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%

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.
Unit 5: Trigonometry	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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