MATH089 Fast Track Mathematics

Department of Science, Technology, Engineering & Mathematics: Mathematics

I. Course Number and Title
MATH089 Fast Track Mathematics
II. Number of Credits
1 credit
III. Minimum Number of Instructional Minutes Per Semester
750
IV. Prerequisites
Math Placement Test
Corequisites
None
V. Other Pertinent Information

This course will not satisfy the general elective category for students who entered their program of study in or after the 2007 fall semester. It is intended for those students who feel the results of their placement test do not accurately reflect their mathematical ability, and who want to demonstrate their mastery of mathematical topics for purposes of placement in a course.

Students work in a web-based platform, ALEKS.

VI. Catalog Course Description
This course reviews various mathematical concepts from Pre-Algebra through Pre-Calculus. After taking the math placement test, students work with math software to strengthen their mathematical knowledge and potentially increase their placement score through the software, leading to continue with other courses within a program of study earlier.
VII. Required Course Content and Direction
  1. Learning Goals:

    1. Course Learning Goals with a College Placement Score of a 1 or 3

    2. Students will:
      1. accurately perform mathematical computations involving whole numbers;
      2. accurately perform mathematical computations involving signed numbers;
      3. accurately perform mathematical computations involving fractions, decimals and percents;
      4. correctly analyze and apply mathematical operations in applied problem solving situations;
      5. solve linear equations and use linear equations to solve applications;
      6. add, subtract, multiply polynomials and divide polynomials by monomials;
      7. factor simple polynomials and solve quadratic equations by factoring;
      8. add, subtract, multiply, and divide rational expressions
      9. graph a linear equation;
      10. find the slope of a line; and
      11. evaluate and simplify radicals, specifically square roots.

    3. Course Learning Goals with a College Placement Score of a 5
    4. Students will:
      1. solve linear equations and inequalities, including fractional, absolute value, and literal equations and do relevant applications;
      2. perform the operations of adding, subtracting, multiplying, and dividing polynomials;
      3. factor polynomials by distributive property, reverse foil, grouping, the difference of squares, sum and difference of cubes;
      4. simplify expressions using the rules of exponents;
      5. add, subtract, multiply, and divide rational expressions and do synthetic division;
      6. perform operations with radical expressions, including rationalizing denominators of monomials and binomials and to solve radical equations;
      7. solve quadratic equations by factoring, quadratic formula, and completing the square and relevant applications;
      8. graph linear equations using the slope and y-intercept, find equations of lines given two points, and solve simultaneous equation;
      9. graph quadratic, exponential, and logarithmic functions and describe the domain and range of a relation; and
      10. use function notation, properties of logarithms to compute common and natural logarithmic values.

    5. Course Learning Goals with a College Placement Score of a 7:
    6. Students will:
      1. develop an understanding and apply the concepts and procedures for solving equations and inequalities and for simplifying expressions;
      2. demonstrate the techniques of solving a variety of applications of equations;
      3. develop a proficiency in solving linear, quadratic, polynomial, and rational functions, and in mastering techniques for graphing these functions and describing their domain and range;
      4. develop skill in using a graphing calculator;
      5. accurately use logarithmic and exponential functions and develop the skill to graph and solve logarithmic and exponential equations;
      6. simplify algebraic expressions involving operations of arithmetic, exponents, radicals, fractions and factoring of polynomials;
      7. solve linear, quadratic, polynomial, absolute value, radical, exponential, logarithmic equations and systems of linear equations;
      8. solve applications of linear and quadratic equations;
      9. solve linear, quadratic, polynomial, absolute value, and rational inequalities and write the solutions in interval notation;
      10. graph linear, quadratic, polynomial, exponential, absolute value, radical, logarithmic, and rational functions and conic sections;
      11. perform operations of functions, find composition of functions, and describe increasing, decreasing, constant intervals, domain, range, and points of discontinuity;
      12. find equations of lines, given two points, a point and the slope, parallel or perpendicular lines, and a point; and
      13. find the distance between, and the midpoint of, the segment, given two points.

    7. Course Learning Goals with College Placement Score of a 8:
    8. Students will:
      1. develop an understanding of trigonometric functions and the skill of graphing these periodic functions;
      2. develop a proficiency in the use of the unit circle to find exact values of trigonometric expressions;
      3. develop the skill of using a graphing calculator for trigonometric computations, graphing trigonometric functions, and finding values for inverse trigonometric ratio functions; and
      4. demonstrate an understanding of the concept of conic sections and develop the skill of deriving the equations and graphing the equations of conic sections.

    9. Course Learning Goals with College Placement Score of a 9:
    10. Students will:
      1. apply and extend algebraic skills;
      2. analyze calculus-related concepts, such as limits, tangent to a curve, and the difference quotient;
      3. apply the properties of functions, such as finding the domain and range and developing the skill to graph them;
      4. accurately use a graphing calculator to find transformations of graphs;
      5. perform operations of functions: addition, subtraction, multiplication, division, and composition;
      6. find the inverse function and its graph;
      7. construct mathematical models with functions, using real-world applications or formulas;
      8. determine zeros of a function, symmetries of a function; use limits to determine end behavior of a function;
      9. solve problems involving maximizing and minimizing a quadratic function, both algebraically and graphically;
      10. find vertical, horizontal, and slant asymptotes for rational functions and graph;
      11. graph exponential and logarithmic functions, and accurately use the properties of logarithms and the definition of e;
      12. solve exponential and logarithmic equations and application problems, using exponents and logarithms;
      13. define trigonometric functions, using the unit circle and right triangle definition;
      14. graph trigonometric functions, find the inverse trigonometric functions, and verify trigonometric identities and formulas; and
      15. solve trigonometric equations and solve problems, using real-world applications.

    11. Core (if applicable)
    12. This course is not included in the Core.
  2. Planned Sequence of Topics and/or Learning Activities:

    The following is a list of the minimum amount of course material to be covered. Topics may vary depending on individual performance within the assessment program.

    Placement Score of a 1 or 3
    1. Operations with Whole Numbers
      1. addition, subtraction, multiplication, and division of whole numbers
      2. exponents and order of operations
      3. variables and variable expressions
    2. Operations with Integers
      1. addition, subtraction, multiplication and division of integers
      2. order of operations with signed numbers
    3. Solving Equations and Problem Solving
      1. simplifying expressions
      2. solving equations using the Addition Property
      3. solving equations using the Multiplication Property
    4. Fractions
      1. equivalent fractions
      2. proper, improper fractions and mixed numbers
      3. multiplication and division of fractions
      4. addition and subtraction of fractions with like denominators
      5. addition and subtraction of fractions with unlike denominators
      6. solving equations containing fractions
    5. Decimals
      1. introduction to decimals
      2. adding and subtracting decimals
      3. multiplying decimals
      4. dividing decimals
      5. converting fractions to decimals and decimals to fractions

    Placement Score of a 5
    1. Linear Equations and Inequalities
      1. linear equations
      2. word problems and formulas
      3. applications of algebra
      4. linear inequalities
      5. equations and inequalities with absolute value
      6. linear functions
      7. slope-intercept form
      8. point-slope form
      9. applications of graphing functions
    2. Exponents and Factoring Polynomials
      1. exponent rules
      2. operations with polynomials
      3. factoring polynomials
      4. second degree equations
      5. applications of second degree equations
    3. Rational Expressions and Equations
      1. operations with rational expressions
      2. complex fractions
      3. rational equations
      4. applications of rational equations
      5. systems of linear equations
    4. Radical Expressions, Radical Equations, Quadratic Formula
      1. simplifying radical expressions
      2. rational exponents
      3. operations with radical expressions
      4. complex number expressions
      5. quadratic formula
      6. radical equations
      7. applications of quadratic equations
    5. Exponential and Logarithmic Functions
      1. exponential functions
      2. exponential to logarithmic form
      3. logarithmic functions

    Placement Score of a 7
    1. Review Topics
      1. the real numbers
      2. the field axioms
      3. operations on polynomials (+, -, x, /)
      4. factoring
      5. algebraic fractions (reduction, +, -, x, /)
      6. exponents (integer, rational)
      7. radicals and radical expressions
      8. complex numbers
    2. Solution of Equations and Inequalities
      1. first degree equations
      2. formula manipulation
      3. first degree inequalities (visualize solution set)
      4. absolute value equations
      5. absolute value inequalities
      6. quadratic equations (factoring, completing the square, quadratic formula)
      7. quadratic inequalities
      8. radical equations
      9. applications (1st and 2nd degree)
      10. rational inequalities
    3. Relations and Functions
      1. Cartesian coordinate system and the distance formula
      2. relations (domain, range, rule, graph)
      3. functions (domain, range, rule, graph)
      4. functional notation
      5. algebra of functions (+, -, x, /)
      6. composition of functions
      7. linear functions (slope-intercept form, graphs)
      8. quadratic functions
      9. system of equations (2x2, 3x3)
    4. Polynomial Functions
      1. division of polynomials
      2. synthetic division
      3. remainder and factor theorem
      4. rational root theorem
      5. graphs of polynomial functions
      6. rational functions
    5. Exponential and Logarithmic Functions
      1. inverse functions (existence, rule, domain, range)
      2. exponential functions (rule, domain, range)
      3. logarithmic functions (rule, domain, range)
      4. laws of logarithms
      5. logarithmic and exponential equations
      6. applications of logs

    Placement Score of an 8
    1. Trigonometric Functions
      1. angle measurement (degree and radian measure)
      2. angle relationships and similar triangles
      3. definitions of trigonometric functions
      4. trigonometric functions of acute and non-acute angles
    2. Right Triangle Trigonometry
      1. solving right triangles
      2. applications
    3. Circular Functions
      1. circular functions of real numbers
      2. linear and angular velocity
      3. graphs of the basic trigonometric functions
      4. vertical and horizontal translations of basic graphs
    4. Identities
      1. Pythagorean and reciprocal identities
      2. sum and difference identities
      3. half and double angle identities
      4. verifying identities
    5. Inverse Functions
      1. definitions and graphs of inverse functions
      2. solving equations
    6. Solving Oblique Triangles
      1. law of sines
      2. law of cosines
      3. area formulas
      4. applications
    7. Vectors
      1. magnitude and direction angle
      2. addition, subtraction, and scalar multiplication
      3. dot product
      4. applications
    8. Complex Numbers
      1. trigonometric and rectangular form
      2. multiplication and division
      3. powers and roots of complex numbers
    9. Polar Equations and Graphs
    10. Parametric Equations and Graphs
    11. Analytic Geometry
      1. parabola
      2. ellipse
      3. hyperbola

    Placement Score of a 9
    1. Review Topics
      1. exponents & scientific notation
      2. radicals & rational exponents
      3. polynomials
      4. factoring polynomials
      5. rational expressions
      6. linear equations
      7. quadratic equations
      8. linear inequalities
    2. Graphs, Functions, and Models
      1. graphs& graphing utilities
      2. lines and slopes
      3. distance & midpoint formulas, circles
      4. basic functions
      5. graphs of functions
      6. transformations of functions
      7. combinations of functions, composite functions
      8. inverse functions
      9. modeling with functions
    3. Polynomial & Rational Functions
      1. complex numbers
      2. quadratic functions & applications
      3. polynomials functions, application & graphs
      4. dividing polynomials; remainder and factor theorem
      5. zeros of polynomial functions
      6. rational functions and graphs polynomial & rational inequalities
    4. Exponential & Logarithmic Functions
      1. exponential functions
      2. logarithmic functions
      3. properties of logarithms
      4. exponential & logarithmic equations
      5. optional; modeling with exponential and logarithmic functions
      6. trigonometric functions & analytical trigonometry
      7. angles and their measure
      8. trigonometric functions; the unit circle
      9. right triangle trigonometry
      10. trigonometric functions of any angle
      11. graphs of sine and cosine functions
      12. graphs of other trigonometric functions
      13. inverse trigonometric functions
      14. applications of trigonometric functions
      15. verifying trigonometric identities
      16. sum and difference formulas
      17. double angle and half angle identities
    5. Additional Topics in Trigonometry
      1. optional: product to sum and sum to product formulas
      2. trigonometric equations
      3. the law of sines
      4. the law of cosines
  3. Assessment Methods for Core Learning Goals:

    1. Course
    2. The assessment of course learning goals is based on successful completion of the individual program designed for the student using a math software. This software also determines a student’s final placement score according to personalized assessments within the software.

    3. Core (if applicable)
    4. This course is not included in the Core.
  4. Reference, Resource, or Learning Materials to be used by Students:

    This course uses departmentally selected online instructional software. See Course format.
VIII. Teaching Methods Employed
Section VIII is not being used in new and revised syllabi as of 12/10/08.

Review/Approval Date - 5/2011