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Basic Math for Electronics

Mathematics related to basic electronics. It includes basic algebra, right triangle trigonometry, scientific notation, with applications to DC and AC circuitry.

During this course, the student will be expected to:

1. Perform basic arithmetic operations .
 1.1 Define and give an example of the following types of numbers:
  a. Whole number
  b. Fraction (numerator and denominator).
   1) proper fraction
   2) improper fractions
  c. Mixed number
  d. Decimal number
 1.2 Perform basic arithmetic operations using whole numbers, longhand and with a calculator.
 1.3 Explain the rules for adding and subtracting fractions and then use these rules to solve problems.
 1.4 Define a factor as "Part of a Product". For example, the factors of the expression "2ab" are: 2, a, and b.
 1.5 Define a prime factor as "A part of a product that contains no other factors other than +1 or -1 and plus or minus itself".
 1.6 Factor a whole number into its prime factors (powers may be used.....for example, the prime factors of 18 are: 32, 2)
 1.7 Define the Lowest Common Denominator (LCD) as "The product of all prime factors of all denominators to their highest power".
 1.8 Find the LCD for any given group of denominators.
 1.9 Explain the rules to multiply and divide fractions and then use these rules to solve problems.
 1.10 Explain what can be done to a fraction without changing its value.
 1.11 Use cancellation of common factors to simplify fractions and reduce them to their lowest terms.
 1.12 Convert from one unit of measure to another using standard conversions and the "Cancellation Factor Method" (canceling the units of measurement themselves to insure the result is dimensionally correct before working with the numbers).
 1.13 Change a mixed number to an improper fraction.
 1.14 Perform basic arithmetic functions using decimal numbers longhand.
 1.15 Convert fractions to decimal form.


2. Demonstrate an understanding of advanced arithmetic operations to solve electric/electronic problems.
 2.1 Define an integer.
 2.2 List the names of the positions in a decimal number between "millions and millionths".
 2.3 Identify the " signs of equality and inequality".
 2.4 Perform basic arithmetic functions using signed numbers long hand.
 2.5 Define what the reciprocal of a number is and illustrate how to take the reciprocal of any number.
 2.6 Identify the base and the exponent of an exponential number.
 2.7 Calculate the value of a number to a given power.
 2.8 Identify the radical sign, radicand, and index of a radical number.
 2.9 Convert from exponential form to radical form and visa versa.
 2.10 Find the principal nth root of a number using approximation (trial and error).
 2.11 Find the principal nth root of a number by converting radical form to exponential form and then using the exponential key on a calculator ("Yx" key or equivalent).
 2.12 Perform operations involving the number "zero".
 2.13 Convert the following:
  2.13.1 Decimal number to a Percent.
  2.13.2 Common fraction/ratio to a Percent
  2.13.3 Percent to decimal
 2.14 Find a number which is a given percent of another number (base).
 2.15 Find the percent one number is of the other number.
 2.16 Calculate the percent efficiency of a device/system.

3. Relate Significant Figures/Digits and Scientific Notation to Numbers and Electrical/Electronic Calculations.
4. Define the following:
 4.1 Approximate number
 4.2 Exact number
 4.3 Significant digits
 4.4 Accuracy of a decimal number
 4.5 Precision of a decimal number
5. Determine the number of significant digits of a decimal numbers
 5.1 all nonzero digits
 5.2 zeros between nonzero digits
 5.3 zeros used only as placeholders to locate the decimal point
 5.4 trailing zeros after the decimal point
 5.5 zeros before the decimal point

6. Round off decimal numbers to a desired accuracy or precision.
7. Perform conversions between numbers in decimal form and powers of ten.
8. List the standard electronics engineering prefix notations from "tera" to "pico" by name, abbreviated symbols, and equivalent power of ten (refer to appendix B).
9. Convert a number from one prefix form to another prefix form.
10. Write numbers in scientific notation (standard form).
11. Convert decimal numbers to scientific notation and visa versa.
12. Perform basic arithmetic functions using numbers in scientific notation form.

13. Demonstrate an understanding of how to solve problems in electricity/electronics using Algebra.
 13.1 Explain why the use of letters are sometimes preferable to the use of numbers (main purpose of algebra).
 13.2 Identify the letters that are typically used to represent known numbers/constants and the letters typically used to represent unknown numbers/variables.
 13.3 Explain what a negative number means.
 13.4 Illustrate positive and negative numbers relative to "0" using a vertical line graph.
 13.5 List the signs and symbols used in algebra (refer to the appendix).
 13.6 State the following definitions word for word:
  a) A "term" is part of an algebraic expression separated by a plus or minus sign.
  b) A "factor" is part of a product within a term.
 13.7 Identify the terms of given algebraic expressions.
 13.8 Identify the factors within each term of given algebraic expressions.
 13.9 Show how factors within each term may be cancelled if common to the numerator and denominator, but show that terms of an algebraic expression cannot be cancelled.
 13.10 Translate word statements into algebraic expressions using algebraic symbols.
 13.11 Translate algebraic symbols into word statements.
 13.12 Solve an algebraic expression by substituting numbers for letters.
 13.13 Define the absolute value of a number and give some examples.
 13.14 State the rules for adding, subtracting, multiplying and dividing positive and negative (signed) numbers. Then solve these types of problems by applying the rules.
 13.15 Define "similar terms" and show how only similar terms can be added.


14. Demonstrate an understanding of how to solve electrical/electronic equations for any unknown parameter.
 14.1 Define an equation.
 14.2 Explain how to transpose a term from one side of an equation to the other.
 14.3 List the four rules for transposing a quantity from one side of the equation to the other side.
 14.4 Show how to take the reciprocal of both sides of an equation.
 14.5 Show how fractions within an equation may be eliminated by multiplying both sides of the equation by the LCD of both sides of the equation.
 14.6 Solve problems given as word statements by using algebra.
 14.7 Show how the "symbols of grouping ( parenthesis , brackets, braces)" are used in algebraic equations.
 14.8 Show how to eliminate symbols of grouping in an algebraic expression by using the distributive law : a(b+c) = ab+ac.
 14.9 Show how to "factor out" a common factor (or factors) using the distributive law.
 14.10 Show how to use factoring to isolate a variable which is originally contained in more than one term of an algebraic equation. (solve the equation for this variable).
 14.11 Multiply/divide quantities containing numbers, letters, and exponents.
 14.12 Check the solution of an algebraic equation by substituting real numbers for the letters.
 14.13 Use subscripts to distinguish one quantity from another.
 14.14 Define the following and illustrate with examples:
  14.14.1 Proportion
  14.14.2 Ratio
  14.14.3 Extreme and means of a proportion
  14.14.4 Direct proportion
  14.14.5 Indirect proportion
 14.15 Solve algebraically given equations for any unknown.


15. Demonstrate an understanding of the evaluation of problems involving angles, similar triangles and the Phythagorean Theorem.
 15.1 Describe how an angle is formed.
 15.2 Define the following and illustrate with examples:
  15.2.1 Acute angle
  15.2.2 Obtuse angle
  15.2.3 Complementary angle
  15.2.4 Supplementary angle
  15.2.5 Right triangle
 15.3 Use a protractor to draw or measure angles.
 15.4 Generate an angle in standard position and label the initial side, vertex, and terminal side.
 15.5 Generate a positive or negative angle.
 15.6 Identify the quadrant the terminal side of an angle is in when the angle is drawn in standard position.
 15.7 Explain how a degree is subdivided into minutes and seconds.
 15.8 Find the complement or supplement of a given angle.
 15.9 Define the radian relative to angular measurement and degree.
 15.10 Convert degrees to radians and visa versa.
 15.11 State the following rule: "The sum of the three angles of any triangle is always 180 degrees".
 15.12 Illustrate examples of similar triangles.
 15.13 Explain how proportions are used to solve similar triangles.
 15.14 Solve for missing parts of similar triangles.
 15.15 Draw a right triangle in standard position and label "a" for the altitude, "b" for the base, and "c" for the hypotenuse.
 15.16 State the "Pythagorean Theorem" in word form and equation form.
 15.17 Solve the Pythagorean Theorem for each side (a & b) of a right triangle and for the hypotenuse (c).
 15.18 Solve for missing parts of a right triangle using the Pythagorean Theorem (do NOT use trigonometric functions at this time).

UNIT 7 – Alternative Numbering Systems

16. Demonstrate an understanding of the use of alternative numbering systems in telecommunications.
 16.1 Understand the binary numbering system.
  16.1.1 Convert from decimal to binary and vice versa.
  16.1.2 Demonstrate the ability to perform basic mathematic functions such as addition, subtraction, multiplication and counting in binary.
 16.2 Understand the octal numbering system.
  16.2.1 Convert from decimal, binary and octal and vice versa.
  16.2.2 Demonstrate the ability to count in the octal numbering system.
 16.3 Understand the hexadecimal numbering system.
  16.3.1 Convert from decimal, binary and octal and vice versa.
  16.3.2 Understand the hexadecimal number system.


17. Solve problems involving logarithms.
 17.1 Convert from exponential form to logarithmic form and visa versa.
 17.2 Solve simple logarithmic equations.
 17.3 List the equations involving the "Laws of Logarithms" for products, quotients, powers, and roots.
 17.4 Discuss the difference between common and natural logarithms.
 17.5 Use scientific notation to write a number in the standard for N x 10P (where "p" is called the "characteristic"). Use Log Tables (Appendix G) to find the mantissa of N. Combine the characteristic and mantissa to form the common log of the original number.
 17.6 Use a calculator to find the common logarithm of a number.
 17.7 Find a number when given its common logarithm (using antilogarithms).
 17.8 Perform arithmetic computations using the "Laws of Logarithms" and common logs.
 17.9 Solve exponential equations by taking the logarithms of both sides of the equation and using standard algebraic techniques.
 17.10 Find the natural log of a number using a calculator.
 17.11 Find the value of a number when given its natural log value.
 17.12 Use the exponential growth and decay equations to solve related problems


18. Demonstrate an understanding of solving electrical/electronic circuit problems involving decibels.
 18.1 Define decibels related to logarithms.
 18.2 List some common applications of decibels.
 18.3 Describe the relationship between ratios and decibels.
 18.4 Give the equation for the "bel" in terms of a power ratio.
 18.5 Give the equation for the "decibel" in terms of a power ratio.
 18.6 Explain how power reference levels are used in decibel expressions ("dbm", "6 mw").
 18.7 Explain the following:
  18.7.1 VU
  18.7.2 dBRN and DBA
  18.7.3 dBRAP
  18.7.4 dBW
  18.7.5 dBk
  18.8 List the equations for expressing voltage and current ratios in decibels (assuming the input and output impedances are equal).
 18.9 Explain dBV and write the equation for it.
 18.10 Describe how decibels are used to find antenna power gain.
 18.11 Solve miscellaneous problems involving the use of decibels.

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