51. Graph the solution set: x 7 > 3x 5 or 3x 5 x + 11 - PDF document

CHAPTER 1 & 2 REVIEW NAME ____________________________________________________ Circle T or F to tell whether each statement is TRUE or FALSE. T F 1. The disjunction of the two statements, x < 2, x > 3, is the null set. T F 2. The conjunction of the two statements, x < 2, x > 3, is the null set. 3. The disjunction of the two statements, x < 2, x > – 3, is all real numbers. T F 4. The equation 2x + 4 = 3x + 7 – x is an identity. T F 5. The degree of the polynomial 7m 3 n 2 + 2mn 3 – 4n 4 is 4. T F T F 6. {0, 1, 2, 3, 4, . . . } is the set of natural numbers. 7. Any rational number can be expressed as the ratio of two integers a and b where b  0. T F T F 8. The IF clause of a conditional statement is called the hypothesis. T F 9. The converse of a true statement is true. T F 10. Subtraction is commutative. T F 11. If ab = 0, then a = 0 or b = 0. T F 12. If ab = 2, then a = 2 or b = 2. T F 13. For real numbers a, b and c, if a > b, then ac > bc. T F 14. For real numbers a and b, if a > b, then | a | > | b |. 15. For real numbers a and b, if | a | > | b |, then a 2 > b 2 . T F T F 16. For real numbers a, b and c, if | a | < | b |, then | a + c | < | b + c |. 17. For real numbers a and b, if | ab | = | a | ● | b |. T F T F 18. If |p| > |q|, then p is closer to the origin than is q. T F 19. |p| < 0. 20. If |p| < |q|, then p 3 < q 3 . T F T F 21. If p < 0 and q < r, then pq > pr. 22. If |p – 2| < 7, then p is less than 7 units from 2. T F 23. The equation |p – 2| = 7 has more than one solution. T F T F 24. The solution set of | x | < 5 is a disjunction. T F 25. The solution set of | x | > 5 is a disjunction. 26. The solution set of | x | < – 5 is {all real numbers}. T F 27. For real numbers a and b, the equation | a – 5 | = b may contain at most two solutions. T F 28. 0.13131313… is rational. T F 29. 0.131331333… is rational. T F T F 30. The set of whole numbers is closed under addition. T F 31. The set of whole numbers is closed under division. T F 32. The set of integers is closed under multiplication. Multiple Choice. Fill in the blank with ALL correct responses for each. _____________ 33. Which of the following numbers are rational? G. 4 4 E. 2  B. 4.24224222422224 … C. 4.2424242424… D. 2 A. 4.2222 F. 42 _____________ 34. Which of the following illustrates the reflexive property A. If a = b, then b = a B. ab = ba C. ab = ab D. a + 0 = a E. a + -a = 0 _____________ 35. Which of the following illustrates the identity property of addition? A. If a = b, then b = a B. ab = ba C. ab = ab D. a + 0 = a E. a + -a = 0 _____________ 36. Which of the following is equivalent to “x is no more than 7 units from 3? A. | x – 3 |  7 C. | x – 3 |  7 D. | x – 7 |  3 B. | -3 – 7 | < x E. | x – 7 | < 3 _____________ 37. Which of the following is equivalent to | 5 + x | < 2? A. 5 is less than 2 units from x B. x is less than 2 units from -5 C. 5 is less than x units from 2 D. 2 is less than x units from 5 E. 2 is more than x units from -5 Write the name of the property in the blank. Assume variables represent any real number. _____________________________________________ 38. x + -x = 0 _____________________________________________ 39. If (x + 1) > 0 and a < 0, then (x + 1)a < 0. _____________________________________________ 40. If (x + 1)a = 0, then x + 1 = 0 or a = 0. _____________________________________________ 41. Only one of the following is true: x < y, x = y, or x >y _____________________________________________ 42. If x + 1 = y + 1, then x = y.

_____________________________________________ 43. If x + 1 = y + 1, then y + 1 = x + 1. _____________________________________________ 44. x + 1 = 1 + x _____________________________________________ 45. (3.2 + 5.7) + 2.3 = 3.2 + (5.7 + 2.3) _____________________________________________ 46. 1x = x _____________________________________________ 47. If x < y and y < z, then x < z. _____________________________________________ 48. (2)(1/2) = 1 Show all work needed. Place the correct answer in the blank. _________________________________ 49. Write the solution set: | 5x – 1 | – 7 = 2. _________________________________ 50. Write the solution set: | 2x – 3 | + 5 = 2. 51. Graph the solution set: x – 7 > 3x – 5 or 3x – 5 ≥ x + 11 _________________________________ 52. Write the solution set: x – 7 < 3x – 5 < x + 11 _________________________________ 53. Write the solution set: 6 + 5| 2x – 3 |  4 _________________________________ 54. Write the solution set: – 2| x – 1 |  – 6 Show all work needed. Explain what each variable represents, write an equation and label your answer properly. _________________ 55. Al left Alston at 10:00am driving toward Bob Bay at 62 mph. Bob left Bob Bay at 11:00am driving toward Alston at 55 mph. If the distance between Alston and Bob Bay is 296 miles, what time is it when Al and Bob meet each other? _________________ 56. The length of a rectangle is three more than twice the width and the perimeter is at least 42 cm. Find the smallest possible dimensions of the rectangle? _________________ 57. A bus is to be hired to take students to a hockey game in Madison. The basic fare is $11.00 per passenger. If more than 30 people go, everyone's fare will be reduced $0.40 for every person over this number (30). At least how many people must go to make the fare less than $7.50 per passenger? (Show algebra – no points for guess & check or arithmetic methods.)

Solutions to Chapter 1 & 2 Review 1. F – should be {all real numbers} 24. F – it is {x: -5 < x < 5} 2. T – no numbers satisfy both 25. T – it is {x: x < -5 or x > 5} 3. T – "arrows" in opp directions 26. F – it is null set 4. F – Null set (If an identity  {all reals}) 27. T – it may have 0, 1, or 2 solutions 5. F – degree 5, highest sum of powers in each term 28. T – repeating decimals can be written as fractions 6. F – natural/counting #s begin with 1 29. F – never terminates, never repeats 7. T – this is the def of rational number 30. T – sum of whole numbers is whole 8. T – then is called the conclusion 31. F 7/2 =a non-whole # (alien baby) 9. F – sometimes T, sometimes F 32. T – product of ints is an integer 10. F 7 – 8 is not equal to 8 – 7 33. A, C, D, G 11. T – this is Zero Product Property 34. C something is equal to itself 35. D – adding 0 the value is identical 12. F – counter-example a = 4 and b = ½ 36. A 13. F – if c < 0, must reverse sign 37. B 14. F – counter-example: a = -1 and b = -2. 38. Inverse Prop of Addition or Prop of Opposites 15. T – bigger abs. value has bigger square 39. Multiplicative Prop of Order 16. F – counter-example: a=-1, b =-2 & c=5 40. Zero Product Prop 17. T 41. Comparison or Trichotomy Principle 18. F – q is closer to origin 42. Cancellation Prop or Addition Prop of Equality 43. Symmetric Prop (of Equality) 19. F – never happens 44. Commutative Prop (of Addition) 20. F – counterexample p=1 & q= -2 45. Associative Prop (of Addition) 21. T – this is the Mult Prop of Order 46. Identity Prop of Multiplication 22. T – def of dist between two pts 47. Transitive Prop of Order 23. T – {-5, 9} 48. Inverse Prop of Mult or Property of Reciprocals 49. | 5x – 1 | – 7 = 2. 50. | 2x – 3 | + 5 = 2. 51. x – 7 > 3x – 5 or 3x – 5 ≥ x + 11 52. Write the solution set: x – 7 < 3x – 5 < x + 11 53. 6 + 5| 2x – 3 |  4 54. – 2| x – 1 |  – 6

_________________ 55. Al left Alston at 10:00am driving toward Bob Bay at 62 mph. Bob left Bob Bay at 11:00am driving toward Alston at 55 mph. If the distance between Alston and Bob Bay is 296 miles, what time is it when Al and Bob meet each other? _________________ 56. The length of a rectangle is three more than twice the width and the perimeter is at least 42 cm. Find the smallest possible dimensions of the rectangle? _________________ 57. A bus is to be hired to take students to a hockey game in Madison. The basic fare is $11.00 per passenger. If more than 30 people go, everyone's fare will be reduced $0.40 for every person over this number (30). At least how many people must go to make the fare less than $7.50 per passenger? (Show algebra – no points for guess & check or arithmetic methods.)