Math 1050
Practice Exam 1
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. π ∈
/Q
2. (4, 6] ⊆ [4, 7)
3. Z ⊆ Q
For #4-6, decide whether the given sequence is arithmetic, geometric, or neither.
4. 4, 1, −2, −5, . . .
5. 7, 11, 22, 15, . . .
6. 7, 21, 63, 189, . . .
7. Find
15
!
3
i=1
8. Find
70
!
i
i=1
9. Find
5
!
i=1
(i2 − i)
10. What is the 52nd term in the sequence 4, 8, 16, 32, . . .?
11. What is the 101st term in the sequence 6, 10, 14, 18, . . .?
12. What is the sum of the first 35 terms of the sequence 20, 25, 30, 35, . . .?
13. What does the following series equal: 18 + 6 + 2 + 23 + . . .?
Page 2
14. You are choosing a class council. Out of 32 students, you must select a president, vice
president, secretary, and treasurer. How many different class councils are possible?
15. You’re buying a car. You know which model you want to buy, but you are given the
option of 2 interior colors, 5 exterior colors, and 3 sound systems. How many different
types of car could you buy?
16. The faculty needs to nominate a panel of three members for a special committee. If
there are 132 faculty members, how many different committees are possible?
17. There are 150 students in this class. How many different ways are there to assign seats
for the first exam?
! "
8
18. What is
? (Your answer should be a natural number in standard form.)
6
Page 3
19. If f (x) = x + 1 and g(x) = x3 , what is f ◦ g(x)?
20. What is the implied domain of f (x) = 21x2 + 7?
1
?
x−4
21. What is the implied domain of g(x) =
Below is the graph of a function f (x). Use this graph to answer questions #22-27.
3
2
1
-5
-4
-3
-2
-1
-1
-2
-3
22. What is f (2)?
23. What is the domain of f ?
24. What is the range of f ?
25. What are the x-intercepts of the graph of f ?
26. What is the y-intercept of the graph of f ?
Page 4
1
2
3
4
5
27. Is the picture below the graph of a function?
6
28. Write out! the
" product (x − 2y) so that your final answer doesn’t include numbers that
n
look like k .
29. Graph id.
30. Graph f (x) = 4.
31. Graph x2 .
32. Graph x3 .
33. Graph x1 .
34. Graph
1
.
x2
35. Graph g : [−2, 1) → R where g(x) = x.
36. Graph h : {2, 3, 4} → R where h(x) = x2 − 3.
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.
27.
Page 6
28.
********************************************************************************
29. id
30. f (x) = 4
32. x3
33.
35. g(x)
36. h(x)
1
x
31. x2
32.
Page 7
1
x2