# Developmental Mathematics

Sections to Cover

This textbook contains TWO (2) Chapter 8s. To designate, the Chapter 8 in the back of the book will be referred to as Supplemental Chp. 8

 Chapter or Appendix Section Topic Notes Chp. 6 All Geometry Appendix E Sets Solving inequalities involving Absolute Value Not in Text; Sample HW problems provided by Math Division . Chp. 9 All Graphs of Linear Equations Chp. 13 All Systems of Equations (2 Equations; 2 Variables) Systems of Equations (3 Equations; 3 Variables) Not in Text; Sample HW problems provided by Math Division. Appendix L Systems of Linear Inequalities Chp. 11 11.8 Pythagorean Theorem Chp. 15 All Quadratic Equations Supplemental Chp. 8 All (8.7 optional) Exponential and Logarithmic Functions

MAT 101
Learning Outcomes and Standards

 Learning Outcome Standard(s) 1. Apply techno logy to assist in solving mathematical applications. 1a/5a. Create a linear equation that models a given problem and use this equation to find the solution to the problem graphically, algebraically and with the assistance of technology. 1b/6c. Evaluate the system of linear equations and inequalities with graphing technology (calculators or computers). 2. Utilize triangular relationships to model and solve applications. 2a. Evaluate the lengths of sides and segments of sides of triangles utilizing properties of congruence. 2b. Evaluate the lengths of sides and segments of sides of triangles utilizing properties of similarity. 2c. Evaluate the lengths of sides and segments of sides of triangles utilizing Pythagorean Theorem. 3. Evaluate geometric measurement formulas fol lowing appropriate orders of operations . 3. Represent a given problem with an appropriate geometric figure (circle, rectangle, sphere, etc.), identify the appropriate quantity (perimeter, area, volume etc.) and apply the appropriate formula to solve the problem. 4. Define when a relation is a function and discuss the domain and range relative to a function. 4a. Given a function in symbolic or graphed form state the domain and range of the function. 4b. Given relation pairs state if the relation is a function. 4c. From a graph of a relation utilize the Vertical Line Test to decide if the relation is a function. 5. Construct linear models and graphs given different representations of the function. 1a/5a. Create a linear equation that models a given problem and use this equation to find the solution to the problem graphically, algebraically and with the assistance of technology. 5b. Given a graph of a linear function create the symbolic representation of the function and use this model to project potential function values. 6. Solve systems of linear equations and systems of inequalities in two variables. 6a. Apply the two basic algebraic techniques, substitution and elimination , to solve a simple linear system of equations. 6b. Graphically represent the solution region of a linear system of inequalities. 1b/6c. Evaluate the system of linear equations and inequalities with graphing technology (calculators or computers). 7. Apply multiple techniques of solving systems of linear equations in three variables. 7a. Solve systems of linear equations in three variables with the Elimination Method . 1c/7b. Solve systems of linear equations in three variables utilizing the graphing calculator or computer software. 8. Apply set theory terminology to assist in solving problems. 8a. Apply terms such as set, intersection, union, disjoint, and empty to assist in solving inequalities, absolute value inequalities and systems of inequalities in two variables. 9. Apply the properties of exp onents and logarithms to simplify and solve problems. 9a. Reduce the complexity of exponential and logarithmic equations with the appropriate properties. 9b. Convert logarithmic equations to exponential equations and vice versa. 9c. Apply the appropriate form (exponential or logarithmic) to solve an equation. 10. Describe and graph exponential, logarithmic and inverse functions. 10a. Graph an exponential or logarithmic function and its inverse. 10b. Discuss the connections between the points of a logarithmic or exponential function and its inverse.
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