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Trigonometry / Advanced Math Topics
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Course Description: This is a
preparatory course for students intending to take
college level or AP Calculus. This year long course is based primarily
on the
California State Standards for Trigonometry and Mathematical Analysis.
In
addition, we will incorporate some probability and statistics, and
analytic
geometry. Assessment: Grades are
based on: 30% homework 50% tests and projects Text: Precalculus 6th
Edition Authors: Larson,
Hostetler Publisher: Houghton
Mifflin, 2004 Content: Functions
and their Graphs Evaluate functions and find
their domains Analyze graphs of functions Identify and graph shifts,
reflections, and non rigid transformations of functions Find arithmetic
combinations and compositions of functions Find inverses of functions
graphically and algebraically Polynomial
and Rational Functions Sketch and analyze graphs
of quadratic and polynomial functions Use long division and
synthetic substitution to divide polynomials Determine the number of
rational and real zeros Perform operations with
complex numbers and plot Determine the domain, find
asymptotes, and sketch rational functions Exponential
and Logarithmic Functions Recognize, evaluate, and
graph exponential and logarithmic functions Rewrite logarithmic
functions with different bases Use properties of Logs Solve exponential and
logarithmic equations Use exponential growth,
decay and Gaussian models Fit exponential and
logarithmic models to data Trigonometric
Functions Describe an angle and
convert between degree and radian measures Identify a unit circle and
its relationship to real numbers Evaluate trigonometric
functions of any angle Use trigonometric
identities Sketch graphs of
trigonometric functions Compositions of
trigonometric functions Model real life problems
using trigonometric functions Analytic
Trigonometry Use fundamental identities
to evaluate trigonometric functions Verify trigonometric
identities Solve trigonometric
equations using inverses Use sum an difference
formulas, product and sum formulas, multi-angle formulas, power
reducing
formulas, half-angle formulas to rewrite and evaluate trigonometric
functions. Additional
topics in Trigonometry Use law of sines an cosines Find areas of oblique
triangles Represent vectors as
directed lines and perform mathematical operations on vectors. Find direction angles of
vectors Find the dot product of two
vectors Multiply and divide complex
numbers written in trigonometric form Find powers and nth root
for complex numbers System
of Equations and Inequalities Solve systems of equations
by substitution, by elimination, by Gaussian elimination, and
graphically Recognize linear systems in
row-echelon form and to use back substitution to solve the system Solve nonsquare systems of
equations Sketch the graphs of
inequalities in two variables and solve systems of inequalities Solve linear programming
problems Model real life problems Matrices
and Determinants Write matrices, identify
their order and perform row operations Use Gaussian elimination
and Gaussian-Jordan elimination with matrices to solve a system Perform operations with
matrices Inverses with matrices Determinants of square
matrices Uses crammer's rule to
solve a system Sequences,
Series, and Probability Use sequence, factorial,
summation notation to writer terms and sums of sequences Write arithmetic and
geometric sequences Prove statements using
induction Use Binomial Theorem and
Pascal’s triangle to calculate binomial coefficients and write
binomial
expansion Solve counting problems
using the Fundamental Counting Principles, permutations and combinations Find the probability of
events and their complements Topics
in Analytic Geometry Write the equations,
analyze and sketch the graphs of parabolas, ellipses, and hyperbolas Rotate the coordinate axis
to eliminate the xy-term in equations of conics and use the
discriminant to
identify conics Solve systems of quadratic
equations Rewrite sets of parametric
equations and find sets of parametric equations for graphs Write equations in polar
form, graph polar equations Write equations of conics
in polar form |