ALGEBRA AND TRIGONOMETRY
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1 ALGEBRA AND TRIGONOMETRY correlated to the Alabama Course of Study for Algebra 2 with Trigonometry CC2 6/
2 Algebra and Trigonometry 2004 correlated to the Number and Operations Students will: 1. Determine the relationships of subsets of complex numbers. Example: using Venn diagrams or tree diagrams to show how subsets of complex numbers are related PE/IAE: Student Success Organizer, Section Simplify expressions involving complex numbers, using order of operations and including conjugate and absolute value. Examples: simplifying v-8, (4-2i) 2, and (3+i) / (3-i) PE/IAE: IAE Only: P.1 P Student Success Organizer, Sections P.1 P
3 Algebra 3. Analyze families of functions, including shifts, reflections, and dilations of y = x/k (inverse variation), y = kx (direct variation/linear), y = [x] (greatest integer), y = x 2 (quadratic), y = ax (exponential), and y = logax (logarithmic). Example: comparing the graphs of y = 2 x, y = 2 x + 1, y = 2 x + 1, and y = -2 x PE/IAE: Student Success Organizer, Sections Identifying the domain and range of a relation given its graph, a table of values, or its equation, including those with restricted domains Example: finding the domain of y = 1/ (x - 3) or y = vx - 2 PE/IAE: IAE Only: Student Success Organizer, Sections
4 Identifying real-world situations corresponding to families of functions PE/IAE: Student Success Organizer, Sections Determine approximate real zeros of functions graphically and numerically and exact real zeros of polynomial functions. PE/IAE: Student Success Organizer, Sections Using the zero product property, completing the square, and the quadratic formula PE/IAE: IAE Only: P Student Success Organizer, Sections P
5 Deriving the quadratic formula PE/IAE: Identify the characteristics of quadratic functions from their roots, graphs, or equations. PE/IAE: Student Success Organizer, Sections Generating an equation when given its roots or graph PE/IAE: Graphing a function when given its equation Examples: graphing equations of the form y = a(x-h) 2 + k; graphing equations of the form y = ax 2 + bx + c PE/IAE: Student Success Organizer, Sections
6 Determining the maximum or minimum values of quadratic functions both graphically and algebraically PE/IAE: Student Success Organizer, Sections Applying functions to real-world problems PE/IAE: Student Success Organizer, Sections Perform operations on functions, including addition, subtraction, multiplication, division, and composition. PE/IAE: IAE Only: Student Success Organizer, Section 2.6 5
7 Determining the inverse of a function or a relation PE/IAE: Student Success Organizer, Section 2.7 Performing operations on polynomial and rational expressions containing variables Example: simplifying 3 / (x + 5) + 5 / (x 2 + 6x + 5) PE/IAE: P.2 P.3 P.5 P.6 Student Success Organizer, Sections P.2 P.3 P.5 P.6 Constructing graphs by analyzing their functions as sums, differences, or products PE/IAE:
8 7. Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratics over the complex numbers, as well as simple trigonometric, exponential, and logarithmic functions. Example: solving x 2-8x > -12, 3 x = 81, 2 sin 2 x + sin x = 0, or log x 2 = 5 PE/IAE: Student Success Organizer, Sections Solving equations using laws of exponents, including rational and irrational exponents PE/IAE: Expressing the solution of an equation, inequality, or applied problem as a graph on a number line or by using set or interval notation PE/IAE: IAE Only: P Student Success Organizer, Sections P
9 8. Solve systems of linear equations or inequalities in two or three variables using algebraic techniques, including those involving matrices. Example: solving a system of linear equations using augmented matrices and row operations, matrix operations of a graphing calculator, or substitution PE/IAE: Student Success Organizer, Sections 9.1, 9.2, 9.3, 10.1, 10.5; Chapter 10 Project: Solving Systems of Equations Evaluating the determinant of a 2x2 or 3x3 matrix PE/IAE: IAE Only: Student Success Organizer, Section 10.4 Solving word problems involving real-life situations PE/IAE:
10 9. Graph trigonometric functions of the form y=a sin(bx), y=a cos(bx), and y=a tan(bx). PE/IAE: Determining period and amplitude of sine, cosine, and tangent functions from graphs or basic equations Example: solving problems involving harmonic motion PE/IAE: IAE Only: Determining specific unit circle coordinates associated with special angles PE/IAE: Geometry 10. Solve general triangles, mathematical problems, and real-world applications using the Law of Sines and the Law of Cosines. PE/IAE: Student Success Organizer, Sections
11 Deriving formulas for Law of Sines and Law of Cosines PE/IAE: Determining area of oblique triangles PE/IAE: Student Success Organizer, Sections 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. PE/IAE: Verify simple trigonometric identities using Pythagorean and/or reciprocal identities. Example: verifying cos 2 a + tan 2 a cos 2 a = 1 PE/IAE: Student Success Organizer, Section
12 Data Analysis and Probability 13. Use different forms of representation to compare characteristics of data gathered from two populations. PE/IAE: Evaluating the appropriateness of the design of an experimental study This standard is taught in a statistics course. Describing how sample statistics reflect values of population parameters This standard is taught in a statistics course. 14. Determine an equation of linear regression from a set of data. PE/IAE: Appendix A.3; Chapter 9 Project: Fitting Models to Data Examining data to determine if a linear, quadratic, or exponential relationship exists and to predict outcomes PE/IAE: Calculate probabilities of events using the laws of probability. PE/IAE: Student Success Organizer, Section
13 Using permutations and combinations to calculate probabilities PE/IAE: IAE Only: Student Success Organizer, Section 11.6 Calculating conditional probability PE/IAE: , Calculating probabilities of mutually exclusive events, independent events, and dependent events PE/IAE: Student Success Organizer, Section
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