Download Math 365 Review: Problems on Arithmetic Sequences, Real Numbers, and Algebra - Prof. Sherr and more Study notes Mathematics in PDF only on Docsity!
1. Negate, “All apples are red or some pears are yellow.”
2. Find the sum of the first 21 terms of an arithmetic sequence in which the eighteenth term is 31 117 5 and
the thirty-third term is 331 222 5.
3. Of the four main operations on real numbers, which ones are commutative?
4. GCD (2332, 1590) =
5. Prove or disprove: If a b c d , , , and b c d , , 0 , then
a b c d
is a rational number.
7. Using the definition of less than, show 3 29 4.
8. Fully simplify
2 1 8 4 14 4 5 x y z y z
9. If U = {a, b, c, d, e}, F = {b, c}, G = {d}, and H = {c, d, e}, find the following.
a. F G
b. n U ( )
c. G H
d. n G ( H )
e. How many proper subsets does H have? List one non-empty proper subset of H.
10. Over the rational numbers, factor completely:
48 a^8 243
11. What is the contrapositive of the statement, “A whippet is a dog.”
12. Fully simplify:
2 3 3 1 0 4 5 5 2 x yz x y z
19. If r is a real number, prove
a. 0 , 0
0 r r
b. r
r 1
c.
0 r
is undefined.
20. What are the steps in Polya’s Four–Step Problem-Solving Process?
21. Give the first 6 terms in the Fibonacci sequence.
22. Define place value.
23. Give a one-to-one correspondence between the even natural numbers, E , and the natural numbers, N.
24. Be able to model addition, subtraction, multiplication, and division, where applicable, of the sets we have
studied. Be able to perform the arithmetic algorithms we studied.
25. Which sets, that we have studied, are closed under the four main operations?
26. What is the Fundamental Counting Principle? Be able to apply it.
27. What are the relationships among the operations of addition, subtraction, multiplication and division?
28. ^4
2 0 5 8 4 9 4 80 4 2 20 8 5 7 3 2 16 x y z
29. What are the properties of the additive inverse?
30. If f ( x ) = 3 x – 7 and g ( x ) = 6 x + 9, find and simplify
g f f g o 2 3
. What is its domain?
31. Give an example of a relation that is transitive, but not reflexive nor symmetric.
32. Give an example of an equivalence relation.
33. Give an example of the Division Algorithm and why it is needed.
34. Which of the following numbers divide 8415?
35. Prime factor 3864. How many positive divisors does 3864
19
have?
36. What is the largest prime you would need to check to see if 517 is prime?
51. Justify each step.
(27.1)(3.9) a. = (2 * 10^1 + 7 * 10^0 + 1 * 10-1)(3 * 10^0 + 9 * 10-1) b. = 2 * 10^1 * 3 * 10^0 + 2 * 10^1 * 9 * 10-1^ + 7 * 10^0 * 3 * 10^0 + 7 * 10^0 * 9 * 10-1^ + 1 * 10-1^ *3 * 10^0 + 1 * 10-1^ * 9 * 10- c. = 2 * 3 * 10^1 * 10^0 + 2 * 9 * 10^1 * 10-1^ + 7 * 3 * 10^0 * 10^0 + 7 * 9 * 10 0
d. = 6 * 10^1 * 10^0 + 18 * 10^1 * 10-1^ + 21 * 10^0 * 10^0 + 63 * 10^0 * 10-1^ + 1 * 3 * 10-1^ *10^0 + 1 * 9 * 10-1^ * 10- e. = 6 * 10 1
63 * 10^0 * 10-1^ + 3 * 10-1^ *10^0 + 9 * 10-1^ * 10- f. = 6 * 10^1 + 18 * 10^0 + 21 * 10^0 + 63 * 10-1^ + 3 * 10-1^ + 9 * 10- g. = 6 * 10^1 + (1 * 10^1 + 8 * 10^0 ) * 10^0 + (2 * 10^1 + 1 * 10^0 ) * 10^0 + (6 * 10^1 + 3 * 10^0 ) * 10-1^ + 3 * 10-1^ + 9 * 10- h. = 6 * 10^1 + 1 * 10^1 * 10^0 + 8 * 10^0 * 10^0 + 2 * 10^1 * 10^0 + 1 * 10^0 * 10^0 + 6 * 10^1 * 10-1^ + 3 * 10^0
- 10-1^ + 3 * 10-1^ + 9 * 10- i. = 6 * 10^1 + 1 * 10^1 + 8 * 10^0 + 2 * 10^1 + 1 * 10^0 + 6 * 10^0 + 3 * 10-1^ + 3 * 10-1^ + 9 * 10- j. = 6 * 10^1 + 1 * 10^1 + 2 * 10^1 + 8 * 10^0 + 1 * 10^0 + 6 * 10^0 + 3 * 10-1^ + 3 * 10-1^ + 9 * 10- k. = (6 + 1) * 10^1 + 2 * 10^1 + (8 + 1 + 6) * 10^0 + (3 + 3) * 10-1^ + 9 * 10- l. = 7 * 10 1
- 2 * 10 1
- 15 * 10 0
- 6 * 10
m. = 7 * 10^1 + 2 * 10^1 + (1 * 10^1 + 5 * 10^0 ) * 10^0 + 6 * 10-1^ + 9 * 10- n. = 7 * 10^1 + 2 * 10^1 + 1 * 10^1 * 10^0 + 5 * 10^0 * 10^0 + 6 * 10-1^ + 9 * 10- o. = 7 * 10^1 + 2 * 10^1 + 1 * 10^1 + 5 * 10^0 + 6 * 10-1^ + 9 * 10- p. = (7 + 2 + 1) * 10^1 + 5 * 10^0 + 6 * 10-1^ + 9 * 10- q. = 10 * 10^1 + 5 * 10^0 + 6 * 10-1^ + 9 * 10- r. = (1 * 10^1 + 0 * 10^0 ) * 10^1 + 5 * 10^0 + 6 * 10-1^ + 9 * 10- s. = 1 * 10^1 * 10^1 + 0 * 10^0 * 10^1 + 5 * 10^0 + 6 * 10-1^ + 9 * 10- t. = 1 * 10^2 + 0 * 10^1 + 5 * 10^0 + 6 * 10-1^ + 9 * 10- u. = 105.
