Accelerated Trigonometry Scope & Sequence



The Hybrid Trigonometry/CC Algebra 2 Course for 2015-2016 ONLY

***italicized items indicate CC topic only

***bolded items indicate Trigonometry topic only

|Topic |Notes |Text Section(s) |CC Module Section(s) |# Classes |

|Functions | | | | |

|The Language of Mathematics |set theory, density, closure, interval notation | |supplement |2 |

|Families of Functions: Domains & Ranges |include onto functions |2-1, 2-3 | |2 |

|Composition of Functions | | | |1 |

|Transforming Functions I: Shifting Functions |rules of transformations |2-6 | |1.5 |

| |even/odd functions, increasing/decreasing, extrema | | | |

|Transforming Functions II: Vertex Form |complete the square |4-2 | |1.5 |

|Inverse Functions |one-to-one functions |6-7 | |1 |

| | | | | |

| | | | | |

|Rational Expressions | | | | |

|Operating on Polynomials |adding/subtracting/multiplying |supplement |M1- L2 |1 |

|Factoring a Polynomial Completely |GCF, difference of perfect squares, trinomial, grouping |4-4 & supplement |M1-L13 |2 |

|Reduce to Lowest Terms | |8-3, 8-4 |M1-L22, L23 |1 |

|Multiplication & Division | |8-4 & supplement |M1-L24 |1 |

|Addition & Subtraction |include complex fractions |8-5 |M1-L25 |2 |

|Complex Fractions | |8-5 |M1-L25 |1.5 |

|Rational Equations |include word problems, graphical solutions, asymptotic behavior |8-6 |M1-L26, L27 |2 |

|Rational Inequalities | |supplement | |1 |

|Absolute Value Equations & Inequalities |inequalities |1-6 | |1 |

| |include word problems | | | |

| | | | | |

|Roots & Radicals | | | | |

|nth degree & Simplifying | |6-1 |M1-L9 |1 |

|Operations | |6-2, 6-3 |M1-L9 |1 |

|Rationalizing | |6-2 & supplement |M1-L9 |1 |

|Radical Equations |graphical solutions |6-8 |M1- L28, L29 |1.5 |

|Complex Numbers | | | | |

|Complex & Imaginary Numbers | |4-8 & Supplement |M1-L37 |2 |

|Solving Quadratic Equations with Imaginary Roots | |4-8 |M1-L38 |1 |

|Operating on Complex Numbers |include magnitude |Supplement | |2 |

| | | | | |

|Quarter I Exam | | | | |

| | | | | |

|Polynomial Functions | | | | |

|The Parabolic Function & Quadratic Models | |4-1, 4-2, 4-5 | |1 |

|Solving Quadratic Equations by Completing the Square | |4-2, 4-6 | |1 |

|Writing the Equation of a Circle by Completing the Square | |10-3 & supplement | |0.5 |

|Discriminant & Nature of the Roots | |4-7 & NY-2 | |2 |

|Solving Quadratic Inequalities | |Concept Byte p. 256 | |1 |

|Solving Linear-Quadratic Systems of Equations | |4-9 |M1-L31 |1 |

|Inverse Variation | |2-2, 8-1 | |1 |

|Graphs of Polynomial Functions | end behavior | |M1-L15 |1 |

|Solving Higher Order Polynomial Functions |graphically, algebraically, Fundamental Theorem of Algebra |5-2, 5-3 |M1-L14, M1-L39 |2 |

| | | | | |

|Exponents | | | | |

|Laws of Exponents: Negative & Zero Exponents |scientific notation |7-1, 7-2, p. 360 |M3-L1, L2 |2 |

|Fractional Exponents | |6-4 |M3-L3, L4 |2 |

|Equations with Fractional/Negative Exponents | |6-5 | |1 |

|Exponential Equations |graphical solutions as well |7-5 |M3-L7, L24 |2 |

| | | | | |

| | | | | |

|Logarithms | | | | |

|The Logarithmic Form of an Equation | |7-3 |M3-L8 |1 |

|The Logarithmic Function/Change of Base | | |M3-L13, M3-L17, L19, L20, L21|2 |

|Product, Quotient, & Power Rules | |7-4 |M3- L11, L12 |2 |

|Logarithmic Equations | |7-5 |M3-L14 |3 |

|Applications |compound and continuous interest formulas, Newton’s Law of Cooling | |M3-L26, M3-L28 |1 |

| | | | | |

|Sequences & Series | | | | |

|Recursive Sequences | | | |1 |

|Arithmetic Sequences & Series | |9-1, 9-2, 9-4 | |1 |

|Geometric Sequences & Series |exponential growth & decay |9-1, 9-3, 9-5 |M3-L25, M3-L29 |2 |

|Sigma Notation | |9-4 |M3-L29 |1 |

|Applications of Geometric Series | | |M3-L30, L31, L32, L33 |1 |

| | | | | |

|Midterm Exam | | | | |

| | | | | |

|Trigonometric Functions | | | | |

|Angles & Their Measure | |13-2 | |1 |

|Right Triangle Trigonometry & The Unit Circle | |13-8, 14-1, NY-3 |M2-L4, L6, L7 |2 |

|Cofunctions | |14-6 | |1 |

|Reference Angles | |Supplement |M2-L5 |1 |

|Using Triangles to Find Unknown Trig Values | |14-3 | |1 |

|Radian Measure | |13-3 |M2-L9 |1.5 |

|Degrees/Minute/Seconds | |Supplement | |.5 |

| | | | | |

|Trigonometric Graphs | | | | |

|Graphs of y = sin x, y = cos x, y = tan x | |13-4, 13-5, 13-6 |M2-L8, L14 |2 |

|Amplitude, Period, & Frequency | |13-1 & Supplement |M2-L11 |1 |

|Transformations of Trigonometric Graphs | |13-7 |M2-L1, L2, L3, L12, L13 |2 |

|Inverse Trigonometric Functions | |14-2 | |2 |

| | | | | |

|Trigonometric Applications | | | | |

|Area of a Triangle | |14-4 | |1 |

|Law of Sines | |14-4 | |1 |

|The Ambiguous Case | |Concept Byte p. 927 | |1 |

|Law of Cosines | |14-5 | |1 |

|Solving Triangles | |Supplement | |3 |

| | | | | |

|Trigonometric Equations & Identities | | | | |

|Pythagorean Identities | |14-1 |M2-L15, M2-L16 |1 |

|Sum/Difference of Angles Identities | |14-6 & Supplement | |1 |

|Double Angle Identities | |14-7 | |1 |

|Half Angle Identities | |14-7 | |1 |

|Solving Trigonometric Equations | |14-2 & Supplement | |3 |

| | | | | |

|Quarter III Exam | | | | |

| | | | | |

|Probability | | | | |

|Combinations, Permutations, & The Counting Principle | |11-1 | |2 |

|Basic Probability |Events, Sample Spaces, Venn Diagrams |11-2, 11-3 |M4-L1, L5 |2 |

|Bernoulli Experiments: “At Least/At Most” | |Supplement | |2 |

|The Binomial Theorem | |11-8, Concept Byte p. 325 | |2 |

| | | | | |

|Statistics | | | | |

|Data Collection |sample surveys, experiments, observational studies |11-7 |M4-L12 |1 |

|Measures of Central Tendency | |11-5 | |0.5 |

|Measures of Dispersion | |NY-1, 11-6 |M4-L8, L9 |1 |

|The Normal Curve | |11-9 & Concept Byte p. 740 |M4-L10, L11 |2 |

| | | | | |

|Math Modeling | | | | |

|Plotting Data | |2-5 | |2 |

|Recognizing & Fitting Curves |correlation coefficient, residual plots |2-5, 4-3, 5-8 |M3-L23, L27 |2 |

| | | | | |

|Additional CC Topics |

|Polynomial Functions | | | | |

|Graphs of Polynomial Functions | end behavior | |M1-L15 | |

|Solving Higher Order Polynomial Functions |graphically, algebraically, Fundamental Theorem of Algebra | |M1-L14, M1-L39 | |

|Dividing Polynomials |divide poly by poly, division algorithm | |M1- L3, L4 | |

|The Remainder Theorem | | |M1- L18, L19 | |

|Modeling with Polynomial Functions | | |M1-L16, L20, L21 | |

|Prove Polynomial Identities |generate Pythagorean Triples | |M1-L10 | |

|The Parabolic Function |focus/directrix | |M1-L33, L34, L35 | |

| | | | | |

|Probability | | | | |

|Two-Way Tables |independence, conditional probability | |M4-L2, L3 | |

|Basic Rules | | |M4-L6, L7 | |

| | | | | |

|Inferential Statistics | | | | |

|Using Samples to Estimate Populations | | |M4-L13 | |

|Sampling Variability in the Sample Proportion | | |M4-L14 | |

|Sampling Variability in the Population Proportion | | |M4-L15 | |

|Margin of Error: Population Proportion |application problems in L22 | |M4-L16, L17, L22 | |

|Sampling Variability in the Sample Mean | | |M4-L18, L19 | |

|Margin of Error: Population Mean |application problems in L22 | |M4-L20, L21, L22 | |

|Experimental Design |randomization in experimental design | |M4-L23, L24 | |

|Ruling out Chance |use data from randomized experiments to compare treatments to decide if the | |M4-L26, L27, L28, L29, L30 | |

| |differences in parameters are significant; real world applications | | | |

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