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Core Content and Skills
Math Precalculus H
2007-2008
BOE Approved

Algebra Skills  Content   Skills  Factoring review Factoring perfect cubes and by grouping Operations on Rational Expressions Complex Fractions   Simplify quadratic expressions by factoring Simplify sums and differences of cubes Simplify expressions by grouping 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 Domain and Range of functions Compositions of functions Inverses of functions Modeling functions   Identifying the graphs of basic functions Sketching the graphs of functions by using transformations of basic 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 Polynomials of degree 3 or higher Roots of polynomials Synthetic Division Graphs of polynomial functions   Express a quadratic equation in vertex form Maximize or minimize quadratic functions Determining the number of rational, real, and complex roots of a polynomial function 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   Skills  Graphs of rational functions Rational equations and inequalities   Sketching graphs of rational functions based on transformations of y = 1/x Sketching graphs of rational functions by finding asymptotes and intercepts Solving applications of rational functions     Exponential, Logarithmic, and Logistic functions  Content   Skills  Rational Exponents Exponential functions and graphs Logarithmic functions and graphs Logistic functions Applications of exponential, logarithmic, and logistic functions   Evaluating expressions with rational and negative exponents Writing exponential functions Evaluating exponential 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 Applications with trigonometric graphs   Determining position around the unit circle based upon the angle from the positive x-axis 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 Sum and difference trigonometric identities Multiple angle identities Solving trigonometric equations Trigonometric laws   Verify Pythagorean identities Verify sum and difference identities Sketch graphs of sums of sinusoids Verify double angle identities 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 Projectile Motion Polar coordinates Polar functions Trigonometric form of complex numbers Complex equations   Model horizontal and vertical motion Derive parametric equations to model projectile motion Convert rectangular coordinates to polar form 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 Matrix Algebra Multivariable systems and row operations Partial Fractions Systems of inequalities   Solving systems of equations in 2 variables Define matrices Perform operations on matrices Solve systems of linear equations with matrices using row reduction 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 Ellipses Hyperbolas Parabolas Applications of conic sections   Write the equation of a circle passing through 3 non-collinear points Write the equation of a circle in standard form Solve a system of circles algebraically 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 Series Mathematical Induction   Determine if a sequence is arithmetic or geometric 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 Derivatives by definition Derivatives by rule Applications of the derivative Graphs of polynomial functions   Find limits of functions Determine an expression for the slope of a function Write the equation of a line tangent to a curve at a specific point 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