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td.MONTH {cursor:pointer;} Teacher: Core PreCalcH Year: 2006-2007 Course: Math Precalculus H Algebra Skills Content Skills Factoring review Simplify quadratic expressions by factoring Factoring perfect cubes and by grouping Simplify sums and differences of cubes Operations on Rational Expressions Simplify expressions by grouping Complex Fractions Simplify expressions involving negative exponents Multiply and divide rational expressions Combine rational expressions using addition and subtraction Simplify complex rational expressions Operations with Functions Content Skills Graphical transformations Identifying the graphs of basic functions Domain and Range of functions Sketching the graphs of functions by using transformations of basic functions Compositions of functions Inverses of functions Modeling functions Identifying the domain and range of a function graphically and algebraically Create functions that are sums, differences, products, quotients, and compositions of functions Determining the inverse of a function both algebraically and graphically Create a function from a given situation Create functions from formulas Polynomial functions Content Skills Quadratic functions Express a quadratic equation in vertex form Polynomials of degree 3 or higher Maximize or minimize quadratic functions Roots of polynomials Determining the number of rational, real, and complex roots of a polynomial function Synthetic Division Graphs of polynomial functions Identifying the number of roots of a given polynomial Finding the roots of a polynomial Sketching graphs of polynomial functions from its roots Writing the equation of a polynomial when given its graph, x- and y- intercepts, and turning points Rational Functions Content Graphs of rational functions Skills Sketching graphs of rational functions based on transformations of y = 1/x and y=1/x^2 Rational equations and inequalities Sketching graphs of rational functions by finding asymptotes and intercepts Solving applications of rational functions Exponential, Logarithmic, and Logistic functions Content Skills Rational Exponents Evaluating expressions with rational and negative exponents Exponential functions and graphs Writing exponential functions Logarithmic functions and graphs Evaluating exponential functions Logistic functions Applications of exponential, logarithmic, and logistic functions Solving exponential equations with logarithms Evaluating and solving logistic equations Modeling exponential, logarithmic, and logistic functions Solving applications of exponential functions Trigonometry graphs Content Skills Graphs and trigonometric values Determining position around the unit circle based upon the angle from the positive x-axis Applications with trigonometric graphs Sketch y = sin x and y = cos x Sketch graphs of transformations of trigonometric functions Sketch graphs of other trigonometric functions Modeling sinusoidal functions to represent real-life phenomena Sketch graphs of inverse trigonometric functions Analytic Trigonometry Content Skills Pythagorean and reciprocal identities Verify Pythagorean identities Sum and difference trigonometric identities Verify sum and difference identities Multiple angle identities Sketch graphs of sums of sinusoids Solving trigonometric equations Verify double angle identities Trigonometric laws Derive multiple angle identities Solve linear and quadratic trigonometric equations Derive and apply the Law of Sines and Cosines Apply Heron's Formula to find the area of a triangle Parametric and Polar functions Content Skills Parametric functions Model horizontal and vertical motion Projectile Motion Derive parametric equations to model projectile motion Polar coordinates Convert rectangular coordinates to polar form Polar functions Trigonometric form of complex numbers Complex equations Sketch graphs of polar functions such as cardioids, limacon, spirals, and roses Convert complex numbers to trigonometric form Perform operations on complex numbers in trigonometric form Solve complex equations Systems and Matrices Content Skills Systems of Equations Solving systems of equations in 2 variables Matrix Algebra Define matrices Multivariable systems and row operations Perform operations on matrices Partial Fractions Solve systems of linear equations with matrices using row reduction Systems of inequalities Solve systems of equations using matrices and the graphing calculator Decomposing a fraction into its partial fractions Solving a system of linear inequalities Solving linear programming applications Conic Sections Content Skills Circles Write the equation of a circle passing through 3 non-collinear points Ellipses Write the equation of a circle in standard form Hyperbolas Solve a system of circles algebraically Parabolas Applications of conic sections Derive the equation of an ellipse from its definition Given an ellipse in standard form, find its center, vertices, and foci by completing the square Derive the equation of a hyperbola from its definition Given a hyperbola in standard form, find its center, vertices, and asymptotes by completing the square Derive the equation of a parabola from its definition Given a parabola in standard form, find its vertes, foci, and directrix by completing the square Discrete Mathematics Content Skills Sequences Determine if a sequence is arithmetic or geometric Series Mathematical Induction Define a sequence either explicitly or recursively Find the specific term of an arithmetic or geometric sequence Find the sum of a finite sequence Find the sum of an infinite geometric series Use Mathematical Induction to prove facts in number theory Introduction to Calculus Content Skills Limits Find limits of functions Derivatives by definition Determine an expression for the slope of a function Derivatives by rule Applications of the derivative Write the equation of a line tangent to a curve at a specific point Graphs of polynomial functions Determine the derivative of functions using the power, product, quotient, reciprocal, and chain rules Solve max/min applications Sketch the graph of a polynomial function by finding turning points and points of inflection