Course title
AP PrecalculusPre-requisite
College Algebra H with C or better OR Algebra II H with teacher recommendationCourse description
Students will explore everyday situations using mathematical tools and lenses. Through regular practice, students build deep mastery of modeling and functions, and they examine scenarios through multiple representations including graphically, numerically, verbally, and analytically. Students will gain deeper understanding of the nature and behavior of polynomial, rational, exponential, logarithmic, trigonometric, and polar functions. Optional topics are functions involving parameters, vectors, and matrices. Students will have opportunities to: Define domain and range in the real-world context. Calculate, interpret, and use average rate of change. Use multiple representations offunction models appropriately. Work with different families of functions beyond linear and quadratic functions including but not limited to exponential, logarithmic, rational, polynomial, logistic, radical, and piecewise- defined functions. Graph rational functions including those whose graphs contain horizontal asymptotes, vertical asymptotes, oblique asymptotes, and/or holes. Make sense of radian measure. Use the unit circle as a tool to graph the trig functions in radians and degrees. Develop fluency with the unit circle. Include opportunities beyond the special angles, for example, explain why sin(l.1) > sin(0.3) in radians. Graph sine, cosine, tangent functions in radians and degrees and analyze/explain the characteristics of each. Explore the reciprocal trig functions using technology. Model real-world situations with the sum, difference, product, or quotient of other function models. Describe relationships of quantities in functions and within a composition of those functions. Find an inverse algebraically, for example given y = f(x) algebraically find x = f-l(y). Work with exponential and logarithmic functions, and quadratic and square root functions at a minimum Understand that restricting a trigonometric function to a domain on which it is monotonic allows its inverse to be constructed. Describe the meaning of f1(20) given a function f that takes hours as an input and gives miles as an output. Make sense of the covarying quantities when modeling with inverse functions Explore conics as loci of points satisfying stipulated conditions. Explore conic sections with technology and manipulatives. Connect the geometric and algebraic relationships of conics. Use the method of completing the square to put the equation of the conic section into standard form. Become fluent in working with arithmetic and geometric sequences and series. Explore several types of sequences, including but not limited to Fibonacci, telescoping, harmonic, alternating. Work with tasks without using formal limit notation, such as, "as n approaches infinity, what happens to s,?"