MTH 081 Technical Mathematics 1

Lecture Hours: 4
Credits: 4

Offers the first course of a two-term technical mathematics sequence designed to meet the needs of technology students from various disciplines and lay the groundwork for applying mathematical concepts and problem solving in the technical fields of engineering, drafting, mechanical design, forestry and electronics. Covers fundamental algebra concepts, graphing, ratio, proportions and variation, basic right angle trigonometry, statistics and empirical methods, operations with linear, quadratic and rational expressions, solutions of linear, quadratic and rational equations. Emphasizes using mathematics and technology to solve applied problems.

Prerequisite: MTH 070 with a grade of C or better, or equivalent course as determined by instructor; or consent of instructor.
Student Learning Outcomes:

Use mathematical problem-solving techniques involving linear, quadratic, rational equations, systems of equations and trigonometric functions. Techniques include the use of graphical, symbolic, narrative, and tabular representations.
Create mathematical models of real-world situations using systems of linear equations, trig ratios and quadratic equations.
Use inductive reasoning to develop mathematical conjectures involving linear, quadratic, rational equations, systems of equations and trigonometric functions.
Use deductive reasoning to verify and apply mathematical arguments involving these models.
Make mathematical connections to, and solve problems from, other disciplines involving ratios, proportions, variation, systems of linear equations, rational equation, quadratic equations, and trigonometric functions.
Use oral and written skills to individually and collaboratively communicate about applications involving linear, quadratic, rational equations, systems of equations and trigonometric functions.
Use appropriate technology to enhance mathematical thinking and understanding, to solve mathematical problems involving linear, quadratic, rational equations, systems of equations and trigonometric functions, and judge the reasonableness of their results.
Do projects that encourage independent, nontrivial exploration of mathematical concepts involving ratios, proportions, linear, quadratic, rational equations, systems of equations, trigonometric functions, and statistics.

Content Outline

Fundamental Algebraic Concepts
- Measurements
  - Accuracy and Precision
  - Errors Concepts
  - Unit Analysis
  - Scientific and Engineering Notation
- Algebraic Expressions and Operation with Polynomials
- Equations, Formulas and Their Application
- Ratio, Proportion and Variations
  - Direct and Inverse Variation
  - Joint and Combined Variation
Right Triangle Trigonometry
- Trigonometric Ratios
  - Angles
  - Angle Measure Degrees and Radians
  - Values of Trigonometric Functions
Linear Analytical Geometry
- Relations and Functions
- Graphing Functions
- Slope and Equation of a Line
Systems of Linear Equations
- Two Linear Equations
  - Graphical Method
  - Algebraic Methods
- Three Linear Equations
- Determinants
  - Evaluating Determinants
  - Cramer’s Rule of Solving Linear Equations
Factoring and Rational Expressions
- Factoring Algebraic Expressions
- Operations with Rational Expressions
  - Multiplication of Rational Expressions
  - Division of Rational Expressions
  - Addition of Rational Expressions
  - Subtraction of Rational Expressions
  - Simplifying Complex Fractions
- Solving Rational Equations
  - Formulas and Applications
  - Formulas Manipulations
  - Quadratic Equations
- Solving Quadratic
  - Factoring
  - Completing the Square
  - Quadratic Formula
  - Graphic Method
- Application Problems Involving Quadratic Equations
Statistics and Empirical Methods
- Probability
  - Classical and Empirical Approaches
  - Outcome and Sample Space
  - Trial and Events
- Measures of Central Tendency
  - Frequency Distribution
  - Graphs of Histogram
  - Mean, Median and Mode
  - Quartiles and Box Plots
- Measures of Dispersion
  - Variance and Standard Deviation
  - Normal Distribution Curve