Practice Exam 1
Name:
Instructions:
Give yourself 50 minutes to complete this practice exam.
Justify each answer.
Use the last two pages to record your answers.
Each answer has equal weight.
For # 1-3, decide whether the following sequences are either arithmetic, geometric, or
neither.
1.
5, 8, 12, 17, . . .
2.
1, −1, 1, −, 1, . . .
3.
5, 25, 125, 625, . . .
4.
What is the 68th term in the sequence 18, 25, 32, 39, . . .?
5.
What is the 10th term in the sequence 100, 150, 225, 675
, . . .?
2
6.
Write
4
X
(3i + 5) as an integer in standard form.
i=1
7.
Write
42
X
i as an integer in standard form.
i=1
8.
Write
200
X
32 as an integer in standard form.
i=1
9.
10.
What is the sum of the first 60 terms of the sequence 3, −3, −9, −15, . . .? (Your
answer should be an integer in standard form.)
What does the following sum equal: 16 + 6 + 94 +
27
32
+ ···?
11.
You have to wear formal attire for a fancy party. You own 3 jackets, 7 ties, and 5
pairs of shoes. How many different types of combinations can you wear?
12.
There are 60 guests at a costume party. You need to select one guest as the winner
of a costume contest, one as a runner up, and one as the worst costume. How many
different ways can you judge the contest?
13.
You work at a kennel that has 99 puppies. You need to decide to give each one a
distinct ID collar. How many different decisions can you make?
14.
You can buy 24 different kinds of bagels at a bagel shop. You need to choose 13
different types of bagels. How many different selections do you have to choose from?
15.
9
What is
? (Your answer should be a natural number in standard form.)
5
16.
If f (x) = x2 − 1 and g(x) = 4x + 1, then what is g ◦ f (x)?
17.
What is the implied domain of f (x) = 10x2 − 4x + 11?
18.
What is the implied domain of g(x) =
x2 + 9
?
5x − 2
Below is a graph of a function f (x). Use this graph to answer questions # 19 - 23.
19.
What is f (2)?
20.
What is the domain of f ?
21.
What is the range of f ?
22.
What are the x-intercepts of the graph of f ?
23.
What is the y-intercept of the graph of f ?
24. Is the picture below the graph of a function?
25. Write the product (2x − 1)3 using
the Binomial Theorem. Your answer should not
n
include numbers that look like
.
k
26. Graph id.
27. Graph f (x) = −3.
28. Graph g(x) = x2 .
29. Graph h(x) = x3 .
30. Graph f (x) =
1
.
x
31. Graph g(x) =
1
.
x2
32. Graph f : [−2, 2) → R where f (x) = x2 .
33. Graph g : {1, 2, 3, 4} → R where h(x) = x − 6.
1.
13.
2.
14.
3.
15.
4.
16.
5.
17.
6.
18.
7.
19.
8.
20.
9.
21.
10.
22.
11.
23.
12.
24.
**
25.
**
**
**
**
**
**
**
**
26. id
28. g(x) = x2
30. f (x) =
1
x
27. f (x) = −3
29. h(x) = x3
31. g(x) =
1
x2
32. f (x)
33. g(x)