El Camino College - Division of
Mathematical Sciences
Math
40
Elementary Math
4 units; 4 hours lecture
Grading
Method: Letter
Associate Degree Credit --- Does Not Transfers to
CSU and
Does
Not Transfers to UC
Prerequisite: Mathematics 23 or
Mathematics 25 with a minimum grade of
C in prerequisite, or qualification by testing (El Camino College
Mathematics Placement Test) and assessment.
Catalog Description:
This
course reviews
introductory algebraic concepts, and includes the study of real
numbers, the solutions and applications of linear equations and
inequalities as well as systems of linear equations, and introduces
coordinate graphing of linear equations, factoring techniques,
simplification of rational and radical expressions, and the solution of
quadratic equations.
Note: Mathematics 40 is equivalent to one year of high school algebra.
Note: Mathematics 40 was formerly numbered Mathematics A.
Course
Objectives and Methods
of Evaluation:
- Course objectives (list
the major
objectives stated as student outcomes in behaviorally measurable
terms.)
- Use the specialized
vocabulary
describing the real number system and its properties as well as the
fundamentals of algebra.
- Manipulate (evaluate,
simplify, or
factor) algebraic expressions, including expressions with fractions and
radicals.
- Solve linear equations
and
inequalities, systems of linear equations, and quadratic equations.
- Solve various
application problems
which feature the mathematics under study using elementary
modeling techniques.
- Graph linear equations
and systems of
linear equations on a coordinate plane, isolating features such as
intercepts and slope.
- Methods of Evaluation -
Associate
Degree Credit Course
- Substantial writing
assignments are
inappropriate for this degree applicable course because:
- The course is primarily
computational
in nature
- The course primarily
involves skill
demonstrations or problem solving.
- Computational or
non-computational
problem-solving demonstrations, including:
- Exam
- Quizzes
- Homework problems
- Objective examinations,
including
- Multiple choice
Outline of Subject
Matter
|
Approximate
Time
|
Major
Topic
|
|
8
hours
|
I. The Specialized Vocabulary of Algebra
- Comparing and
Contrasting:
- constant, variable
- natural, whole, real
number, and
integer
- absolute value
- rational and irrational
number
- prime and composite
number
- odd and even number
- factor, divisor,
multiple
- base, exponent, power,
square root
- expression, equation,
and inequality
- solution, solution set
- identities,
contradictions, equivalent
equations
- linear and quadratic
equations
- polynomial, monomial,
binomial,
trinomial
- coefficient, term,
degree
|
|
16
hours
|
II. Basic
Operations and Manipulations with Algebraic
Expressions
- Review of expressions
with grouping
and mixed operations, including exponents, order of operations
- Review of operations
with signed
numbers
- Operations with
polynomials (including
long division, integer exponents). The Commutative, Associative, and
Distributive Properties.
- Factorization of
polynomials by
recognizing common monomial factors, the difference of squares,
patterns or grouping in simple and general trinomials, perfect square
trinomials.
- Algebraic fractions,
operations with
rational expressions.
- Radical expressions,
combining
radicals; products and quotients of expressions involving radicals.
|
|
16
hours
|
III. Equations
and Inequalities
- Review of first degree
equations in
one variable using the properties of equality
- Linear inequalities in
one variable
- Systems of equations in
two variables:
substitution and linear combination (elimination or addition)
- Literal equations
- Quadratic equations,
factoring, the
square root property, completing the square, and the quadratic formula.
|
|
8
hours
|
IV. Applications
- Review of algebraic
techniques in the
solution of problems involving geometric formulas (Perimeter, Area,
Volume, and the Pythagorean Theorem).
- Translation of
situations described in
word problems to mathematical expressions, equations and inequalities
and solving problems involving such topics as percentage relationships,
ratio and proportion, direct and inverse variation, and scientific
notation.
- Algebraic strategies
for word problems
such as "work," "distance," and "mixture" problems.
|
|
12
hours
|
V. Graphing
- Graphing of solution
sets of linear
inequalities in one variable on a number line
- Graphing of ordered
pairs on a
coordinate plane
- Interpretation of
graphs
- Graphing of linear
equations in two
variables using intercepts and using slope
- Analysis of effects of
changes in 'm'
and 'b' on graphs of lines
- Finding the slope of a
line from graph
or from equation
- Finding the equation of
a line using
slope and y-intercept; or given two points on the line
- Solving of systems of
linear equations
in two variables using graphing
|
|
12
hours
|
Examinations
|
|
Total:
|
72
Hours
|
Return
to the
top of the page.
Planned Instructional Activities:
Lecture,
class discussion and problem solving, individual assistance.
Entrance
Skills and Knowledge:
List the required skills
and/or knowledge without which a student would be highly unlikely to receive a grade of A, B,
C, or Credit (or for Health and Safety, would endanger self or others) in the
Target Course.
- Use arithmetic operations with whole
numbers, fractions,
decimals, and percents.
- Perform operations (at the Pre-Algebra
level) on real
numbers, using order of operations and exponents.
- Solve elementary linear equations and apply
their solution
to standard situations such as geometric formulas and proportional
relationships.
Source of
information: Course Outline of Record dated November, 2001
Last Updated On: 4/20/06