Honors Algebra II Syllabus
Teacher: B. Goforth
Email: bmgoforth@clevelandcountyschools.org
Web Site: http://www.bgoforth.net
Overview:
Honors
Algebra II continues students' study of advanced algebraic concepts including
functions, polynomials, rational expressions, systems of functions and
inequalities, and matrices. students will be expected to describe and translate
among graphic, algebraic, numeric, tabular, and verbal representations of
relations and use those representations to solve problems. The course includes all topics
covered in Algebra II, but is characterized by more rigorous assignments, an
increased pace of study, and independent projects completed outside of
class. An emphasis will be placed on mathematical theory and higher order
thinking skills that impact practical and increasingly complex
applications, modeling, and algebraic proof. Technology will be used regularly
for instruction and assessment.
Objectives:
The
learner will:
·
Simplify
and perform operations with rational exponents and logarithms (common and
natural) to solve problems.
·
Define
and compute with complex numbers.
·
Operate
with algebraic expressions (polynomial, rational, complex fractions) to solve
problems.
·
Operate
with matrices to model and solve problems.
·
Model
and solve problems using direct, inverse, combined and joint variation.
·
Use
the composition and inverse of functions to model and solve problems and
justify the results.
·
Use
quadratic functions and inequalities to model and solve problems; justify the
results; solve using tables, graphs, and algebraic properties; interpret the
constants and coefficients in the context of the problem.
·
Use
exponential functions to model and solve problems; justify the results; solve
using tables, graphs, and algebraic properties; interpret the constants,
coefficients, and bases in the context of the problem.
·
Create,
justify, and use beat-fit mathematical models of linear, exponential,
quadratic, and cubic functions to solve problems involving sets of data;
interpret the constants, coefficients, and bases in the context of the data;
check the model for goodness-of-fit and use the model, where appropriate, to
draw conclusions or make predictions.
·
Use
rational equations to model and solve problems and justify results; interpret
the constants and coefficients in the context of the problem; identify the
asymptotes and intercepts graphically and algebraically.
·
Use
polynomial equations (third degree and higher) to model and solve problems;
solve using tables and graphs; interpret constants and coefficients in the
context of the problem.
·
Use
equations with radical expressions to model and solve problems and justify
results; solve using tables, graphs, and algebraic properties; interpret the
degree, constants, and coefficients in context of the problem.
·
Use
equations and inequalities with absolute value to model and solve problems and
justify results; solve using tables, graphs, and algebraic properties;
interpret the constants and coefficients in context of the problem.
·
Identify,
compare, and construct the conic sections to model and solve problems; describe
parabolas and circles algebraically according to definitions, characteristics,
and constituent parts; identify and distinguish among the conic sections using
tables, graphs, and algebraic properties.
·
Use
systems of two or more equations or inequalities to model and solve problems
and justify results; solve using tables, graphs, matrix operations, algebraic
properties, and linear programming.
Minimum Topic Coverage
Ø
Function concepts
§
Definition
as a set of ordered pairs, as a rule, compared with relations
§
Function
notation
§
Independent
and dependent variable; domain and range
§
Graphs
of functions and relations
§
Introduction
to 3-dimensional graphing
§
Arithmetic
operations on functions
§
Inverse
of a function
§
Piece-wise
defined functions
§
Composition
§
Inverse
functions
·
Graphical
meaning and in terms of ordered pairs
·
How
to compute
·
Whether
an inverse exists
§
Even
and odd functions
§
Linear
transformations and their effect on graphs
§ Applications and modeling
Ø Linear functions and relations
§
Slope-intercept
and point-slope form
§
Graphs
and use of a coordinate system
§
Geometric
interpretation of slope as a rate
§
solving
linear equations
§
Linear
regression
§
Linear
inequalities in one and two variables
§
Absolute
value equations and inequalities - solved by graphing
§
Applications
and modeling
Ø Systems of linear equations and inequalities
§
Solving
algebraically (substitution and elimination) and by graphing
§
Use
calculator to solve arbitrary systems (not necessarily linear)
§
Linear
programming
§
Graphing
in three variables
§ Applications and modeling
Ø Matrix algebra
§
Matrix
concepts
·
Terminology:
row, column, identity, inverse
·
Calculator
use
§
Operations
·
Addition,
subtraction, and scalar multiplication
·
Multiplication
by calculator
·
Multiplication
by hand
§
Identity
and inverse matrices
·
Finding
inverses by calculator
·
Finding
inverses using formulas and/or by hand
§
Solve
systems of equations
·
Using
inverses to solve AX=B
·
Cramer's
Rule
§
Selected
applications and modeling such as inventory, cost and profit
Ø Quadratics
§
Terminology:
intercept, root, zero, solution
§
Graphing:
roots, y-intercept, vertex, symmetric points, axis of symmetry
§
Vertex
form
§
Solving
·
Common
factor and quadratic factoring
·
Completing
the square
·
Ways
to find the vertex: vertex form, -b/2a, symmetry, graphing calculator
·
Quadratic
formula
·
Relationship
between factoring and the quadratic formula
·
Relationship
between discriminant and roots
§
Complex
numbers
·
The
imaginary unit i
·
Solving
quadratics with complex roots
·
Add,
subtract, multiply, divide conjugates
·
The
complex plane
§
Finding
a parabola from three points
§
Applications
and modeling such as motion, gravitational constant
Ø Polynomials
§
Vocabulary:
degree, coefficient, leading coefficient, term, nth degree, constant term,
root, solution, zero, x-intercept, complete factoring
§
Multiplying,
binomial theorem
§
Factoring
·
Common
factor
·
Difference
of squares, perfect squares
·
Sum
and difference of cubes
·
Long
division algorithm
·
Synthetic
division
§
Finding
roots
·
The
factor/remainder theorem
·
The
rational roots theorem
·
Use
of calculator to solve
§
Graphs
and curve sketching
·
End
behavior
·
Number
of roots/changes in sign
·
Turning
points
·
Finding
a function from a graph
§ Applications and modeling
Ø Powers, roots, and radicals
§
nth
roots
§
Solving
radical equations by graphing
§ Applications and modeling
Ø Rational equations and functions
§
Inverse,
joint, combined, and direct variation
§
Solving
rational equations by graphing
§
Add,
subtract, multiply, and divide rational expressions
§
Vertical
and horizontal asymptotes
§
Applications
and modeling
Ø Exponents and logarithms
§
Basic
laws of exponents, negative and rational exponents, roots
§
Logarithm
as the inverse of exponentiation
·
Logarithmic
notation
·
Log
rules (product, quotient, power, and change of base rule)
§
Solve
exponential equations, with and without calculator
§
Solve
log equations
§
Find
an exponential equation from two points
§
Base
e, ln
§
Graphs
of exponential and logarithmic functions
§ Applications and modeling such as growth and decay, bank interest and depreciation
Ø Conic sections
§
Circles
§
Ellipses
§
Hyperbolas
§ Parabolas
Ø Sequences and series
§
Recursive
and explicit definitions of functions
§
Arithmetic
and geometric sequences and series
§
Arithmetic
and geometric means
§
Applications
and modeling
Ø Counting principles and probability
§
Counting
problems
§
Binomial
theorem, Pascal's triangle
§ Rules of probability
Ø Statistics
§
Modeling
real world data using scatterplots
§
Prediction
equations
§
Correlation
Methodology
There are several methodological approaches for this
course. Lectures are important for introducing new material and connecting it
to previously learned material. Group work will be used frequently. In addition
to the homework that is assigned each night, students will have worksheets that
go beyond what has been taught, requiring that they read supplemental material
in order to complete the assignment. Students will also work in pairs to
complete two projects during the year.
Evaluation
Tests - 70%
Homework - 30%
**Projects will count as a double test grade
Resources
Houghton-Mifflin Algebra 2 and Trigonometry
Glencoe/McGraw Hill Algebra 2
Technology
Resources
TI-83/TI-83 Plus Graphing
Calculator
TI Smartview
TI-Interactive
Internet
Excel
Interwrite School Board
Evaluation
of Projects
Rubrics will be developed
specific to the project.
Course Outline
|
Dates |
Topic |
Activities |
|
August 25 – September 3 |
Sets and symbols; axioms for real numbers; properties of real number system; theorems and proofs |
“White shirt gorillas” video clip |
|
September 4 – September 15 |
Transforming equations and solving problems |
Worksheet 2.08 |
|
September 16 – September 25 |
Linear functions and relations |
Movie clip |
|
September 26 – October 8 |
Systems of linear equations or inequalities |
Worksheet 2.10 |
|
October 9 – October 22 |
Graphs in space; determinants |
Movie clip |
|
October 28 – November 18 |
Polynomials and rational expressions |
Worksheet 1.03 Worksheet 2.05 |
|
November 19 – December 9 |
Radicals and irrational numbers; * midterm exam review begins |
Worksheet 2.03 Worksheet 2.07 Movie clip |
|
January 5 – January 9 |
Complex numbers |
Movie clip |
|
January 12 - January 28 |
Sequences and series |
|
|
January 29 – February 19 |
Polynomial functions |
Worksheet 2.02 |
|
February 20 – March 10 |
Quadratic relations and systems |
Worksheet
2.09 Worksheet
1.05 Project Variation |
|
March 11 – March 26 |
Exponents and logarithms |
Worksheets
1.01, 2.01 Project Crime Watch |
|
April 1 – April 9 |
Matrices |
Worksheet
1.04 |
|
April 20 - April 21 |
Modeling real world data using scatterplots |
|
|
April 22 – April 23 |
Prediction equations |
Worksheet 2.04 |
|
April 24 – April 27 |
Correlation |
Anscombe
data set |
|
April 28 - April 29 |
Binomial theorem |
|
|
April 30 - May 1 |
Horizontal and vertical asymptotes |
|
|
May 4 - |
Benchmarks & Review for EOC’s |
|