MAT 0028 Introductory Algebra
Review Problems
There will be 30 questions on the Departmental Final Exam. Some questions will be multiple choice.
Some questions will be free response. There will be no
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Section 9.1-9.2: Symbols and Sets of Numbers & Properties of Numbers
Definitions:
Set a collection of objects
Element each object or member of a set
Natural numbers cfw_1, 2, 3, 4,
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Section 11.6: Solving Quadratic Equations by Factoring
Quadratic Equation: A quadratic equation is one that can be written in the form
ax2 + bx + c = 0
where a, b, and c are real num
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Section 10.5-10.6: Multiplying Polynomials and Special Products
Recall: To multiply two monomials, you multiply numbers and then multiply variables, using
the commutative and associa
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Section 10.2: Negative Exponents and Scientific Notation
Simplifying Expressions Containing Negative Exponents:
x2
Lets look at this example: 5
x
Negative Exponents:
If a is a real n
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Section 12.3: Adding and Subtracting Rational Expressions with the Same Denominator and
Least Common Denominator
Addition and subtraction of rational expressions is similar to additi
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Section 12.2: Multiplying and Dividing Rational Expressions
Multiplying and dividing rational expressions is similar to multiplying and dividing number
fractions.
Fractions
Rational
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Section 11.7: Quadratic Equations and Problem Solving
Example 1: Since the 1940s, one of the top tourist attractions in Acapulco, Mexico, is watching
the cliff divers off La Quebrada
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Section 9.6: Linear Inequalities and Problem Solving
Graphing Inequalities on a Number Line:
Example 1: Graph x -1.
0
Example 2: Graph -1 > x.
0
Example 3: Graph -4 < x 2.
0
Using th
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Section 11.1: The Greatest Common Factor
The process of writing a polynomial as a product is called factoring the polynomial.
Multiplying:
Factoring:
Finding the Greatest Common Fact
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Section 12.1: Simplifying Rational Expressions
Recall: A rational number is a number that can be written as a quotient of integers.
Rational Expression: A rational expression is an e
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Section 9.3: Further Solving Linear Equations
Definition: A linear equation in one variable can be written in the form Ax + B = C, where A, B,
and C are real numbers and A 0.
To Solv
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Section 9.4: Further Problem Solving
Solving Direct Translation ProblemsFinding an Unknown Number:
Example 1: Twice a number, added to seven, is the same as three subtracted from the
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Introductory Algebra
Test #1 Review: Chapter 4 + Sections 6.1, 8.7
From Chapter 4:
1.
45a2b3
Write the fraction in simplest form.
48ab5
Perform the indicated operation an
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Section 12.4: Adding and Subtracting Rational Expressions with Different Denominators
Recall: To add or subtract numerical fractions with unlike denominators, we used the LCD and
wri
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Section 11.5: Factoring Perfect Square Trinomials and the Difference of Two Squares
Recall: (x + 3)2 = x2 + 6x + 9 and (x 3)2 = x2 6x + 9
When factoring, if the trinomial is of the f
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Sections 10.3-10.4: Introduction to Polynomials, Adding and Subtracting Polynomials
Defining Term and Coefficient:
Terms are separated by _.
Coefficient: the numerical factor of each
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Introductory Algebra
Test #4 Review: Chapters 11-12: Sections 11.1-11.7 and 12.1-12.4
From Chapter 11:
1.
Find the GCF for the list of numbers: 18, 24, 36, 48
1. _
2.
2.
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Section 10.7: Dividing Polynomials
Dividing by a Monomial:
To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.
ab a b
, c0
c
c c
Example 1: Div
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Introductory Algebra
Test #2 Review: Chapter 9, Sections 9.1-9.6 + 6.6-6.7
Section 9.1:
Insert <, >, or = to make the statement true.
1.
-2 _ 0
3.
Write the sentence as a
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Section 9.5: Formulas and Problem Solving
Using Formulas to Solve Problems:
Ex:
d=rt
Sales Tax = tax rate (as a decimal) purchase price
P = 2L + 2W
Total Price = purchase price + sal