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Algebra 2 and Trigonometry

Algebra 2 and Trigonometry. Opening September 2009 Coming to A School Near You! Prepared and presented by Susan Sladowski, Sonia Buszwatiuk, Sharon Hoosak and Celia Foster . What’s Your I.A. - IQ?. True or False

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Algebra 2 and Trigonometry

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  1. Algebra 2 and Trigonometry Opening September 2009 Coming to A School Near You! Prepared and presented by Susan Sladowski, Sonia Buszwatiuk, Sharon Hoosak and Celia Foster.

  2. What’s Your I.A. - IQ? True or False 1. The Algebra2/Trig Course will be like the 11th year math course of the ’70s. 2. The Algebra2/Trig Course will be just like Course III. 3. The Algebra 2/Trig will be the same as Math B Terms 2 and 3.

  3. What’s Your I.A. - IQ? True or False 1. The Algebra2/Trig course will not include probability or statistics. 2. The Algebra2/Trig course will have additional indicators on topics from Pre-Calculus. 3. The Algebra2/Trig Regents will be easier than Math B.

  4. Algebra 2 and Trigonometry Content and Process Strands True or False The content strands are what teachers teach and the process strands are how they teach it.

  5. True The content strands are what teachers teach and the process strands are how they teach it.

  6. Algebra 2 and Trigonometry TRUE OR FALSE The five process strands are • discover • conjecture • justify • explain • investigate

  7. False The five process strands are NOT • discover • conjecture • justify • explain • investigate

  8. Algebra 2 and Trigonometry TRUE OR FALSE The five process strands are • reasoning and proof • problem solving • connections • representation • communication

  9. True The five process strands continue to be: • reasoning and proof • problem solving • connections • representation • communication

  10. Algebra 2 and Trigonometry True or False Since process strands describe how teachers present the content, the NYSED list of performance indicators for Algebra 2 and Trig is the same list as was given for Integrated Algebra and for Geometry.

  11. False The NYSED list of performance indicators for Algebra 2 and Trig lists many of the same indicators BUT has indicators specific to the Algebra 2 and Trig course.

  12. Algebra 2 and Trigonometry True or False The NYSED lists specific performance indicators for each of the five process strands.

  13. True The NYSED lists specific performance indicators for each of the five process strands

  14. Sample Process Strands • A2.PS10: Evaluate the relative efficiency of different representations and solution methods of a problem. • A2.RP.8: Evaluate written arguments for validity. • A2.CM.9: Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or conjectures of others.

  15. Sample Process Strands • A2.RP.3: Evaluate conjectures and recognize when an estimate or approximation is more appropriate than an exact answer. • A2.RP4: Recognize when an approximation is more appropriate than an exact answer.

  16. Sample Process Strands • A2.R.6 Use mathematics to show and understand physical phenomena (e.g., investigate sound waves using the sine and cosine functions). • A2.R.7 Use mathematics to show and understand social phenomena (e.g., interpret the results of an opinion poll). • A2.R.8 Use mathematics to show and understand mathematical phenomena (e.g., use random number generator to simulate a coin toss).

  17. Algebra • A2.A.5 Use DIRECT and inverse variation to solve for unknown values. • A2.A.23 Solve rational equations and INEQUALITIES. • A2.A.24 Know and apply the technique of COMPLETING THE SQUARE.

  18. Algebra • A2.A.26 Find the solution to polynomial equations of higher degree that can be solved using factoring and/or the quadratic formula. • A2.A.50 Approximate the solution to polynomial equations of higher degree by inspecting the graph.

  19. SEQUENCES & SERIES NEW UNIT FROM PRECALCULUS!

  20. SEQUENCES & SERIES • A2.A.29 Identify an arithmetic or geometric sequenceand find theformula for its nth term. • A2.A.30 Determine the common difference in an arithmetic sequence. • A2.A.31 Determine the common ratio in a geometric sequence.

  21. SEQUENCES & SERIES • A2.A.32 Determine a specified term of an arithmetic or geometric sequence. • A2.A.33 Specify terms of a sequence, given its recursive definition. • A2.A.35 Determine the sum of the first n terms of an arithmetic or geometric series.

  22. A2.A.34 Represent the sum of a series, using sigma notation Use sigma notation to represent the sum of the following series: 3 + 6 + 9 + 12 + … for the first 33 terms -3 + 6 -12 + 24 … for the first 50 terms 6 + 2 + 1/3 + 1/6 + … for n terms

  23. STANDARD FORM OF THE EQUATION OF A CIRCLE STUDENTS WILL NEED TO KNOW HOW TO COMPLETE THE SQUARE! • x2 + y2 + Cx + Dy + E = 0.

  24. A2.A.47 Determine the center-radius form for the equation of a circle in standard form Use the technique of completing the square to convert the equation x2 + y2 - 4x - 6y+ 8 = 0 into center-radius form. What is the center and what is the radius of this equation?

  25. WHAT’S NEW IN FUNCTIONS? • A2.A.43 Determine if a function is one-to-one, onto, or both. • A2.A.45 Determine the inverse of a function and use composition to justify the result. • A2.A.46 Perform transformations with functions and relations:f(x+a) , f(x)+a , f(-x), -f(x) , af(x)

  26. …transformations of functions • Given the graph of the function f(x), sketch the graphs of

  27. WHAT’S NEW IN EXPONENTIAL AND LOGARITHMIC FUNCTIONS? • Base e • Evaluate: • Natural logarithm: ln x • Sketch and label the following graphs y = ex • Rewrite logarithmic expressions in equivalent forms: i.e.

  28. WHAT’S NEW IN TRIGONOMETRIC FUNCTIONS? • Graphs of reciprocal functions • Phase Shift • More Emphasis on restricting the domain of inverse trig functions

  29. …. and phase shift A pet store clerk noticed that the population in the gerbil habitat varied sinusoidally with respect to time, in days. He carefully collected data and graphed his resulting equation. From the graph, determine amplitude, period, frequency, and phase shift.

  30. Write trigonometric function: Reciprocal functions & phase shift A2.A.72 Write the trigonometric function that is represented by a given periodic graph.

  31. Statistics • A2.S.1 Understand the differences among various kinds of studies (e.g., survey, observation, controlled experiment). • A2.S.2 Determine factors which may affect the outcome of a survey.

  32. Statistics • A2.S.4 Calculate measures of dispersion (range, quartiles, inter-quartile range, standard deviation, variance) for both samples and populations.

  33. Probability (A2.S9 – A2.S16) • Permutations • Combinations • Fundamental Principle of Counting • Theoretical Probabilities, including geometric applications • Use the normal distribution as an approximation for binomial probabilities

  34. What has been eliminated? Fields/Groups/Operations defined by tables? • Step Functions • Transformations of Points, Triangles, Line Segments (Done in Geometry) • Parallelogram of Forces • Systems of Trig Equations • Proving Complex Trig Identities • Deriving Double Angle and Half Angle Formulas – just have to “Apply…” them

  35. Other Resources • Core Curriculum • Crosswalk • Sample Tasks • Tool Kits • News www.emsc.nysed.gov/ciai/mst/math/html

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