Download Name: Tracy Hanzal

Syllabus
Algebra II
2010-2011
Name: Tracy Hanzal
Email: [email protected]
Telephone: 701-224-1789
Course Description: Algebra II is a review and extension of material covered in Algebra
I including some Trigonometry topics. This material includes Inequalities, Linear
Equations, Functions, Polynomials, Quadratic Equations, Logarithms, Trigonometric
Applications, and Matrices.
Required Course Materials: Student text: Algebra and Trigonometry: Structure and
Method, Book. McDougal Littell/Houghton Mifflin
Supplies: Notebook paper, folder, pencil and TI-84 Plus calculator. You may bring your
own TI-84 Plus calculator. If you do not have one, the school will provide a calculator
for classroom use.
Course Requirements: Course requirements include daily problems done at the
beginning of every class period, notes, homework assignments, quizzes, and tests.
Participation is also required as we will be correcting assignments together in class and
will include work at the board during each lesson and from assignments.
Evaluation: Students’ progress in the course will be evaluated based upon formal and
informal assessment techniques as discussed under course requirements and grading.
Instructional Strategies: Instructional strategies will include lecture, note-taking, class
participation, students working examples at the board, small group activities, and
individualized instruction.
Accountability for Assignments: Students are expected to begin working on the daily
problem immediately when they get to class. Students will have a specified amount of
time to complete the daily problem and will have it checked as soon as it is completed by
the teacher. Students not completing the daily problem efficiently as determined by the
teacher will receive and zero for that daily problem. Assignments given in class are due
the next class period. Work not finished in school is expected to be finished at home. If
assignments are handed in late, the student will lose five points for that assignment for
each day it is late. Students are also expected to participate in class (board work and
answering questions) and to be prepared for quizzes and tests.
Grading System: (based on %)
A+
100
A
94-99
A92-93
B+
89-91
B
85-88
B83-84
C+
80-82
C
76-79
C74-75
D+
71-73
D
67-70
D65-66
If You Have A Disability: Any accommodations or modifications will be coordinated
with the special education case manager.
Class Schedule (Subject to Change):
Week
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
Topics and Standards Addressed
Introduction, Syllabus Review, Simplifying Expression, Sums and
Differences, Products, Quotients, Solving Equations
9.2.2.1, 9.2.2.2
Problem Solving with Equations, Solving Inequalities and Combined
Inequalities, Solving Absolute Value Sentences
9.2.3.1
Open Sentences in Two Variables, Graphs of Linear Equations in Two
Variables, Slope of a Line, Find an Equation of a Line
9.2.2.3
Systems of Linear Equations in Two Variables, Problem Solving: Using
Systems
9.2.2.1
Linear Inequalities in Two Variables, Functions, Relations, Polynomials,
Laws of Exponents
9.2.1.1, 9.2.1.2, 9.2.2.6, 9.2.3.1, 9.2.3.2
Using Prime Factorization, Factoring Polynomials, Factoring Quadratic
Polynomials
9.2.3.3,
Solving Polynomial Equations, Solving Polynomial Inequalities
9.2.4.1
Quotients, Monomials, Zero and Negative Exponents, Rational
Expressions
9.2.2.4
Complex Fractions, Fractional Coefficients and Equations
9.2.3.4, 9.2.3.5
Roots of Real Numbers, Properties and Sums of Radicals, Binomials and
Week 11
Week 12
Week 13
Week 14
Week 15
Week 16
Week 17
Week 18
Equations Containing Radicals
9.2.4.7
Rational and Irrational Numbers, Imaginary and Complex Numbers
9.2.3.4, 9.2.3.7
Completing the Square, Quadratic Formula
9.2.4.1
Discriminant, Quadratic Formula and Functions
9.2.2.1, 9.2.4.1
Direct Variation and Proportion, Dividing Polynomials, Synthetic
Division, Finding Rational Roots
9.2.4.1
Exponential and Logarithmic Functions, Sequences
9.2.2.3, 9.2.2.5
Trigonometric Functions, Solving Right Triangles, Law of Cosines, Law
of Sines
9.3.4.1, 9.3.4.2
Matrices, Matrix Multiplication, Determinants
Review, Final
Minnesota Standards
Strand
Standard
No.
Benchmark
Understand the definition of a function. Use functional
notation and evaluate a function at a given point in its
9.2.1.1 domain.
For example: If
9,
10,
11
Algebra
f  x 
1
x2  3
, find f (-4).
Understand the
concept of
Distinguish between functions and other relations defined
9.2.1.2
function, and
symbolically, graphically or in tabular form.
identify important
features of
Find the domain of a function defined symbolically,
functions and
graphically or in a real-world context.
other relations
9.2.1.3
For example: The formula f (x) = πx2 can represent a function whose
using symbolic
domain is all real numbers, but in the context of the area of a circle, the
and graphical
domain would be restricted to positive x.
methods where
Obtain information and draw conclusions from graphs of
appropriate.
functions and other relations.
9.2.1.4 For example: If a graph shows the relationship between the elapsed flight
time of a golf ball at a given moment and its height at that same moment,
identify the time interval during which the ball is at least 100 feet above the
ground.
Strand
Standard
No.
Benchmark
Identify the vertex, line of symmetry and intercepts of the
parabola corresponding to a quadratic function, using
9.2.1.5 symbolic and graphical methods, when the function is
expressed in the form f (x) = ax2 + bx + c, in the form
f (x) = a(x – h)2 + k , or in factored form.
9.2.1.6
Identify intercepts, zeros, maxima, minima and intervals of
increase and decrease from the graph of a function.
Understand the concept of an asymptote and identify
9.2.1.7 asymptotes for exponential functions and reciprocals of linear
functions, using symbolic and graphical methods.
9.2.1.8
Make qualitative statements about the rate of change of a
function, based on its graph or table of values.
For example: The function f(x) = 3x increases for all x, but it increases faster
when x > 2 than it does when x < 2.
Determine how translations affect the symbolic and graphical
forms of a function. Know how to use graphing technology to
9.2.1.9 examine translations.
For example: Determine how the graph of f(x) = |x – h| + k changes as h and
k change.
Represent and solve problems in various contexts using linear
and quadratic functions.
9,
10,
11
Algebra
Recognize linear,
quadratic,
exponential and
other common
functions in realworld and
mathematical
situations;
represent these
functions with
tables, verbal
descriptions,
symbols and
graphs; solve
problems
involving these
functions, and
explain results in
the original
context.
9.2.2.1 For example: Write a function that represents the area of a rectangular
garden that can be surrounded with 32 feet of fencing, and use the function
to determine the possible dimensions of such a garden if the area must be at
least 50 square feet.
Represent and solve problems in various contexts using
9.2.2.2 exponential functions, such as investment growth,
depreciation and population growth.
Sketch graphs of linear, quadratic and exponential functions,
and translate between graphs, tables and symbolic
9.2.2.3
representations. Know how to use graphing technology to
graph these functions.
Express the terms in a geometric sequence recursively and by
giving an explicit (closed form) formula, and express the
partial sums of a geometric series recursively.
9.2.2.4
For example: A closed form formula for the terms tn in the geometric
sequence 3, 6, 12, 24, ... is tn = 3(2)n-1, where n = 1, 2, 3, ... , and this
sequence can be expressed recursively by writing t1 = 3 and
tn = 2tn-1, for n  2.
Another example: The partial sums sn of the series 3 + 6 + 12 + 24 + ... can
be expressed recursively by writing s1 = 3 and
sn = 3 + 2sn-1, for n  2.
Strand
Standard
No.
Benchmark
Recognize and solve problems that can be modeled using
finite geometric sequences and series, such as home mortgage
9.2.2.5 and other compound interest examples. Know how to use
spreadsheets and calculators to explore geometric sequences
and series in various contexts.
9.2.2.6
Sketch the graphs of common non-linear functions such as
f  x   x , f  x   x , f  x   1 , f (x) = x3, and translations of
x
these functions, such as f  x   x  2  4 . Know how to use
graphing technology to graph these functions.
Strand
9,
10,
11
Algebra
Standard
Generate
equivalent
algebraic
expressions
involving
polynomials and
radicals; use
algebraic
properties to
evaluate
expressions.
No.
Benchmark
Evaluate polynomial and rational expressions and expressions
9.2.3.1 containing radicals and absolute values at specified points in
their domains.
9.2.3.2
Add, subtract and multiply polynomials; divide a polynomial
by a polynomial of equal or lower degree.
Factor common monomial factors from polynomials, factor
quadratic polynomials, and factor the difference of two
9.2.3.3 squares.
For example: 9x6 – x4 = (3x3 – x2)(3x3 + x2).
Add, subtract, multiply, divide and simplify algebraic
fractions.
9.2.3.4
For example:
1
x

1 x 1 x
is equivalent to
1  2x  x 2
1  x2
.
Strand
Standard
No.
Benchmark
Check whether a given complex number is a solution of a
quadratic equation by substituting it for the variable and
evaluating the expression, using arithmetic with complex
numbers.
9.2.3.5
For example: The complex number
2
1 i
is a solution of 2x2 – 2x + 1 = 0,
2
since 2  1  i   2  1  i   1  i  1  i   1  0 .
 2 
 2 




Apply the properties of positive and negative rational
exponents to generate equivalent algebraic expressions,
including those involving nth roots.
9.2.3.6
For example:
2  7  2 2  7 2 14 2  14 . Rules for computing
1
1
1
directly with radicals may also be used: 3 2  3 x  3 2x .
Justify steps in generating equivalent expressions by
identifying the properties used. Use substitution to check the
equality of expressions for some particular values of the
9.2.3.7
variables; recognize that checking with substitution does not
guarantee equality of expressions for all values of the
variables.
Represent relationships in various contexts using quadratic
equations and inequalities. Solve quadratic equations and
inequalities by appropriate methods including factoring,
completing the square, graphing and the quadratic formula.
Find non-real complex roots when they exist. Recognize that
a particular solution may not be applicable in the original
context. Know how to use calculators, graphing utilities or
9.2.4.1
other technology to solve quadratic equations and
inequalities.
9,
10,
11
Algebra
Represent realworld and
mathematical
situations using
equations and
inequalities
For example: A diver jumps from a 20 meter platform with an upward
involving linear,
velocity of 3 meters per second. In finding the time at which the diver hits
the surface of the water, the resulting quadratic equation has a positive and
quadratic,
a negative solution. The negative solution should be discarded because of
exponential and
the context.
th
n root functions.
Represent relationships in various contexts using equations
Solve equations
and inequalities 9.2.4.2 involving exponential functions; solve these equations
graphically or numerically. Know how to use calculators,
symbolically and
graphing utilities or other technology to solve these equations.
graphically.
Interpret solutions
Recognize that to solve certain equations, number systems
in the original
need to be extended from whole numbers to integers, from
context.
integers to rational numbers, from rational numbers to real
9.2.4.3
numbers, and from real numbers to complex numbers. In
particular, non-real complex numbers are needed to solve
some quadratic equations with real coefficients.
Strand
Standard
No.
Benchmark
Represent relationships in various contexts using systems of
linear inequalities; solve them graphically. Indicate which
9.2.4.4
parts of the boundary are included in and excluded from the
solution set using solid and dotted lines.
9.2.4.5
Solve linear programming problems in two variables using
graphical methods.
Represent relationships in various contexts using absolute
value inequalities in two variables; solve them graphically.
9.2.4.6
Strand
9,
10,
11
Algebra
Standard
No.
For example: If a pipe is to be cut to a length of 5 meters accurate to within
a tenth of its diameter, the relationship between the length x of the pipe and
its diameter y satisfies the inequality | x – 5| ≤ 0.1y.
Benchmark
Solve equations that contain radical expressions. Recognize
that extraneous solutions may arise when using symbolic
methods.
Represent realworld and
mathematical
For example: The equation x  9  9 x may be solved by squaring both
situations using
9.2.4.7
equations and
sides to obtain x – 9 = 81x, which has the solution x   9 . However, this
80
inequalities
is not a solution of the original equation, so it is an extraneous solution that
involving linear,
should be discarded. The original equation has no solution in this case.
quadratic,
Another example: Solve 3  x 1  5 .
exponential and
th
n root functions.
Solve equations
and inequalities
Assess the reasonableness of a solution in its given context
symbolically and
and compare the solution to appropriate graphical or
9.2.4.8
graphically.
numerical estimates; interpret a solution in the original
Interpret solutions
context.
in the original
context.
Conceptual Framework
Dakota Memorial Students (DMS) students are becoming adults who are prepared to be
responsible citizens and life long learners in an ever-changing world. DMS students are
becoming knowledgeable, reflective, humanistic, and creative.
Knowledgeable: DMS students display competency in their subject matter, based upon a
solid core curriculum and an extensive choice of electives. DMS students will pursue
vocational and/or college preparatory opportunities. As life-long learners, DMS students
engage in complex thinking and understand the value of volunteerism. DMS students
will strive to be ethical and respectful of the viewpoints of others.
Reflective: DMS students will engage in thoughtful analysis of the meaning and
significance of their actions, decisions, and results with regard to their work in order to
assess progress in meeting this guiding principle. DMS students will learn to think about
theory and practice, and respectfully question content, processes, and procedures.
Humanistic: DMS students will value the personal worth of each individual. This is
based on a belief in people’s potential and innate ability to develop to their fullest. DMS
students are grounded in the knowledge of the influence of culture and history, ethnicity,
language, gender and socioeconomics of one’s life. This knowledge base informs
students’ decision-making as they embrace environments that promote freedom,
compassion, and success for all. DMS students are fair-minded in their interactions with
others, as well as sensitive to and accepting of individual differences. DMS students
have an understanding of aesthetics and the diversity that is part of the human experience
and they will incorporate this knowledge into their work.
Creative: DMS students understand the powerful resources of the arts and sciences.
DMS students recognize the important role creativity plays in instruction and the
classroom environment. They will show academic curiosity when introduced to new
topics. They will seek solutions to issues and problems.