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# ALGEBRA II

The Department’s Educational Philosophy
The study of mathematics will enhance the ability of all students to problem solve and to reason. Through a strong standardized
departmental program that emphasizes problem solving, communicating, reasoning and proof, making connections, and using
representations, students will develop self-confidence and a positive attitude towards mathematics.

Our curriculum matches that of the Massachusetts Mathematics Curriculum Framework, and we are philosophically aligned with the
National Council of Teachers of Mathematics Standards.

Guiding Principles
• Mathematical ideas should be explored in ways that stimulate curiosity, create enjoyment of mathematics, and develop depth of
understanding.
• Effective mathematics programs focus on problem solving and require teachers who have a deep knowledge of the discipline.
• Technology is an essential tool in a mathematics education, and all students should gain facility in using it where advantageous.
• All students should have a high-quality mathematics program.
• Assessment of student learning in mathematics should take many forms to inform instruction and learning.
• All students should understand the basic structure of mathematics.
• All students should recognize that the techniques of mathematics are reflections of its theory and structure.
• All students should gain facility in applying mathematical skills and concepts.
• All students should understand the role of inductive and deductive reasoning in mathematic and real life situations.

Course Frequency: Full-year course, five times per week
Credits Offered: Five
Prerequisites: A final grade of at least 70 in both Algebra I and Geometry

Background to the Curriculum
This course uses the Houghton Mifflin text by Dolciani et al., Algebra 2 and Trigonometry, 1992 edition. It is the third course in our
accelerated/enriched (AE) program, and the majority of the students enrolled have taken Algebra I AE and Geometry AE. This
specific text has been used since 1992; this course has used older editions of this same text since the late 1960s. The text is followed
quite closely; however, the material on Trigonometry and Probability/Statistics is not covered. The text matches the 2000 edition of
the Massachusetts State Framework recommendations for a second-year Algebra course and is philosophically aligned with the spirit
of the National Council of Teachers of Mathematics curriculum standards. Teachers bring in other material where appropriate and
make minor changes as to emphasis on certain topics, after consultation with the RDL.

Core Topics/Questions/Concepts/Skills
Solving equations and inequalities in one variable
Working with linear relations and functions
Solving systems of linear equations and inequalities
Analyzing and graphing quadratic relations and functions
The algebra of rational expressions and rational/fractional equations
Exponential and Logarithmic Functions
Theory of Polynomial Equations
Using sequences and series

Course-End Learning Objectives

 Learning objectives Corresponding state standards, where applicable 1] Solve linear equations and inequalities, including those with absolute values Algebra II.P.8 2] Graph linear equations and inequalities Algebra I.P.3 3] Find the equation of a line given various information Algebra I.P.5 4] Find the equations of parallels and perpendiculars Algebra I.P.6 5] Solve equations in 2 or 3 variables Algebra II.P.10 6] Fit a model to data Algebra I.D.2 7] Use appropriate technology to solve problems Algebra II.P.8 8] Simplify monomial and polynomial expressions Algebra I.P.7 9] Factor polynomials Algebra II.P.8 10] Solve quadratic equations by factoring or quadratic formula Algebra II.P.7 11] Simplify radical expressions Algebra II.N.2 12] Simplify expressions with complex numbers Algebra II.N.1 13] Simplify expressions with negative/fractional exponents Algebra II.N.2 14] Graph and apply quadratic functions Algebra I.P.11 15] Apply the distance and midpoint formulae Geometry.G.12 16] Graph the equations of conic sections centered at origin Precalculus.P.8 17] Solve systems of simultaneous quadratic equations Algebra II.P.8 18] Find the composition and inverse of functions Algebra II.P.5 19] Solve variation problems Algebra II.P.11 20] Solve rational/fractional equations Algebra II.P.8 21] Simplify complex algebraic rational expressions Algebra II.P.8 22] Understand and use arithmetic sequences and series Algebra II.P.2 23] Understand and use geometric sequences and series Algebra II.P.2 24] Solve algebraic word problems Algebra II.P.8 25] Draw graphs in 3-space Geometry G.16 26] Perform operations with real numbers as exponents Algebra II.N.2 27] Find the equations of the conic sections, given information in the geometric definitions Precalculus.P.8 28] Explain the theory of equations – Rational Root Theorem and Fundamental Theorem of Algebra Algebra II.P.8 29] Use Synthetic Division and Synthetic Substitution Algebra II.P.8 30] Convert between exponential and logarithmic form Algebra II.P.4 31] Apply the log definition and the log laws Algebra II.P.8 32] Solve Exponential Equations Algebra II.P.10 33] Use determinants in solving systems of equations Algebra II.P.9 34] Study patterns that are iterative and recursive Algebra II.P.1 35] Identify maximum and minimum values of functions Algebra II.P.6 36] Distinguish between polynomial, rational, logarithmic, exponential functions Algebra II.P.11

Assessment
Students are generally assessed by in-class tests and quizzes, which are administered regularly throughout a marking period.
Generally, two quizzes are equivalent to a test. The students’ attitude, effort, and quality of homework preparation will also impact
their term grade to a small degree. Teachers informally assess students every day by asking pivotal questions, as well as questions
involving mechanics or concepts, and the students’ term grades may be positively affected to a small degree based on their responses.
A standardized midyear examination and final examination are administered to all students in this course in order to assess their longterm
retention of the course material.

Technology and Health Learning Objectives Addressed in This Course
(This section is for faculty and administrative reference; students and parents may disregard.)

 Course activity: skills &/or topics taught Standard(s) addressed through this activity 1] Graphing calculators to introduce Quadratic function graphs 2] Graphing calculators to aid in the solution of Polynomial Equations 3] Graphing calculators to contrast graphs with horizontal or vertical shifts

Materials and Resources
Teachers use other texts for supplementary ideas, such as the McDougal Littell Algebra II text and the Glencoe Algebra II text.
Review materials that match both of the departmental examinations are used by all teachers of the course. Some teachers may employ
the software package “Algebra Plotter Plus” to have students investigate a concept at the Mac lab. Teachers may also have students
investigate problems with graphing calculators