C o u n t y
C o l l e g e
M A T H 0 9 5
I n t e r m e d i a t e
A l g e b r a:
C O U R S E
S Y L L A B U S
D i a n e P . V e n e z i a l e
C o u r s e Co o r d i n a t o r 2004 - 2005
S c i e n c e , M a t h e m a t i c s
A n d
T e c h n o l o g y
Math 095: Intermediate Algebra
Division: Science, Mathematics, and Technology
Credit Hours:Four (4) credits
Prerequisites: Elementary Algebra skills/ Math 075 or one year of high school
Algebra
Textbook: Intermediate Algebra: Graphs and Functions, Third Edition, plus free HM3 CD-Rom + free SMARTHINKING, by Ron Larson, Robert Hostetler, Carolyn Neptune, 2003, Houghton Mifflin Company, ISBN: 0-618-28103-7
Course Description: This course is designed to prepare students of developmental
mathematics to make the transition from elementary algebra
to the college level mathematics courses. Topics include graphs and transformations of functions, linear and absolute value equations and inequalities, systems of linear equations and inequalities in 2 variables, radicals and complex numbers, quadratic functions, equations and inequalities, and rational expressions and graphing rational functions.
Required Materials Textbook, as listed above.
for Instruction:
Calculator: a scientific or graphing calculator may be used throughout the course during classroom discussions only. Its use
is NOT permitted on any test or final.
Course Syllabus (in the college store)
Optional Materials: Student Solutions Guide by Carolyn F. Neptune
Instructional Videotapes/DVDs by Dana Mosely (located in both
the Pemberton and TEC libraries)
HM3 Tutorial CD-Rom (Windows)
SMARTHINKING.com Live, On-Line Tutoring
Attendance: Attendance is taken at all class meetings. Please refer to the
Burlington County College catalog for details of the college’s
policy and specifically your instructor for his/her policy.
Course Content: Unit I – Chapter 2: Introduction to Graphs and Functions
1. Ordered Pairs as Solutions; The Distance Formula; The Midpoint Formula
2. Graphs of Equations
3. Slope; Parallel and Perpendicular Lines
4. Relations, Functions, and Function Notation; Finding the Domain of a Function
5. Graphs of Linear and Piecewise-Defined Functions; Vertical Line Test
6. Transformations of Functions
Unit II – Chapters 3 and 4: Linear Functions, Equations, and
Inequalities; Systems of Linear Equations and Inequalities
1. Writing Equations of Lines
2. Linear Inequalities in One Variable: Solving Linear and Compound Inequalities
3. Solving Absolute Value Equations and Inequalities
4. Solving a System of Equations in 2 Variables by Graphing, Substitution, and Elimination
5. Graphs of Linear Inequalities in 2 Variables and Systems of Linear Inequalities in 2 Variables
Unit III – Chapter 5: Radicals and Complex Numbers
1. Integer Exponents and Scientific Notation
2. Rational Exponents and Radicals
3. Simplifying and Combining Radicals
4. Multiplying and Dividing Radicals
5. Solving Radical Equations
6. Complex Numbers and Operations with Complex Numbers
Unit IV – Chapter 6: Quadratic Functions, Equations, and Inequalities
1. The Factoring and Square Root Methods
2. Completing the Square
3. The Quadratic Formula; The Discriminant
4. Graphs of Quadratic Functions; Sketching a Parabola
5. Quadratic Inequalities in One Variable
Unit V – Chapter 7: Rational Expressions and Rational Functions
1. Simplifying Rational Expressions
2. Multiplying and Dividing Rational Expressions
3. Adding and Subtracting Rational Expressions
4. Solving Rational Equations
5. Graphing Rational Functions
Evaluation: There are five (5) tests – one each on Units I, II, III, IV, and V.
Each test will be graded using the following scale:
|
Percent Correct |
Letter Grade |
|
100 – 90 |
O (Outstanding) |
|
89 – 70 |
P (Passing) |
|
69 – 0 |
U (Unsatisfactory) |
The final exam, to be administered during exam week, is comprehensive and MUST be passed with a score of 70% or better. There are 40 multiple-choice questions on the exam.
The course grade will be determined from the final test average. Adding the percent grades for each test, along with the score for the final exam (which must be at least 70%), and dividing this sum by six will compute the final test average. The letter grades listed in the above scale will be used to determine the course grade.
Grades of “I” or “X” are assigned at the discretion of the instructor.
Unit I: – Chapter 2: Introduction to Graphs and Functions
Objectives: Upon completion of this unit, the student should be able to define, explain,
symbolize, and/or illustrate the following:
ordered pairs rectangular coordinate system origin
Cartesian plane x-axis/y-axis quadrants
coordinates solution point collinear
Distance Formula Midpoint Formula graph
linear equation intercepts (x- and y-) slope
slope-intercept form relation function
domain/range independent/dependent variable
linear function constant function
Upon completion of this unit, the student should be able to:
1. Plot points on a rectangular coordinate system
2. Given a linear equation, determine ordered pairs that are solutions
3. Use the Distance Formula to determine the distance between two points
4. Given a line segment joining two points, find the midpoint
5. By plotting points, sketch the graph of an equation
6. Find and use the x- and y- intercepts to sketch a graph
7. Determine the slope of a line through two points
8. Write a linear equation in slope-intercept form and sketch it using slope and y-intercept
9. Use slope to determine whether two lines are parallel, perpendicular, or neither
10. Given a relation, find the domain and range of the relation
11. Determine if a relation is a function
12. Given a function and a value for x, evaluate the function
13. Using function notation, find the domain and range of the function
14. Sketch graphs of functions on a rectangular coordinate system
15. Use the Vertical Line Test to determine if a graph represents a function
16. Identify and sketch transformations of graphs of functions
________________________________________________________________________
Unit II – Chapters 3 and 4: Linear Functions, Equations, and
Inequalities; Systems of Linear Equations and Inequalities
Objectives: Upon completion of this unit, the student should be able to define, explain,
symbolize, and/or illustrate the following:
point-slope form general form algebraic inequalities
solution set graph of an inequality bounded intervals
unbounded intervals equivalent inequalities compound inequality
double inequality conjunctive disjunctive
intersection union system of equations
solution of a system consistent system dependent system
inconsistent system substitution method elimination method
linear inequality (in 2 variables) solution of a linear inequality
system of linear inequalities solution of a system of linear inequalities
Upon completion of this unit, the student should be able to:
1. Write an equation of a line using the point-slope form
2. Write the equation of a line of a horizontal, vertical, parallel, or
perpendicular line
3. Sketch the graph of inequalities in one variable
4. Solve linear inequalities in one variable
5. Solve compound inequalities
6. Solve absolute value equations and inequalities
7. Determine if an ordered pair is a solution of a system of equations
8. Solve a system of equations graphically, by substitution, and by the elimination method
9. Verify a solution to a linear inequality in two variables
10. Sketch graphs of linear inequalities in two variables
11. Solve systems of linear inequalities in two variables
________________________________________________________________________
Unit III – Chapter 5: Radicals and Complex Numbers
Objectives: Upon completion of this unit, the student should be able to define, explain,
symbolize, and/or illustrate the following:
zero exponents negative exponents scientific notation
square root cube root nth root of a
principal nth root of a index radical symbol
radicand perfect squares perfect cubes
rational exponents domain of a radical function radical function
conjugates extraneous solution imaginary unit i
i – form complex number imaginary number
standard form (of a complex number) complex conjugates
Upon completion of this unit, the student should be able to:
1. Use properties of exponents to simplify algebraic expressions
2. Write very large and very small numbers in scientific notation
3. Determine the nth roots of numbers and evaluate radical
expressions
4. Use the properties of exponents to evaluate and/or simplify
expressions with rational exponents
5. Evaluate radical functions and find the domains of radical
functions
6. Simplify radical expressions by using the Multiplication and
Division Properties
7. Simplify radical expressions by rationalizing
8. Add and subtract “like” radical expressions by using the
Distributive Property
9. Multiply radical expressions using the Distributive Property
or the FOIL method
10. Determine the product of conjugates
11. Simplify quotients involving radicals by rationalizing the
Denominators
12. Solve radical equations, identifying any extraneous solution
13. Write the square roots of negative numbers in i – form and
perform operations on numbers in i – form
14. Determine the equality of two complex numbers
15. Add, subtract, and multiply complex numbers
16. Divide complex numbers by using the complex conjugates
________________________________________________________________________
Unit IV – Chapter 6: Quadratic Functions, Equations, and Inequalities
Objectives: Upon completion of this unit, the student should be able to define, explain,
symbolize, and/or illustrate the following:
quadratic form of an equation solving quadratic equations
extracting square roots completing the square
Quadratic Formula The Discriminant parabola
vertex of a parabola axis of a parabola
standard form of a quadratic function zeros
critical numbers test intervals
general form of a quadratic inequality
Upon completion of this unit, the student should be able to:
1. Solve quadratic equations by factoring
2. Solve quadratic equations by extracting square roots
3. Solve quadratic equations with imaginary solutions
4. Rewrite quadratic expressions in completed square form
5. Solve quadratic equations by completing the square
6. Solve quadratic equations using the Quadratic Formula
7. Determine the number and types of solutions of quadratic
equations using the discriminant
8. Determine the vertices of parabolas by completing the square
9. Sketch parabolas
10. Determine the test intervals for polynomials
11. Solve quadratic inequalities in one variable using the test
intervals
________________________________________________________________________
Unit V – Chapter 7: Rational Expressions and Rational Functions
Objectives: Upon completion of this unit, the student should be able to define, explain,
symbolize, and/or illustrate the following:
rational expression domain of a rational expression
rational function domain of a rational function
simplified (or reduced) form complex fractions
least common multiple (LCM) least common denominator (LCD)
asymptote vertical asymptote
horizontal asymptote
Upon completion of this unit, the student should be able to:
1. Find the domain of a rational function
2. Simplify rational expressions
3. Multiply rational expressions
4. Divide rational expressions
5. Simplify complex fractions
6. Add and subtract rational expressions with “like” denominators
7. Add and subtract rational expressions with “unlike” denominators
8. Solve rational equations containing constant denominators
9. Solve rational equations containing variable denominators
10. Use a table of values to sketch graphs of rational functions
11. Determine horizontal and vertical asymptotes of rational functions
12. Use asymptotes and intercepts to sketch graphs of rational functions
________________________________________________________________________
Week # 1: Introduction to the Course/Chapter 2: Introduction to Graphs and Functions
Recommended Assignment: (Review of Algebra Skills):
Chapter 1, Pg. 78 # 1-32 all
Recommended Assignment: Pgs. 91-93 # 1-11 odd, # 19-29 odd,
# 43-51, 65-77 odd, # 85-93 odd
3. Section 2.2 – Graphs of Equations
Recommended Assignment: Pgs.105, 106 # 1-20, # 25-30, # 37-46
________________________________________________________________________
Week # 2: 1. Section 2.3 – Slope:An Aid to Graphing Lines
RecommendedAssignment: Pgs. 118, 119 # 1-26, # 29-45 odd
# 47-64, # 67-83
2. Section 2.4 – Relations, Functions, and Function Notation
Recommended Assignment: Pgs. 130-132 # 1-4, # 11-16,
# 19-24, # 27-37, # 41-44, # 47-63 odd
________________________________________________________________________
Week # 3: 1. Section 2.5 – Graphs of Functions
Recommended Assignment: Pgs. 140, 141 # 1-7 odd, # 11- 24,
# 33-36, # 37-57 odd
2. Section 2.6 – Transformations of Functions
Recommended Assignment: Pgs. 149, 150 # 1-11 odd, # 13-26,
# 33- 45 odd
Week # 4: 1. Review of Chapter 2
Recommended Assignments: Pgs. 153-156 # 9-18, # 19-25 odd,
# 31-35 odd, 43-61 odd, # 65-71 odd, # 73, 77,
# 81-89 odd, # 93 –97 odd, 103-109 odd
Pgs. 157 # 1-14
Sample Test I(included here on P.12,13)
Week # 4 (continued):
2. TEST # 1 – Chapter 2
3. Unit II - Chapters 3 and 4: Linear Functions, Equations, and
Inequalities; Systems of Linear Equations and Inequalities Section 3.1 – Writing Equations of Lines
Recommended Assignment: Pgs. 168,169 # 1-20, # 21-29 odd,
# 33-43 odd, # 55-73 odd
4. Section 3.4 – Linear Inequalities in One Variable
Recommended Assignment: Pgs. 210,211 #1-16, # 17,21,25,…,49,
# 55-63 odd
________________________________________________________________________
Week # 5: 1. Section 3.5 – Absolute Value Equations and Inequalities
Recommended Assignment: Pgs. 220,221 # 1-8 all,
# 9, 13, 17,…, 37, #43 – 51 odd,
61, 63, # 69-99 odd, # 111-116
2. Section 4.1 – Systems of Linear Equations in Two Variables
Recommended Assignment: Pgs. 244,245 # 1-9 odd, #11, 17, 19,
# 21, 29, 31, 41-49 odd, 55-65 odd
________________________________________________________________________
Week # 6: 1. Section 4.5 – Linear
Inequalities in Two Variables
Recommended Assignment: Pgs. 293, 294 # 1-6, # 9, 13, 15, 19,
# 23, 27, # 45-61 odd
2. Review of Unit II – Chapter 3.1, 3.4, 3.5, 4.1, 4.5
Recommended Assignments: Pgs. 224, 225 # 1-23 odd, 55-79 odd
Pgs. 298-300 # 1-7 odd, # 13-22,
# 79-83, # 85-88
Sample Test II(included here on P.13,14)
________________________________________________________________________
Week # 7: 1. TEST # 2 – parts of Chapters 3 and 4
Recommended Assignment: Pg. 12 # 45-90 all (review of
exponent rules)
2. Unit III – Chapter 5: Radicals and Complex Numbers
Section 5.1 – Integer Exponents and Scientific Notation
Recommended Assignment: Pg. 311 # 1-75 odd
Week # 7 (continued):
3. Section 5.2 – Rational Exponents and Radicals
Recommended Assignment: Pgs. 321, 322 # 7-41 odd,
# 51-111 odd
________________________________________________________________________
Week # 8: 1. Section 5.3 – Simplifying and Combining Radicals
Recommended Assignment: Pgs. 329, 330 # 1-45 odd, 51-73 odd,
# 81-105 odd, # 109-112
2. Section 5.4 – Multiplying and Dividing Radicals
Recommended Assignment: Pgs. 337, 338 # 1-29 odd, 39-71 odd,
# 81, 83
3. Section 5.5 – Solving Radical Equations
Recommended Assignment: Pg. 346 # 1-51 odd
________________________________________________________________________
Week # 9: 1. Section 5.6 – Complex Numbers
Recommended Assignment: Pgs. 354, 355 # 1-87 odd
2. Review of Unit III – Chapter 5
Recommended Assignments: Pgs. 357-359 #1-103 odd,
# 111-123 odd, # 129-140
Pg. 360 # 1-19
Sample Test III(included here on P.14,15)
3. TEST # 3 – Chapter 5
_______________________________________________________________________
Week # 10: 1. Unit IV – Chapter 6: Quadratic Functions, Equations, and Inequalities
Section 6.1 – The Factoring and Square Root Methods
Recommended Assignment: Pgs. 372, 373 # 1-57 odd, 89-99 odd
2. Section 6.2 – Completing the Square
Recommended Assignment: Pg. 381 # 1-41 odd
3. Section 6.3 – The Quadratic Formula and the Discriminant
Recommended Assignment: Pg. 389 # 13-33 odd, # 43-65 odd
Week # 11: 1. Section 6.5 – Graphs of Quadratic Functions
Recommended Assignment: Pgs. 408, 409 # 1-53 odd, # 79-85 odd
2. Section 6.6 – Quadratic Inequalities in One Variable
Recommended Assignment: Pg. 419 # 1-35 odd
3. Review of Unit IV – Chapter 6
Recommended Assignments: Pgs.422, 423 # 1-21 odd, 39-49 odd,
# 55-73 odd, 79-91 odd
Pg. 425 # 1-9, 11, 14
Sample Test IV(included here on P.15,16)
4. TEST # 4 – Chapter 6
_______________________________________________________________________
Week # 12: 1. Unit V – Chapter 7: Rational Expressions and Rational Functions
Section 7.1 – Simplifying Rational Expressions
Recommended Assignment: Pgs. 435, 436 # 1-55 odd, 59, 61
2. Section 7.2 – Multiplying and Dividing Rational Expressions
Recommended Assignment: Pgs. 443, 444 # 1-57 odd
3. Section 7.3 – Adding and Subtracting Rational Expressions with
“like” and “unlike” denominators
Recommended Assignment: Pgs. 452, 453 # 1-65 odd, 79-89 odd
_______________________________________________________________________
Week # 13: 1. Section 7.5 – Solving Rational Equations
Recommended Assignment: Pg. 474 # 1-41 odd
2. Section 7.6 – Graphing Rational Functions (asymptotes)
Recommended Assignment: Pgs. 483, 484 # 1-35 odd
3. Review of Unit V – Chapter 7
Recommended Assignments: Pgs. 494-496 # 1-35 odd, 39,
# 55-63 odd, 69-83 odd
Pg. 497 # 1-10, 14, 16
Sample Test V(included here on P.16,17)
Week # 14: 1. TEST # 5 – Chapter 7
Recommended Assignment: Final Review on Pgs. 22-27 (here)
11
Week # 14 (continued)
2. Final Exam Review:
Complete Pgs. 28-33 of Syllabus (Final Exam Review)
Additional Recommended Assignments: Pgs. 581, 582 # 1-14,
#19-22, 27-33
Pgs. 639 # 3-9, 11-19, 21-26
Review all Sample Tests
Week # 15: FINAL EXAM: (comprehensive)