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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)

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TMAT 103

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  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

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