# COURSE OUTLINE FOR ALGEBRA II

COURSE DESCRIPTION:

This course is designed for college preparatory students . Major units include the real number
system and its properties, the function concept, rational algebraic expressions , linear equations and
inequalities, quadratic equations, systems of equations, variation, irrational numbers and
applications of algebra to real world situations.

MISSION RELATED GOALS:

This class will provide the student with a variety of opportunities to demonstrate academic
excellence and intellectual curiosity by communicating effectively, solving complex problems , and
working with others toward a common goal .

Students will be afforded opportunities to apply mathematical concepts to real-world applications.
A variety of teaching methods will be used to foster an environment that promotes self-confidence
and respect for others throughout the school and global community.

GENERAL PERFORMANCE OBJECTIVES:

The student will be able to:
1. Use properties of real numbers to evaluate expressions
2. Solve first degree equations and inequalities with one variable , including proportion,
percent, number, and consecutive integer problems
3. Solve absolute value equations, literal equations , compound inequalities and absolute value
inequalities
4. Organize data into a matrix and perform addition, subtraction , scalar multiplication, and
matrix multiplication
5. Apply the rules of exponents to expressions
6. Add, subtract, multiply, divide and factor polynomials
7. Solve polynomial equations
8. Create and interpret a variety of graphs
9. Understand and use the concepts of relations and functions
10. Graph and write linear equations utilizing points, slope, or intercepts
11. Understand and use the concepts of inverse and composition of functions
12. Solve and graph systems of equations and inequalities

MASSACHUSETTS FRAMEWORKS STRANDS:

• Number Sense and Operations
• Patterns, Relations, and Algebra
• Geometry
• Data Analysis, Statistics, and Probability

CURRICULUM FRAMEWORK LEARNING STANDARDS:

I. Identify and use the properties of operations on real numbers, including the associative,
commutative, and distributive properties ; the existence of the identity and inverse elements
for addition and multiplication; the existence of nth roots of positive real numbers for any
positive integer n; and the inverse relationship between taking the nth root of and the nth
power of a positive real number. (10.N.1)

II. Simplify numerical expressions, including those involving positive integer exponents or the
absolute value and apply such simplifications in the solution of problems. (10.N.2)

III. Describe, analyze, and generalize a wide variety of patterns. (10.P.1)

IV. Demonstrate an understanding of the relationship between various representations of a line.
Determine a line’s slope and x- and y-intercepts from its graph or from a linear equation
that represents the line. Find a linear equation describing a line from a graph or a geometric
description of the line. Explain the significance of a positive, negative, zero , or undefined
slope. (10.P.2)

V. Add, subtract, and multiply polynomials. Divide polynomials by monomials . (10.P.3)

VI. Demonstrate facility in symbolic manipulation of polynomial and rational expressions by
rearranging and collecting terms ; factoring; identifying and canceling common factors in
rational expressions; and applying the properties of positive integer exponents. (10.P.4)

VII. Find solutions to quadratic equations with real roots by factoring , completing the square or

VIII. Solve equations and inequalities including those involving absolute value of linear
expressions and apply to the solution of problems. (10.P.6)

IX. Solve everyday problems that can be modeled using linear, quadratic or exponential
functions. (10.P.7)

X. Solve everyday problems that can be modeled using systems of linear equations or
inequalities. (10.P.8)

XI. Using rectangular coordinates, calculate midpoints of segments, slopes of lines and
segments, and distances between two points and apply the results to solutions of problems.
(10.G.7)

XII. Find linear equations that represent lines, either perpendicular or parallel to a given line and
through a given point. (10.G.8)

XIII. Create and interpret an appropriate graphical representation for a set of data and use
appropriate statistics to communicate information about the data. (10.D.1)

XIV. 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)

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

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

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

XVIII. 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)

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

XX. 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)

XXI. 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 variation. (12.P.11)

XXII. 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)

XXIII. Demonstrate an understanding of relations and functions. Identify the domain, range,
dependent, and independent variables of functions. (AI.P.3)

XXIV. Translate between different representations of functions and relations: graphs, equations,
point sets, and tabular. (AI.P.4)

UNITS AND THEMES:

 I. Tools of Algebra (14 days) 10.N.1, 10.N.2, 10.P.6, 12.P.8 II. Functions, Equations, & Graphs (15 days) 10.P.1, 10.P.2, 10.P.7, 10.G.7, 10.G.8, 10.D.1, 12.P.8, 12.P.11, AI.P.3, AI.P.4 III. Solving Systems (12 days) 10.P.8, 12.P.8, 12.P.10 IV. Matrices and Determinants (15 days) 12.P.9 V. Quadratic Equations & Functions (16 days) 10.N.1, 10.P.1, 10.P.4, 10.P.5, 10.P.7, VI. Rational Equations (7 days) 10.D.1, 12.N.1, 12.P.7, 12.P.8, 12.P.11 VII. Polynomials & Polynomial Functions (7 days) 10.N.2, 10.P.1, 10.P.3, 10.P.4, 10.P.7, 12.P.8, 12.P.11, 12.P.13 VIII. Review, Midterm and Final (4 days)
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