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 webbased platform, ALEKS.
 VI. Catalog Course Description
 This course reviews various mathematical concepts from PreAlgebra through PreCalculus. 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


Learning Goals:
 Course Learning Goals with a College Placement Score of a 1 or 3
 accurately perform mathematical computations involving whole numbers;
 accurately perform mathematical computations involving signed numbers;
 accurately perform mathematical computations involving fractions, decimals and percents;
 correctly analyze and apply mathematical operations in applied problem solving situations;
 solve linear equations and use linear equations to solve applications;
 add, subtract, multiply polynomials and divide polynomials by monomials;
 factor simple polynomials and solve quadratic equations by factoring;
 add, subtract, multiply, and divide rational expressions
 graph a linear equation;
 find the slope of a line; and
 evaluate and simplify radicals, specifically square roots.
 Course Learning Goals with a College Placement Score of a 5 Students will:
 solve linear equations and inequalities, including fractional, absolute value, and literal equations and do relevant applications;
 perform the operations of adding, subtracting, multiplying, and dividing polynomials;
 factor polynomials by distributive property, reverse foil, grouping, the difference of squares, sum and difference of cubes;
 simplify expressions using the rules of exponents;
 add, subtract, multiply, and divide rational expressions and do synthetic division;
 perform operations with radical expressions, including rationalizing denominators of monomials and binomials and to solve radical equations;
 solve quadratic equations by factoring, quadratic formula, and completing the square and relevant applications;
 graph linear equations using the slope and yintercept, find equations of lines given two points, and solve simultaneous equation;
 graph quadratic, exponential, and logarithmic functions and describe the domain and range of a relation; and
 use function notation, properties of logarithms to compute common and natural logarithmic values.
 Course Learning Goals with a College Placement Score of a 7: Students will:
 develop an understanding and apply the concepts and procedures for solving equations and inequalities and for simplifying expressions;
 demonstrate the techniques of solving a variety of applications of equations;
 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;
 develop skill in using a graphing calculator;
 accurately use logarithmic and exponential functions and develop the skill to graph and solve logarithmic and exponential equations;
 simplify algebraic expressions involving operations of arithmetic, exponents, radicals, fractions and factoring of polynomials;
 solve linear, quadratic, polynomial, absolute value, radical, exponential, logarithmic equations and systems of linear equations;
 solve applications of linear and quadratic equations;
 solve linear, quadratic, polynomial, absolute value, and rational inequalities and write the solutions in interval notation;
 graph linear, quadratic, polynomial, exponential, absolute value, radical, logarithmic, and rational functions and conic sections;
 perform operations of functions, find composition of functions, and describe increasing, decreasing, constant intervals, domain, range, and points of discontinuity;
 find equations of lines, given two points, a point and the slope, parallel or perpendicular lines, and a point; and
 find the distance between, and the midpoint of, the segment, given two points.
 Course Learning Goals with College Placement Score of a 8: Students will:
 develop an understanding of trigonometric functions and the skill of graphing these periodic functions;
 develop a proficiency in the use of the unit circle to find exact values of trigonometric expressions;
 develop the skill of using a graphing calculator for trigonometric computations, graphing trigonometric functions, and finding values for inverse trigonometric ratio functions; and
 demonstrate an understanding of the concept of conic sections and develop the skill of deriving the equations and graphing the equations of conic sections.
 Course Learning Goals with College Placement Score of a 9: Students will:
 apply and extend algebraic skills;
 analyze calculusrelated concepts, such as limits, tangent to a curve, and the difference quotient;
 apply the properties of functions, such as finding the domain and range and developing the skill to graph them;
 accurately use a graphing calculator to find transformations of graphs;
 perform operations of functions: addition, subtraction, multiplication, division, and composition;
 find the inverse function and its graph;
 construct mathematical models with functions, using realworld applications or formulas;
 determine zeros of a function, symmetries of a function; use limits to determine end behavior of a function;
 solve problems involving maximizing and minimizing a quadratic function, both algebraically and graphically;
 find vertical, horizontal, and slant asymptotes for rational functions and graph;
 graph exponential and logarithmic functions, and accurately use the properties of logarithms and the definition of e;
 solve exponential and logarithmic equations and application problems, using exponents and logarithms;
 define trigonometric functions, using the unit circle and right triangle definition;
 graph trigonometric functions, find the inverse trigonometric functions, and verify trigonometric identities and formulas; and
 solve trigonometric equations and solve problems, using realworld applications.
 Core (if applicable) This course is not included in the Core.
Students will:

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 Operations with Whole Numbers
 addition, subtraction, multiplication, and division of whole numbers
 exponents and order of operations
 variables and variable expressions
 Operations with Integers
 addition, subtraction, multiplication and division of integers
 order of operations with signed numbers
 Solving Equations and Problem Solving
 simplifying expressions
 solving equations using the Addition Property
 solving equations using the Multiplication Property
 Fractions
 equivalent fractions
 proper, improper fractions and mixed numbers
 multiplication and division of fractions
 addition and subtraction of fractions with like denominators
 addition and subtraction of fractions with unlike denominators
 solving equations containing fractions
 Decimals
 introduction to decimals
 adding and subtracting decimals
 multiplying decimals
 dividing decimals
 converting fractions to decimals and decimals to fractions
Placement Score of a 5 Linear Equations and Inequalities
 linear equations
 word problems and formulas
 applications of algebra
 linear inequalities
 equations and inequalities with absolute value
 linear functions
 slopeintercept form
 pointslope form
 applications of graphing functions
 Exponents and Factoring Polynomials
 exponent rules
 operations with polynomials
 factoring polynomials
 second degree equations
 applications of second degree equations
 Rational Expressions and Equations
 operations with rational expressions
 complex fractions
 rational equations
 applications of rational equations
 systems of linear equations
 Radical Expressions, Radical Equations, Quadratic Formula
 simplifying radical expressions
 rational exponents
 operations with radical expressions
 complex number expressions
 quadratic formula
 radical equations
 applications of quadratic equations
 Exponential and Logarithmic Functions
 exponential functions
 exponential to logarithmic form
 logarithmic functions
Placement Score of a 7 Review Topics
 the real numbers
 the field axioms
 operations on polynomials (+, , x, /)
 factoring
 algebraic fractions (reduction, +, , x, /)
 exponents (integer, rational)
 radicals and radical expressions
 complex numbers
 Solution of Equations and Inequalities
 first degree equations
 formula manipulation
 first degree inequalities (visualize solution set)
 absolute value equations
 absolute value inequalities
 quadratic equations (factoring, completing the square, quadratic formula)
 quadratic inequalities
 radical equations
 applications (1st and 2nd degree)
 rational inequalities
 Relations and Functions
 Cartesian coordinate system and the distance formula
 relations (domain, range, rule, graph)
 functions (domain, range, rule, graph)
 functional notation
 algebra of functions (+, , x, /)
 composition of functions
 linear functions (slopeintercept form, graphs)
 quadratic functions
 system of equations (2x2, 3x3)
 Polynomial Functions
 division of polynomials
 synthetic division
 remainder and factor theorem
 rational root theorem
 graphs of polynomial functions
 rational functions
 Exponential and Logarithmic Functions
 inverse functions (existence, rule, domain, range)
 exponential functions (rule, domain, range)
 logarithmic functions (rule, domain, range)
 laws of logarithms
 logarithmic and exponential equations
 applications of logs
Placement Score of an 8 Trigonometric Functions
 angle measurement (degree and radian measure)
 angle relationships and similar triangles
 definitions of trigonometric functions
 trigonometric functions of acute and nonacute angles
 Right Triangle Trigonometry
 solving right triangles
 applications
 Circular Functions
 circular functions of real numbers
 linear and angular velocity
 graphs of the basic trigonometric functions
 vertical and horizontal translations of basic graphs
 Identities
 Pythagorean and reciprocal identities
 sum and difference identities
 half and double angle identities
 verifying identities
 Inverse Functions
 definitions and graphs of inverse functions
 solving equations
 Solving Oblique Triangles
 law of sines
 law of cosines
 area formulas
 applications
 Vectors
 magnitude and direction angle
 addition, subtraction, and scalar multiplication
 dot product
 applications
 Complex Numbers
 trigonometric and rectangular form
 multiplication and division
 powers and roots of complex numbers
 Polar Equations and Graphs
 Parametric Equations and Graphs
 Analytic Geometry
 parabola
 ellipse
 hyperbola
Placement Score of a 9 Review Topics
 exponents & scientific notation
 radicals & rational exponents
 polynomials
 factoring polynomials
 rational expressions
 linear equations
 quadratic equations
 linear inequalities
 Graphs, Functions, and Models
 graphs& graphing utilities
 lines and slopes
 distance & midpoint formulas, circles
 basic functions
 graphs of functions
 transformations of functions
 combinations of functions, composite functions
 inverse functions
 modeling with functions
 Polynomial & Rational Functions
 complex numbers
 quadratic functions & applications
 polynomials functions, application & graphs
 dividing polynomials; remainder and factor theorem
 zeros of polynomial functions
 rational functions and graphs polynomial & rational inequalities
 Exponential & Logarithmic Functions
 exponential functions
 logarithmic functions
 properties of logarithms
 exponential & logarithmic equations
 optional; modeling with exponential and logarithmic functions
 trigonometric functions & analytical trigonometry
 angles and their measure
 trigonometric functions; the unit circle
 right triangle trigonometry
 trigonometric functions of any angle
 graphs of sine and cosine functions
 graphs of other trigonometric functions
 inverse trigonometric functions
 applications of trigonometric functions
 verifying trigonometric identities
 sum and difference formulas
 double angle and half angle identities
 Additional Topics in Trigonometry
 optional: product to sum and sum to product formulas
 trigonometric equations
 the law of sines
 the law of cosines

Assessment Methods for Core Learning Goals:
 Course 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 studentâ€™s final placement score according to personalized assessments within the software.
 Core (if applicable) This course is not included in the Core.

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