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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.