Algebra II and Trigonometry Honors
Course Description:
Algebra II & Trigonometry Honors is an advanced
instructor-led algebra course focusing on topics of
systems, equations, polynomial arithmetic, complex numbers , solutions of
quadratic equations, exponential
and logarithmic functions , sequences, series, graphs of polynomial functions,
conic sections, and
applications of mathematics. Students completing this accelerated course are
prepared for future
coursework in math, physics, and engineering. This course is three weeks long,
with five hours of inclass
work for five days a week (75 hours total class time). Daily outside homework is
required.
Outcomes:
Upon successful completion of this course, students will
have mastered all the material in second-year
high school mathematics course and be prepared for a full year of PreCalculus
leading to an Advanced
Placement Calculus course. Students will be graded on daily homework and unit
tests, and occasional
quizzes may be used to further assess student comprehension.
Resources and Materials:
Text: Algebra 2, Larson, Boswell, Kanold, and Stiff
(McDougal Littell), 2007.
Students are required to have a graphing calculator, however no specific
manufacturer and model is
favored.
Student Evaluation and Grading Policies for Credit
Courses Only:
a. CTD Grading Scale (A+ is at instructor's discretion; an
instructor can use 97-100 A)
A+ |
100-98% |
A |
97-93% |
A- |
92-90% |
B+ |
89-87% |
B |
86-83% |
B- |
82-80% |
C+ |
79-77% |
C |
76-73% |
C- |
72-70% |
D+ |
69-67% |
D |
66-63% |
D- |
62-60% |
F |
below 60% |
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b. Students will be grade as follows:
Daily Homework: 15% of the final grade
Unit Tests (5 total tests): Each test is 13% of the final grade
Final Exam (cumulative): 20% of the final grade
Instructor Biography:
Lori Alvin is a Ph.D. student at the University of
Wisconsin-Milwaukee, where she is studying
Mathematics and more specifically the area of Real Dynamics . She has taught a
variety of
undergraduate courses for the mathematics department at the university including
Intermediate Algebra,
College Algebra, and several math courses for elementary school teachers. This
is her first year working
with Northwestern University's Center for Talent Development Summer Program, but
she has 8 years
experience working with gifted and talented students. She received her
bachelor's degree from the
University of Wisconsin-Oshkosh and her master's degree from the University of
Wisconsin-
Milwaukee.
Schedule:
Mathematics is not an isolated venture, and collaboration
is a necessity in this field. Therefore some
emphasis will be placed on group (including partner) work. Instruction will vary
from class to class to
allow some one-on-one time, lecture, and student presentations of homework
problems. Students should
anticipate covering a chapter a day.
Tests will address a wide variety of concepts,
applications and various problem solving and deduction
skills.
Unit |
Chapter |
Concepts to be covered |
Unit 1: Linear Equations,
Inequalities, Functions, and
Systems |
1-Equations and
Inequalities |
Apply properties of real numbers, evaluate and
simplify algebraic expressions, solve linear equations ,
rewrite formulas and equations, use problem solving
strategies and models, solve linear inequalities, solve
absolute value equations and inequalities. |
2-Linear
equations and
Functions |
Represent relations and functions, find slope and
rate
of change, graph equations of lines, write equations of
lines, model direct variation, draw scatter plots and
best-fitting lines, use absolute value functions and
transformations, graph linear inequalities in two
variables. |
3-Linear Systems
and Matrices |
Solve Linear systems by graphing, solve linear
systems algebraically, graph systems of linear
inequalities, solve systems of linear equations in three
variables, perform basic matrix operations, multiply
matrices, evaluate determinants and apply Cramer’s
Rule, use inverse matrices to solve linear systems. |
Unit 2: Quadratic,
Polynomial, and Radical
Functions |
4-Quadratic
Functions and
Factoring |
Graph quadratic functions in standard form, graph
quadratic functions in vertex or intercept form, solve
x² + bx + c = 0 by factoring, solve ax² + bx + c = 0 by
factoring, solve quadratic equations by finding square
roots, perform operations with complex numbers,
complete the square, use the quadratic formula and the
discriminant, graph and solve quadratic inequalities,
write quadratic functions and models. |
5-Polynomials
and Polynomial
functions |
Use properties of exponents, evaluate and graph
polynomial functions, add, subtract, and multiply
polynomials, factor and solve polynomial equations,
apply the remainder and factor theorems, find rational
zeros, apply the fundamental theorem of algebra,
analyze graphs of polynomial functions, write
polynomial functions and models. |
6-Rational
Exponents and
Radical Functions |
Evaluate nth roots and use rational exponents,
apply
properties of rational exponents, perform function
operations and composition, use inverse functions,
graph square root and cube root functions, solve
radical equations. |
Unit 3: Other Nonlinear
Functions and Relations |
7-Exponential
and Logarithmic
Function |
Graph exponential growth functions, graph
exponential decay functions, use functions involving
e, evaluate logarithms and graph logarithmic
functions, apply properties of logarithms, solve
exponential and logarithmic equations, write and
apply exponential and logarithmic functions. |
8-Rational
Functions |
Model inverse and joint variation, graph simple
rational functions, graph general rational functions,
multiply and divide rational expressions, add and
subtract rational expressions, solve rational equations. |
9-Quadratic
Relations and
Conic Sections |
Apply the distance and midpoint formulas, graph
and
write equations of parabolas, graph and write
equations of circles, graph and write equations of
ellipses, graph and write equations of hyperbolas ,
translate and classify conic sections, solve quadratic
systems. |
Unit 4: Probability, Data
Analysis, and Discrete Math |
10-Counting
Methods and
Probability |
Apply the counting principle and permutations,
use
combinations and the binomial theorem, define and
use probability, find probabilities of disjoint and
overlapping events, find probabilities of independent
and dependent events. |
11-Data Analysis
and Statistics |
Find measures of central tendency and dispersion,
apply transformations to data, use normal
distributions , select and draw conclusions from
samples, chose the best model for two- variable data . |
12-Sequences and
Series |
Define and use sequences and series, analyze
arithmetic sequences and series, analyze geometric
sequences and series, find sums of infinite geometric
series, use recursive rules with sequences and series. |
Unit 5: Trigonometry |
13-Trigonometric
Ratios and
Functions |
Use trigonometry with right triangles, define
general
angles and use radian measure, evaluate trigonometric
functions of any angle, evaluate inverse trigonometric
functions, apply the law of sines , apply the law of
cosines. |
14-Trigonometric
Graphs, Identities
and Equations |
Graph sine, cosine, and tangent functions,
translate
and reflect trigonometric graphs, verify trigonometric
identities, solve trigonometric equations, write
trigonometric models, apply sum and difference
formulas, apply double-angle and half-angle formulas. |
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