Download 6.5 Honors Trig-Adv. Math

Honors Trigonometry and Advanced Mathematics
Concepts
Trigonometric
Functions
Competencies
Convert decimal degrees to degrees, minutes and seconds and vice versa; define
and use coterminal and reference angles
Assessment Standards
Hwk
CC.2.3.HS.A.7
Find the values of the six trigonometric rations for acute angles of right
triangles.
Use the mnemonic SOHCAHTOA
Develop the unit circle from the 2 special right triangles, 30-60-90 and 45-45-90
Use SOHCAHTOA to find the measures of the sides of right triangles.
Use SOHCAHTOA to find the measures of the angles of right triangles
Solve real world applications of right triangles
Use the Law of Sines to find measures of sides and angles of triangles that are
not right triangles
Find areas of non-right triangles
Use the Ambiguous Case of the Law of Sines to determine if zero, one, or two
triangles can be constructed from given information
Use the Law of Cosines to find the measure of a side or angle of a non-right
triangle when Law of Sines is not applicable
Hwk
CC.2.3.HS.A.7
CC.2.2.HS.C.9
Hwk/Quiz
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Hwk/Quiz
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CC.2.3.HS.A.7
CC.2.3.HS.A.7
CC.2.3.HS.A.14
CC.2.3.HS.A.7
CC.2.3.HS.A.3
Hwk
CC.2.3.HS.A.3
Hwk/Quiz
CC.2.3.HS.A.3
Unit test
Concepts
Graphs of the
Trigonometric
Functions
Competencies
Change from radian measure to degree measure, and vise versa.
Find the arc length of a circle, and find area of a sector of a circle
Assessment Standards
Hwk
CC.2.3.HS.A.8
CC.2.2.HS.C.7
Find linear and angular velocity
Derive and draw the graphs of the Sine and Cosine Functions
Define and find the amplitude and period to draw graphs of the Sine and Cosine
Functions.
Write equations given amplitude and period for Sine and Cosine Functions
Define and find the phase shift and vertical translation to draw graphs of the
Sine and Cosine Functions
Model real world data using Sine and Cosine Functions
Hwk/Quiz
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Graph the Remaining Trig Functions: Tangent, Secant, Cosecant, Cotangent,
Graph the inverse Trig Functions
CC.2.2.HS.C.8
CC.2.2.HS.C.4
CC.2.2.HS.C.8
Hwk/Quiz
CC.2.2.HS.C.4
Hwk
CC.2..3HS.A.14
Hwk
Hwk
Unit test
CC.2.2.HS.C.8
CC.2.2.HS.C.4
Concepts
Trigonometric
Identities
and Equations
Competencies
Identify and use Reciprocal Identities, Quotient Identities, and Pythagorean
Identities to simplify expressions.
Assessment
Standards
Hwk
CC.2.2.HS.C.9
Verify Trigonometric Identities
Use the Sum and Difference Identities for Sine, Cosine, and Tangent
Use the Double and Half-Angle Identities for Sine, Cosine, and Tangent
Solve Trigonometric Equations
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Unit test
CC.2.2.HS.C.9
Concepts
Polar Coordinates and
Complex Numbers
Competencies
Graph points in polar coordinates, graph polar equations, determine the distance
between 2 points with polar coordinates.
Graph various polar equations; such as cardiod, limacon, rose, etc
Convert between polar and rectangular coordinates, and vice versa
Write and graph the polar from of a linear equation
Perform all the operations on complex numbers in rectangular form
Graph complex numbers in the complex number and convert them to polar from
and vice versa
Multiply and Divide Complex Numbers in Polar Form
Find Powers and Roots of Complex Numbers in polar form using De Moivre’s
Theorem
Assessment
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Hwk/Quiz
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Unit test
Standards
CC.2.1.HS.F.6
Concepts
Conic Sections
Competencies
Find the distance and midpoint between 2 points on the coordinate plane
Use and determine the standard form of a circle by determining the center and
radius
Use and determine the standard form of an ellipse by determining the center,
vertices, and foci
Use and determine the standard form of a hyperbola by determining the center,
the vertices, the foci, and the asymptotes
Use and determine the standard form of a parabola by determining the vertex,
the focus, the directrix, and axis of symmetry
Assessment Standards
Hwk
Hwk/Quiz CC.2.3.HS.A.10
Hwk/Quiz
CC.2.3.HS.A.10
Hwk/Quiz
CC.2.3.HS.A.10
Hwk/Quiz
CC.2.3.HS.A.10
Unit test
Concepts
Exponential and
Logarithmic Functions
Competencies
Use the properties of exponents, and simplify rational exponents
Assessment Standards
Hwk
CC.2.1.HS.F.1
Graph exponential functions. Solve problems using exponential growth and
decay
Use the natural base e to graph functions, solve problems using e.
Evaluate expressions using logarithms, solve logarithmic equations, graph
Logarithmic equations
Use natural logs, ln, to solve equations, Graph natural log, ln, functions
Hwk
Solve real world problems using natural logarithmic functions
Hwk/Quiz
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Unit test
CC.2.2.HS.C.5
CC.2.2 HS.D.9
CC.22.HS.D.10
CC.2.2.HS.C.5
CC.2.2 HS.D.9
CC.2.2.HS.C.5
CC.2.2 HS.D.9
CC.2.2.HS.C.5
CC.2.2 HS.D.9
Concepts
Sequences and Series
Competencies
Define and use arithmetic sequence and series to find the nth term of a sequence
and find the sum of n terms of an arithmetic series
Define and use geometric sequence and series to find the nth term of a sequence
and find the sum of n terms of a geometric series
Find the limit of the terms of an infinite sequence. Find the sum of an infinite
Geometric series
Define convergent and divergent series and determine whether a series is which
of the two
Use sigma notation to find sums and be able to express a series in sigma notation
Use the Binomial Theorem and Pascal’s Triangle to expand binomials
Assessment Standards
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Hwk/Quiz
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Unit test
Concepts
Combinatorics and
Probability
Competencies
Solve problems using the Basic Counting Principle, solve problems using
Permutations and Combination s
Solve problems that involve permutations with repetitions and circular
permutations
Find the probability of an event, find the odds for the success and failure of an
event.
Find the probabilities of: independent and dependent events, and mutually
Inclusive and Exclusive events
Find the probability of an event given the occurrence of another event
Assessment Standards
Hwk
Find the probability of an event using the Binomial Theorem
Hwk/Quiz
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CC.2.4.HS.B.7
Hwk/Quiz
CC.2.4.HS.B.7
Hwk
CC.2.4.HS.B.7
CC.2.4.HS.B.6
CC.2.4.HS.B.7
Unit test
Concepts
Statistics and Data
Analysis
Competencies
Draw, analyze, and use bar graphs and histograms. Organize data into a frequency
Distribution.
Find the mean, median, and mode of a set of data. Construct and analyze a stem
and leaf plot
Construct a box and whisker plot. Find interquartile range, mean and standard
Deviations.
Use the normal distribution curve
Assessment Standards
Hwk
CC.2.4.HS.B.1
Find the standard error of the mean to predict the true mean of a population with
a certain level of confidence
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Hwk/Quiz
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unit test
CC.2.4.HS.B.1
CC.2.4.HS.B.2
CC.2.4.HS.B.1
CC.2.4.HS.B.2
CC.2.4.HS.B.1
CC.2.4.HS.B.4
CC.2.4.HS.B.4
CC.2.4.HS.B.5
Concepts
Calculus
Competencies
Calculate limits algebraically and by using a calculator
Find derivatives and antiderivatives of polynomials
Find areas of integrals of polynomial functions and find the areas under their
graphs.
Assessment Standards