Download Review Problem for Final

MATH 211 FINAL EXAM REVIEW PROBLEMS
1. 32 ÷ 4 in the partitive or sharing interpretation of division, base ten pieces
2. 32 ÷ 4 in the measurement interpretation of division, base ten pieces
3. Sharing concept
Circle groups of Xs to illustrate
18 ÷ 6
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
4. Measurement concept
Circle groups of Xs to illustrate
18 ÷ 6
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Write a short and simple story problem for each:
5. Illustrating 18 ÷ 6 for the sharing concept of division.
6. Illustrating 18 ÷ 6 for the measurement concept of division.
7. Illustrating 12 - 7 for the take away concept of subtraction
8. Illustrating 12 - 7 for the comparison concept of subtraction
9. Illustrating 12 - 7 for the missing addend concept of subtraction
10.
The number 24 •33 • 52 • 71 has exactly this many different factors:
11.
The number 24 •33 • 52 • 71 has exactly this many different PRIME factors:
12.
The number 354,109,373,276,4x0 will be divisible by 6 if x is replaced by
13. The Uris satellite circles the earth every 308 hours. The Arub satellite
circles the earth every 660 hours. If both satellites were above Monroe,
Louisiana at 7 AM on April 12, the earliest time they will both again be above
Monroe is in this many hours:
Math 211 Final Practice Problems, Page 1
14.
Which one of the following pair of numbers is relatively prime?
(10, 20), (23, 46), (16, 30), (15, 42), (32, 125)
15. For this problem: Choose all, if any, that are correct.
The number 354,109,373,286,460 is divisible by: 2, 3, 4, 5, 6, 9, 10, 11?
16.
Find the LCM (1125, 70) using any method (no calculator).
17.
Find the GCF (1125, 70) using any method (no calculator).
18. What is the greatest prime that must be checked to determine if 179 is prime
or composite? Show your work.
Rewrite each statement in the form a | b.
19.
20.
21.
22.
17 divides 391
14 is a factor of 638
533 is a multiple of 13
665 is divisible by 19
23. The GCF of two numbers, x and y, is 10. Their LCM is 900. x < y < 150.
Find x and y.
24.
Explain why 22 • 32 • 15 is not a prime factorization of 540.
25.
26.
27.
28.
29.
If a number is not divisible by 6, can it be divisible by 3?
If a number is not divisible by 3, can it be divisible by 6?
If a number is not divisible by 6, can it be divisible by 9?
If a number is not divisible by 2, can it be divisible by 4?
If a number is not divisible by 4, can it be divisible by 2?
Math 211 Final Practice Problems, Page 2
Explain.
Explain.
Explain.
Explain.
Explain.
30. Maria has two lengths of ribbon, one 150 inches long and the other 135
inches long. She wants to cut lengths into equal length pieces. What is the
longest such piece she can cut so that no ribbon is left over?
Black and red tiles models: R for red tiles and B for black tiles, write clearly.
31. 7 + (- 5)
32. 4 - 6
33. 3 - (- 1)
34. 2 • - 4
35. -2 • - 4
36. -2 • 4
37. - 9 ÷ 3
38. - 9 ÷ -3
Closed or not?
39. The set of integers for multiplication.
40. The set of integers for division.
41. The set of negative integers for addition.
42. The set of positive integers for subtraction.
43. The set of even whole numbers (multiplication)
Commutative or not?
44. The set of integers for multiplication.
45. The set of integers for division.
46. The set of negative integers for addition.
47. The set of even integers for subtraction.
Associative or not?
48. The set of whole numbers for multiplication?
49. The set of integers for multiplication.
50. The set of integers for division.
51. The set of negative integers for addition.
52. The set of even integers for subtraction.
53. Valid or invalid?
All children love to draw.
Cindy is a child.
Math 211 Final Practice Problems, Page 3
Therefore, Cindy loves to draw.
54. Valid or invalid?
Some educated people are rascals.
Doctors are educated people.
Therefore, doctors are not rascals.
Rewrite each of the following using a) converse, b) inverse and c) contrapositive.
In each case use a Venn diagram to show whether the new statement is valid or
invalid.
55.
56.
57.
If I buy apples then I have fruit to eat.
I will wash my dog if it is hot out.
I will not take Math 212 in the winter if I don’t study for the math 211 final
58.
Write 1247ten in expanded form (base 10).
59.
How many units are in 1847nine?
60.
Convert 1847ten to base 60
61. Sketch the base four number pieces representing this addition, including all
regroupings. Show the addition algorithm and record the resulting base four
numeral.
2311four + 203four
62. Sketch the base four number pieces representing this subtraction, including
all regroupings. Show the subtraction algorithm and record the resulting base
four numeral.
222four - 133four
Math 211 Final Practice Problems, Page 4
63. Select 4 flats, 6 longs, and 2 units from your base ten pieces. Using only
these pieces (all of them), and making no exchanges, form a rectangle.
Neatly sketch the rectangle you made, label the edge dimensions and the partial
products and show the final product it represents.
Study the pattern below.
1st
64.
65.
2nd
3rd
4th
If this pattern of tiles continues, draw the 5th figure.
If this pattern of tiles is extended to the 150th figure, describe the 150th figure.
The following sequence of figures begins repeating in the fifth figure.
Figure 1
66.
Figure 2
Figure 3
Figure 4
Figure 5
Describe and draw the 6th figure.
67. How many triangles will there be in the 163rd, the 164th and the 166th
figures? Explain clearly for credit, a long list of numbers will receive no credit.
68. Arithmetic, geometric or finite differences
Find a pattern in the following sequence and write the next two terms of the
sequence.
2, 5, 8, 11, 14, …
69. Arithmetic, geometric or finite differences
Find a pattern in the following sequence and write the next two terms of the
sequence.
2, 5, 12, 24, 42, ….
70. Arithmetic, geometric or finite differences
Find a pattern in the following sequence and write the next two terms of the
sequence.
3, 12, 48, 192, …
Math 211 Final Practice Problems, Page 5
71. Arithmetic, geometric or finite differences
Find a pattern in the following sequence and write the next two terms of the
sequence.
0, 1, 7, 18, 34, …
Equation of line
72. Between (2,6) and (-3, 4)
73. Between (2,-2) and (-3, 4)
74. Parallel to y = 3x -4
75. Perpendicular to y = 3x -4
Simplify or solve
76.
77.
78.
2(x + 3) – 3( x + 2) = 4x
-3x < -7x + 14
2(x + 1) – 4(x + 6) + 2(x – 4)
SET A
SMALL CIRCLES
SET E
RED PIECES
SET B
CIRCLES
SET F
BLUE PIECES
SET C LARGE HEXAGONS
SET D
SET G YELLOW PIECES
HEXAGONS
79.
Set _____ ⊂ Set _____
80.
Set A ∪ Set D?
81.
Set A ∪ Set B ∪ Set F?
82.
a) Set A ∩ Set D? b) Set A ∩ Set E? c) Set C ∩ Set E?
83.
(Set A ∪ Set D) ∩ Set E?
84.
(Set B ∩ Set D) ∪ Set E?
and
Math 211 Final Practice Problems, Page 6
Set _____ ⊂ Set _____