If You Have Any Questions, Please Contact Melissa Shields s1

July 2, 2013

Below is a checklist for the Algebra II with Trig Course of Study. You can utilize it as a bird’s- eye view of course expectations and/or as a framework to ensure you’ve addressed all content requirements. Feel free to edit it to suit your needs. You may wish to delete provided examples to conserve space.

If you have any questions, please contact Melissa Shields.

2010 Math Course of Study and Resources: http://www.ecboe.org/mathccrs

Lessons for every standard, as well as really helpful descriptions of each (“unpacking” the standards). Click http://alex.state.al.us/browseMath.php and then the Alabama Insight graphic. Etowah County user name: guest28. Password: guest.

ECBOE Teachers’ Corner Math Website: http://www.ecboe.org/math

Curriculum Correlations – Mark the pages in your text (or other curricular resources) that relate to this standard. Add links, reminders, tools, etc. to help remind you next year how best to teach that standard.

Additional Column Heading Suggestions: AMSTI Strategies, Standards Revisited Mathematical Practice Standards, Project-Based Lessons, Interdisciplinary Lessons

Etowah County Schools – Algebra II with Trig State Standards (Correlated with ACT QualityCore EOCT) Glencoe Correlations added in blue print (8-25-13) (*)Skills will likely need continued attention in higher grades. NUMBER AND QUANTITY – The Real Number System EOC Glencoe Curriculum T Correlations Correlation Corr. Perform arithmetic operations with complex numbers. 2 Students will be 1. Know there is a complex number i such that i = –1, and every complex C1a 4.4 required to find number has the form a + bi with a and b real. [N-CN1] quotients of complex numbers on QualityCore assessment. 2. Use the relation i2= –1 and the commutative, associative, and distributive C1b 4.4 properties to add, subtract, and multiply complex numbers. [N-CN2] 3. (+) Find the conjugate of a complex number; use conjugates to find moduli C1a 4.4 and quotients of complex numbers. [N-CN3] Use complex numbers in polynomial identities and equations. (Polynomials with real coefficients.) 4. Solve quadratic equations with real coefficients that have complex E1c 4.5 solutions. [N-CN7] Example: x2 + 4 5. Extend polynomial identities to the complex numbers. [N-CN8] 4.5 = (x + 2i)(x-2i) Use the 6. Know the Fundamental Theorem of Algebra; show that it is true for F2c 4.6 discriminant quadratic polynomials. [N-CN9] E1b to analyze the zeros. Vector and Matrix Quantities EOC Glencoe Curriculum T Correlations Correlation Corr. s Perform operations on matrices and use matrices in applications. 7. (+) Use matrices to represent and manipulate data, e.g., to represent I1f 3.5 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 I1f 3.6 when all of the payoffs in a game are doubled. [N-VM7] I1b I1f 9. (+) Add, subtract, and multiply matrices of appropriate dimensions. I1a 3.5 [N-VM8] I1f 10. (+) Understand that, unlike multiplication of numbers, matrix I1a- 3.5 multiplication for square matrices is not a commutative operation, but b still satisfies the associative and distributive properties. [N-VM9] I1f 11. (+) Understand that the zero and identity matrices play a role in I1c-e 3.8 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] ALGEBRA – Seeing Structure in Expressions EOC Glencoe Curriculum T Correlations Correlation Corr. s Interpret the structure of expressions. (Polynomial and rational.) Expressions are 12. Interpret expressions that represent a quantity in terms of its context.* [A- G1a 4.1 investigated in SSE1] 2.6 Algebra I. Focus should be on a. Interpret parts of an expression such as terms, factors, and coefficients. [A- 4.6 using the expressions SSE1a] to solve equations and b. Interpret complicated expressions by viewing one or more of their parts as apply. a single entity. [A-SSE1b] 13. Use the structure of an expression to identify ways to rewrite it. [A-SSE2] F1b 4.5 G1c 6.5 Write expressions in equivalent forms to solve problems. 14. Derive the formula for the sum of a finite geometric series (when the 10.2 common ratio is not 1), and use the formula to solve problems.* [A-SSE4] 10.3 Example: Calculate mortgage payments. ALGEBRA – Arithmetic with Polynomials and Rational Expressions EOC Glencoe Curriculum T Correlations Correlation Corr. s Perform arithmetic operations on polynomials. (Beyond quadratic.) Adding and 15. Understand that polynomials form a system analogous to the integers; A1b 5.1 subtracting namely, they are closed under the operations of addition, subtraction, and F1a are covered in Algebra I. multiplication; add, subtract, and multiply polynomials. [A-APR1] Understand the relationship between zeros and factors of polynomials. 16. Know and apply the Remainder Theorem: For a polynomial p(x) and a F1a- 5.6 number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if b (x – a) is a factor of p(x). [A-APR2] F2c Teach Rational 17. Identify zeros of polynomials when suitable factorizations are available, F1b 5.7 Root and use the zeros to construct a rough graph of the function defined by the F2a- Theorem polynomial. [A-APR3] b E1a F2d Use polynomial identities to solve problems. For example: 18. Prove polynomial identities and use them to describe numerical 4.3 special relationships. [A-APR4] 4.6 cases such as factoring 5.5 of cubics; difference of squares, etc. (5.5) Rewrite rational expressions. (Linear and quadratic denominators.) 19. Rewrite simple rational expressions in different forms; write a(x)/b(x) in F1b 5.2 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] Creating Equations* EOC Glencoe Curriculum T Correlations Correlation Corr. s Create equations that describe numbers or relationships. (Equations using all available types of expressions, including simple root functions.) Include 20. Create equations and inequalities in one variable and use them to solve D2b 4.5 completing the problems. Include equations arising from linear and quadratic functions, and E1a (and square with and without simple rational and exponential functions. [A-CED1] E1d throughout technology. (4.5) E2a book) G1a With and without 21. Create equations in two or more variables to represent relationships D2a- 3.1 technology. between quantities; graph equations on coordinate axes with labels and b 3.2 scales. [A-CED2] D1c 4.2 E1d 6.3 E2a E2c With and without 22. Represent constraints by equations or inequalities, and by systems of D2a 3.1 technology equations and/or inequalities, and interpret solutions as viable or nonviable D2b 3.3 options in a modeling context. [A-CED3] E2c Example: Represent inequalities describing nutritional and cost constraints on combinations of different foods. 23. Rearrange formulas to highlight a quantity of interest, using the same 1.3 reasoning as in solving equations. [A-CED4] 4.6 Example: Rearrange Ohm’s law V = IR to highlight resistance R. Reasoning with Equations and Inequalities EOC Glencoe Curriculum T Correlations Correlation Corr. s Understand solving equations as a process of reasoning and explain the reasoning. (Simple rational and radical.) Include 24. Solve simple rational and radical equations in one variable, and give G1b- 6.5 simplifying examples showing how extraneous solutions may arise. [A-REI2] g 6.6 rational 6.7 exponents. (6.6) 8.6 Solve equations and inequalities in one variable. 25. Recognize when the quadratic formula gives complex solutions, and write 4.6 them as a ± bi for real numbers a and b. [A-REI4b] Solve systems of equations. Include solving 26. (+) Find the inverse of a matrix if it exists and use it to solve systems of I1e 3.8 systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). equations with three [A-REI9] variables algebraically. (3.4 and 3.7) Represent and solve equations and inequalities graphically. (Combine polynomial, rational, radical, absolute value, and exponential functions.) Solve linear 27. Explain why the x-coordinates of the points where the graphs of the D1a- 3.1 inequalities using equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = b absolute value. (1.6) g(x); find the solutions approximately, e.g., using technology to graph the Solve compound inequalities. (1.6) 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] Conic Sections EOC Glencoe Revisited T Correlations Corr. Understand the graphs and equations of conic sections. (Emphasize understanding graphs and equations of circles and parabolas.) 28. Create graphs of conic sections, including parabolas, hyperbolas, E3a- Chapter 9 d (emphasize ellipses, circles, and degenerate conics, from second-degree equations. general Example: Graph x2 – 6x + y2 – 12y + 41 = 0 or y2 – 4x + 2y + 5 = 0. characteristics of graphs & a. Formulate equations of conic sections from their determining eq of circles characteristics. and parabolas); more in-depth in Precal FUNCTIONS – Interpreting Functions EOC Glencoe Revisited T Correlations Corr. Interpret functions that arise in applications in terms of the context. (Emphasize selection of appropriate models.) 29. Relate the domain of a function to its graph and, where applicable, to the E2a- 2.1 quantitative relationship it describes.* [F-IF5] b 8.3 Example: If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. Analyze functions using different representations. (Focus on using key features to guide selection of appropriate type of model function.) 30. Graph functions expressed symbolically, and show key features of the F2d 2.6, 2.7 graph, by hand in simple cases and using technology for more complicated G2a 6.3, 6.4 cases.* [F-IF7] 5.4, 5.7 7.1, 7.3 a. Graph square root, cube root, and piecewise-defined functions, including 12.7, 12.8 step functions and absolute value functions. [F-IF7b] b. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. [F-IF7c] c. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. [F-IF7e] For example: 31. Write a function defined by an expression in different but equivalent E3a- 4.2, 4.3 Changing forms to reveal and explain different properties of the function. [F-IF8] d 4.5, 4.7 from standard form to vertex form. (4.2, 4.7) 32. Compare properties of two functions each represented in a different way 2.2 (algebraically, graphically, numerically in tables, or by verbal descriptions). [F- 2.7 IF9] Example: Given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. FUNCTIONS – Building Functions EOC Glencoe Curriculum T Correlations Correlation Corr. s Build a function that models a relationship between two quantities. (Include all types of functions studied.) Include 33. Write a function that describes a relationship between two quantities.* C1d 6.1 composition [F-BF1] and determining domain and a. Combine standard function types using arithmetic operations. [F-BF1b] range. Example: 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 model. Build new functions from existing functions. (Include simple radical, rational, and exponential functions; emphasize common effect of each transformation across function types.) 34. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and E2b 2.7, 4.7 f(x + k) for specific values of k (both positive and negative); find the value of k 5.3, 6.3 given the graphs. Experiment with cases and illustrate an explanation of the 7.1, 7.3 effects on the graph using technology. Include recognizing even and odd 8.3, 12.8 functions from their graphs and algebraic expressions for them. [F-BF3] f(x) = c does not 35. Find inverse functions. [F-BF4] 6.2 imply the a. Solve an equation of the form f(x) = c for a simple function f that has an constant function. inverse, and write an expression for the inverse. [F-BF4a] FUNCTIONS – Linear, Quadratic, and Exponential Models* EOC Glencoe Curriculum T Correlations Correlation Corr. s Construct and compare linear, quadratic, and exponential models and solve problems. (Logarithms as solutions for exponentials.) ct Include graphing 36. For exponential models, express as a logarithm the solution to ab = d G2b 7.1, 7.2 exponential and where a, c, and d are numbers, and the base b is 2, 10, or e; evaluate the 7.3, 7.8 logarithmic functions logarithm using technology. [F-LE4] with and without technology. (7.1) FUNCTIONS – Trigonometric Functions EOC Glencoe Curriculum T Correlations Correlation Corr. s Extend the domain of trigonometric functions using the unit circle. 37. Understand radian measure of an angle as the length of the arc on the unit 12.2, 12.6 circle subtended by the angle. [F-TF1] 38. Explain how the unit circle in the coordinate plane enables the extension of 12.6 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 12.1 triangle, coordinates on the unit circle, and the reciprocal of other functions. Model periodic phenomena with trigonometric functions. 40. Choose trigonometric functions to model periodic phenomena with 12.7, 12.8 specified amplitude, frequency, and midline.* [F-TF5] STATISTICS AND PROBABILITY – Using Probability to Make EOC Glencoe Curriculum T Correlations Correlation Decisions Corr. s Use probability to evaluate outcomes of decisions. (Include more complex situations.) 41. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a H1a- 11.4 random number generator). [S-MD6] f 42. (+) Analyze decisions and strategies using probability concepts (e.g., H1a- 11.3, 11.4 product testing, medical testing, pulling a hockey goalie at the end of a game). f 11.6 [S-MD7] STATISTICS AND PROBABILITY - Conditional Probability and the EOC Glencoe Curriculum T Correlations Correlation Rules of Probability Corr. s Understand independence and conditional probability and use them to interpret data. (Link to data from simulations or experiments.) 43. Describe events as subsets of a sample space (the set of outcomes), using 0.5 characteristics (or categories) of the outcomes, or as unions, intersections, or 0.6 complements of other events (“or,” “and,” “not”). [S-CP1] 44. Understand the conditional probability of A given B as P(A and B)/P(B), H1f 0.5 and interpret independence of A and B as saying that the conditional 11.3 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] 45. Construct and interpret two-way frequency tables of data when two H1d 0.5 categories are associated with each object being classified. Use the two-way H1f 0.6 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 H1d 0.5 independence in everyday language and everyday situations. [S-CP5] H1f 0.6 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. Use the rules of probability to compute probabilities of compound events in a uniform probability model. 47. Find the conditional probability of A given B as the fraction of B’s H1f 0.6 outcomes that also belong to A, and interpret the answer in terms of the model. [S-CP6] 48. Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret H1d 0.5 the answer in terms of the model. [S-CP7] 49. (+) Apply the general Multiplication Rule in a uniform probability model, H1d 0.6 P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. [S-CP8] 50. (+) Use permutations and combinations to compute probabilities of H1b 0.4 compound events and solve problems. [S-CP9]

Updated July 2013

Quick Chart – Copied from ALEX http://alex.state.al.us/ccrs/node/76