Math Hammy

- Sine and cosine functions - Amplitude, period, frequency - Transformation of sine and cosine functions - Graphing sine and cosine functions - construct a sinusoid given the amplitude and period that goes through a given point - state the amplitude and period of the sinusoid, and (relative to the basic function) the phase shift and vertical translation - constructing a sinusoidal model using time (tide) - applications involving sine and cosine functions - Tangent and cotangent Functions - Graph

- Identifying Polynomial Functions and their degrees - write a LINEAR equation given two ordered pairs - average rate of change - vertex from of a quadratic equation - Matching quadratic equation to their graphs - Graphing a quadratic function in vertex form- - Finding the vertex and axis of symmetry of a quadratic function - Rewriting a quadratic equation in Vertex Form by Completing the Square - Writing the equation from the graph of a quadratic function - Application of quadratic functions-

- Graphing parametric equations on a graphing calculator - Graphing parametric equations by hand - Eliminate the parameter and identify the graph of the parametric curve - Eliminate the parameter to obtain the rectangular equation for the curve and Plot the points to graph the curve - Finding Parametric Equations for a line or line segment - Finding Parametric Equations for a circle - Applications involving parametric equations

- Converting between degrees and DMS - Converting between degrees and radians - Using the arc length formula - Compass reading - Angular speed - Applications involving angle and arc length measure - Conversion between statute and nautical miles - Using one trigonometric ratio to find the remaining 5 - Memorizing the Unit Circle - Evaluating trig functions for 30, 60, and 45 degree angles - Evaluating Trigonometric Functions using a Calculator - Solving for theta - Solving a right triangle - Appl

- Use the Product, quotient, and power rules for logarithms to rewrite logarithmic expression as a single logarithm and vice versa - Change of base formula for logarithms - Write expression using only common and natural logarithms - Identify transformation and Graphing logarithmic functions - Matching logarithmic functions to their graphs - Applications of logarithmic functions - One-to-one properties - Solving exponential equations algebraically - Solving logarithmic, natural log, and equations

- Identifying Exponential functions - Computing exponential function values - Find an Exponential Function from its Table of Values or from its Graph - Exponential functions and the base e - describe Transformations and graph Exponential Functions - exponential growth and decay - logistic growth functions - Population Growth Application problems - Solving Exponential Functions - Exponential population model - Finding grown and decay rates - Determine exponential function from data - Half life -

- Vertical Line Test - Defining a Function in Equation Form - Finding the Domain of a Function - Finding the Range of a Function - Continuity of Functions - Removable and nonremovable discontinuity - Identifying points of discontinuity - Finding Local Maximum and Minimums - Identifying Intervals where function is increasing, decreasing, and constant - Determining Boundedness of a Function - Checking functions for Symmetry Algebraically - Checking functions for Symmetry Graphically - Finding Vert

- Pythagorean Identities - Reciprocal identities - Quotient identities - Use identities to simplify expressions - Co-function identities - Odd-even identities - Simplify expressions by factoring and using identities - Simplify expressions by expanding and using identities - Simplify expressions by combining fractions and using identities - Solving Trigonometric Equations - Proving identities - Identifying and proving an identity - Setting up difference of squares to prove an identity - More str

- finding points determined parametrically - Eliminating the Parameter - Using a graphing calculator in parametric mode - Horizontal line test - One-to-One functions - Finding the Inverse of a Function - Finding the domain of the inverse of a function - Graphing the Inverse of a Function - find the inverse of a non-invertible function by restricting its domain - Inverse Composition Rule - Writing a linear equation from 2 ordered pairs - Use composite functions to determine whether two functions

- Match the numerical model to the corresponding graphical model and algebraic model: - Find an algebraic model to represent the data - Solving Equations Algebraically - Solving Equations Graphically - Grapher Failure - Hidden behavior - Solving equations Graphically - Scatter plots - Regression equations - Vertical Line Test - Defining a Function in Equation Form - Finding the Domain of a Function - Finding the Range of a Function - Continuity of Functions - Removable and nonremovable discont

- Two-dimensional vector - Head minus tail rule - Magnitude of a vector - Component form of a vector - Determining if two vectors are equal - Vector addition and scalar multiplication - Representing a vector in rectangular coordinates and finding its magnitude - Unit Vectors - Resolving the vector - Finding the direction angle of a vector - Velocity - Component form of a velocity vector - Writing a vector whose magnitude and direction are given - Finding resultant force - Using vectors to find s

- Interest compounded annually - Interest compounded k times a year - Interest compounded continuously - Future value of an annuity - Present value of an annuity - Finding time period of an investment - Finding the interest rate - Applications involving Annuities

- determine whether a given function is a power function - direct variation and inverse variation - determine whether a given function is a Monomial function - graphing power functions - Analyze Power Functions: Domain, Range, Continuity, Symmetry, Boundedness, Local Extrema, Asymptotes, End Behavior: (use limit notation) - Write statements as a power function equation - Write a sentence that expresses the relationship in a formula, using the language of variation or proportion - Using a graphe

- Determine whether the function is periodic. If it is, find the period - Composite Trigonometric Functions - Find the Domain, Range, and Period of a function - Find the equations of parallel lines a function oscillates between: - Sums and differences of sinusoids - Identify a sinusoid - Express the sum of sinusoids as a sinusoid - Showing A function is Periodic but not a Sinusoid - Identifying Damped Oscillation - Applications of damped oscillation

- Law of Sines - Solving a triangle given 2 angles and a side - The Ambiguous Case (two sides and an angle opposite one of them) - State whether given measurements determine zero, one, or two triangles - Applications involving Law of sines

- solving rational equations - extraneous solutions - solving rational equations graphically - showing extraneous solutions graphically - applications involving rational equations - mixture problems, maximizing/minimizing perimeter problems and Volume problems

- Law of Cosines - Solving a triangle (SAS) - Solving a triangle (SSS) - Finding area of a triangle when you know 2 sides and an angle - Finding the area of a regular polygon inscribed in a circle - Finding area of a triangle when you know 3 sides (Heron’s Theorem) - Decide whether a triangle can be formed with the given side lengths - Applications involving Law of Cosines

- Graphing rational functions - Identify and graph transformations of rational functions - End behavior, vertical, and horizontal asymptotes - x and y intercepts - evaluating left and right hand limits of a graph of a function - matching rational functions to their graphs - more on graphing rational functions

- The 12 Basic Functions - Transformations and equations of the 12 Basic Functions - Matching graphs to transformation equations of the 12 basic functions - Using a graphing Calculator to determine the domain and range of the function - Analyze a Function (symmetry, boundedness, asymptotes, relation to 12 basic functions etc…) - Graphing piecewise functions and identifying points of discontinuity

- Pythagorean Identities - Reciprocal identities - Quotient identities - Use identities to simplify expressions - Co-function identities - Odd-even identities - Simplify expressions by factoring and using identities - Simplify expressions by expanding and using identities - Simplify expressions by combining fractions and using identities - Solving Trigonometric Equations