Practice Test Midterm 1 (1050-005)
Ntniir;
1.
(it)
ID: U
3 point 1ff: R —R aiidg :i —*R r: lunctioiis (1(tfnu(1
y
g(x)
(b)
()
—
2 poilits
[
)1
0111t5
Ix g tb
fliii find
fog and q of.
i1ivrs of
f?
Fiiid the doniaiii and
f(a)
=2F —1
and
Lxphiin iH itbur case.
rLie
1 1ie lhllowing fiuie inn given b its
LJ
gr1J)h.
2.
(a)
(b)
5 points Lut
Vnhii( of x.
f
: R
-
R 1w a
Find flw iiiipimd
3 points
fnhl(tjon
(lonliun
siwli that
of tli(
hIil(-tion
fnnution.
(u)
15 points
Ciru
tii graph of
f(x)
us
bolow
iiuid
f(/
f(.)
—
1)
=
3 and
2x + 1
uiid
tin graph of
y
-4
(a)
f(:u
--
1), (1
-3
) f(r) + 1, ()
-2
x
f(2x) and (d) —2f(x)
Pagv 2
2
f (3)
thou
=
2. Thn find flic
find fin iuivrs of th
3. (a) 2 points What is the 8th number of the sequence 2000, 200, 20, 2, . . . ?
(b) 5 points Find the sum of first 53 terms of the sequence 140, 137, 134, 131, . . . .
(c) 5 points Find the sum of all terms of the geometric sequence 1,
1 1
2, 4,
1
8, . . .
(d) 5 points Suppose that you expect to pay $400 for gas for your car next year, and that each year
after that you plan your yearly gas expenditures will increase by $20. How much will you spend on
the gas in the next 8 years?
Page 3
4. (a) 5 points Suppose you are on boat with 10 people. The boat is sinking and there is only one lift
raft that seats 6. How many di↵erent options are there for which 6 people to put in the raft?
(b) 5 points 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 di↵erent flavor on top of that, and a third
di↵erent 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 di↵erent sundaes can you make?
5. (a) 5 points How many 5 digits numbers can be formed using the digits 1, 2, . . . , 9?
(b) 8 points Find the values of
expand (x
1)4 .
✓ ◆ ✓ ◆ ✓ ◆ ✓ ◆ ✓ ◆
4
4
4
4
4
,
,
,
,
and then use the Binomial Theorem to
0
1
2
3
4
Page 4
6. (a) 2 points (True/False) x = 1 is a root of the polynomial 7x5 + 13x4
explanation for your answer.
(b) 5 points Solve the inequality for x:
(c) 5 points Divide:
6x5 + 5x4
12
3
x
2x2 + 50x
x 3
24
13
Page 5
3x3
7x2
9x
1. Give an
7. (a) 5 points Compute the discriminant of the quadratic x2 + 2x 1. Decide how many distinct real
roots does it have if there is any and then find the root(s) if exist.
(b) 7 points Suppose you shoot a feather straight up into the air, and that t is the time measured
in seconds that follow after you shoot the feather into air. If the height of the feather at time t is
given by 2t2 + 20t feet, then what is the maximum height that the feather reaches? How many
seconds does it take for the feather to reach its maximum height?
8. 10 points (Bonus Problem) How many 3 digits number can be formed using the digits 0, 1, 2, . . . , 9
Page 6
3. (a) 2 points What is the 8th number of the sequence 2000, 200, 20, 2, . . . ?
(b) 5 points Find the sum of first 53 terms of the sequence 140, 137, 134, 131, . . . .
(c) 5 points Find the sum of all terms of the geometric sequence 1,
1 1
2, 4,
1
8, . . .
(d) 5 points Suppose that you expect to pay $400 for gas for your car next year, and that each year
after that you plan your yearly gas expenditures will increase by $20. How much will you spend on
the gas in the next 8 years?
Page 3
4. (a) 5 points Suppose you are on boat with 10 people. The boat is sinking and there is only one lift
raft that seats 6. How many di↵erent options are there for which 6 people to put in the raft?
(b) 5 points 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 di↵erent flavor on top of that, and a third
di↵erent 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 di↵erent sundaes can you make?
5. (a) 5 points How many 5 digits numbers can be formed using the digits 1, 2, . . . , 9?
(b) 8 points Find the values of
expand (x
1)4 .
✓ ◆ ✓ ◆ ✓ ◆ ✓ ◆ ✓ ◆
4
4
4
4
4
,
,
,
,
and then use the Binomial Theorem to
0
1
2
3
4
Page 4
6. (a) 2 points (True/False) x = 1 is a root of the polynomial 7x5 + 13x4
explanation for your answer.
(b) 5 points Solve the inequality for x:
(c) 5 points Divide:
6x5 + 5x4
12
3
x
2x2 + 50x
x 3
24
13
Page 5
3x3
7x2
9x
1. Give an
7. (a) 5 points Compute the discriminant of the quadratic x2 + 2x 1. Decide how many distinct real
roots does it have if there is any and then find the root(s) if exist.
(b) 7 points Suppose you shoot a feather straight up into the air, and that t is the time measured
in seconds that follow after you shoot the feather into air. If the height of the feather at time t is
given by 2t2 + 20t feet, then what is the maximum height that the feather reaches? How many
seconds does it take for the feather to reach its maximum height?
8. 10 points (Bonus Problem) How many 3 digits number can be formed using the digits 0, 1, 2, . . . , 9
Page 6