PARAMUS PUBLIS SCHOOLS, Paramus, New Jersey
Fundamentals of Algebra 2
CURRICULUM OUTLINE
DEPARTMENT: Mathematics
COURSE:
Fundamentals of Algebra II
LEVEL:
11.12-Full Year
DATE:
REV. DATE:
November 2004
Jan 1990, Aug 1993, February
1995 (no content change), July
1995 (text change). 1987
This course description incorporates the New Jersey Core Curriculum Content Standards for Mathematics Standards and Strands 2003 appropriate for grade 12: 4.1, 4.3, 4.4, 4.5
I
COURSE DESCRIPTION:
This course is designed for those who need mathematics credits for college, find the study of mathematics
difficult, and desire a less rigorous course and more individualized instruction. The course reviews the basic
structure of algebra and the real number system. Further study is made of polynomials. Emphasis is on relations
and functions including inequalities, linear and quadratic functions, number system to the complex number system.
Students are exposed to logarithms, graphing conic sections and the solution of word problems.
II
COURSE OBJECTIVES:
1. To perform basic operations of addition, subtraction, multiplication, and division with real and complex numbers
and with polynomials having real number coefficients. 2. To translate narrative problems into algebraic sentences
and determine their solution. 3. To solve open sentences, linear and quadratic, in one and two variables having real
and complex roots. 4. To construct and analyze graphs of relations and functions.
III
MAJOR CONCEPTS & TOPICS:
1.
Axioms for real numbers.
2.
Equations and Inequalities.
3.
Linear Relations and Functions
4.
Systems of Equations and Inequalities.
5.
Polynomials
6.
Roots
7.
Quadratic equations.
8.
Quadratic Relations and Functions
9.
Conics
10.
Rational Polynomial Expressions
11.
Exponents
12.
Exponential and Logarithmic Functions
13.
Trigonometry (elementary)
14.
Vertex-Edge Graphs and Algorithms
This document is for use by current faculty and current students of Paramus School District, Paramus, New Jersey. No part of this document may be used or reproduced, stored in a
retrieval system, or transmitted in any form or by any means, electronic. mechanical, photocopying, recording, scanning, or otherwise, without the prior written permission of the Board of
Education, Paramus School District, 145 Spring Valley Road Paramus, New Jersey, 07652.
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PARAMUS PUBLIS SCHOOLS, Paramus, New Jersey
IV. STUDENT SKILL OBJECTIVES
1.
Linear Functions [Review]
a.
Concept of relation, function, and the differences between these concepts
b.
Concept of linear function
c.
Graphing linear equations
d.
Concept of x-intercept, y-intercept, slopes, parallel lines, perpendicular lines, vertical lines, and
horizontal lines
e.
Forms of linear equations: slope intercept, y- intercept, general form
f.
Deriving the equation of a line in various forms using 2 points, 1 point and a slope, parallel lines,
perpendicular lines, and x-intercepts and y-intercepts
2.
a.
b.
c.
d.
Solving and Graphing Linear Inequalities [Review]
Solving inequalities in one variable
Compound inequalities
Absolute Value and inequalities
Graphing Linear inequalities in two variables
3. Solving Linear Equations [Review]
a. Solving Equation
b. Solving equation with variable on both sides
c. Solving Equations with Decimals
4. Solving Systems of Linear Equations [Review]
a. Solution linear system by graphing
b. Solution of linear system by substitution
c. Solution of linear system by linear combination
5. Monomials
a. concept of degree of a monomial
b. rules for multiplying, adding, dividing, and subtracting monomials
8. Polynomials
a. Polynomials and functions
b. Addition and subtraction of polynomials
c. Multiplication of polynomials
d. Division of polynomials, synthetic division
e. The Remainder and Factor theorems
f. Roots and zeros
g. Rational Zero theorem
h. Zeros of Polynomial functions
i. Composition of functions
7. Quadratic relations and functions
a. Solving quadratic equations
b. Completing the square
c. Discriminants and roots
d. Quadratic techniques to solve polynomial functions
e. Graphing quadratic functions
f. Applications of quadratic functions
g. Graphing quadratic inequalities
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PARAMUS PUBLIS SCHOOLS, Paramus, New Jersey
8. Exponentials & radicals
a. Roots of real numbers
b. Products and quotients of radicals
c. Computing with radicals
d. Rational exponents
e. Simplifying expressions with rational exponents
f. Solving equations containing radicals
g. Imaginary numbers
h. Complex numbers
i. Simplifying expressions containing complex numbers
9. Exponential and logarithmic functions
a. Real exponents and exponential functions
b. Logarithms and logarithmic functions
c. Properties of logarithms
d. Common logarithms
e. Natural logarithms
f. Exponential equations
g. Applications of logarithms
10. Trigonometry
a. Angles and the unit circle
b. Sine and cosine functions
c. Simple uses of trigonometry
12. Discrete Mathematics
a. Vertex-Edge Graphs and Algorithms
V.
EVALUATION PROCEDURES:
Evaluation of success will be based upon homework, class work, quizzes, unit tests and
examinations.
VI.
SUGGESTED MATERIALS:
“Algebra 2” Haenisch AGS Publishing 2004
*
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