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 partial credit for incorrect answers.
Calculators are N
MAT0028
Colarusso
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,
Whole numbers cfw_0, 1, 2, 3, 4,
Integers cfw_, -3, -2
MAT0028
Colarusso
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 numbers and a 0. This form of the equation is called stand
MAT0028
Colarusso
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 associative properties.
Example 1: Multiply.
(a)
6x 4x
(b)
-7x
MAT0028
Colarusso
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 number other than 0 and n is an integer, then
1
1
an n
a
MAT0028
Colarusso
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 addition and subtraction of
rational numbers.
Fractions
Ratio
MAT0028
Colarusso
Section 12.2: Multiplying and Dividing Rational Expressions
Multiplying and dividing rational expressions is similar to multiplying and dividing number
fractions.
Fractions
Rational Expressions
P
R
and are rational expressions, then
Q
S
MAT0028
Colarusso
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. The divers platform is about 144 feet above the sea.
MAT0028
Colarusso
Section 10.1: Exponents
Evaluating Exponential Expressions:
Example 1: Evaluate each expression.
(a)
23
(b)
(d)
-42
(e)
31
1
2
(c)
(-4)2
(f)
4x2
2
Example 2: Evaluate each expression for the given value of x.
(a)
2x3 when x = 5
(b)
9
w
MAT0028
Colarusso
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 the Addition Property:
If a, b, and c are real numbers, t
MAT0028
Colarusso
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 Factor of a List of Numbers:
When do we use the factoring o
MAT0028
Colarusso
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 expression that can be written in the form
P
Q
where P a
MAT0028
Colarusso
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 Solve Linear Equations in One Variable:
1)
If an equation c
MAT0028
Colarusso
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 number.
Find the number.
Example 2: Twice the sum of a
MAT0028
Colarusso
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
write equivalent fractions with like denominators. The sam
MAT0028
Colarusso
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 form a2 + 2ab + b2, then the factored form is (a + b)2.
MAT0028
Colarusso
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 term.
Example 1: Complete the table for the expression
MAT 0028
S. Colarusso
Name: _
Introductory Algebra
Test #3 Review: Chapter 10, Sections 10.1-10.7
Section 10.1: Exponents
Evaluate each expression.
1.
-32
3
2.
1
3
3.
7 24
Evaluate each expression with the given replacement values.
4.
x3 when x = -3
5.
MAT 0028
S. Colarusso
Name: _
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. _
Find the GCF for the list of terms:
12m3n2, 18m5n4, 3
MAT0028
Colarusso
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: Divide.
(a)
(6m2 + 2m) 2m
(b)
25x 3 5x 2
5x 2
(c)
9 x 5 12
MAT 0028
S. Colarusso
Name: _
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 mathematical statement:
Eleven is less than or equal t