Syllabus

Course Syllabus for 1st Quarter

#312 Algebra 2 (5 credits)

 

Prerequisites:  Algebra 1 and Geometry

 

Text:  McDougall Little, Algebra 2 Apps. Eqs. Graphs (2001)

                                               

Required Materials:  Text, Notebook and pen/pencil, TI-83/83 graphing calculator or comparable calculator

  

Course Outline:

 

First Quarter – Linear Inequalities, Quadratic Functions

 

Topics:

Topic 1:        Linear Inequalities; Systems of Linear Inequalities (A2.P.10)

Topic 2:        Absolute Value Equations; Graphs of Absolute Value Equations (A2.P.13)

Topic 3:        Graphing Quadratic Functions  (A2.P.7)

Topic 4:        Solving Quadratic Equations by Factoring (A2.P.7)

Topic 5:        Solving Quadratics Equations by Finding the Square Roots (A2.P.7)

Topic 6:        Complex Numbers (A2.N.1)

Topic 7:        Completing the Square (A2.P.7)

Topic 8:        Quadratic Formula and the Discriminant (A2.P.7)

Topic 9:        Graphing and Solving Quadratic Inequalities (A2.P.8)

 

Student Prior Knowledge:

  • Translate word problems into equations
  • Should be able to graph
  • Linear equations
  • Linear inequalities
  • Absolute value equations
  • graphing
  • substitution
  • elimination

·         Should be able to coordinate and interpret equations and graphs

  • Solve systems of equations by various methods

 

Student Objectives:

  • Should be able to graph

o   Quadratic equations

  • Quadratic inequalities
  • Graph using Technology
  • Elimination
  • Should be able to coordinate and interpret quadratic equations their related graphs
  • Solve Quadratic equations by various methods
  •  
    • Completing the Square
    • Substitution

 

Assessments: 

  • Line Project
  • Systems of Equations Project
  • Absolute Value Poster
  • Collins on Completing the Square
  • Graphing Calculator project finding the maximum values of quadratic functions.

 

Grading:

  • Each test counts as 1 major grade (2 -3 per quarter)
  • Every 2-3 quizzes count as 1 major grade
  • Notebook counts as 1 major grade
  • Homework counts as 2 major grades
  • Collins assignment counts as 1 major grade
  • Projects count as 1 or 2 major grades depending on duration and difficulty
  • Midterm and Final exams count as 2 major grades

 

Course Syllabus for 2nd  Quarter

#312 Algebra 2 (5 credits)

 

Prerequisites:  Algebra 1 and Geometry

 

Text:  McDougall Littell, Algebra 2 Apps. Eqs. Graphs (2001)

                  

Required Materials:  Text, Notebook and pen/pencil, TI-83/83 graphing calculator or comparable calculator

 

Course Outline:

 

Second Quarter – Evaluating and Graphing Polynomial Equations and Functions

 

Topics:

Topic 1:        Properties of Exponents (A2.N.2)

Topic 2:        Graphing and Evaluating Polynomials Functions (A2.P.6)

Topic 3:        Adding, Subtracting and Multiplying Polynomial Equations  (A2.P.6)

Topic 4:        The Remainder and Factor Theorems (A2.P.6)

Topic 5:        Finding Rational Zeros and the Fundamental Factor Theorem

Topic 6:        Analyzing and Modeling Polynomial Functions (A2.P.11)

Topic 7:        Rational Exponents (A2.N.2)

Topic 8:        Power Functions and Function Operations (A2.P.4)

 

Student Objectives:  

  • Add, Subtract and Multiply Polynomial Equations
  • Apply Polynomial Functions in real world situations.
  • Should be able to graph
  • Polynomial Functions
  • Graph using Technology
  • Difference of two cubes
  • Sum of two cubes
  • Factor Polynomial equations by various methods
  • Grouping
  • Should be able to coordinate and interpret Polynomial Functions their related graphs

.

Assessments: 

  • Collins on Difference of Two Cubes
  • Graphing Calculator activity on Approximating Real Zeros
  • Graphing Calculator activity on Solving Polynomial Equations

 

Grading:

  • Each test counts as 1 major grade (2 -3 per quarter)
  • Every 2-3 quizzes count as 1 major grade
  • Notebook counts as 1 major grade
  • Homework counts as 2 major grades
  • Collins assignment counts as 1 major grade
  • Projects count as 1 or 2 major grades depending on duration and difficulty.
  • Midterm and Final exams count as 2 major grades

                  

 

Course Syllabus for 3rd Quarter

#312 Algebra 2 (5 credits)

 

Prerequisites:  Algebra 1 and Geometry

 

Text:  McDougall Littell, Algebra 2 Apps. Eqs. Graphs (2001)

                  

Required Materials:  Text, Notebook and pen/pencil, TI-83/83 graphing calculator or comparable calculator

 

Course Outline:

 

Third Quarter – Inverse Functions, Exponential Functions, Logarithmic Functions

 

Topics:

Topic 1:        Inverse Functions (A2.P.5)

Topic 2:        Graphing Square Root and Cube Root Functions (A2.N.2)

Topic 3:        Solving Radical Equations  (A2.N.2)

Topic 4:        Exponential Growth and Decay (A2.P.4)

Topic 5:        The Number e (A2.P.4)

Topic 6:        Logarithmic Functions (A2.P.4)

Topic 7:        Properties of Logs (A2.P.4)

Topic 8:        Solving and Modeling Exponential and Logarithmic Functions (A2.P.11)

Topic 9:        Inverse and Joint Variation (A2.P.5)

Topic 10:       Graphing Rational Functions (A2.P.6)

         

Student Objectives:

  • Solve and apply Polynomial Functions in real world situations
  • Solve and apply Logarithmic Functions in real world situations
    • Should be able to graph
    • Inverse, Exponential and logarithmic Functions
    • Graph using Technology
  • Solve and graph radical functions

 

Assessments: 

  • Graphing Inverse Functions using Technology
  • Exponential Growth and Decay
  • Graphing Logarithmic Functions
  • Graphing Rational Functions

 

Grading:

  • Each test counts as 1 major grade (2 -3 per quarter)
  • Every 2-3 quizzes count as 1 major grade
  • Notebook counts as 1 major grade
  • Homework counts as 2 major grades
  • Collins assignment counts as 1 major grade
  • Projects count as 1 or 2 major grades depending on duration and difficulty
  • Midterm and Final exams count as 2 major grades

 

Course Syllabus for 4th  Quarter

#312 Algebra 2 (5 credits)

 

Prerequisites:  Algebra 1 and Geometry

 

Text:  McDougall Littell, Algebra 2 Apps. Eqs. Graphs (2001)

 

Required Materials:  Text, Notebook and pen/pencil, TI-83/83 graphing calculator or comparable calculator

 

Course Outline:

 

Fourth Quarter – Rational Equations and Functions, Conic Sections, Sequences and Series

 

Topics:

Topic 1:        Multiplying and Dividing Rational Expressions (A2.P.6)

Topic 2:        Solving Rational Equations (A2.P.6)

Topic 3:        Circles and Ellipses (A2.G.3)

Topic 4:        Hyperbolas (A2.G.3)

Topic 5:        Graphing and Classifying Conics (A2.G.3)

Topic 6:        Solving Quadratic Systems (A2.P.10)

Topic 7:        Arithmetic Sequences and Series (A2.P.2)

Topic 8:        Geometric Sequences and Series (A2.P.2)

Topic 9:        Recursive Rules for Sequences (A2.P.1)

         

Student Objectives:

  • Students should be able to
    • Multiply and Divide Rational Expressions
    • Solve Rational Equations
    • Solve Quadratic Systems
    • Graph Circles, Ellipses and Hyperbolas

 

Assessments: 

  • Operations with Rational Expressions
  • Graphing Circles
  • Working with Sequences
  • Geometric Series
  • Evaluating Recursive Rules

 

Grading:

  • Each test counts as 1 major grade (2 -3 per quarter)
  • Every 2-3 quizzes count as 1 major grade
  • Notebook counts as 1 major grade
  • Homework counts as 2 major grades
  • Collins assignment counts as 1 major grade
  • Projects count as 1 or 2 major grades depending on duration and difficulty
  • Midterm and Final exams count as 2 major grades


Learning Standards for Algebra II[1]

 

Note: The parentheses at the end of a learning standard contain the code number for the corresponding standard in the two-year grade spans.

 

Number Sense and Operations

Understand numbers, ways of representing numbers, relationships among numbers, and number systems

Understand meanings of operations and how they relate to one another

Compute fluently and make reasonable estimates

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:

AII.N.1      Define complex numbers (e.g., a + bi) and operations on them, in particular, addition, subtraction, multiplication, and division. Relate the system of complex numbers to the systems of real and rational numbers. (12.N.1)

AII.N.2      Simplify numerical expressions with powers and roots, including fractional and negative exponents. (12.N.2)

 

 

 

Patterns, Relations, and Algebra

Understand patterns, relations, and functions

Represent and analyze mathematical situations and structures using algebraic symbols

Use mathematical models to represent and understand quantitative relationships

Analyze change in various contexts

 

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:

AII.P.1       Describe, complete, extend, analyze, general­ize, and create a wide variety of patterns, including iterative and recursive patterns such as Pascal’s Triangle. (12.P.1)

AII.P.2       Identify arithmetic and geometric sequences and finite arithmetic and geometric series. Use the properties of such sequences and series to solve problems, including finding the formula for the general term and the sum, recursively and explicitly. (12.P.2)

AII.P.3       Demonstrate an understanding of the binomial theorem and use it in the solution of problems. (12.P.3)

AII.P.4       Demonstrate an understanding of the exponential and logarithmic functions.

AII.P.5       Perform operations on functions, including com­position. Find inverses of functions. (12.P.5)

AII.P.6       Given algebraic, numeric and/or graphical representations, recognize functions as polynomial, rational, logarithmic, or exponential. (12.P.6)

AII.P.7       Find solutions to quadratic equations (with real coefficients and real or complex roots) and apply to the solu­tions of problems. (12.P.7)

AII.P.8       Solve a variety of equations and inequalities using algebraic, graphical, and numerical methods, including the quadratic formula; use technology where appropriate. Include polynomial, exponential, and logarithmic functions; expressions involving the absolute values; and simple rational expressions. (12.P.8)

AII.P.9       Use matrices to solve systems of linear equations. Apply to the solution of everyday problems. (12.P.9)

AII.P.10    Use symbolic, numeric, and graphical methods to solve systems of equations and/or inequalities involving algebraic, exponential, and logarithmic expressions. Also use technology where appropriate. De­scribe the relationships among the methods. (12.P.10)

AII.P.11    Solve everyday problems that can be modeled using polynomial, rational, exponential, logarithmic, and step functions, absolute values and square roots. Apply appropriate graphical, tabular, or symbolic methods to the solution. Include growth and decay; logistic growth; joint (e.g., I = Prt, y = k(w1 + w2)), and combined (F = G(m1m2)/d2) variation. (12.P.11)

AII.P.12    Identify maximum and minimum values of func­tions in simple situations. Apply to the solution of problems. (12.P.12)

AII.P.13    Describe the translations and scale changes of a given function f(x) resulting from substitu­tions for the various parameters a, b, c, and d in y = af (b(x + c/b)) + d. In particular, describe the effect of such changes on polynomial, rational, exponential, and logarithmic functions. (12.P.13)

 

 

Geometry

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

Specify locations and describe spatial relationships using coordinate geometry and other representational systems

Apply transformations and use symmetry to analyze mathematical situations

Use visualization, spatial reasoning, and geometric modeling to solve problems

 

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:

AII.G.1      Define the sine, cosine, and tangent of an acute angle. Apply to the solution of problems. (12.G.1)

AII.G.2      Derive and apply basic trigono­metric identities (e.g., sin2q + cos2q = 1, tan2q + 1 = sec2q) and the laws of sines and cosines. (12.G.2)

AII.G.3      Relate geometric and algebraic representations of lines, simple curves, and conic sections. (12.G.4)

 

 


 


Data Analysis, Statistics, and Probability

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

Select and use appropriate statistical methods to analyze data

Develop and evaluate inferences and predictions that are based on data

Understand and apply basic concepts of probability

 

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:

AII.D.1      Select an appropriate graphical representation for a set of data and use appropriate statistics (e.g., quartile or percentile distribution) to communicate information about the data. (12.D.2)

AII.D.2      Use combinatorics (e.g., “fundamental counting principle,” permutations, and combinations) to solve problems, in particular, to compute probabilities of compound events. Use technology as appropriate. (12.D.6)

 

 

 

[1] Massachusetts Department of Education, Mathematics Curriculum Frameworks 2000.  Malden, MA

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