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

SLIDE 1

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.

T F

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 7m3n2 + 2mn3 – 4n4 is 4.

T F

6. {0, 1, 2, 3, 4, . . . } is the set of natural numbers.

T F

7. Any rational number can be expressed as the ratio of two integers a and b where b  0.

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 |.

T F

15. For real numbers a and b, if | a | > | b |, then a2 > b2.

T F

16. For real numbers a, b and c, if | a | < | b |, then | a + c | < | b + c |.

T F

17. For real numbers a and b, if | ab | = | a | ● | b |.

T F

18. If |p| > |q|, then p is closer to the origin than is q.

T F

19. |p| < 0.

T F

20. If |p| < |q|, then p3 < q3.

T F

21. If p < 0 and q < r, then pq > pr.

T F

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

24. The solution set of | x | < 5 is a disjunction.

T F

25. The solution set of | x | > 5 is a disjunction.

T F

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

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?

A. 4.2222
B. 4.24224222422224…
C. 4.2424242424… D.

4 E. 2

F.

2

G. 4

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
B. | -3 – 7 | < x
C. | x – 3 |  7
D. | x – 7 |  3
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.

CHAPTER 1 & 2 REVIEW

SLIDE 2

_______________________ 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.)

SLIDE 3

Solutions to Chapter 1 & 2 Review

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

SLIDE 4

_________________ 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.)