SCHOOLofBUSINESS AND TECHNOLOGY
Department of Mathematics and Computer Science
MATH 101 Intermediate Algebra
Course Outline
Course Description
Topics in this Intermediate Algebra course include the algebra of signed numbers, solving linear equations and inequalities, quadratic equations, operations on algebraic expressions, and graphing. This course does not satisfy the General Education Requirement in Mathematics.
Course Outcomes:
1.Use a problem solving approach to investigate and understand mathematical content.
2.Use mathematical vocabulary, notation, and structure to represent ideas, describe relationships, and model situations.
3.Read and write presentations of mathematics with understanding.
4.Use and analyze algorithms.
5.Apply mathematical content and processes to model and solve problems from situations within and outside mathematics.
6.Develop understanding of and appreciation for biographical and historical development of mathematics.
Course Outline
This topic outline is intended as a scope and sequence for a regular semester.
It is highly recommended to all students to study and understand the following topics before taking a practice test. You will be assigned to take Math 101 or Math 109 based on placement test score. There is a sample test on departmental Web-site to practice your skill.You should score 70% or better on the practice test to be considered for Math 109.
Required test book for Math 101: Martin-gay, E.K.,” Intermediate Algebra”, Upper Saddle river, Prentice Hall, NJ, ISBN: 0536962499
1.1Tips for Success in Mathematics
1.2Algebraic Expressions and Sets of Numbers
1.3Operations on Real Numbers
1.4Properties of Real Numbers
2.1Linear Equations in One Variable
2.2Introduction to Problem Solving
2.3Formulas and Problem Solving
2.4Linear Inequalities and Problem Solving
2.5Compound inequalities
2.6Absolute Value Equations
2.7Absolute Value Inequalities
3.1Graphing Equations
3.2Introduction to Functions
3.3Graphing Linear Functions
3.4Slope of a Line
3.5Equations of Lines
3.6Graphing Linear Inequalities
5.1Exponents and Scientific Notation
5.2More Work with Exponents and Scientific Notation
7.1Radicals and Radical Functions
7.2Rational Exponents
5.3Polynomials and Polynomial Functions
5.4Multiplying Polynomials
5.5Greatest Common Factor and Factoring by Grouping
5.6Factoring Trinomials
5.7Factoring by Special Products
5.8Solving Equations by Factoring and Problem Solving
8.1Solving Quadratic Equations by Completing the Square
8.2Solving Quadratic Equations by the Quadratic Formula
6.1Rational Functions and Multiplying and Dividing Rational Expressions
6.2Adding and Subtracting Rational Expressions
6.3Simplifying Complex Fractions
6.4Dividing Polynomials
6.6Solving Equations Containing Rational Expressions
6.7Rational Equations and Problem Solving
6.8Variation and Problem Solving
Sample Test
Name______
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the value of the algebraic expression at the given replacement value.
1)
4x - ywhen x = 9 and y = 2
1)
______
A)
72
B)
34
C)
6
D)
38
Complete the statement to illustrate the given property.
2)
t + 0 = Additive identity property
2)
______
A)
0
B)
1
C)
0 + t
D)
t
Simplify the expression.
3)
3)
______
A)
5
B)
-6
C)
6
D)
-5
Write the sentence using mathematical symbols.
4)
The sum of -19 and x is -20.
4)
______
A)
-19 + x = -20
B)
x = -19 + 20
C)
x - 20 = -19
D)
-19 - 20 = x
Write the following as an algebraic expression.
5)
If 6x is an even integer, represent the next even integer as an expression in x.
5)
______
A)
6x + 1
B)
8x
C)
12x
D)
6x + 2
Write the solution set using interval notation.
6)
( 10x - 64) ≥ x - 4
6)
______
A)
(-∞, 16)
B)
[ 16, ∞)
C)
( 16, ∞)
D)
(-∞, 16]
Solve the absolute value equation.
7)
| 5x + 4| + 10 = 8
7)
______
A)
,
B)
-, -
C)
-, -
D)
∅
8)
| 10x| = 39
8)
______
A)
0, 3.9, -3.9
B)
-3.9
C)
3.9
D)
3.9, -3.9
Solve the equation.
9)
x - 16.3 = -12.4
9)
______
A)
3.9
B)
28.7
C)
-28.7
D)
-3.9
Solve.
10)
Cindy has scores of 71, 84, 83, and 89 on her biology tests. Use a compound inequality to find the range of scores she can make on her final exam to receive a C in the course. The final exam counts as two tests, and a C is received if the final course average is from 70 to 79.
10)
______
A)
70 ≤ final score ≤ 79
B)
11.5 ≤ final score ≤ 34
C)
93 ≤ final score ≤ 147
D)
46.5 ≤ final score ≤ 73.5
Determine whether the equation is linear or not.
11)
y = 8
11)
______
A)
linear
B)
not linear
Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y-intercept.
12)
Slope ; y-intercept (0, 0)
12)
______
A)
y =
B)
y = -x
C)
y = x
D)
y = -
Find the domain and the range of the relation. Then determine whether the relation is a function.
13)
{( -2, -7), ( 0, 3), ( 3, -4), ( 7, -1)}
13)
______
A)
domain: { -7, 3, -4, -1}
range: { -2, 0, 3, 7}
function
B)
domain: { -2, 0, 3, 7}
range: { -7, 3, -4, -1}
not a function
C)
domain: { -2, 0, 3, 7}
range: { -7, 3, -4, -1}
function
D)
domain: { -7, 3, -4, -1}
range: { -2, 0, 3, 7}
not a function
Find the domain and the range of the relation. Use the vertical line test to determine whether the graph is the graph of a function.
14)
14)
______
A)
domain: [3]
range: (-∞, ∞)
function
B)
domain: (-∞, ∞)
range: [3]
not a function
C)
domain: (-∞, ∞)
range: [3]
function
D)
domain: [3]
range: (-∞, ∞)
not a function
Graph the inequality.
15)
y ≥ -3x
15)
______
A)
B)
C)
D)
Simplify.
16)
If Q(x) = - 5, find Q( -5).
16)
______
A)
100
B)
-10
C)
20
D)
25
Factor the polynomial completely.
17)
- 81
17)
______
A)
B)
C)
(x + 9)(x - 9)
D)
prime polynomial
Factor. Assume that variables used as exponents represent positive integers.
18)
25 - 49
18)
______
A)
( 5 + 7)( 5 - 7)
B)
( 5 + 7)2
C)
( 5 - 7)2
D)
prime polynomial
Factor the polynomial completely.
19)
12 + 31(a + 3) + 20
19)
______
A)
( 4a + 5)( 3a + 4)
B)
( 4a + 8)( 3a + 7)
C)
( 4a + 17)( 3a + 13)
D)
( 4a + 16)( 3a + 14)
Simplify. Write the answer with positive exponents.
20)
20)
______
A)
-
B)
y
C)
D)
Simplify.
21)
21)
______
A)
B)
5 s + 8 t
C)
D)
8 s + 5 t
Solve the equation for the specified variable.
22)
P = for t
22)
______
A)
t =
B)
t =
C)
t = P - rA
D)
t =
Simplify the rational expression.
23)
23)
______
A)
x - 2y + 1
B)
C)
x - y
D)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Fill in the blank with one of the words or phrases listed below.
24)
The ofa list of rational expressions is a polynomial of least degree whose factors include the denominator factors in the list.
24)
______
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve.
25)
The amount of paint needed to cover the walls of a room varies jointly as the perimeter of the room and the height of the wall. If a room with a perimeter of 40 feet and walls requires of paint, find the amount of paint needed to cover the walls of a room with a perimeter of 55 feet and 6-foot walls.
25)
______
A)
330 quarts
B)
33 quarts
C)
6.6 quarts
D)
3.3 quarts
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Fill in the blank with one of the words or phrases listed below.
26)
The of a number is written as .
26)
______
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the product rule to multiply. Assume all variables represent positive real numbers.
27)
∙
27)
______
A)
5
B)
5
C)
25
D)
125
28)
∙
28)
______
A)
-56
B)
56
C)
-1
D)
15
Use radical notation to write the expression. Simplify if possible.
29)
29)
______
A)
2187
B)
81
C)
6561
D)
19,683
Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
30)
( + 2)( - 2)
30)
______
A)
11
B)
3
C)
5
D)
7 - 2
Solve the inequality. Graph the solution set and write the solution set in interval notation.
31)
4+ 24- 9x - 54 0
31)
______
A)
(-∞, -6] ∪ [ -, ]
B)
(-∞, -6) ∪ ( -, )
C)
( -6, -) ∪ (, ∞)
D)
[ -6, -] ∪ [, ∞)
32)
(4x - 1)(x + 2) ≤ 0
32)
______
A)
(-∞, -2] ∪ [, ∞)
B)
(-∞, ]
C)
[ -2, ∞)
D)
[ -2, ]
Use the discriminant to determine the number and type of solutions of the equation.
33)
- 6x + 9 = 0
33)
______
A)
two complex but not real solutions
B)
two real solutions
C)
one real solution
Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial.
34)
x2-x + ______
34)
______
A)
x2-x + =
B)
x2-x +=
C)
x2-x +=
D)
x2-x + =
Use the square root property to solve the equation.
35)
x2= 36
35)
______
A)
6
B)
18
C)
-7, 7
D)
-6, 6
1)
B
2)
D
3)
B
4)
A
5)
D
6)
B
7)
D
8)
D
9)
A
10)
D
11)
B
12)
C
13)
C
14)
C
15)
B
16)
C
17)
C
18)
A
19)
C
20)
B
21)
D
22)
B
23)
C
24)
least common denominator
25)
D
26)
cube root
27)
A
28)
B
29)
B
30)
B
31)
C
32)
D
33)
C
34)
C
35)
D