Adlai E. Stevenson High School Course Description

Transcription

1 Adlai E. Stevenson High School Course Description Division: Content Objectives: By the end of this course, students will be able to: Exponents/Logs Intro to Functions Inverse Trig Polynomials Probability Rational Functions Statistics Trig Graphing Trig Identities Trig Laws Unit Circle College Readiness Objectives: By the end of this course, students will be able to: Expressions, Equations & Inequalities Functions Numbers: Concepts & Properties Probability, Statistics & Data Analysis Properties of Plane Figures Content Learning Targets Exponents/Logs A. Evaluate and approximate logarithms B. Simplify expressions or solve equations using properties of logarithms C. Sketch the graphs of exponential functions D. Sketch the graphs of logarithmic functions E. Solve equations using exponents F. Solve exponential equations using logarithms G. Write and apply continuousgrowth/decay models Intro to Functions A. Classify a function as even, odd, neither B. Combine functions using composition and evaluate composed functions C. Determine a function s inverse

2 D. Evaluate basic functions and relations E. Identify the symmetry of a graph by reflecting a given point/ line/ graph over another line or point F. Recognize the relationship between a function/relation and its domain and range G. State a relation given its domain and related equation H. Write the equations or sketch the graphs of transformations of basic functions Inverse Trig A. Applying the Sum and Difference identities B. Evaluating inverse trig expressions using a single trig function C. Evaluating inverse trig expressions using multiple trig functions D. Solving trig equations using algebra E. Solving trig equations using identities. F. Understanding basic notation of inverse trig Polynomials A. Determine all roots of a polynomial equation containing at least one set of irrational or imaginary roots B. Determine the number and type of roots of a polynomial equation C. Divide using synthetic division D. Identify the possible rational roots of a polynomial equation E. Sketch the graph of a polynomial using the given information F. Understand how the equation of a polynomial relates to its x-int(s), zeros, and roots G. Understand the relationship between end behavior and a polynomial equation H. When dividing a polynomial by a binomial factor, determine the remainder; determine whether a binomial is a factor; determine whether a value is a root Probability A. Apply the basic counting principle B. Calculate the number of combinations C. Calculate the number of permutations D. Determine a conditional probability E. Determine the probability of multiple events F. Determine the probability of single events Rational Functions A. Identify the horizontal asymptote of rational functions; relate the horizontal asymptote to equations and graph of B. Identify the point(s) of discontinuity of rational functions; relate the point(s) of discontinuity to equations and graph of C. Identify the vertical asymptote(s) of rational functions; relate the vertical asymptote(s) to equations and graphs of D. Identify the x intercept(s) of rational functions; relate the x intercept(s) to equations and graphs of

3 E. Identify the y intercept of rational functions; relate the y intercept to equations and graphs of F. Use prerequisite skills including factoring. Statistics A. Construct and interpret boxplots B. Construct and interpret histograms C. Construct and interpret stemplots D. Find and interpret summary data E. Use normal distribution data to find a boundary or interval where at least 1 z-score is an integer value F. Use normal distribution data to find a boundary or interval where the z-score is an integer value G. Use normal distribution data to find a percentage where at least 1 z-score is a non-integer value H. Use normal distribution data to find a percentage where the z-score is an integer value Trig Graphing A. Determine the amplitude and period of a trig function's graph B. Determine the shifts in a trig function's graph C. Recognize the properties of Secant/Cosecant functions D. Recognize the properties of Sine/Cosine functions E. Recognize the properties of Tangent/Cotangent functions F. Sketch the graph of a trig function given its equation or properties. G. Write the equation of a trig function given its graph or properties. Trig Identities A. Recognize and apply the basic trig identities (Reciprocal, Quotient, Pythagorean) B. Simplify basic trig expressions using few identities C. Simplify complex trig expressions using several identities D. Use and apply Advanced Algebra skills to simplify expressions (factoring, multiplying binomials, using operations with common denominators and complex fractions) E. Use identities to verify trig equations Trig Laws A. To interpret word problems/diagrams. B. To use right triangle trigonometry to determine missing triangle measurements. C. To use the Law of Cosines to determine missing triangle measurements. D. To use the Law of Cosines to solve the ambiguous case. E. To use the Law of Sines to determine missing triangle measurements. Unit Circle A. Convert angle measure (degrees to radians. radians to degrees) B. Determine the basic trig functions for unit circle angles

4 C. Determine the quadrant in which the terminal side of an angle lies D. Determine the reciprocals of basic trig functions for unit circle angles E. Determine the reference angle of a given angle F. Evaluate basic trig functions given orde/red pairs or ratios G. Evaluate reciprocals of basic trig functions given ordered pairs or ratios H. Identify angles coterminal to a given angle College Readiness target Expressions, Equations & Inequalities A. XEI702: Write equations and inequalities that require planning, manipulating, and/or solving. Functions A. FUN501: Evaluate polynomial functions, expressed in function notation, at integer values. B. FUN502: Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths. C. FUN601: Evaluate composite functions at integer values. D. FUN602: Apply basic trigonometric ratios to solve right-triangle problems. E. FUN701: Write an expression for the composite of two simple functions. F. FUN702: Use trigonometric concepts and basic identities to solve problems. G. FUN703: Exhibit knowledge of unit circle trigonometry. H. FUN704: Match graphs of basic trigonometric functions with their equations. Numbers: Concepts & Properties A. NCP604: Apply rules of exponents. B. NCP605: Multiply two complex numbers. C. NCP702: Exhibit knowledge of logarithms and geometric sequences. Probability, Statistics & Data Analysis A. PSD202: Perform a single computation using information from a table or chart. B. PSD301: Calculate the average of a list of numbers. C. PSD302: Calculate the average, given the number of data values and the sume of the data values. D. PSD303: Read tables and graphs. E. PSD304: Perform computations on data from tables and graphs. F. PSD305: Use the relationship between the probabiliy of an event and the probability of its complement. G. PSD401: Calculate the missing data value, given the average and all data values but one. H. PSD402: Translate from one representation of data to another. I. PSD403: Determine the probability of a single event. J. PSD404: Exhibit knowledge of simple counting techniques. K. PSD501: Calculate the average, given the frequency counts of all the data values.

5 L. PSD502: Manipulate data from tables and graphs. M. PSD503: Computer straightforward probabilities for common situations. N. PSD504: Use Venn diagrams in counting. O. PSD602: Interpret and use information from figures, tables, and graphs. P. PSD603: Apply counting techniques. Q. PSD604: Compute a probability when the event and/or sample space are not given or obvious. R. PSD701: Distinguish between mean, median, and mode for a list of numbers. S. PSD702: Analyze and draw conclusions based on information from figures, tables, and graphs. T. PSD703: Exhibit knowledge of conditional and joint probability. Properties of Plane Figures A. PPF601: Appy properties of , , similar, and congruent triangles.