MATH 015 - Elementary Algebra

Prerequisites:

Mat 012 - Review of Math Fundamentals or greater than or equal to 94 in computation and 20-66 in algebra

Corequisites: None

Course Hours and Credits: 4:0:4

Course Description: A review of elementary algebra, including operations on real numbers, simplification and evaluation of algebraic expressions , solving equations and inequalities , solving word problems, exponents, polynomials, factoring, graphing, simultaneous equations , radicals and algebraic fractions .

Required Text: Kaufmann, J. & Schwitters, K. (2006). Elementary and Intermediate Algebra: A Combined Approach (4^th ed.). Belmont, CA: Thomson Brooks/Cole

Materials: Scientific Calculator or Graphing Calculator Graph paper

Method of Instruction: Lecture

Manuals: Review for Final Exam

Disclaimer: None

CORE COURSE PERFORMANCE OBJECTIVES :

The student will be able to:

1. Perform basic operations on real numbers. (CCC 7)
2. Perform operations with algebraic expressions including applications.(CCC2,7)
3. Perform basic operations with exponents and scientific notation . (CCC 7)
4. Perform basic operations and factoring of polynomials . (CCC 7)
5. Graph functions. (CCC 7)
6. Solve equations and inequalities including applications. (CCC 2,7)
7. Solve systems of simultaneous equations including applications. (CCC 2,7)
8. Perform operations on radicals and radical expressions. (CCC 7)
9. Perform basic operations on algebraic functions . (CCC7)

MEASURABLE PERFORMANCE OBJECTIVES

The Elementary Algebra student will be tested on the following measurable performance objectives:

1. Perform basic operations on real numbers. (CCC 7)

1.1 Use the names of different types of numbers, add signed numbers with same signs and add signed numbers with opposite signs.
1.2 Subtract signed numbers.
1.3 Multiply and divide signed numbers.
1.4 Write numbers in exponent form; evaluate numerical expressions that contain exponents.
1.5 Recognize polynomials; use the distributive property to multiply a polynomial by a monomial .
1.6 Identify like terms, combine like terms.
1.7 Use the order of operations to simplify numerical expressions involving addition, subtraction, multiplication, division and exponents.
1.8 Evaluate a variable expression for a specified value; evaluate a formula by substitution .
1.9 Simplify variable expressions with several grouping symbols.
1.10 Evaluate a square root of a perfect square and approximate a square root to the nearest thousandth.
1.11 Simplify radical expressions.
1.12 Add or subtract radical expressions.
1.13 Multiply radical expressions.

2. Perform operations with algebraic expressions . (CCC 2, 7)

2.1 Solve equations of the form x + b = c using the addition principle.
2.2 Solve equations of the form x/a = b and ax = b.
2.3 Solve equations of the form ax + b = c and equations with parentheses.
2.4 Solve equations with fractions.
2.5 Solve formulas for a specified variable.
2.6 Interpret an inequality statement and graph an inequality on a number line.
2.7 Solve an inequality.
2.8 Write an algebraic expression for two or more quantities that are being compared.
2.9 Use equations to solve word problems.
2.10 Solve word problems involving comparisons.
2.11 Solve applied problems with periodic rate changes, percent problems, investment problems involving simple interest, and coin problems.
2.12 Solve word problems using geometric formulas.
2.13 Use inequalities to solve word problems.

3. Perform basic operations with exponents and scientific notation. (CCC 7)

3.1 Multiply and divide exponential expressions with like bases and raise exponential expressions to a power.
3.2 Use negative exponents and write numbers in scientific notation.

4. Perform basic operations and factoring of polynomials. (CCC 7)

4.1 Add and subtract polynomials.
4.2 Multiply polynomials.
4.3 Multiply binomials of the type (a + b)(a - b), (a + b)^2 and (a - b)^2; multiply polynomials with more than two terms.
4.4 Divide a polynomial by a monomial and by a binomial.
4.5 Factor polynomials containing a common factor in each term.
4.6 Factor problems with four terms by grouping.
4.7 Factor polynomials of the form x^2 + bx + c.
4.8 Factor a trinomial of the form by the trial and error method and by the grouping method.
4.9 Recognize and factor problems of the type a^2 - b^2 and the type a^2 + 2ab + b^2.
4.10 Identify and factor any polynomial that can be factored.
4.11 Solve a quadratic equation by factoring.

5. Graph functions. (CCC 7)

5.1 Plot a point given the coordinates, name the coordinates of a plotted point, and find ordered pairs for a given linear equation.
5.2 Graph a straight line by plotting points, by finding its x- and y-intercepts, and graph horizontal and vertical lines.
5.3 Graph linear inequalities in two variables.

6. Solve equations and inequalities including applications. (CCC 2, 7)
6.1 Find the slope given (a) two points and (b) the equation of a line; write the equation of a line given the slope and y-intercept, graph using slope y-intercept and find slope of lines that are parallel or perpendicular.
6.2 Write the equation of a line given (a) a point and a slope, (b) two points, and (c) from a graph of a line.

7. Solve systems of simultaneous equations including applications. (CCC 2, 7)

7.1 Solve a system of linear equations by graphing.
7.2 Solve a system of linear equations by the substitution method.
7.3 Solve a system of linear equations by the addition method (elimination method).
7.4 Choose an appropriate method to solve a system of linear equations algebraically.
7.5 Solve word problems using a system of linear equations.

8. Perform operations on radicals and radical expressions. (CCC 7)

8.1 Simplify a fraction involving radicals.
8.2 Use the Pythagorean Theorem and solve radical equations.
8.3 Solve problems involving direct and inverse variations.
8.4 Simplify an algebraic fraction by factoring.
8.5 Multiply and divide algebraic fractions and write the answer in simplest form.
8.6 Add and subtract algebraic fractions with the same denominator and with different denominators.

9. Perform basic operations on algebraic functions. (CCC 7)

9.1 Simplify complex rational expressions.
9.2 Solve equations involving algebraic fractions.
9.3 Solve problems involving ratio and proportion, similar triangles, distance problems and work problems.

EVALUATION CRITERIA

Students will demonstrate proficiency on all Measurable Performance Objectives at least to the 75% level. The final grade will be determined using the College Grading System:

Students should refer to the Student Handbook for information on Academic Standing Policy, Academic Honesty Policy, Students Rights and Responsibilities and other policies relevant to their academic progress.

Syllabus for College Algebra

1. Protocol

1. Course Name: College Algebra
2. Course Number: MAT 181
3. Credits: Three (3)
4. Prerequisite: Passing score on Part A and Part B of University
Mathematics Placement Exam or Grade of C or better
in DMA 092 or DMA 094

2. Objectives of the Course

Upon completion of this course, the student will be able to:

1. Identify the elements and properties of the real number systems.
2. Add, subtract, multiply, and divide polynomials.
3. Simplify algebraic expressions .
4. Factor polynomials.
5. Add, subtract, multiply, and divide rational expressions, and write rational
expressions in simplified form .
6. Simplify exponential expressions with integral and rational expressions.
7. Simplify radical expressions .
8. Solve linear equations.
9. Identify a complex number and elementary properties of the complex number
system.
10. Perform operations on complex numbers.
11. Solve quadratic equations by appropriate methods: factoring, applying the
square root property, completing the square, and using the quadratic formula.
12. Solve equations involving rational expressions by clearing of fractions.
13. Solve formulas for an indicated variable.
14. Explain the steps int he derivation of the quadratic formula and theorems of
algebra.
15. Apply theorems, rules, and definitions of algebra in problem solving .
16. Model real-world applications mathematically.
17. Solve real-world applications.
18. Demonstrate efficiency in problem solving.
19. Use induction and deduction as methods of reasoning.
20. Solve radical equations and equations that are quadratic in form.
21. Solve linear inequalities; graph solutions and write solutions in interval notation.
22. Solve quadratic and rational and rational inequalities; graph solutions and write
solutions in interval notation.
23. Solve equations and inequalities involving absolute value; graph solutions and
write solutions in interval notation.
24. Find the distance and midpoint between two points.
25. Test an equation algebraically for symmetry with respect to the y-axis, x-axis,
and origin.
26. Graph linear equations.
27. Analyze the graph of a linear equation and determine the slope , the intercepts,
and the equation of the graph.
28. Determine algebraically if two lines are parallel , perpendicular, or neither.
29. Derive the general and standard form of the equation of a line under given
conditions: given a point and the slope, given two points, given a point and the
equation of a line parallel or perpendicular to the line.
30. Graph circles given the equation of a circle in either standard or general form.
31. Derive the equation of a circle given the center and radius of the circle.
32. Determine if a given relation is a function.
33. Determine if a given equation is a function.
34. Determine the domain and range of a given function and apply the rule of
maximum domain if the domain is not specified.
35. Evaluate functions.
36. Perform operations on functions.
37. Form a composite function given two functions and find the domain of the
composite function.
38. Identify even and odd functions given an equation of a function.
39. Determine if a given graph is the graph of a function.
40. Analyze the graph of a function and determine if the function is even or odd; the
symmetry of the function; the intercepts; the domain and range; if the function is
continuous; intervals where the function is increasing, decreasing, or constant;
and the value of the function at a given point.
41. Graph functions using transformations.
42. Graph quadratic functions.
43. Analyze quadratic functions and determine the maximum or minimum point, the
intercepts, points on the graph using symmetry, the range, if the graph will be
concave up or down, the intervals where the function is increasing or
decreasing.
44. Graph polynomial functions .
45. Find the domain and range of rational functions.
46. Find and graph the asymptotes of rational functions.
47. Graph rational functions.
48. Use synthetic division and the remainder theorem to evaluate a polynomial.
49. Find the zeros of polynomial functions of degree greater than two.
50. Solve systems of linear equations and related applications by the following
methods: substitution, elimination, and matrices (if time permits).

3. Catalog Description: Fundamental operations; factoring and fractions, exponents, and
radicals; functions and graphs; equations and inequalities; systems of equations.
Prerequisite: MAT 099 or high school algebra. (3 cr.)

4. Descriptive Overview of Course

1. Outline of Course Content:

1. Basic Algebraic Operations
(1) Review of the real number system
(2) Polynomials
(3) Factoring polynomials
(4) Rational expressions
(5) Integral exponents
(6) Rational exponents
(7) Radical expressions

2. Equations and Inequalities
(1) Linear equations
(2) Applications of linear equations
(3) Linear inequalities
(4) Equations and inequalities involving absolute value
(5) Complex numbers
(6) Quadratic equations
(7) Radical equations and equations that are quadratic in form
(8) Polynomial and rational inequalities

3. Graphing and Functions
(1) Rectangular coordinate system
(a) Distance formula
(b) Midpoint formula
(2) Graphs of equations
(a) Introduction to graphing
(b) Intercepts
(c) Symmetry
(3) Equations and graphs of lines
(4) Parallel and perpendicular lines
(5) Circles
(6) Functions

(a) Determining where a function is increasing, decreasing,
or constant
(b) Determining even and odd functions
(c) Graphs of functions

(7) Graphing using transformations
(8) Graphing quadratic functions
(9) Operations on functions
(10) Composite functions

4. Polynomial and Rational Functions
(1) Polynomial functions
(2) Rational functions
(3) Synthetic division
(4) The real zeros of a polynomial function
(5) Isolating real zeros
(6) Rational Root Theorem
(7) Approximating real zeros
(8) Fundamental Theorem of Algebra

5. Systems of Linear Equations
(1) Solving systems of linear equations by substitution and
elimination methods
(2) Solving systems of linear equations using matrices

2. Teaching Methodology: This course will be taught using the lecture/discussion
format. Small group and individual work will be assigned at the discretion of the
instructor. Use of appropriate technology for concept exploration will be used
at the discretion of the instructor.

3. Text and Other Support Materials
1. Barnett, R. & Ziegler, M. (1993). College Algebra, 5^th ed. New
York: McGraw Hill.
2. Scientific calculator

4. Methods of Evaluation and Assessment: The final grade will be determined as a
percentage from the following evaluation methods with varying weights at the
discretion of the instructor:

1. Written examinations
2. Quizzes
3. Homework assignments
4. Attendance
5. Performance

COLLEGE ALGEBRA

I: Algebra
Students will be able to:
1. Perform operations on polynomials : +, -, x, ÷, including synthetic ÷, and raising to a power

2. Factor expressions
a. by grouping
b. by synthetic division that are the sum or difference of cubes
c. containing negative and fractional exponents

3. Perform operations on rational expressions
a. Reduce, +, -, x, ÷
b. Simplify a complex fraction

4. Perform operations on radical expressions
a. Simplify, +, -, x, ÷, raise to a power including complex numbers
b. Rewrite radicals using fractional exponents

5. Perform operations on expressions with fractional and negative exponents
a. Simplify, +, -, x, ÷, raise to a power
b. Rewrite fractional exponents using radicals

6. Solve the following Equations algebraically and graphically on the TI- 83 Plus calculator
a. Linear
b. Quadratic -- Algebraically by : Factoring, Quadratic Formula with Real and Complex Roots, Extracting the Roots with Real and Complex Roots, Completing the Square Method with Real and Complex Roots
c. Higher Degree (Polynomials)
d. Rational
e. Radical
f. Absolute Value

7. Solve the following Inequalities algebraically and graphically on the TI- 83 Plus calculator and express the solution in Interval Notation
a. Linear
b. Quadratic
c. Rational
d. Absolute value

8. Perform the following in regard to Relations and Functions
a. Find the value of a function using functional notation
b. Determine whether a relation represents a function (from a set of ordered pairs and from a graph)
c. Find the domain and range of a function
d. Find the sum, difference, product and quotient of two functions
e. Find the composite of a pair of functions (and its domain)
f. Find the Difference Quotient of a Polynomial, Rational, and Radical Function

9. Hand graph the following functions
a. Linear using Slope Y-Intercept (find the slope of a line and write an equation of a line ).
b. Quadratic (Find x and y-intercepts, find the axis of symmetry, and find the vertex
c. Cubic
d. Rational and determine asymptotes
e. Radical
f. Absolute Value
g. Restricted domain, Split domain or Piecewise
h. Greatest Integer

10. Using the graphing calculator
a. To graph a function and find/determine (x-and y-intercepts, zeros, intervals on which the function is increasing and decreasing, maximum and minimum and local minima and maxima, obtain information from or about the graph of a function
b. Regression Program to find the Curve of Best Fit (linear, quadratic, power, polynomial – cubic, exponential, logarithmic)

11. Solve systems of equations algebraically and graphically , by hand and graphing calculator
a. That are linear and nonlinear, two variables
b. *That are linear, three variables

II. Trigonometry
Students will be able to:
1. Solve a right triangle using Right Triangle Trig and The Pythagorean Theorem
2. Convert between degrees , minutes, seconds and decimal form for angles
3. Convert from degrees to radians and from radians to degrees
4. Find the trigonometric functions of an angle of any size
5. Solve oblique triangles using the Law of Sines and Law of Cosines
6. Graph trigonometric functions
7. *Graph and solve vector problems

III. Elementary Transcendental Functions
Students will be able to:
1. Use the Properties of logarithms to expand a log expression, and vice versa
2. Solve logarithm equations algebraically and graphically on the calculator
3. Graph logarithmic functions by hand and graphing calculator
4. Solve exponential equations algebraically and graphically on the calculator
5. Graph exponential functions by hand and the graphing calculator