Download Algebra Assistance/College Algebra – MATH 0999/MATH 1111

Algebra Assistance/College Algebra – MATH 0999/MATH 1111
Course Outline
Fall 2014
Co-requisite: MATH 1111
Credit: (0-2-1) for institutional use only
MyMathLab Course ID: sharpe37304
[Algebra & Trigonometry, 9th Edition, Sulllivan]
(Beginning & Intermediate Algebra, 5th Edition, Martin-Gay)
{MyMathLab using Algebra & Trigonometry, 9th Edition, Sullivan, Chapters 15-18 Algebra Review}
(MATH 1111 in black, MATH 0999 in red)
SESSION
1
2
TOPIC
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Solve a linear equation
Recognize identities and equations with no solutions
Recognize polynomials
Add, subtract, and multiply polynomials
Find the Greatest Common Factor of a list of terms
Factor out the Greatest Common Factor from a polynomial
Factor a polynomial containing four terms by grouping in
pairs
Factor perfect square trinomials
Factor trinomials
Factor binomials
3
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4
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Solve a quadratic and higher degree polynomial equations
by factoring.
5
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Find and approximate square roots
Use the product and quotient rules to simplify radicals
Add, subtract, and multiply radical expressions
Rationalize denominators
Solve quadratic equations by using the square root method
Complete the square
Solve quadratic equations by completing the square
Solve quadratic equations using the Quadratic Formula
Classify numbers
Write square roots of negative numbers in the form bi
Add, subtract, multiply, and divide complex numbers
Raise i to powers
Solve quadratic and higher degree polynomial equations in
the complex number system
Determine the character of the solutions of a quadratic
equation by using the discriminant
6
7
8
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RESOURCES
[R.4, 1.1]
(2.3, 5.2, 5.3, 5.4)
{MML 16.2-16.4}
[R.5]
(6.1, 6.3)
{MML 16.6-16.8}
[R.5]
(6.2, 6.3, 6.5)
{MML 16.7, 16.8}
[R.5, 1.2, 1.4]
(6.6)
{MML 16.6-16.8}
[R.2, R.8, 1.2]
(10.1, 10.3-10.5)
{MML 18.2, 18.3}
[R.5, 1.2]
(11.1, 11.2)
[R.1, R.8, 1.3]
(10.1, 10.3, 10.7)
{MML 15.2, 18.5}
[1.3]
(11.2, 11.3)
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Work with nth roots
Simplify radicals with nth roots
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Understand the meaning of 𝑎− 𝑛
Use the Laws of Exponents to simplify expressions that
contain rational exponents
Use rational exponents to simplify radical expressions
Solve radical equations
11
12
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Unit 1 Test
Find the domain of a rational expression
Reduce a rational expression to lowest terms
Multiply and divide rational expressions
13
15
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Find the Least Common Multiple
Solve rational equations
Use interval notation
Use properties of inequalities
Solve linear inequalities
Solve linear compound inequalities
Solve equations involving absolute value
16
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Solve inequalities involving absolute value
17
18
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19
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20
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Unit 2 Test
Define the Rectangular Coordinate System and plot
ordered pairs of numbers
Use the Pythagorean Theorem
Use the Distance Formula
Use the Midpoint Formula
Graph a linear equation by finding and plotting ordered
pair solutions
Find intercepts from a graph
Find intercepts from an equation
Test an equation for symmetry with respect to the x-axis,
the y-axis, and the origin
Find the slope of a line given its graph
Find the slope of a line using the slope formula given two
points
Find the slope of a line given its equation
Compare the slope of parallel and perpendicular lines
9
10
14
21
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𝑚
[R.2, R.8]
(5.1, 5.5, 10.1,
10.2)
{MML 16.1, 18.1,
18.3, 18.4}
[R.8, 1.4]
(10.6)
[R.2, R.7]
(7.1, 7.2, 7.3)
{MML 15.8, 17.2,
17.3}
[R.7]
(7.5-7.7)
[R.1, R.2, 1.5]
(2.8, 9.1)
{MML 15.7}
[R.2, 1.6]
(9.2)
{MML 15.5}
[1.6]
(9.3)
[R.3, 2.1]
(3.1, 6.7, 10.3)
[2.2]
(3.1-3.3)
[2.2]
[2.3]
(3.4)
22
23
24
25
26
27
28
29
30
31
32
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Graph a linear equation by finding and plotting its
intercepts
 Use slope-intercept form to graph a linear equation
 Graph vertical and horizontal lines
 Use slope-intercept form or point-slope form to write an
equation for a non-vertical line
 Write equations for vertical lines
 Write equations for parallel and perpendicular lines
 Write the standard form of the equation of a circle
 Graph a circle
 Work with the general form of the equation of a circle
 Solve problems involving direct variation
 Solve problems involving inverse variation
 Solve problems involving joint variation
 Solve problems involving combined variation
Unit Test 3
 Determine whether a relation represents a function
 Find the value of a function
 Find the domain of a polynomial, rational, or radical
function defined by an equation
 Add and subtract rational expressions
 Simplify complex rational expressions
 Form the sum, difference, product, or quotient of two
functions
 Identify the graph of a function using the Vertical Line Test
 Obtain information from or about the graph of a function
 Graph linear functions using slope-intercept form
 Use average rate of change to identify linear functions
 Determine whether a linear function is increasing,
decreasing, or constant
 Graph variations of 𝑓(𝑥) = 𝑥 2 , illustrating vertical or
horizontal shifts, vertical compressions or stretches, and a
reflection about the x-axis
 Graph a quadratic function using transformations
 Identify the vertex and axis of symmetry of a quadratic
function
 Derive the formula for the x-coordinate of the vertex
 Graph a quadratic function using its vertex and one other
point
 Find a quadratic function given its vertex and one other
point
 Find the maximum or minimum value of a quadratic
function
[2.3]
(3.3, 3.4)
[2.3]
(3.5)
[2.4]
(13.1)
[2.5]
(8.4)
[3.1]
(3.6, 8.2)
[R.7, 3.1]
(7.3, 7.4, 7.7, 12.1)
{MML 17.4, 17.5}
[3.2]
(3.3, 3.6, 8.2)
[4.1]
(8.1)
[3.5, 4.3]
(8.2, 11.5, 11.6)
[4.3]
(11.6)
33
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34
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35
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Identify polynomial functions and their degree
Identify the real zeros of a polynomial function and their
multiplicity
Describe the behavior near each zero
Describe the end behavior and the number of turning
points given the polynomial function
Analyze the graph of a polynomial function
Solve polynomial inequalities
36
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Solve rational inequalities
37
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Divide a monomial by a monomial
Divide a polynomial by a monomial
Divide a polynomial by another polynomial using long
division
Divide a polynomial by a linear binomial with a leading
coefficient of 1 by synthetic division
Use the Remainder and Factor Theorems
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38
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40
41
42
43
44
45
46
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Unit 4 Test
 Form a composite function
 Find the domain of a composite function
 Determine whether a function is one-to-one
 Apply the Horizontal Test
 Determine the inverse of a function defined by a map or
roster
 Obtain the graph of the inverse function from the graph of
the function
 Find the inverse of a function defined by an equation
 Evaluate exponential functions
 Graph exponential functions
 Define the number e.
 Solve exponential equations which can be written in the
form 𝑏 𝑥 = 𝑏 𝑦 , 𝑏 > 0 𝑎𝑛𝑑 𝑏 ≠ 1
 Change exponential statement to logarithmic statements
and vice versa
 Evaluate logarithmic expressions
 Determine the domain of a logarithmic function
 Graph logarithmic functions
 Solve logarithmic equations by converting to exponential
form
Unit 5 Test
[5.1]
{MML 16.2}
[5.1]
[5.4]
(11.4)
[5.4]
(11.4)
[R.4, R.6]
(5.6, 5.7)
{MML 16.5}
[5.5]
(5.7)
[6.1]
(12.1)
[6.2]
(12.2)
[6.3]
(12.3)
[6.3]
(12.3)
[6.4]
(12.5)
[6.4]
(12.5)
47
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48
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49
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Work with the properties of logarithms
Write a logarithmic expression as a sum or difference of
logarithms
Write a logarithmic expression using a single logarithm
Evaluate logarithms whose base is neither 10 nor e using
the Change of Base Formula
Solve logarithmic equations
50
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Solve exponential equations
51
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52
53
54
55
56
57
58
59
60
Final
Exam
Determine the future value of a lump sum of money
Determine the present value of a lump sum of money
Determine the rate of interest or time required to double a
lump sum of money
Unit 6 Test
 Determine if an ordered pair is a solution of a system of
equations
 Solve systems of two linear equations in two variables by
graphing
 Identify inconsistent systems
 Express the solution of a system of dependent linear
equations in two variables
 Solve systems of two linear equations in two variables by
substitution or elimination
 Solve systems of at most three linear equations in three
variables
 Solve a system of nonlinear equations in two variables
using substitution
 Solve a system of nonlinear equations in two variables
using elimination
Unit 7 Test
Final Exam Review
Learning Support Math Exit Exam
Final Exam (
)
Revised: 3/27/2014
[6.5]
(12.6)
[6.5]
(12.6, 12.7)
[6.6]
(12.8)
[6.6]
(12.8)
[6.7]
(12.7, 12.8)
[12.1]
(4.1)
[12.1]
(4.2, 4.3)
[12.1]
(4.4)
[12.6]
[12.6]