CURRICULUM MAP TEMPLATE. Framework Standard

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1 HONORS PRECALCULUS COURSE 231 CURRICULUM MAP TEMPLATE Essential Questions & Content Framework Standard Skills Assessment & Learner Expectations September/ October How do you define real life data verbally, numerically, graphically and algebraically? Function Domain/range/zeroes Maximum/minimum Even/odd Composite Reflection/symmetry Phase shifts Rigid/nonrigid transformation Asymptotes Distance/midpoint formulas Vertical/horizontal line test Linear/quadratic/cubic/quartic Absolute value/radical Greatest integer function Piecewise Circle Parent AII.P.7 AII.P.8 12.P.5 12.G.4 Identify a function Identify domain, range and zeros Create inverse and composite Use symmetry/reflections in graphing Identify even and odd Create a function of one variable from a verbal description Graph based upon changes to parent function Solve and graph polynomial Use math models of to solve verbal

2 Increasing/decreasing Relative maximum/minimums November/ December How can you predict behavior of polynomial? Polynomial Degree Constant Cubic Quartic Quintic Rational/complex Synthetic/direct Intermediate value Integral coefficients Odd/even multiplicity Critical points 12.N.1 PC.P.2 12.P.7 12.P.8 12.P P.12 AII.P.8 AII.P.12 Use direct/synthetic substitution to evaluate polynomials Find roots/binomial factors synthetically and graphically with multiple theorem support Use technology to approximate roots Recognize visual representations of higher degree polynomials and their characteristics Design polynomial to represent realworld applications Analyze graphs of rational Solve polynomial/rational inequalities CIM- Make Open Box GSP- Polynomial Surprises December/ January Synthetic substitution/division Rational zero test Factor/remainder theorems Intermediate value theorem Leading coefficient test Upper/lower bound rules Asymptotes Sign analysis How can exponents and logarithms apply to real-life situations? Integral Rational 12.N.2 12.P.4 12.P.8 12.P.10 Define and apply integral exponents Define and apply rational exponents Define and use exponential

3 Exponential Logarithmic Growth/decay Half life Natural logarithms Common logarithms Change of base Properties of exponents Exponential Logarithmic Growth and decay formula Common/natural logarithms Base e 12.P.12 Prove and apply laws of logarithms Solve exponential Apply exponents to model population growth, business/finance, health/medicine, and physics/science Understand the relationships between exponential and logarithmic Use the graphing calculator to solve real life February/ March What is the meaning of trigonometry? Angle Initial/terminal ray Unit circle Degree/minute/second Radian Standard position Coterminal/quadrantal Arc/sector Revolution Sine/cosine/tangent Secant/cosecant/cotangent Reference angle PC.M.1 PC.M.2 PC.M.3 12.G.1 12.G.2 12.G.4 12.G.5 12.M.2 Convert radians to degree and degrees to radians Graph all trig Identify domain and range Evaluate trig expressions Solve simple trig Find arc length/central angles Find areas of sectors Apply trigonometry to real-world. CIM- Trigonometry Unit circle

4 Trigonometric relationships Types of angle measurement March/April May How does the study of trigonometry relate to real-world periodic phenomena? Period/amplitude Phase shift Trigonometric identity Periodic Trigonometric models Reciprocal/Pythagorean/ Cofunction/Negative Trigonometric Relationships Periodic behavior Application of Sine/Cosine Waves What connections exist between trigonometry and geometry? Right triangle trigonometry Angles of elevation/depression Navigation/compass bearings SOHCAHTOA s Regular Law of Sines Law of Cosines PC.P.3 PC.P.5 PC.P.6 12.P.4 PC.G.1 Solve trigonometric Simplify trigonometric expressions/identities Sketching graphs Model real-world applications Use technology to solve trigonometric Extract information from trigonometric and graphs Solve a right triangle Apply law of sines/cosines/area formulas Model real-world applications including navigation, aviation, and surveying Sketch appropriate trigonometric models

5 June Navigation Trigonometric/geometric relationships Area formulas of polygons Solving right triangles What other relationships are available to help in solving more challenging? Sum and difference formulas Double angle formulas Sum and difference formula and relationship to double angle formula PC.P.5 Generate double angle formulas Interpret more advanced trig graphs Convert between rectangular and polar coordinates Input data into graphing calculator for parametric