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Mathematics and Technical Foundation Skills

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.

Addition and Subtraction

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 check your answers to both addition and subtraction problems.
  • 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.

    • Algebra: Quadratic Equations

    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:

  • Simplify several radicals and then add like terms.
  • 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.

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