Strath Haven High School Syllabus
Course Title:
Level:
I.
Algebra II
Course Number: 3242/3263 Grade: 9-12
College Prep / Career College Prep
Course Description/Overview
This course continues the study of functions addressed in Advanced Algebra 1. It begins by
experimenting 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 complex numbers and the arithmetic of complex
numbers. The study of functions is then extended to include exponential and logarithmic functions, with
students investigating various transformations of those functions. Other topics include an introduction
to Pascal's Triangle, the Binomial Theorem, and rational functions.
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
Understand the correspondence between the roots of a polynomial and its linear factors
Review basic laws of exponents and develop an understanding of an 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
Develop an understanding of arithmetic and geometric sequences and series
Analyze Pascal’s Triangle and explore its relationship to the Binomial Theorem
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
Decide whether a linear function can reasonably represent a data set
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
Use complex numbers as tools for solving equations
Develop a fluency in complex number arithmetic
C.
Exponential and Logarithmic Functions
Evaluate exponential expressions, including zero, negative and rational exponents
Explore arithmetic and geometric sequences
Provide a geometric sequence to interpret expressions involving 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
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
D.
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
E.
Sequences and Series
Write a closed-form rule for the sum column of a given function
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
𝑛
Generate Pascal’s Triangle and write the nth row, kth column entry as ( )
𝑘
Notice and expand patterns in Pascal’s Triangle
Use the Binomial Theorem to expand expressions of the form (a + b)n
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.