Download Name I Fill in the blank with the correct symbol or word. Please

Math 190 Midterm #1
Trinity Western University
2012 02 05 Page 1
Name
I Fill in the blank with the correct symbol or word. Please place your actual answer in the blank
at the right of the page. [35 marks] You should take 12-15 minutes on this part.
1. How many elements are in the set {Ø} ?
1.
2. You read 4 × 5 in words (not using "times") as
2.
3. If one writes 23 = 4 × 5 + 3, then 3 is the ___of a division 3.
4. In a subtraction a - b = c, the number "b" is called the
4.
5. {1, 5, 8} ∩ {1, 7, 9}
5.
6. {2, 3, 4} ∪ {2, 4, 5}
6.
7. A counting devices with beads on a wire is called
7.
8. Visual aids to picture sets are called
8.
9. The set of elements not in a set A is called the __ of A
9.
10. If every element of A is also an element of C, then
show in symbols the relationship between A and C
10.
11. For a transitive relation called *, if a*b AND b*c then
11.
12. The fact that A ∪ B = B ∪ A is called
12.
5
2
13. Simplify 2 × 4
13.
14. Simplify 45 - 5 × 8
14.
15. If A = {2} and B = {1, 2, 5}, what is B × A?
15.
16. {1, 3, 5, 8} - {2, 5, 7, 9} =
16.
5
2
17. Simplify (3 × 10 ) × (5 × 10 )
17.
18. convert 1246 to decimal
18.
19. In the sequence 0,1,1,2,3,5,8,13,21, what are the next two terms?
19.
20. Reasoning from general rules to particular cases is called 20.
21. What numeration system was based on grouping, but not place value?
21.
22. The primary classroom aid for measurement models of adding
and subtracting is some form of __
22.
23. The fact that the product of two whole numbers is another whole number is called
23.
3 2 2
24. Simplify (12x y )
24.
25. If two sets are equivalent, they have the same
25.
26. What addition shows that x - y = z ?
26.
27. What multiplication shows that 24 divided by 6 equals 4 ? 27.
28. Write: "The complement of B" in symbols
28.
29. Suppose * is an operation, and you know that for all a, b it is the case that
a*b = b*a. What do you call this property?
29.
30. Suppose you find an element e for which a*e = e*a = 1. What would you
call the element e?
30.
31. Write 354110 in expanded notation
31
32. Write 2347 in expanded notation
32.
33. Convert the base two numeral 11001 to base 10
33.
34. "Logarithm" is a synonym for
34.
35. In a division expressed as 14 ÷ 2 = 7 the number 7 is called the 35.
Math 190 Midterm #1
Trinity Western University
II [21] In this section, you may
skip 3 questions. Each is worth 3
36. A set with three elements has how many
2012 02 05 Page 2
marks. Indicate which.
37. Draw a diagram illustrating (A ∪ B)
subsets? List them.
38. Is the set {-1,0,1} closed
under addition? multiplication? Say why.
40. What is the probable next term in the
sequence 5, 23, 91, 269, 641, 1315, . . . ?
39. Disprove the theorem:
"Cross product on sets is commutative."
41. Explain, using the relationship between
multiplication and division, why n ÷ 0 is
undefined. (Work must be shown.)
42. If, whenever x ∈ A we also have x ∈ B,
43. What is the meaning of a7 ?
how are A & B related? (symbols and words)
44. What is the difference between a number and a numeral? 45. What is a magic square?
Math 190 Midterm #1
Trinity Western University
2012 02 05 Page 3
III [9] Explain three of the following. You should in some cases use examples.
46. WADES. 47. A number line model for addition. 48. How to use grouping to assist addition.
49. Why the zero symbol cannot be left out in place value numerals.
50. A model for the idea that 3 < 7 51. A teaching model for 3 times 5.
52. The difference between a take-away approach and a missing addend approach.
IV [8] Simplify, compute, or… (show all steps, or no marks)
3
5
4
53. 1 + 2 × 5 − (3 − 2)
54. 4 ÷ 2
55. ( 2 × 3) × 4 2
56.
127 + 35 + 13 + 45
III Bonus questions. Anything you get here is added to your score.
57. [5] A survey of a flock of chickens revealed
9 fat red roosters 7 thin brown hens
2 fat red hens
18 thin brown roosters
26 fat roosters
6 thin red roosters
37 fat chickens
5 thin red hens
How many chickens were
a) both red and fat? (b) fat, but not male?
58. [3] Is the set of all sets closed under multiplication? Explain.
59. [4] If a,b,c ∈N , explain at least four properties of addition using these symbols (& words).