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COLLEGE ALGEBRA
Text
1. Required: Aufmann|Barker|Nation College Algebra and
Trigonometry 4th ed. (2002) Houghton Mifflin,
Boston.
2. Required: Scientific Calculator; preferably a graphing calculator.
3. Recommended: MathCAD® software if you have your own personal computer. A
version called
StudyWorks is available in the bookstore for only about $35.00. There is a
summary of useful MathCAD®
features at my website. I encourage you to check it out.
Bulletin Description
Manipulation techniques for polynomial, rational,
exponential, and radical expressions.
Properties of the exponential and logarithmic functions. Solutions of systems of
equations and
inequalities. Complex numbers, theory of equations, curve sketching,
combinatorics, sequences and
series, finite induction. Does not apply toward any math or computing program.
Prerequisite: MATH
007 or high school algebra II.
Objectives
1. To develop skills in the classical areas of precalculus-algebra.
2. To provide the student with the manipulative skills necessary for calculus.,
business and/or education
classes.
3. To introduce the student to appropriate mathematical uses of technology
including MathCAD®.
Topics Covered: The wording under “Topics” come directly from the textbook and
California Commission on
Teacher Credentialing “Standards of Quality and Effectiveness for the Subject
Matter Requirement for
the Multiple Subject Teaching Credential” September 6 2001.
| Sections | Topics |
| P.1-P.2 | Real Number System, Intervals, Absolute Value
Distance. Students examine the structure of the whole, integer, rational , and real number systems. They order integer, mixed numbers, rational numbers (including fractions, decimals, and percents) and real numbers. They describe the relationships between algorithms for addition, subtraction, multiplication, and division. They understand the properties of number systems and their relationship to the algorithms. [e.g. 1 is the multiplicative identity; 27 + 34 = 2 × 10 + 3 + 3× 10 + 4 = (2 + 3) × 10 + (7 + 4)]. They perform operations with positive, negative, and fractional exponents, as they apply to whole numbers and fractions. They show an understanding of the order of operations. They estimate and measure length. |
| P.3-P.4 | Integer and Rational Exponents, Polynomials,
scientific notation. Students revise their understanding of base ten place value, including representation of numbers in exponential and scientific notation. They describe the relationships between algorithms for addition, subtraction, multiplication, and division. They perform operations with positive, negative, and fractional exponents, as they apply to whole numbers and fractions. They round numbers and estimate the result of calculations, and place numbers accurately on a number line. |
| P.5-P.6 | Factoring and Rational Expressions. Students
review number theory concepts including prime numbers, greatest common factors. They describe the relationships between algorithms for addition, subtraction, multiplication, and division. They perform operations with positive, negative, and fractional exponents, as they apply to whole numbers and fractions. They use proportional reasoning. Students have a basic understanding of the multiplication, division and factoring of polynomials. Students estimate and measure area. |
| MathCAD® | Introduction to the use of MathCAD® as an
algebraic manipulator. We require all college algebra students to become proficient in the use of MathCAD® for numerical computations, symbolic manipulations and graphing. They take a test devoted entirely to MathCAD® on the last day of the quarter. Besides that students are required to possess and use a scientific calculator on tests. See these requirements listed under the “Text” portion of the Syllabus. |
| 1.1 | Linear Equations. Students demonstrate fluency in
standard algorithms for computation both in this section and through out this course. They are able to find equivalent expressions for equalities. They can explain the meaning of symbolic expressions, and find solutions and represent them on graphs. They recognize and create equivalent algebraic expressions, and represent geometric problems algebraically. They have a basic understanding of linear equations. They interpret graphs of linear and quadratic equations and inequalities including solutions to systems of equations. |
| 1.2 | Formulas and applications. Students evaluate the
correctness of nonstandard algorithms. They round numbers in the solution to equations and estimate the result of calculations, and place numbers accurately on a number line. They recognize and create equivalent algebraic expressions, and represent geometric problems algebraically. They calculate perimeters and areas of two-dimensional objects. They use measures such as miles per hour to analyze and solve problems. |
| 1.3 | Quadratic equations. Students are able to find
equivalent expressions for equalities. They recognize and create equivalent algebraic expressions, and represent geometric problems algebraically. They have a basic understanding of solving quadratic equations through factoring, completing the square and using the quadratic formula. . They interpret graphs of linear and quadratic equations and inequalities including solutions to systems of equations. They understand the Pythagorean theorem and its converse. They use concrete representations, such as coordinate geometry to represent geometric objects.. |
| 1.4 | Other type of equations (higher degree and
radical equations). Students recognize and create equivalent algebraic expressions, and represent geometric problems algebraically. They use concrete representations, such as coordinate geometry to represent geometric objects.. |
| 1.5 | Inequalities (linear and other). Students are able to find equivalent expressions for inequalities. |
| 1.6 | Variation and applications including proportions.
Students round numbers in the solution to equations and estimate the result of calculations, and place numbers accurately on a number line. They represent patterns, including relations and functions through table, graphs, and verbal rules or symbolic rules. They can explain the meaning of symbolic expressions, and find solutions and represent them on graphs. They use measures such as miles per hour to analyze and solve problems. |
| 2.1 | Two-dim Coordinate system and graphs. Students
represent patterns, including relations and functions through tables graphs. They understand the Pythagorean theorem and its converse. |
| Test 1 | |
| 2.2 | Intro to functions. Students represent patterns,
including relations and functions through tables and verbal rules or symbolic rules. Students estimate and measure volume. |
| 2.3 | Linear functions. Students interpret graphs of
linear and quadratic equations and inequalities including solutions to systems of equations. |
| 2.4 | Quadratic functions. Students interpret graphs of
linear and quadratic equations and inequalities including solutions to systems of equations. They use concrete representations, such as coordinate geometry to represent geometric objects.. |
| 2.5 | Properties of graphs. Students interpret graphs
of linear and quadratic equations and inequalities including solutions to systems of equations. |
| 2.6 | The algebra of functions. Students estimate and
measure surface areas and volumes of three-dimensional objects. see question 65. |
| 3.1 | Polynomial division and synthetic division.
Students have a basic understanding of the multiplication, division and factoring of polynomials. |
| Test 2 | |
| 3.2 | Polynomial Functions. Students represent
patterns, including relations and functions through tables and verbal rules or symbolic rules. Students have a basic understanding of the multiplication, division and factoring of polynomials. They use concrete representations, such as coordinate geometry to represent geometric objects.. |
| 3.3 | Zeros of polynomial functions |
| 3.4 | Fundamental Theorem of Algebra |
| 11.1 | Infinite sequences and summation notation.
Students represent patterns, including relations and functions through tables, graphs, and verbal rules or symbolic rules. |
| 11.5 | The binomial theorem |
| 3.5 | Rational functions and their graphs. Students use
proportional reasoning. They estimate and measure surface areas and volumes of three-dimensional objects (see question 66). |
| 9.1 | Systems of linear equations in two dimensions.
Students are able to find equivalent expressions for equalities. They can explain the meaning of symbolic expressions, and find solutions and represent them on graphs. They have a basic understanding of linear equations. Students interpret graphs of linear and quadratic equations and inequalities including solutions to systems of equations. |
| 9.2 | Systems of linear equations in three dimensions.
Students are able to find equivalent expressions for equalities. They have a basic understanding of linear equations. Students interpret graphs of linear and quadratic equations and inequalities including solutions to systems of equations. They use concrete representations, such as coordinate geometry to represent geometric objects.. |
| 10.1 | Gaussian elimination method and matrices.
Students interpret graphs of linear and quadratic equations and inequalities including solutions to systems of equations. |
| Test 3 | |
| 10.2 | Algebra of matrices |
| 10.3 | Inverse of matrices. Students interpret graphs of
linear and quadratic equations and inequalities including solutions to systems of equations. |
| 4.1 | Inverse functions |
| Thanksgiving Week | |
| 4.2 | Exponential functions and their graphs. Students
represent patterns, including relations and functions through tables, graphs, and verbal rules or symbolic rules. |
| 4.3 | Logarithmic functions and their graphs. Students
represent patterns, including relations and functions through tables, graphs, and verbal rules or symbolic rules. |
| 4.4 | Properties of logarithms. They can explain the
meaning of symbolic expressions, and find solutions and represent them on graphs. |
| 4.5 | Exponential and logarithmic equations. Students are able to find equivalent expressions for equalities. |
| 4.6 | Applications of exponential equations and
logarithmic equations. They can explain the meaning of symbolic expressions, and find solutions and represent them on graphs. |
| Review | |
| Review | |
| Test 4 | MathCAD use |