1 / 58

TMAT 103

TMAT 103. Chapter 1 Fundamental Concepts. TMAT 103. § 1.1 The Real Number System. § 1.1 – The Real Number System. Integers Positive, Negative, Zero Rationals Irrationals Reals Real number line Complex Numbers Primes. § 1.1 – The Real Number System. Properties of Real Numbers (FYI)

leo-dorsey
Download Presentation

TMAT 103

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. TMAT 103 Chapter 1 Fundamental Concepts

  2. TMAT 103 §1.1 The Real Number System

  3. §1.1 – The Real Number System • Integers • Positive, Negative, Zero • Rationals • Irrationals • Reals • Real number line • Complex Numbers • Primes

  4. §1.1 – The Real Number System • Properties of Real Numbers (FYI) • Commutative Property of Addition • Commutative Property of Multiplication • Associative Property of Addition • Associative Property of Multiplication • Distributive Property of Multiplication over Addition • Additive inverse • Multiplicative inverse • Additive identity • Multiplicative identity

  5. §1.1 – The Real Number System • Signed Numbers • Absolute Value • Adding 2 signed numbers • Subtracting 2 signed numbers • Multiplying 2 signed numbers • Dividing 2 signed numbers

  6. §1.1 – The Real Number System • Examples – Calculate the following • |–101| • (- 1½) + (- 2¼) • Bill, a diver, is 120 feet below the surface of the Pacific Ocean. Heather is directly above Bill in a balloon that is 260 feet above the Pacific Ocean. Find the distance between Bill and Heather.

  7. TMAT 103 §1.2 Zero and Order of Operations

  8. §1.2 – Zero and Order of Operations • Operations with 0

  9. §1.2 – Zero and Order of Operations • Examples – Calculate the following • Find values of x that make the following meaningless:3x – 7 2x + 1 • Find values of x that make the following indeterminate: 2 – x . (2x – 7)(x – 2)

  10. §1.2 – Zero and Order of Operations • Order of Operations – PEMDAS • Parenthesis • Exponents • Multiplications and Divisions in the order they appear left to right • Additions and Subtractions in the order they appear left to right

  11. §1.2 – Zero and Order of Operations • Examples – Calculate the following

  12. TMAT 103 §1.3 Scientific Notation and Powers of 10

  13. §1.3 – Scientific Notation and Powers of 10 • Powers of 10 • Laws

  14. §1.3 – Scientific Notation and Powers of 10 • Scientific Notation • Changing a number from decimal form to scientific notation • Changing a number from scientific notation to decimal form

  15. §1.3 – Scientific Notation and Powers of 10 • Examples – Calculate the following • Write the following in scientific notation 23700 17070000 .00325 • Write the following in decimal form 7.23 x 106 6.2 x 10-3

  16. TMAT 103 §1.4 Measurement

  17. §1.4 – Measurement • Measurement • Comparison of a quantity with a standard unit • In past, units not standard (1 pace, length of ear of corn, etc.) • Necessity dictated universally standard units • Approximate vs. exact • Accuracy (significant digits) • Precision

  18. §1.4 – Measurement • Accuracy (Significant Digits) Rules • All non-zero digits are significant • All zeros between significant digits are significant • Tagged zeros are significant • All numbers to the right of a significant digit AND a decimal point are significant • Non-tagged zeros to the right in a whole number are not significant • Zeros to the left in a measurement less than one are not significant

  19. §1.4 – Measurement • Examples – Calculate the following • Find the accuracy (number of significant digits) of the following: 14.7 .000000000008 1404040 1404040.00030

  20. §1.4 – Measurement • Precision • The smallest unit with which a measurement is made. In other words, the position of the rightmost significant digit. • Ex: The precision of 239,000 miles is 1000 miles. • Ex: The precision of 23.55 seconds is .01 seconds

  21. §1.4 – Measurement • Examples – Calculate the following • Find the precision of each of the following: 1.0 m 360 V 350.000030 V

  22. §1.4 – Measurement • Precision and accuracy are different!!! • Ex: Determine which of the following measurements are more precise, and which is more accurate:0.00032 feet 23540000 feet

  23. TMAT 103 §1.5 Operations with Measurements

  24. §1.5 – Operations with Measurements • Adding or subtracting measurements • Convert to the same units • Add or subtract • Round the result to the same precision as the least precise of the original measurements • Multiplying or dividing measurements • Convert to the same units • Multiply or divide • Round the result to the same number of significant digits as the original measurement with the least significant digits

  25. §1.5 – Operations with Measurements • Examples – Calculate the following • Find the sum of: 178m, 33.7m and 100cm • Find the product of: (.065m) and (.9282m)

  26. TMAT 103 §1.6 Algebraic Expressions

  27. §1.6 – Algebraic Expressions • Terminology • Variable • Constant • Term • Numerical coefficient • Monomial, binomial, trinomial, polynomial • Degree of a monomial • Degree of a polynomial

  28. §1.6 – Algebraic Expressions • Operations on Algebraic expressions • Adding expressions • Subtracting expressions • Evaluating expressions given the values of variables

  29. §1.6 – Algebraic Expressions • Examples – Calculate the following • Find the degree of x2y • Find the degree of x2y + w4 + a3b2 • (4y + 11) + (11y – 2) • (x2 + x + 17) – (3x – 4)

  30. TMAT 103 §1.7 Exponents and Radicals

  31. §1.7 – Exponents and Radicals • Laws of Exponents

  32. §1.7 – Exponents and Radicals • Examples – Simplify the following

  33. §1.7 – Exponents and Radicals • Radicals • Simplifying simple radicals • Ex: • Simplifying radicals with the following property: • Ex:

  34. TMAT 103 §1.8 Multiplication of Algebraic Expressions

  35. §1.8 – Multiplication of Algebraic Expressions • Distributive Property • FOIL • Vertical multiplication • Multiplication of general polynomials

  36. §1.8 – Multiplication of Algebraic Expressions • Examples – Calculate the following • x2(y3 + z – 2) • (x + 2)(x – 2) • (3x2 + 4x – 1)(2y – 3z + 7)

  37. TMAT 103 §1.9 Division of Algebraic Expressions

  38. §1.9 – Division of Algebraic Expressions • Division by a monomial • Division by a polynomial

  39. §1.9 – Division of Algebraic Expressions • Examples – Calculate the following • 14x2 – 10x 2x • 6x4 + 4x3 + 2x2 – 11x + 1 (x – 2) • 4y3 + 11y – 3 (2y + 1)

  40. TMAT 103 §1.10 Linear Equations

  41. §1.10 – Linear Equations • Four properties of equations • The same value can be added to both sides • The same value can be subtracted from both sides • The same non-zero value can be multiplied on both sides of the equation • The same non-zero value can divided on both sides of the equation

  42. §1.10 – Linear Equations • Examples – Calculate the following • x – 4 = 12 • 4(2y – 3) – (3y + 7) = 6 • ¼(½x + 8) = ½(x – 16) + 11

  43. TMAT 103 §1.11 Formulas

  44. §1.11 – Formulas • Formula – equation, usually expressed in letters, that show the relationship between quantities • Solving a formula for a given letter

  45. §1.11 – Formulas • Examples – Calculate the following • Solve f = ma for a • Solve e = ƒx +  for x • Solve for R3:

  46. TMAT 103 §1.12 Substitution of Data into Formulas

  47. §1.12 – Substitution of Data into Formulas • Using a formula to solve a problem where all but the unknown quantity is given • Solve for the unknown • Substitute all values with units • Solve

  48. §1.12 – Substitution of Data into Formulas • Examples – Calculate the following • Solve f = ma for a when f = 3 and m = 17 • Solve e = ƒx +  for xwhen e = 11, ƒ = 3.5 and  = .01 • Solve for R3 when RB,R1, and R2 are all 11

  49. TMAT 103 §1.13 Applications involving Linear Equations

  50. §1.13 – Applications involving Linear Equations • Solving application problems • Read the problem carefully • If applicable, draw a picture • Use a symbol to label the unknown quantity • Write the equation that represents the problem • Solve • Check

More Related