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Math 30 Pure COURSE OUTLINE Textbook: MathPower 12 + Handouts Provided Course Work = 50% Diploma Final Exam = 50% 1. Transformations 9 classes Stretches • vertical and horizontal stretches • stretches about other lines • stretches and the zeros of a function Reflections • vertical and horizontal reflections • combining stretches and reflections • the inverse of a function Translations • vertical and horizontal translations Combining Transformations • the algebra of transformations • graphing transformations • describing transformations The Reciprocal of a Function 2. Exponents and Logarithms 14 classes The Exponential Function • definition and terminology related to exponential functions • graphing the exponential function • transformations of the exponential function Exponential Regression • exponential growth • exponential decay The Logarithmic Function • definition and terminology related to logarithmic functions • graph and analyze the logarithmic function with and without technology • converting between exponetial and logarithmic forms • common logarithms • the laws of logarithms • solve exponential and logarithmic equations • change of base law • applications and problem solving LTCHS M30P Course Outline Sept2011 Page 1 of 4 3. Geometric Sequences and Series 8 classes Geometric Sequences • definition and terminology related to geometric sequences • the general term of a geometric sequence • relationship to exponential functions • applications and problem solving Geometric Series • definition and terminology related to geometric series • sigma notation • finite geometric series • applications and problem solving 4. Trigonometry I 12 classes Trig Theory • rotation angles, coterminal angles, principal angle • the primary and reciprocal trig ratios • reference angles • exact ratios Degree and Radian Measure for Angles • conversion between radians and degrees • arc length of a circle The Unit Circle • the CAST rule • special triangle relationships - exact values Graphing Trig Functions • graphing the basic sine, cosine, and tan functions with and without technology • understand the characteristics of the primary trig functions – amplitude, vertical translation, period, phase shift, range, max/min values • understand, interpret, and analyze the primary trig functions • transformations as they apply to the primary trig functions • graphs and terminology related to the reciprocal trig functions • use the sine curve to represent and solve related problems • develop and apply sine regression models which represent periodic data with and without technology LTCHS M30P Course Outline Sept2011 Page 2 of 4 5. Trigonometry II 8 classes Trig Identities • verify trig identities numerically, algebraically and graphically • understand and apply the various trig identities to simplify and verify trig expressions and equations Solve Trig Equations (0 ≤ θ < 2π) • solve trig equations graphically and algebraically: linear, quadratic, multiple angle, double function equations • relate graphs and solutions to trig equations • determine general solutions 6. Conics 8 classes The Geometry of Conics • definitions and terminology related to conics • slicing the cone – the geometric model • classify conics according to shape and according to the vertex angle • recognize degenerate conics The Algebra of Conics • classify conics according to AC rules • general form Ax2 + Cy2 + Dx + Ey + F = 0 • standard form - study the effects of changing various parameters: h, k, a, b • transformations as they relate to conics • convert between general and standard forms • terminology - center, vertex, domain, range, intercepts, asymptotes • sketch conics from the equation, given key points, or a transformation • write the equation when given key points or a transformation 7. Combinatorics and Probability 14 classes The Fundamental Counting Principle • construct and interpret tree diagrams • understand and apply the fundamental counting principle • dealing with various restrictions • factorial notation Linear Permutations • definition and terminology related to permutations • permuting a part of a set • permutations involving various restrictions • distinguishable permutations Combinations • definition and terminology related to combinations • combinations involving various restrictions The Algebra of Factorial Notation • simplifying algebraic expressions involving perms and combs • solving algebraic equations involving perms and combs LTCHS M30P Course Outline Sept2011 Page 3 of 4 Pathway Problems • solve simple pathway problems • solve compound two-dimensional pathway problems with a given diagram • solve two-dimensional pathway problems without a given diagram • solve three-dimensional pathway problems The Binomial Theorem • definition and terminology related to the binomial theorem • relationship to combinations • expanding binomials of various degrees • understand and apply patterns as they relate to the binomial theorem Probability • determine probability by using the fundamental counting principle where order is important and where order is not important • determine the probability of one event in which permutations or combinations are involved • determine the probabilities for two or more events in which permutations or combinations are involved • solve probability problems 8. Statistics 7 classes Review of Mean and Standard Deviation • definitions and terminology – mean, median, mode, range, standard deviation • use technology to calculate the mean and standard deviation using ungrouped and grouped data The Normal Distribution Curve • definition and properties of the normal curve • use and apply the z-score formula • use and apply the area under the normal curve chart to solve problems • solve manufacturers’ guarantees problems The Binomial Distribution • definition and terminology related to a binomial experiment • solve and apply binomial experiment problems with and without technology LTCHS M30P Course Outline Sept2011 Page 4 of 4