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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