Las Positas College
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Course Outline for Mathematics 55A
INTERMEDIATE ALGEBRA A
I.
CATALOG DESCRIPTION:
MATH 55A — INTERMEDIATE ALGEBRA A — 3 units
Concepts covered in the first half of Mathematics 55 including complex numbers, quadratic
equations, radical expressions, radical equations, rational exponents, absolute value
equations and inequalities, and functions and their graphs. Prerequisite: Mathematics 65
or 65B or 65Y (completed with a grade of C or higher) or an appropriate skill level
demonstrated through the Mathematics assessment process. May not receive credit if
Mathematics 55 or Mathematics 55X has been completed. 3 hours lecture, 0-1 laboratory
hour.
II.
NUMBER OF TIMES COURSE MAY BE TAKEN FOR CREDIT: One
III.
PREREQUISITE AND/OR ADVISORY SKILLS:
Before entering this course, the student should be able to:
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
K.
L.
M.
N.
O.
P.
IV.
demonstrate ability to use set theory;
add, subtract, multiply, and divide polynomials;
perform real number operations;
solve linear equations in one variable;
solve and graph linear inequalities in one variable;
develop and graph linear equations in two variables using various methods;
factor difference of two squares, perfect squares, and general trinomials;
add, subtract, multiply, and divide, and simplify rational expressions;
apply the laws of integer exponents;
use algebraic methods to solve word problems;
solve quadratic equations by factoring, completing the square, and using the
quadratic formula;
solve systems of equations by the addition method and substitution;
solve literal linear equations for any given variable;
solve equations involving rational expressions;
add, subtract, multiply, divide, and simplify expressions involving square roots;
graph basic quadratic equations.
EXPECTED OUTCOMES FOR STUDENTS:
Upon completion of both Math 55A and Math 55B, the student will be able to:
A.
B.
C.
D.
E.
F.
G.
H.
perform basic operations on complex numbers;
find complex roots of a quadratic equation;
sketch graphs of conic sections;
sketch the graphs of functions and relations;
sketch the graph of algebraic functions using synthetic division;
sketch the graph of logarithmic and exponential functions;
solve exponential and logarithmic functions;
apply the concepts of logarithmic and exponential functions to other fields;
Course Outline for Mathematics 55A
INTERMEDIATE ALGEBRA A
I.
J.
K.
L.
M.
N.
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solve systems of linear equations in two and three unknowns using elimination and
substitution;
solve systems of nonlinear equations in two unknowns using elimination and
substitution;
understand the properties of and perform operations with rational and irrational
exponents;
solve equations and inequalities involving absolute values;
solve equations involving radicals;
find rational roots of polynomials with integral coefficients.
V.
CONTENT:
Content for Math 55A will consist of topics from the list below as covered in the first half of
the selected textbook.
A.
Review solving linear equations and inequalities
B.
Absolute value equations and inequalities
C.
Review exponents, operations with polynomials and factoring
D.
Review operations with rational expressions
E.
Synthetic division
F.
Review simplifying and operations with radicals
G.
Rational and irrational exponents
H.
Solving equations with radicals
I.
Complex numbers
J.
Quadratic equations
1.
The quadratic formula
2.
The discriminant
K.
Solving nonlinear and rational inequalities in two variables
L.
Solving equations involving quadratic forms
M.
Graphing linear equations and inequalities in two variables
N.
Distance, midpoint, and the slope of a line
O.
Variation
P.
Introductions to functions
1.
Types(even and odd functions)
2.
Operations
3.
Composite
4.
Inverse
Q.
Graphing polynomial and rational functions with synthetic division
R.
Find rational roots of polynomials
S.
Exponential and logarithmic functions
1.
Definition
2.
Equations
3.
Graphing
4.
Applications
T.
Conic sections
1.
Parabola
2.
Ellipse
3.
Hyperbola
4.
Circles
5.
Translation of axes
U.
System of non-linear equations and inequalities
V.
Systems of linear equations
VI.
METHODS OF INSTRUCTION:
A.
Lectures
B.
Discussion
C.
Collaborative learning where applicable
D.
Individual assistance during lab hour
Course Outline for Mathematics 55A
INTERMEDIATE ALGEBRA A
Page 3
VII.
TYPICAL ASSIGNMENTS:
A.
Homework. Assign exercises from the exercise sets at the end of each section.
Assignments should include a good mix of beginning and intermediate level
problems, with a few harder problems also assigned. While the length of a
assignment may vary depending on the material, typically between 20 and 30
problems per section may be assigned. Typical problems would be
1.
Solve and graph the solution set: |3 – x| 5
2.
Using any method, solve the system of equations {3x – 2y = -10, 6x + 5y =
25}.
3.
Find the equation of the line that is perpendicular to the line 2x – 5y = 10 and
that has the same y-intercept.
B.
Collaborative activity. Have students form small groups and solve problems
together.
1. Write a system of equations and use it to solve the following problem: An artist
makes three types of ceramic statues at a monthly cost of $650 for 180 statues.
The manufacturing costs for the three types are $5, $5, and $3. If the statues
sell for $20, $12, and $9, respectively, how many of each type should be made
to produce $2,100 in monthly revenue?
VIII.
EVALUATION:
A.
Methods of evaluation
1.
Examinations
2.
Final Exam
3.
Any or all of the following at the discretion of the instructor
a. homework
b. quizzes (announced or unannounced, in class, take home or on-line)
c. collaborative group activities or labs
B.
Frequency of evaluation
1.
Recommended minimum of 3 exams plus the final
C.
Types of problems:
1.
Most questions should be open-ended.
a.
Factor: y3 -216
b.
Solve the equation: 5m(m-1) = 2(1-m)
c.
Simplify i35
d.
Carmen and Paul can clean the house together in 2 hours. Working
alone, it takes Carmen ½ hour longer than it takes Paul to do the job.
How long would it take Carmen alone?
2.
Use the multiple choice and true-false questions at a minimum and only where
appropriate.
a.
Find the degree of the following polynomial: x6 + x3 + 2x + 1 a) 10 b) 9
c) 3 (d) 6 e) none of the answers
b.
True or False: In the expressions 4x2 + 3x + 2, “4” is called the leading
coefficient.
IX.
TYPICAL TEXTS:
A.
Lial, Hornsby, Miller, Intermediate Algebra, 6thEdition, Boston, Addision Wesley,
1998.
B.
Tussy, Gustafson, Intermediate Algebra, 2nd Edition, Pacific Grove, Brooks/Cole,
2002.
X.
OTHER MATERIALS REQUIRED OF STUDENTS:
A calculator may be required
Creation Date: 1/94
Revised Date: 12/94, 3/03
Course Outline for Mathematics 55A
INTERMEDIATE ALGEBRA A
Date Approved by Curriculum Committee: 5/14/03
Effective Date: Fall 2003
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