EXERCISES 1.1
20. The set of people who voted in the last election
Use both the roster and the rule method to specify the sets in
Problems 1 through 10.
1. The RGEP courses you are enrolled in this se
Word Problems
Objectives
Upon completion, you should be able to:
Translate English statements into
mathematical statements
Use the techniques learned in solving
linear, quadratic and systems of
equati
RATIONAL EXPONENTS &
RADICALS
OBJECTIVES
na
Upon completion, you should be able to
Define the principal nth root of numbers;
Simplify radicals; and
Perform addition, subtraction, multiplication
and
EQUATIONS &
INEQUALITIES
MATH 11
COLLEGE ALGEBRA
Chapter Outline
Equality Axioms
Linear and Quadratic Equations
Equations involving Radicals
Equations in Quadratic Form
Linear and Quadratic Inequaliti
INEQUALITIES and
ABSOLUTE VALUE
MATH 11
College Algebra
Objectives
Upon completion, you should be able to
define order relations between numbers
enumerate order properties of
define
absolute value of
PART 3
THINKING
MATHEMATICALL
Y
3.1 MATHEMATICS
AS AN AXIOMATICDEDUCTIVE SYSTEM
ALGEBRA: The Language of Mathematics
Algebra may be described as a
generalization and extension of arithmetic.
Arithme
CHAPTER 1.3
THE COMPLEX
NUMBER SYSTEM
Solvable Equations in R
ax b 0 is always solvable in R.
b
x
a
Solvable Equations in R
x 9 is solvable in R.
The solutions are 3 and 3
2
x 3 is solvable in R.
2
Th
ALGEBRAIC
EXPRESSIONS
Math Division, IMSP, UPLB
Learning Objectives
Upon completion, you should be able to
Give examples of algebraic
expressions; and
Perform operations involving integer
exponents.
2
RATIONAL
EXPRESSIONS
Learning objectives
Upon completion, you should be able to
Simplify
rational expressions;
Perform
addition, subtraction,
multiplication and division on rational
expressions; and
OPERATIONS ON
POLYNOMIALS
OPERATIONS ON POLYNOMIALS
Learning Objectives
Upon completion you should be able to
perform the following operations on
polynomials:
ADDITION
SUBTRACTION
MULTIPLICATION
D
SPECIAL PRODUCTS AND
FACTORING
Special Products and Factoring
Upon completion, you should be able to
Find special products
Factor a polynomial completely
2
Special Products
rules for finding product
RATIONAL EXPONENTS &
RADICALS
OBJECTIVES
na
Upon completion, you should be able to
Define the principal nth root of numbers;
Simplify radicals; and
Perform addition, subtraction, multiplication
and
ALGEBRAIC
EXPRESSIONS
MathDivision,IMSP,UPLB
LearningObjectives
Upon completion, you should be able to
Give examples of algebraic
expressions; and
Perform operations involving integer
exponents.
2
Mat
Equations in Linear and
Quadratic Forms
At the end of this section, you should be
able to solve equations that are convertible
to equations in linear or quadratic forms:
Equations involving rational
EXERCISES 1.2
1. Tell which of the axioms of the real numbers justifies each of
the following statements:
a.
b.
c.
d.
e.
2. True or false: If true, provide a proof. Otherwise, give a
counterexample.
a
EXERCISES 1.4
In each of the following, a) find the sum of the
polynomials, and b) subtract the second from the
first.
1.
2.
3.
4.
In each of the following, remove the symbols of
grouping and combine
EXERCISES 1.5
Perform the indicated operations and simplify.
Final answers should be in simplest form.
1.
2.
3.
4.
5.
6.
7.
x 2 xy
3x 2 x3
24 x 2
6x2 9x
a 2 4a 4
a2 4
x 2 3x 4
x 2 x 12
2a 2 5a 12
4a 2
EXERCISES 1.3
In problems 1 through 10, carry out the indicated operations and express your answer in the
form
.
1. a)
b)
2. a)
b)
3. a)
b)
4. a)
b)
c)
d)
5. a)
b)
6. a)
1
a bi
7. a)
b)
1
a bi
b)
A. Write SET if the statement is a set,
otherwise write NOT SET
1.
2.
3.
Collection of planets in the solar system
Collection of provinces near Laguna
Collection of intelligent students
B. Given: S =
6/20/2012
NOTION OF A SET
Learning objectives:
Upon completion you should be able to:
Give examples of a well-defined set;
Name the elements of a set;
Describe a set using the roster and rule
metho
Learning Objectives
At the end of the lesson, you should be able to
define subtraction and division operations
enumerate the properties of real numbers
illustrate the closure property for real numb
6/27/2012
Learning Objectives: upon completion,
you should be able to perform the
following operations:
Union
Intersection
Complement
Difference
Cross product
S
E
T
O
P
E
R
A
T
I
O
N
S
2
Uses a clos
Learning Objectives
Subsets of the Set of Real
Numbers
Mathematics Division, IMSP, UPLB
At the end of the lesson, you should be able to
identify subsets of the set of real numbers
recognize the vari
RATIONAL
EXPRESSIONS
Learning objectives
Upon completion, you should be able to
Simplify
rational expressions;
Perform
addition, subtraction,
multiplication and division on rational
expressions; and
SPECIAL PRODUCTS AND
FACTORING
Special Products and Factoring
Upon completion, you should be able to
Find special products
Factor a polynomial completely
2
Special Products
rules for finding product
OPERATIONS ON
POLYNOMIALS
OPERATIONS ON POLYNOMIALS
Learning Objectives
Upon completion you should be able to
perform the following operations on
polynomials:
ADDITION
SUBTRACTION
MULTIPLICATION
D
INEQUALITIES and
ABSOLUTE VALUE
MATH 11
College Algebra
Objectives
Upon completion, you should be able to
define order relations between numbers
enumerate order properties of
define
absolute value of