BASIC ELECTRICITY MATHEMATICS

TABLE OF CONTENTS 1 ALGEBRA Tasks This lesson is common to all missile repairer tasks Requirements Hours Instructions and Certification Instruction Arithmetic of Grouping Mathematics Equations Radicals and Complex Numbers Equations EXERCISES of a Logarithm the Logarithm of a Number Characteristics with Logarithms of Ten Prefixes 2 LOGARITHMS Tasks This lesson is common to all missile repairer tasks 3 TRIGONOMETRY Tasks This lesson is common to all missile repairer tasks 4 VECTOR ALGEBRA Tasks This lesson is common to all missile repairer tasks EXERCISES Functions Measure Representation EXERCISES Quantities Notation Vectors Representation and Subtraction a Vector to a Power of a Vector EXERCISES EXAMINATION SOLUTIONS INQUIRY SHEET is the first of three subcourses that are an introduction to or refreshers your knowledge of basic electricity This reviews the mathematics you need understand the basic operating principles of guided missile systems and and radar circuits Covered are algebra logarithms trigonometry vector algebra Requirements Hours are no supplementary requirements in material or personnel for this You will need only this book and will work without supervision credit hours will be awarded for the successful completion of this score of at least 75 on the end of subcourse examination Instructions Sheets If a change sheet has been sent to you with this subcourse be you post the changes in the book before starting the subcourse on TSC Form 59 Before you begin this subcourse make sure that the already typed on your TSC Form 59 ACCP Examination Response Sheet correct You will find the correct subcourse number and subcourse edition on the front cover of this book If any of the information on your TSC 59 is incorrect write to Army Institute for Professional Development IPD Army Training Support Center News VA 23628 0001 new correctly filled out form will be sent to you Do not correct the form or send it to IPD Changes Corrections If you have questions about enrollment or administrative matters write to IPD If a change occurs or a correction to be made in your status name grade rank address unit of assignment notify IPD as soon as possible These kinds of changes or corrections can sent along on a separate sheet of paper with your completed TSC Form 59 with IPD In any correspondence with IPD always write your Social Security Number and the school code of your enrollment on each and Certification Instructions you have completed the subcourse review any of the material covered that are not sure of Then take the end of subcourse examination When you have the examination in the book you must transfer your answers to TSC 69 The instructions on the form itself tell you how to mark your answers the instructions carefully you have transferred your answers to the TSC Form 59 fold the form as it folded when sent to you Do not staple or mutilate this form Place the in the self addressed envelope provided and mail it to IPD No postage is TSC Form 59 is the only material that you are required to return to If you return it as soon as you have completed this subcourse you will your next subcourse sooner The highest score possible on the end of subcourse examination is 100 grade structure for all ACCP subcourses is given below 95 100 85 94 75 84 0 74 TSC Form 59 will be machine graded and you will be notified of the Your grade on the examination will be your grade for the subcourse credit is given for grades below satisfactory 75 When you have completed the subcourse successfully IPD will send a subcourse completion certificate Keep it with your other personal copies personnel material Subcourse completion certificates can be used to support and other personnel actions IMPORTANT NOTICE PASSING SCORE FOR ALL ACCP MATERIAL IS NOW 70 DISREGARD ALL REFERENCES TO THE 75 REQUIREMENT Lesson 1 1 The skills and knowledge taught in this subcourse are common to all missile repairer tasks When you have completed this lesson you should be able to correctly solve equations using algebraic and involving exponents radicals and complex numbers You will have this subcourse book and work without supervision You must score at least 75 on the end of subcourse examination that covers this lesson and lessons 2 3 4 answer 23 of the 30 questions correctly extends the scope of arithmetic by introducing the concept of negative values and the use of letters for Letters used to represent quantities are called literal numbers An algebraic expression is any combination of numerals and literal numbers For example a b and x 2y are algebraic expressions Signs are used to indicate numbers are positive or negative or they may indicate operations to be performed such as add or ARITHMETIC of two algebraic quantities need not be indicated by a sign Just a position of terms can indicate Thus a X b or a b may be written ab In the expression ab a and b are known as factors of the Each factor of a product is known as the coefficient of the other factor s absolute value of a number refers to its magnitude regardless of the sign preceding it Numbers not preceded by a are assumed to be positive For example 8 is the absolute value of both 8 and 8 To designate absolute value exponent is a number or letter which indicates the power to which a quantity called the base is to be raised It the number of times the quantity is multiplied by itself Thus the expression ex is read e to the x power that e is multiplied by itself x times arithmetical or literal number or the product or quotient of the numbers is called a term For example 4 x 25b x y are terms which have identical literal parts are called similar or like terms while those with unlike literal numbers are as unlike terms Thus 7a and a are like terms while 7a and 7a2 or 8a and 8b are unlike terms terms may be added to or subtracted from each other For example 4x may be added to 5x to produce 9x or 10y2 3y2 equals 7y2 since the literal numbers are the same in each case The sum of numbers such as 4y and 5m2 must be as 4y 5m2 since y and m2 are unlike terms add two numbers with the same sign add their absolute values and write common sign before the sum added to 3 equals 9 added to 3 equals 9 add two numbers with opposite signs take the difference of their absolute values and write the sign of the larger value subtract a quantity from another change the sign of the quantity to be subtracted then add the quantities following rules of addition algebraic expression containing two or more terms joined together by a plus or minus sign is called a Thus the expressions a b c and ab ac are polynomials A polynomial with only two terms is known a binomial one with three terms is known as a trinomial and a single term such as a b 10a2b is a monomial are added and subtracted the same way single terms are symbols such as parentheses brackets and braces are used to group several quantities which are by the same operation and must be treated as a single quantity For example in the expression 4a2 3ab 2ab the entire quantity of 3a2 2ab is subtracted from the first term In removing a symbol or grouping that preceded by a minus sign change the signs of all terms included by the symbol 4ab x becomes 3a2 4ab x one symbol of grouping appears within another it is best to remove one set of grouping symbols at a time with the innermost symbol first Lesson 1 added to 3 equals 3 added to 3 equals 3 3 becomes 6 3 3 6 becomes 3 6 3 3 becomes 6 3 9 3 becomes 6 3 3 2b 3c 6a b 7c 10a 3b 10c 6n2 3m2 8n2 2n2 of Grouping 2a2 5am a2 inside parentheses to obtain 2a2 5am