Download Quaker Valley School District Course Syllabus

Quaker Valley School District Course Syllabus
School: Quaker Valley High School
Course Title: Honors Functions, Statistics, and Trigonometry
Course Number: 4410
Course Description:
Students will work with descriptive and inferential statistics, probability, combinatorics, and various functions,
such as exponential, logarithmic, and trigonometric functions. Algebraic,
statistical and trigonometric concepts will be integrated throughout the course. Mathematical
modeling of problems from the real world will be emphasized. The use of technology will be
emphasized using the TI-83 graphics calculator. This course differs from Functions, Statistics,
and Trigonometry in both the depth and the breadth of the topics within the curriculum.
Although many concepts are taught in both courses, the honors course is more rigorous in
addressing these concepts. Concepts are often addressed at a theoretical and at a practical level
in the honors course.
Text and Materials:
• Functions, Statistics, and Trigonometry, 2nd Edition, The University of Chicago School
Mathematics) Scott Foresman, 1998
• Graphing Calculator
Standards
The curriculum content for this course has been written and aligned in accordance with the academic standards
established by the Pennsylvania Department of Education. For more information regarding specific standards,
you can log onto http://www.pdesas.org/ and click the "Clear Standards" tab.
Major Units:
Exploring Data
• Calculate measures of center and spread for data sets.
• Use sigma-notation to represent a sum, mean, variance, or standard deviation.
• Compare measures of center.
• Compare measures of spread.
• Use samples to make inferences about populations.
• Determine relationships and interpret data presented in a table.
• Use statistics to describe data sets and to compare or contrast data sets.
• Read and interpret bar graphs, circle graphs, and coordinate graphs.
• Read and interpret box plots.
• Read and interpret histograms and dot plots.
• Draw graphs to display data.
Functions and Models
• Evaluate functions described with Euler's notation.
• Identify independent and dependent variables, domain, and range of a function.
• Identify properties of regression lines and of the correlation coefficient.
• Describe properties of quadratic and exponential functions.
• Find and interpret linear models.
• Find and interpret exponential models. Find and interpret quadratic models.
• Use step functions to model situations.
• Graph linear, exponential, quadratic, and step functions.
• Interpret properties of relations from graphs.
• Use scatter plots to draw conclusions about models for data.
Transformations of Graphs and Data
• Find formulas and values of composites of functions.
• Find inverses of functions.
• Use Graph Translation and Graph Scale Changes to find transformation images.
• Describe the effects of translations or scale changes on functions and their graphs.
• Describe the effects of translations or scale changes on measures of center or spread.
• Describe the symmetries of graphs.
• Identify properties of composites and inverses.
• Identify properties of z-scores.
• Use translations, scale change, or z-scores to analyze data.
• Recognize and graph parent functions.
• Apply Graph Translation and Graph Scale-Changes to make or to identify graphs.
• From a graph of a function, determine its symmetries or whether its inverse is a function.
• Graph inverses of functions.
Circular Functions
• Convert between degrees, radians, and revolutions.
• Find lengths of circular arcs and areas of sectors.
• Find sines, cosines, and tangents of angles.
• Apply the definitions of the sine, cosine, and tangent functions.
• Apply theorems about sines, cosines, and tangents.
• Identify the amplitude, period, frequency, phase shift, and other properties of circular
functions.
• Solve problems involving lengths of arcs or areas of sectors.
• Use equations of circular functions to solve problems about real phenomena.
• Find equations of circular functions to model periodic phenomena.
• Use the unit circle to find values of sines, cosines, and tangents.
• Draw or interpret graphs of the parent sine, cosine, and tangent functions.
• Graph transformation images of circular functions.
• State equations for graphs of circular functions.
Trigonometric Functions
• Find sines, cosines, and tangents of angles.
• Evaluate inverse trigonometric functions.
• Use trigonometry to find lengths, angles, or areas.
• Solve trigonometric equations.
• Interpret the Law of Sines, Law of Cosines, and related theorems.
• State properties of inverse trigonometric functions.
• Solve problems using trigonometric ratios in right triangles.
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Solve problems involving the Law of Sines and Law of Cosines.
Write and solve equations for phenomena described by trigonometric and circular functions.
Graph or identify graphs of inverse trigonometric functions.
Root, Power, and Logarithmic Functions
• Solve exponential equations.
• Evaluate logarithms.
• Describe properties of rational power, nth root, and logarithmic functions.
• Use properties of logarithms.
• Use rational exponents to model situations.
• Solve problems arising from exponential or logarithmic models.
• Use rational power functions or logarithmic functions to model data.
• Graph nth root, rational power, and logarithmic functions.
• Interpret graphs of nth root, rational power, and logarithmic functions.
Polynomial Functions
• Use finite differences and systems of equations to determine an equation for a polynomial function from
data points.
• Calculate or approximate zeros and relative extrema of polynomial functions.
• Divide polynomials.
• Factor polynomials and solve polynomial equations using the Factor Theorem, sums or differences or
powers, grouping terms, or trial and error.
• Perform operations with complex numbers.
• Apply the vocabulary of polynomials.
• Apply the Remainder Theorem, the Factor Theorem, and Factor-Solution-Intercept Equivalence
Theorem.
• Apply the Fundamental Theorem of Algebra and Conjugate Zeros Theorem.
• Construct and interpret polynomials that model real situations.
• Represent two or three dimensional figures with polynomials.
• Relate properties of polynomial functions and their graphs.
Probability and Simulation
• List sample spaces and events for probability experiments.
• Compute probabilities.
• Find the number of ways of selecting or arranging objects.
• Evaluate expressions using factorials.
• State and use properties of probabilities.
• Determine whether events are mutually exclusive, independent, or complementary.
• Solve equations using factorials.
• Calculate probabilities in real situations.
• Use Counting principles and theorems to ding the number of ways of arranging objects.
• Design and conduct simulations without technology.
• Design and conduct simulations using technology.
• Construct, graph, and interpret probability distributions.
Sequences, Series, and Combinations
• Find terms of sequences from explicit or recursive formulas.
• Find explicit or recursive formulas for the nth term of an arithmetic or geometric sequence.
• Evaluate arithmetic or geometric series.
• Expand binomials.
• Determine whether a sequence is arithmetic or geometric.
• Determine limits of certain sequences.
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Tell whether an infinite series converges. If it does, give the limit.
Prove and apply properties involving combinations.
Solve problems involving arithmetic and geometric sequences and series.
Use combinations to compute the number of ways of selecting objects.
Determine probabilities in situations involving binomial experiments.
Locate numerical properties represented by the patterns in Pascal's Triangle.
More Work With Trigonometry
• Evaluate reciprocal functions.
• Apply properties of the reciprocal trigonometric functions.
• Prove trigonometric identities.
• Describe singularities of functions.
• Use a calculator to test a proposed identity.
• Given polar coordinates of a point, determine its rectangular coordinates, and vise versa.
• Plot points in a polar coordinate system.
• Graph and interpret graphs of polar equations.
Binomial and Normal Distributions
• Calculate the mean and standard deviation of a binomial probability.
• Use the Standard Normal Distribution to find probabilities.
• Compare and contrast characteristics of different binomial probability distribution graphs.
• Use properties of normal distributions and their parent function.
• Solve probability problems using binomial or normal distributions.
• Use binomial and normal distributions to test hypotheses.
• Apply the Central Limit Theorem.
• Apply confidence intervals to real world problems.
• Graph and interpret a binomial probability distribution.
• Graph and interpret normal distributions.
Major Assessments and Projects:
• Tests, Quizzes, and Projects will be approximately 80% of the student’s grade.
• Homework and Practice will be approximately 20% of the student’s grade.
Technology will be integrated throughout the course.