Math 1050
Exam 1 (Make-up)
February 10, 2012
Answer all questions below. Every question is worth the same number of
points. You may use the available space for work, but must write ALL
answers on the answer sheet.
No cell phones, calculators, or notes are allowed during the exam. These
rules will be strictly enforced.
Name:
Number:
For #1-3 decide whether the statement is true or false.
1. (1, 2] ⊆ [1, 3)
√
2. 2 ∈ Z
3. Z ⊆ N
For #4-6, decide whether the given sequence is arithmetic, geometric, or neither.
4. 6, 8, −7, 8, . . .
5. −1, 1, −1, 1, . . .
6. −10, 10, 30, 50, . . .
7. Find
101
X
8
i=1
8. Find
3
X
(i3 )
i=1
9. Find
52
X
i=1
i
10. What is the 68th term in the sequence 2, −6, 18, −54, . . .?
11. What is the 91st term in the sequence 10, 7, 4, 1, . . .?
12. What does the following series equal:
3
2
+ 1 + 32 + 49 + . . .?
13. What is the sum of the first 50 terms of the sequence 9, 13, 17, 21, . . .?
Page 2
14. You are designing a house for yourself to live in. You can choose the house to be made
out of wood, brick, or metal. The roof can be wood shingles, asphalt shingles, or tin.
You can paint the house brown, red, yellow, or green. You can choose to have two, three,
four, or five bedrooms. How many possibilities are there for the design of your house?
15. You are in an ice cream shop. There are 31 flavors of ice cream. You are building a
sundae with a scoop of ice cream on the bottom, a different flavor on top of that, and a
third different flavor on top of that. If it matters to you which flavor is on the bottom,
in the middle, and on the top, then how many different sundaes can you make?
16. You are on a boat with 200 people. The boat is sinking and there is only one life raft
with 8 seats. How many different options are there for which 8 people to put in the raft?
10
17. What is
? (Your answer should be a natural number in standard form.)
5
Page 3
18. If f (x) = 4x + 1 and g(x) = x3 − 1, what is f ◦ g(x)?
19. What is the implied domain of f (x) = −2x2 + 54x − 3?
20. What is the implied domain of g(x) =
4x3 −8x+2
?
10x−5
Below is the graph of a function f (x). Use this graph to answer questions #22-27.
21. What is f (−1)?
22. What is the range of f ?
23. What is the domain of f ?
24. What is the y-intercept of the graph of f ?
25. What are the x-intercepts of the graph of f ?
Page 4
26. Is the picture below the graph of a function?
4
27. Write out the
product (x + y) so that your final answer doesn’t include numbers that
n
look like k .
28. Graph id.
29. Graph x2 .
30. Graph x3 .
31. Graph f (x) = −15.
32. Graph x1 .
33. Graph
1
.
x2
34. Graph g : [−1, 2) → R where g(x) = 2x − 1.
35. Graph h : {−1, 0, 2} → R where h(x) = x2 + 1.
Page 5
Name:
Number:
1.
14.
2.
15.
3.
16.
4.
17.
5.
18.
6.
19.
7.
20.
8.
21.
9.
22.
10.
23.
11.
24.
12.
25.
13.
26.
Page 6
27.
********************************************************************************
28. id
29. x2
31. f (x) = −15
32.
34. g(x)
35. h(x)
30. x3
1
x
33.
Page 7
1
x2