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Resource T=Textbook O=Other Resource Standardized Tests Graduation Exam Algebra II with Trigonometry Algebra II Date (O=Ongoing) Year: ___________ Continuum of Skills Blount County Schools Course: Algebra II and Algebra II with Trigonometry Math Course of Study Number and Operations 1 1 X 2 2 X 3 3 X Determine the relationships among the subsets of complex numbers. Example: using Venn diagrams or tree diagrams to show how subsets of complex numbers are related Simplify expressions involving complex numbers, using order of operations and including conjugate and absolute value. Example: 2 simplifying -8 , (4-2i) , and 3+i 3+i Algebra Analyze families of functions, including shifts, reflections, and dilations of y =k/x 2 x (inverse variation), y=kx (direct variation/linear), y=x (quadratic), y=a (exponential), and y=log x (logarithmic). a X X X 4 X 4 X X 5 X 5 X X X X X X X X X 6 X 6 X Example: x x x+1 x comparing the graphs of y=2 , y=2 +1 , y=2 , and y=-2 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= x-2 Identifying real-world situations corresponding to families of functions Determine approximate real zeros of functions graphically and numerically and exact real zeros of polynomial functions. Using completing the square, the zero product property, and the quadratic formula Deriving the quadratic formula Identifying the characteristics of quadratic functions from their roots, graphs, or equations. Writing an equation when given its roots or graph Generating an equation when given its roots or graph Graphing a function when given its equation Example: 2 graphing equations of the form y=a(x-h) +k, graphing equations 2 of the form y=ax +bx+c Determining the nature of the solutions of a quadratic equation Determining the maximum or minimum values of quadratic functions both graphically and algebraically Applying functions to real-world problems Perform operations on functions, including addition, subtraction, multiplication, division, and composition. Page 1 of 3 X X 7 Course: Algebra II and Algebra II with Trigonometry Math Course of Study X 7 Continuum of Skills Blount County Schools Resource T=Textbook O=Other Resource X X Standardized Tests Algebra II with Trigonometry X X Graduation Exam Algebra II Date (O=Ongoing) Year: ___________ X Determining the inverse of a function or a relation Performing operations on polynomial and rational expressions containing variables Example: Simplifying 3 + 5 2 x+5 x +6x+5 Constructing graphs by analyzing their functions as sums or differences Constructing graphs by analyzing their functions as sums, differences, or products Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratic over the complex numbers, as well as exponential and logarithmic functions. Example: 2 x solving x -4>0 or 3 =81 Solving equations using laws of exponents, including rational and irrational exponents Expressing the solution of an equation, inequality, or applies problem as a graph on a number line or by using set or interval notation 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: 2 x 2 solving x -8x>-12, 3 =81, 2 sin x+sin x=0, or log 2=5 x X X 8 8 X X X X 9 X X X Solving equations using laws of exponents, including rational and irrational exponents Expressing the solution of an equation, inequality, or applies problem as a graph on a number line or by using set or interval notation Solve systems of linear equations or inequalities in two variables using algebraic techniques, including those involving matrices. Example: using the matrix operations of a calculator to solve a system of linear equations Evaluation the determinant of a 2x2 or 3x3 matrix Solving word problems involving real-life situations Graph trigonometric functions of the form y=a sin (bx), Y=a cos (bx), and y=a tan (bx). X Determining period and amplitude of sine, cosine, and tangent functions from graphs or basic equations Example: solving problems involving harmonic motion Determining specific unit circle coordinates associated with special angles Geometry 9 X Solve coordinate geometry problems using algebraic techniques. Page 2 of 3 10 X X X 11 X 12 X Continuum of Skills Blount County Schools Resource T=Textbook O=Other Resource Standardized Tests Graduation Exam Algebra II with Trigonometry Algebra II Date (O=Ongoing) Year: ___________ Course: Algebra II and Algebra II with Trigonometry Math Course of Study Example: finding missing coordinates of vertices of polygons, determining properties of polygons given the coordinates of their vertices, determining perpendicularity of sides of a polygon on a coordinate plane Solve general triangles, mathematical problems, and real-world applications using the Law of Sines and the Law of Cosines. Deriving formulas for Law of Sines and Law of Cosines Determining area of oblique triangles 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. Verify simple trigonometric identities using Pythagorean and/or reciprocal identities. Example: 2 2 2 verifying cos a + tan a cos a =1 Data Analysis and Probability 10 13 X X 11 X X X 14 X 12 X X X 15 X X X X X Use different forms of representation to compare characteristics of data gathered from two populations. Evaluating the appropriateness of the design of an experimental study Describing how sample statistics reflect values of population parameters Determine an equation of linear regression from a set of data. X Examining data to determine if a linear or quadratic relationship exists and to predict outcomes Calculate probabilities of events using the laws of probability. Using permutations and combinations to calculate probabilities Calculating conditional probability Calculating probabilities of mutually exclusive events, independent events, and dependent events Page 3 of 3