# 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 .

**STUDENT EXPECTATIONS FOR LEARNING ADDRESSED:**

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 n^{th} roots of positive real
numbers for any

positive integer n; and the inverse relationship between taking the n^{th}
root of and the n^{th}

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

using quadratic formula. (10.P.5)

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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