Download Strath Haven High School Syllabus

Strath Haven High School Syllabus
Course Title:
Level:
Advanced Algebra II / Trigonometry
Honors
Course Number: 3221 Grade: 9-12
I.
Course Description/Overview
The course experiments with functions used to model real world data, differentiating between explicitly and
recursively defined functions. The definition of a function is formalized and students use polynomial functions to
explore the topics of domain, range, arithmetic of functions, composition of functions, and inverse functions.
Students are introduced to rational and complex numbers and their respective operations. The study of functions
is then extended to include exponential, logarithmic, and trigonometric functions, and students investigate various
transformations of those functions. Other topics include matrices, sequences and series, Pascal's Triangle, the
Binomial Theorem, and combinatorics.
II.
Course Objectives
Revisit the notion of a function through the use of closed-form (explicit) and recursive descriptions
Introduce complex numbers as an extension of the real number system
Explore matrices, understand their properties, and use them to solve systems of equations
Understand the correspondence between the roots of a polynomial and its linear factors
Review basic laws of exponents and develop an understanding of the exponential function
Investigate logarithms and the logarithmic function as it relates to the exponential function
Explore the effects of translating, scaling and reflecting the graphs of basic functions
Perform operations involving rational expressions
Develop an understanding of sequences and series, including arithmetic and geometric
Extend the domain of trigonometric functions past 90o by relating to the coordinates on a unit circle
Use analytic trigonometry to solve triangles for their missing parts
Analyze Pascal’s Triangle and explore its relationship to the Binomial Theorem
Introduce and apply permutations and combinations to solve systematic counting problems
III.
Course Content (Key Concepts/Skills)
A.
Introduction to Functions
Find closed form and recursive functions to fit input-output tables
Use difference tables to determine whether a given table is a linear or quadratic function
Find the balance point and line of best fit for a data set
Define, identify, and evaluate recursive functions including the factorial function
Solve literal equations for a specified variable
B.
Functions and Polynomials
Determine whether a table, graph or closed form rule is a function
Investigate composition of functions
Find the inverse of a function, if it exists
Use linear combinations of polynomials to determine new polynomials
Understand the relationship between roots and factors of polynomials
Divide polynomials by monic linear factors
State and use the Remainder Theorem and the Factor Theorem
Write the general rule of a function that fits a table
Develop advanced techniques for factoring polynomials
Understand complex numbers as an extension of the real number system
Become fluent in complex number arithmetic
Use complex numbers as tools for solving equations
Introduce rational expressions and become fluent with rational operations
C.
Linear Algebra
Extend algebraic techniques to solve systems of three equations with three unknowns
Understand the definition of a matrix as an organized array of numbers
Convert between a system of linear equations and matrix form
Investigate Gaussian Elimination and apply it to solve a system with and without a calc
Compute dot products, sums, differences, products, and inverses of matrices
Interpret and solve problems using matrix calculations
D.
Exponential and Logarithmic Functions
Evaluate exponential expressions, including zero, negative and rational exponents
Convert between exponential and radical forms for rational exponents
Explore the graph characteristics of exponential functions
Determine the equation of an exponential function given two points
E.
H.
G.
I.
Provide an exponential function, in both closed and recursive form, from a table
Define the logarithmic function as the inverse of an exponential function
Review the Laws of Exponents to develop the Laws of Logarithms
Evaluate logarithms of any base with and without a calculator
Use logarithms to solve exponential equations
Explore the graph characteristics of logarithmic functions
Graphs and Transformations
Identify and sketch the basic functions: linear, quadratic, rational, cubic, square root,
absolute value, exponential and logarithmic function
Relate the effect of a translating on both the graph and its equation
Relate the effect of scaling or reflecting on both the graph and its equation
Compose transformations and sketch the effect of a composition on a basic graph
Introduction to Trigonometry
Use special angles to find coordinates on a unit circle
Evaluate the sine, cosine, and tangent functions for any angle
Solve equations involving trigonometric functions
Explore the graph characteristics of the sine, cosine, and tangent functions
Use the graphs of trigonometric functions to solve problems
Prove and use the basic trigonometric identities
Solve a triangle for its missing parts
Derive and use the Law of Sines and the Law of Cosines
Investigate and use Heron’s Formula
Sequences and Series
Write a closed-form rule for the sum of any given definite or indefinite sequence
Use Gauss’s method to find the sum of an arithmetic sequence
Use Euclid’s method to find the sum of a geometric sequence
Convert between ∑ notation and expanded form of the series
Find a closed form for arithmetic and geometric sequences and their associated series
Determine whether a geometric sequence has a limit, and if it does, how to find it
𝑛
Generate Pascal’s Triangle and write the nth row, kth column entry as ( )
𝑘
Identify and expand patterns in Pascal’s Triangle
Use the Binomial Theorem to expand expressions of the form (a + b)n
Combinatorics
Explore combinatorics and the types of problems you can solve with them
Investigate multiple strategies for systematic counting
Develop and use formulas for finding the number of permutations nPr
Develop and use formulas for finding the number of combinations nCr.
Apply counting strategies to solve Pascal’s Paths problem
Relate the coefficients of a binomial expansion to Pascal’s Triangle
IV.
Types of Student Assessments and Evaluations
Quizzes, tests, oral presentations, and graded homework.
V.
Grading Policy
Grades are based on a point system. Averages are calculated by dividing the total points earned by the student
by the total number of possible points. The school scale is used to determine grades: A (90% and above), B
(80% and above), C (70% and above), D (60% and above), and F (59% and below). Final grades are determined
as follows: first marking period (40%), second marking period (40%), and final exam (20%).
VI.
Homework
Homework is given on a regular basis. Most assignments are due the next day.
VII
Resources
Graphing calculators (TI-Nspire recommended), rulers, protractors, compasses, graph paper and CME Project:
Algebra II (CME Project Development Team)
All members of the school community are expected to be respectful of each other. Negative comments about anyone’s
race, nationality, religion, physical appearance or ability, intellectual capabilities, gender identity, sexual orientation, work
ethic, or character are unacceptable and will not be tolerated. Students are encouraged to discuss any concerns with any
adult in the building.