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Mathematics and Technical Foundation Skills

#### Quality Concepts: Terminology for Management

Course #: 186035
Duration: 5 hours
What Students Learn:

• Define quality and quality management, using examples.
• Describe how quality has evolved to where it is today.
• Explain company and personal motivation for quality improvement.
• Describe how quality-conscious organizations have changed for the better.
• Explain how familiar business practices have led to TQM and how other common practices have gotten in the way of TQM.
• Name successful results of TQM programs.

• #### Basic Industrial Math

Course #: Block X21
Duration: 30 hours
What Students Learn: This module of six study units offers the trainee arithmetic and basic mathematics, metric measurement, and calculator fundamentals. The Metric System is an introductory unit which includes metric conversions. Problem exercises and examples in this module are presented in on-the-job scenarios with applications drawn from the industrial context.
Components: Addition and Subtraction (186008); Multiplication and Division (186009); Fractions, Percents, Proportions, and Angles (186010); Metric System (186011); Formulas (186012); Introduction to Algebra (186013);
Special Notes: This updated course replaces lessons contained within Practical Math and Measurements, Block X01. Each study unit contains a progress examination.

Course #: 186008
Duration: 5 hours
What Students Learn:

• Define the terms: whole number, numeral, digit, decimal, place value, addend, sum, minuend, subtrahend, and difference.
• Explain the significance of the digit zero in a number.
• Differentiate between concrete and abstract numbers.
• Properly prepare numbers for addition and subtraction.
• Perform addition and subtraction on numbers.
• How to use a calculator to add and subtract numbers.

#### Multiplication and Division

Course #: 186009
Duration: 5 hours
What Students Learn:

• Define the terms: factor, multiplicand, multiplier, partial product, dividend, divisor, quotient, and remainder.
• Recognize the various signs used for multiplication and division.
• Properly prepare numbers for multiplication and division.
• Perform multiplication and division on whole numbers and decimals.
• How to check your answers to both multiplication and division problems.
• How to find the average of a group of numbers.
• How to use a calculator to multiply and divide numbers.

• #### Fractions, Percents, Proportions, and Angles

Course #: 186010
Duration: 5 hours
What Students Learn:

• Define the terms: fraction, proper fraction, improper fraction, lowest common denominator, percent, ratio, and proportion.
• How to add, subtract, multiply, and divide fractions and decimals.
• How to change fractions to decimals and decimals to fractions.
• Solve problems involving percent.
• How to use a protractor to measure angles.
• Lay out templates for checking angles.
• How to use a calculator to solve percent problems and to convert fractions to decimals.

• #### Metric System

Course #: 186011
Duration: 5 hours
What Students Learn:

• Name the base units most commonly used in the metric system.
• Identify metric prefixes and their values.
• Apply conversion factors to increase or decrease metric base units.
• Estimate lengths in metric units.
• Express temperature in degrees Celsius.
• Define the terms: mass, density, force, torque, and pressure. Identify the metric units used to measure each one.
• How to use a calculator to convert one metric unit to another.

• #### Formulas

Course #: 186012
Duration: 5 hours
What Students Learn:

• Explain the use of letters in formulas.
• Prepare and use formulas to solve problems.
• The use of formulas to calculate the perimeter of a triangle and rectangle, distance, area of a triangle, rectangle, and circle, volume of a pyramid, current in a circuit, and volume of a sphere.
• How to use a calculator to find square root and solve formulas.
• Transform and solve an equation.
• Perform basic arithmetic operations with signed terms.
• Substitute given numerical values for letters in a formula and find the unknown quantity.

Special Notes: This updated course replaces 2468.

• #### Introduction to Algebra

Course #: 186013
Duration: 5 hours
What Students Learn:

• Define the terms: term, constant, coefficient, exponent, monomial, trinomial, and polynomial.
• Identify and combine like terms in an expression.
• Multiply and divide terms containing exponents.
• Remove parentheses from an expression and simplify the expression.
• Perform basic arithmetic operations with signed terms.

• #### Introduction to Algebra, Geometry, and Trigonometry

Course #: Block X02
Duration: 72 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn: This twelve lesson block is for those trainees requiring more advanced math subjects. The subject of algebra is covered in detail and the subjects of geometry and trigonometry are introduced in a practical manner.
Because math skills vary widely, a placement test is available to determine the trainee's specific knowledge of the various areas. Test X0250: Introduction to Algebra, Geometry, and Trigonometry is divided into four sections: lessons X0201 through X0204; lessons X0205 through X0208; lessons X0209 through X0210; and lessons X0211 and X0212.
Components: Algebra: Monomials and Polynomials (X0201); Algebra: Factoring (X0202); Algebra: Addition and Subtraction of Fractions (X0203); Algebra: Multiplication and Division of Fractions (X0204); Algebra: Linear Equations (X0205); Algebra: Simultaneous Linear Equations (X0206); Algebra: Determinants (X0207); Algebra: Quadratic Equations (X0208); Algebra: Exponents (X0209); Algebra: Radicals and Imaginary Numbers (X0210); Applied Geometry (X0211); Practical Trigonometry (X0212); Progress Examination Booklet (X0220); Progress Examination (X0221); Progress Examination (X0222); Progress Examination (X0223); Progress Examination (X0224); Placement Test: Introduction to Algebra, Geometry, and Trigonometry (X0250);

#### Algebra: Monomials and Polynomials

Course #: X0201
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

• Remove grouping symbols from algebraic expressions, dividing by a monomial when indicated.
• Multiply binomials by monomials, trinomials, and other inomials.
• Calculate the square root and the third power of given monomials.
• Find special products involving binomials.
• Divide one polynomial by another polynomial of lower degree.

• #### Algebra: Factoring

Course #: X0202
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

• Find the prime factors of certain binomials and trinomials.
• Factor a given trinomial.
• Use the Factor Theorem to factor a given polynomial.
• Use factoring to find the roots of an equation.
• Divide one polynomial by another polynomial of lower degree.
• Find the lowest common multiple of several polynomials.

• #### Algebra: Addition and Subtraction of Fractions

Course #: X0203
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

• Recognize equivalent algebraic fractions.
• Perform additions and subtractions involving algebraic fractions.
• Reduce an algebraic fraction to its lowest terms.
• Find the least common denominator for a group of algebraic fractions.

• #### Algebra: Multiplication and Division of Fractions

Course #: X0204
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

• Perform multiplications and divisions involving algebraic fractions.
• Reduce an algebraic fraction to its lowest terms.
• Find the least common denominator for a group of algebraic fractions.
• Solve equations involving fractions or decimals.
• Simplify complex fractions.

• #### Algebra: Linear Equations

Course #: X0205
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

• Recognize equations expressing mixture problems and other word problems.
• Solve number problems, digit problems, and age problems.
• Recognize the graph of a linear equation, given the graph or a set of points.

• #### Algebra: Simultaneous Linear Equations

Course #: X0206
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

• Recognize essential steps in the solving of simultaneous linear equations by addition, subtraction, comparison, graphing, and clearing of fractions.
• Identify the classification of a system of equations.
• Solve a system of linear equations.
• Solve interest problems, lever problems, and work-sharing problems.

• #### Algebra: Determinants

Course #: X0207
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

• Evaluate a second-order determinant and expand a third-order determinant.
• Recognize the standard form to be used in solving simultaneous equations by determinants.
• Recognize determinants that represent the solutions of simultaneous equations in two or three unknowns.

Course #: X0208
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

• Recognize the graphical solution of two equations.
• Solve and recognize steps in the solution of systems of quadratic equations and systems of a quadratic and linear equation.
• Solve a fourth-degree polynomial equation in quadratic form.
• Use the quadratic formula to solve a quadratic equation, calculate the discriminant of a quadratic equation, and point out what can be known from a given discriminant.
• Write a quadratic equation which has given roots.
• Solve word problems involving quadratic equations.

• #### Algebra: Exponents

Course #: X0209
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

• Demonstrate an understanding of the meaning of a fractional exponent.
• Apply the rules for positive and negative exponents in multiplication, division, and raising to powers.
• Use radicals to convert fractional exponents and use fractional exponents to convert radicals.
• Write a given number in standard form.

• #### Algebra: Radicals and Imaginary Numbers

Course #: X0210
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

• Rationalize the denominator of a fraction and eliminate an imaginary number from the denominator of a fraction.
• Solve an equation containing several square roots.
• Multiply, divide, and raise to powers terms containing radicals.

• #### Applied Geometry

Course #: X0211
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

• Recognize characteristics of angles and closed plane figures.
• Distinguish between common geometric solids.
• Apply the Pythagorean theorem.
• Calculate perimeters and areas of a polygon, circle, and ellipse.
• Apply the formula for area and volume of geometric solids.

• #### Practical Trigonometry

Course #: X0212
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

• Define trigonometric functions.
• Use trigonometric tables and apply interpolation.
• Solve right triangles.
• Apply the laws of sines and cosines in solving oblique triangles.

• #### Logarithms

Course #: 5254
Duration: 10 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn: Table of Common Logarithms; Table of Useful Numbers; Exponents; Logarithms of Numbers; Determination of Characteristics of a Logarithm; Determination of Mantissa of a Logarithm; Proportional Parts; Determination of Antilogarithms; Multiplication by Use of Logarithms; Division by Use of Logarithms; Finding Powers and Roots by Logarithms; Cologarithms; Hyperbolic Logarithms.

#### Practical Geometry

Course #: 5983A-B
Duration: 20 hours
Course Prerequisites: Introduction to Algebra, Geometry, and Trigonometry (Block X02);
What Students Learn: PART 1 (5983A). Points, Lines, Surfaces, and Angles; Perpendicular and Parallel Lines; Triangles; Quadrilaterals; Other Polygons.
PART 2 (5983B). The Circle; Arcs and Areas of Figures Bounded by Them; Solids; Areas and Volumes of Unusual Figures.

Special Notes: Covers subject at an advanced, in-depth level.

#### Plane Trigonometry

Course #: 2309A-B
Duration: 60 hours
Course Prerequisites: Practical Geometry (5983A-B); Introduction to Algebra, Geometry, and Trigonometry (Block X02);
What Students Learn: PART 1 (2309A). Solving a Triangle; Deriving Trigonometric Functions; Trigonometric and Geometric Identities; Values for the Trigonometric Functions; Using the Table of Natural Trigonometric Functions; Interpolation; Solving the Right Triangle; Solving the Right Triangle by Using Logarithms.
PART 2 (2309B). Angles and Their Measurement; Degrees and Radians; Rectangular Coordinates; The Trigonometric Formulas; Finding the Values of the Functions of Angles; Reduction Formulas; Solving the Oblique Triangle; Law of Tangents; Using Half-Angle Formulas; Area of a Triangle; Radius of an Inscribed Circle; Radius of a Circumscribed Circle.

Special Notes: Covers subject at an advanced, in-depth level.

Course #: 186001
Duration: 5 hours
What Students Learn: Preview
A thorough knowledge of safe practices is an important part of working in any industrial setting. Every industrial worker should be familiar with accident prevention techniques, fire safety mehods, and the use of personal protective equipment.
Injuries in the workplace cost many millions of dollars in medical costs, lost wages, and production losses each year. Many injuries can be prevented by understanding how accidents and injuries can occur. This study unit is designed to help trainees understand why safety is so important, and to present students with information about safety that goes beyond common sense.

Objectives
When a student completes this study unit, he and she will be able to:

• Name the agencies that make and enforce safety regulations and explain an employees responsibilities under those regulations.
• List the physical hazards associated with chemicals and describe how to avoid those hazards.
• Name several electrical shock hazards and the techniques used to prevent shocks.
• List the steps in a lock-out / tag-out procedure.
• Explain the importance of machine guarding and name several types of machine guards.
• Name the four classes of fire and how to extinguish each of them.
• Describe the proper technique used to lift a heavy load.
• Explain how to avoid hand injuries when using hand and power tools.
• List some of the hazards involved in welding and hot cutting operations and how to prevent them.
• Explain how job analysis and the science of ergonomics are used to improve the workplace.
• Explain the importance of personal protective equipment and name several types of PPE.

Contents
Introduction; Safety Regulations; Key safety Issues; Protecting Yourself and Your Co-workers.

• #### Working Safely with Chemicals

Course #: 186002
Duration: 5 hours
What Students Learn: Preview
This study unit deals with the safe use of chemicals in the workplace. The two primary causes of chemical accidents are the misuse of chemicals and the improper disposal of chemical wastes. Understanding the hazards that chemicals can create is the first step in protecting people from harm.
The main goal of this study unit is to provide students with sound, practical knowledge about chemical use and disposal, both in the workplace and at home. You will learn how to recognize common chemical hazards and how to deal with them. Trainees will learn how to perform a job analysis to look for potential chemical dangers in your daily taks. Finally, people will learn how to take precautions to avoid chemical accidents and make all jobs as safe as possible.

Objectives
When a student completes this study unit, he and she will be able to:

• Recognize the six different ways in which a chemical can cause physical injury.
• Name the routes or paths of entry by which chemicals can enter the body.
• Describe the types of injuries caused by chemicals.
• Identify potential chemical dangers in your workplace.
• Describe how to identify, store and label hazardous chemicals.
• List several methods used to prevent chemical accidents.
• Explain why proper training is important to chemical handling.
• Describe the types of personal protective equipment used and worn when handling chemicals.
• Explain the role of governmental agencies in enforcing chemical regulations.

Contents
Introduction: Living with Chemicals; Chemical Injuries; Accident Prevention; Handling Hazardous Wastes.

• #### Preventive Maintenance

Course #: 286085
Duration: 5 hours
Course Prerequisites: Trades Safety: Getting Started (186001); Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn: Preview
The purpose of a preventive maintenance program is to locate possible machine or equipment faults before the machine fails.

Objectives
When a student completes this study unit, he and she will be able to:

• Describe the function of inspection and scheduled maintenance as the basis of preventive maintenance.
• Explain why preventive maintenance is performed and how it's scheduled.
• Identify those within industry who should be part of preventive maintenance planning and execution.
• Discuss the causes, effects, and goals of a successful preventive maintenance program.
• Explain how a computerized preventive maintenance program can be developed and implemented.

Contents
Introduction To Preventive Maintenance; Why Perform Preventive Maintenance?; Scheduling Preventive Maintenance; PM Program Personnel; PM Program Goals; Computerized PM Programs.

• #### Preventive Maintenance Techniques

Course #: 286086
Duration: 5 hours
Course Prerequisites: Trades Safety: Getting Started (186001); Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn: Preview
How to implement a preventive maintenance (PM) program is just as important as the why and when of such a program. It doesn't pay to create a well thought out and scheduled PM program only to have the lubrication, inspection, or repair tasks performed improperly. The objective of this unit is to show you how to perform these tasks safely and properly. This will include showing you typical PM tasks as they are performed on common industrial equipment.

Objectives
When a student completes this study unit, he and she will be able to:

• Explain how to inspect and properly maintain a belt, chain, and gearbox power transmission system.
• Discuss why proper alignment is necessary when operating a power transmission system.
• List the steps needed to properly maintain an AC or DC motor.
• Explain how to perform a start-up or bump test of a motor.
• Describe how to perform PM tasks on pneumatic systems.
• Describe how to maintain both floor and elevated conveyor systems.
• Identify the types of elevators and vertical lifts in your plant and the proper PM procedures for this equipment.
• Explain how to maintain liquid and vacuum pump systems.
• Describe how to perform a basic alignment of in-line shafts.
• List the proper PM procedures for electronic controllers and robot systems.

Contents
PM Of Power Transmission Systems; PM Of Electric Motors And Controllers; PM Of Pneumatic Systems; PM Of Conveyors; PM Of Vertical Lifts; PM Of Vacuum And Fluid Pumps; PM Of Electronic Controllers; PM Of Robots.

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