whether there are zero, one, or infinitely many solutions. Book: Chapter 3 (suggested 3.1, 3.2,.3, 3.4, 3.5) 12 Days Algebra II with Trigonometry 2
Matrices: Chapter 12 Standards I Can Statements Resource s Recommen dation / 7. Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. (Use technology to approximate roots.) [N VM6] 8. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. [N VM7] 9. Add, subtract, and multiply matrices of appropriate dimensions. [N VM8] 10. Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. [N VM9] 11. Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. [N VM10] 26. Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 3 or greater). [A REI9] 1. I can use matrices to represent data in context. 2. I can multiply a matrix by a scalar. 3. I can add subtract and multiply matrices when possible. 4. I can understand matrix multiplication is not commutative. 5. I can understand that the associative and distributive properties do apply. 6. I can calculate the determinant of 2x2 and 3x3 matrices. 7. Honors: I can calculate the determinant of a 3x3 matrix using expansion by minors. Book Chapter 12 (suggested 12.1, 12.2, 12.3, 12.4, 3.6) 10 days Quadratic Function Equations: Chapter 4 (4.1 4.3, 4.6) Algebra II with Trigonometry 3
Standards I Can Statements Resource s Recomme ndation / 20. 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. [A CED1] 21. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A CED2] 29. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [F IF5] 30. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. [F IF7] 31. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F IF8] 32. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F IF9] 33. Write a function that describes a relationship between two quantities. [F BF1] 34. 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. [F BF3] 1. I can create quadratic equations in one variable and use them to solve problems. 2. I can graph equations in two variables on a coordinate plane and label the axes and scales. 3. Given a function, I can identify intercepts in graphs and tables. 4. I can sketch a graph of a function given key features of a function. 5. I can relate the domain of a function to its graph and to the relationship it describes. 6. I can determine intercepts for a function given its equation. 7. I can determine intervals where a function is increasing and decreasing given its equation. 8. I can determine intervals where a function is positive or negative given its equation. 9. I can identify relative maximums and minimums given the equation of a function. 10. I can graph by hand functions given the equation 11. I can translate a given expression into equivalent forms designed to highlight different properties of the function. 12. I can write a function to describe a relationship between two quantities. 13. I can identify the different parts of an expression and explain their meaning within the context of a problem. Book: Chapter 4 (suggested 4.1, 4.2, 4.3, 4.6) 6 days Algebra II with Trigonometry 4
14. I can determine the domain and range of a quadratic function 15. I can 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. 16. I can convert from standard form of a quadratic to vertex form by completing the square. Second 9 weeks Chapter 4, Chapter 10, Chapter 5, Chapter 9 Algebra II with Trigonometry 5
Standards I Can Statements Resource s Recomme ndation / 20. 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. [A CED1] 21. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A CED2] Honors3. Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. [N CN3] Honors5.Extend polynomial identities to the complex numbers. [N CN8] 22. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A CED3] 25. Recognize when the quadratic formula gives complex solutions, and write them as a ± bi for real numbers a and b. [A REI4b] (17 b from Algebra I) 31. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F IF8] 34. 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 I can create quadratic equations in one variable and use them to solve problems. I can determine when the solutions to a quadratic equation will be complex and can write the solutions in the form a±bi. I can create quadratic inequalities in one variable and use them to solve problems. I can graph equations in two variables on a coordinate plane and label the axes and scales. Given a function, I can identify intercepts in graphs and tables. I can sketch a graph of a function given key features of a function. I can determine intercepts for a function given its equation. I can determine intervals where a function is increasing and decreasing given its equation. I can determine intervals where a function is positive or negative given its equation. I can identify relative maximums and minimums given the equation of a function. Book: Chapter 4 (suggested 4.4, 4.5, 4.6, 4.7, 4.8, 4.9) 11 days Algebra II with Trigonometry 6
from their graphs and algebraic expressions for them. [F BF3] 12. Interpret expressions that represent a quantity in terms of its context. [A SSE1] a. Interpret parts of an expression such as terms, factors, and coefficients. [A SSE1a] 17. 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 APR3] 1. Know there is a complex number i such that i2 = 1, and every complex number has the form a + bi with a and b real. [N CN1] 2. Use the relation i 2 = 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. [N CN2] 4. Solve quadratic equations with real coefficients that have complex solutions. [N CN7] I can graph by hand functions given the equation I can translate a given expression into equivalent forms designed to highlight different properties of the function. I can identify the different parts of an expression and explain their meaning within the context of a problem. I can identify the zeros of polynomials when the polynomial is factored. I know that there is a complex number i such that i 2 = 1. I know that every number is a complex number which can be written as a+bi, where a and b are real numbers. I can apply the fact that i 2 = 1. I can use the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. I can use conjugates to divide complex numbers. I can solve quadratic equations with real coefficients that have complex solutions a + bi and a bi. I can use polynomial identities to write equivalent expressions for complex numbers. I can solve quadratic systems graphically with and without technology Algebra II with Trigonometry 7
I can solve quadratic systems algebraically with and without technology I can solve quadratic equations by completing the square I can solve quadratic equations by using the Quadratic Formula I can find the discriminant and use it to determine the number of solutions for a quadratic equation I can graph a system of quadratic inequalities with or without technology I can 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. Conic Sections: Chapter 10 Standards I Can Statements Resource s Recomme ndation / 28.) Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second degree equations. (Alabama) a. Formulate equations of conic sections from their determining characteristics. (Alabama) Example: Write the equation of an ellipse with center (5, 3), a horizontal 1. I can identify conic sections (e.g., parabola, circle, ellipse, hyperbola) from their equations in standard form 2. I can graph circles and parabolas and their translations from given equations 3. I can graph circles and parabolas and their Book: Chapter 10 (suggested 10.1, 10.2, 10.3, 10.4, 10.5) 10 days Algebra II with Trigonometry 8
major axis of length 10, and a minor axis of length 4. 29. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [F IF5] 30. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. [F IF7] 31. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F IF8] 34. 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. [F BF3] translations from given properties 4. I can identify and write equations for circles and parabolas from given characteristics and equations 5. I can sketch a graph of a function given key features of a function. 6. I can relate the domain of a function to its graph and to the relationship it describes. 7. I can determine intercepts for a function given its equation. 8. I can graph by hand functions given the equation 9. I can 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. Polynomials and Polynomial Functions: Chapter 5 Standard I Can Statements Resource s Recomme ndation / 6. Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. [N CN9] 13. Use the structure of an expression to identify ways to rewrite it. [A SSE2] 15.) Understand that polynomials form a system analogous to the 1) I can break down expressions and make sense of the multiple factors and terms by explaining the meaning of the individual parts. 2) I can rewrite algebraic expressions in Book:Chapter 5 (suggested 5.1, 5.2, 5.3, 5.4, 5.5, 5.6) 13 days Algebra II with Trigonometry 9
integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. [A APR1] 16. 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). [A APR2] 18. Prove polynomial identities and use them to describe numerical relationships. [A APR4] Example: The polynomial identity ( x 2 + y 2 ) 2 = ( x 2 y 2 ) 2 + (2 xy) 2 can be used to generate Pythagorean triples 19.) 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. [A APR6] a variety of equivalent forms using factoring, combining like terms, applying properties, or using other operations. 3) I can use factoring techniques such as common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor completely. 4) I understand that polynomial identities include, but are not limited to, the product of the sum and difference of two terms, the difference of two squares, the sum and difference of two cubes, the square of a binomial, etc. 5) I can add, subtract and multiply polynomials. 6) I understand that a is a root of a polynomial function if and only if x a is a factor of the function. 7) I understand how the Remainder Theorem relates to the factoring of a quadratic function. 8) I understand the Remainder Theorem. 9) I understand the Fundamental Theorem of Algebra which states that the number of complex solutions to a polynomial equation is the same as the degree of the polynomial. 10) I can use the zeros of polynomials to sketch a graph of the function defined by the polynomial. Algebra II with Trigonometry 10
11) Given a function, I can identify intercepts in graphs and tables. 12) Given a function, I can identify intervals where a graph is increasing, decreasing, positive, or negative. 13) Given a function, I can identify symmetry given equations, graphs and tables. 14) Given a function, I can identify end behavior given equations, graphs and tables. 15) I can sketch a graph of a function given key features of a function. 16) I can relate the domain of a function to its graph and to the relationship it describes. 17) I can determine intercepts for a function given its equation. 18) I can use technology to graph more complicated functions. 19) I can graph polynomial functions by hand, identifying zeros when factorable and showing end behavior. 20) I can recognize even and odd functions from graphs and equations. 21) I can use technology and experimentation to illustrate the effect on the graph of f(x) for f(x) + k, k f(x), f(kx), and f(x + k). 22) I can approximate solutions to polynomial equations by using technology to graph the equation, creating a table of values, or finding Algebra II with Trigonometry 11
23) I can evaluate and simplify polynomial expressions 24) I can solve polynomial equations 25) I can solve quadratic equations with real coefficients that have complex solutions 26) I can determine the number of rational zeros of a polynomial function 27) I use technology to find the minimum and maximum values of a polynomial function Sequences and Series: Chapter 9 Standards I Can Statements Resources Recomm endation / 14. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. [A SSE4] 1. I can derive the formula for the sum of a finite geometric series when the common ratio is not 1. 2. I can use the formula for a finite geometric series to solve real world problems. 3. I can calculate mortgage payments. 4. I can derive the formula for the sum of a finite arithmetic series 5. I can use the formula for a finite arithmetic series to solve real world problems. 6. I can find the nth term of an arithmetic or geometric sequence. 7. I can find the position of a given term of an arithmetic or geometric sequence. 8. I can find the sum of a finite arithmetic or geometric series. Book: Chapter 9 (suggested 9.1, 9.2, 9.3, 9.4, 9.5) 8 days Algebra II with Trigonometry 12
9. I can use sequences and series to solve real world problems. 10. I can use sigma notation to express sums. Third 9 weeks Chapter 8, Chapter 6, Chapter 7 Standards I Can Statements Resources Recomm endatio n / 21. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A CED2] 1. I can graph equations in two variables on a coordinate plane and label the axes and scales. Book: Chapter 6 and Chater 8 25 days Algebra II with Trigonometry 13
23. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [A CED4] 30. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. [F IF7] 30a. Graph square root, cube root, and piecewise defined functions, including step functions and absolute value functions 33. Write a function that describes a relationship between two quantities. [F BF1] 34. 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. [F BF3] 12. Interpret expressions that represent a quantity in terms of its context. [A SSE1] a. Interpret parts of an expression such as terms, factors, and coefficients. [A SSE1a] b. Interpret complicated expressions by viewing one or more of their parts as a single entity. [A SSE1b] 13. Use the structure of an expression to identify ways to rewrite it. [A SSE2] 24. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A REI2] 27. 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. [A REI11] 35. Find inverse functions. [F BF4] a. 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. [F BF4a] Example: f( x) =2 x 3 or ( x) = ( x+1)/( x 1) for x 1. 2. I can solve multi variable formulas or literal equations for a specific variable. 3. I can use technology to graph more complicated functions. 4. I can write a function to describe a relationship between two quantities. 5. I can explain the difference between the graph of f(x) and the graph of f(x) + k for both positive and negative k values. 6. I can explain the difference between the graph of f(x) and the graph of k f(x) for both positive and negative k values. 7. I can explain the difference between the graph of f(x) and the graph of f(x +k), for both positive and negative k values. 8. I can interpret expressions that represent a quantity in terms of its context. 9. I can identify the different parts of an expression and explain their meaning within the context of a problem 10. I can break down expressions and make sense of the multiple factors and terms by explaining the meaning of the individual parts 11. I can rewrite simple rational expressions, 12. I can use a computer algebra system to rewrite more complicated rational expressions and assist with building a broader conceptual understanding. 13. I can add, subtract, multiply and divide rational expressions. 14. I can provide examples to illustrate how extraneous solutions may arise for a rational or radical equation. Algebra II with Trigonometry 14
15. Given a function, I can identify intercepts in graphs and tables. 16. I can create simple rational inequalities in one variable and use them to solve problems. 17. I can solve multi variable formulas or literal equations for a specific variable 18. I can solve simple radical equations, and recognize extraneous solutions. 19. I can write a function to describe a relationship between two quantities. 20. I can write an expression for the inverse of f(x) = c by interchanging the values of the dependent and independent variables and solving for the dependent variable. 21. I can graph square and cube root functions by hand. 22. I can translate a given expression into multiple functions designed to highlight different properties of the function. 23. I can find the inverse of a function algebraically. Exponential and Logarithmic Functions: Chapter 7 Standard I Can Statements Resources Recomm endatio n / 30c. Graph exponential and logarithmic functions showing intercepts and end behavior; and trigonometric functions, 1. I can break down expressions and make sense of the multiple factors and terms by Book: Chapter 7 (suggested 7.1, 7.2, 15 days Algebra II with Trigonometry 15
showing period, midline, and amplitude. [F IF7c] 33. Write a function that describes a relationship between two quantities. [F BF1] 33a. Combine standard function types using arithmetic operations. [F BF1b] Example for 33a: Build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the mode 30.) Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases. [F IF7] c. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. [F IF7e] 36.) For exponential models, express as a logarithm the solution to ab ct = d where a, c, and d are numbers, and the base b is 2, 10, or e; evaluate the logarithm using technology. [F LE4 ] explaining the meaning of the individual parts. 2. I can create equations in two or more variables to represent relationships between quantities. 3. I can graph exponential functions by hand showing intercepts and end behavior. 4. I can graph logarithmic functions by hand showing intercepts and end behavior. 5. I can translate a given expression into multiple functions designed to highlight different properties of the function. 6. I can combine standard function types, such as linear and exponential, using arithmetic operations. 7. I can compare the key features of two functions presented algebraically, graphically, in tables, or using verbal descriptions. 8. I can use technology to evaluate the logarithm that is the solution to ab ct = d where a, c, and d are numbers, and the base b is 2, 10, or e. 9. I can approximate solutions to exponential equations by using technology to graph the equation, creating a table of values, or finding successive approximations. 10. I can approximate solutions to logarithmic equations by using technology to graph the equation, creating a table o f values, or finding successive approximations. 7.3, 7.4, 7.5, 7.6) Algebra II with Trigonometry 16
Algebra II with Trigonometry 17
Fourth 9 weeks Chapter 13, Chapter 11, Chapter 14 Standards I Can Statements Resources Recom mendati on / 37. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. [F TF1] 38. 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. [F TF2] 39. Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions. [F TF4] 40. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. [F TF5] 30 c. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. [F IF7] 1. I can describe the radian measure of an angle as the length of the arc on the unit circle subtended by the angle. 2. I can use the unit circle to explain how trigonometric functions extend to all real numbers 3. I can explain how radian measures of angles rotated counterclockwise in a unit circle are in a one to one correspondence with the positive real numbers, and that angles rotated clockwise in a unit circle are in a one to one correspondence with the negative real numbers. 4. I can define the six trigonometric functions using ratios of the sides of a right triangle. 5. I can define the six trigonometric functions using Book: Chapter 13 and 14.3 14.5 15 days Algebra II with Trigonometry 18
coordinates on the unit circle. 6. I can define the six trigonometric functions using the reciprocal of other functions. 7. I can identify a trigonometric function to model periodic phenomena with a specific amplitude, frequency, and midline. 8. I can find radian measure of an angle as the length of the arc on the unit circle subtended by the angle 9. I can use the Law of Sines and Cosines to solve non right triangles 10. I can use the Law of Sines and Cosines to solve real world problems 11. I can graph sine and cosine functions with and without technology. Probability and Data Analysis: Chapter 11 Standard I Can Statements Resource s Recom mendat ion / 37. Use the mean and standard deviation of 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, Construct two way frequency tables of data for two categorical variables. Interpret two way frequency tables of data Book Chapter 5.7 15 days Algebra II with Trigonometry 19
spreadsheets and tables to estimate areas under the normal curve [S ID4] Honors 41. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S MD6] Honors 42. Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).[s MD7] 43. Describe events as subsets of a sample space (the set of outcomes), using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ( or, and, not ). [S CP1] 45. Construct and interpret two way frequency tables of data when two categories are associated with each object being classified. Use the two way table as a sample space to decide if events are independent and to approximate conditional probabilities. [S CP4] Example: Collect data from a random sample of students in your school on their favorite subject among mathematics, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. 46. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. [S CP5] Example: Compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. 50. Use permutations and combinations to compute probabilities of compound events and solve problems. [S CP9] 48. Apply the Addition Rule, P(A or B) = P(A) + P(B) P(A and B), and interpret the answer in terms of the model. [S CP7] 49. Apply the general Multiplication Rule in a uniform probability model, P(A and B) for two categorical variables. Use the probabilities from the table to evaluate independence of two variables. The student will be able to recognize and explain the concepts of independence and conditional probability in everyday situations. Identify situations as appropriate for the use of permutation or combination to calculate probabilities Use permutations and combinations in conjunction with other probability method to calculate probabilities of compound events and solve problems Identify two events as disjoint (mutually exclusive). Calculate probabilities using the Addition Rule. Interpret the probability in context. Calculate the probabilities using the General Multiplication Rule. Interpret the results in context. Define and calculate conditional probabilities Use the Multiplication Principal to decide if two events are independent Use the Multiplication Principal to calculate conditional probabilities. Calculate the conditional probabilities 11.1 to 11.8 and 11.10 11.9 is not in the course of study. Algebra II with Trigonometry 20
= P(A)P(B A) = P(B)P(A B), and interpret the answer in terms of the model. [S CP8] Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. [S CP2] 44. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. [S CP3] 47. Find the conditional probability of A given B as the fraction of B s outcomes that also belong to A, and interpret the answer in terms of the model. [S CP6] using the definition the conditional probability of A given B as the fractions of B s outcomes that also belong to A. Interpret the probability in context. The student will be able to make decisions based on expected values. The student will be able to explain in context the decisions made based on expected values. I can use the counting principle to find the number of ways an event can happen. I can use the Binomial Theorem to expand a binomial of any power. Trigonometric Identities and Equations: Chapter 14 Standards I Can Statements Resources Recom mendat ion / 37. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. [F TF1] 38. 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. [F TF2] 39. Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions. [F TF4] 1. I can describe the radian measure of an angle as the length of the arc on the unit circle subtended by the angle. 2. I can use the unit circle to explain how trigonometric functions extend to all real numbers 3. I can define the six trigonometric functions using ratios Book Chapter 14 10 days Algebra II with Trigonometry 21
40. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. [F TF5] 30 c. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. [F IF7e] of the sides of a right triangle. 4. I can define the six trigonometric functions using coordinates on the unit circle. 5. I can find radian measure of an angle as the length of the arc on the unit circle subtended by the angle 6. I can use the Law of Sines and Cosines to solve non right triangles 7. I can use the Law of Sines and Cosines to solve real world problems 8. I can evaluate inverse trigonometric functions 9. I can solve trigonometric equations. 10. I can find missing sides and angles of right triangles 11. I can verify and use sum and difference identities 12. I can verify and use double and half angle identities. Algebra II with Trigonometry 22