First Midterm Exam
Conics
For #1-8, match the numbered quadratic equations in two variables with
their lettered sets of solutions.
2
1.)y=x
=1
2
2.)x
3
D
A)
a)
c)
D.)
OA
2
3.)x
4.) x
2 +y
2
-1
2
5.) x
oE
—
2
y
6.) xy =1c
7.) x
=—1
2
2+y
8.) x
2
0
E.)
1
—
-
.!-
r-
I
t
-
P-
cD
03
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QD
II
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c
II
I
—
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-
cx
F
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00
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(.1%)
t—.-.’
II
-
*
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CD*
.
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-t-
Q
CD
C
•
yq
cJ1
0
•
CD
CD
t
1
4
4
Ii
I
‘—
I
—
a
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
cc
•
cc
16.) Find the product
/
4)
(2
3(2÷ ((-i
75 \
6)
3+
-a(-)+(-i)(z)J
i (-i)
17.) Give the determinant of
(‘t)(z)-(i)(-3 S-3)/
18.) Give the inverse of
—8 3
/s
Lc
(-3)-(-(i)
-
-i
/3
S
-I\
L}
/ -\
-
************************************************
Lines
19.) Give an equation for a line in the plane that has slope 4 and passes
through the point (0, 0).
20.) Give an equation for a line in the plane that has slope —2 and passes
through the point (6 5 1).
(-i-z()
21.) Give the slope of the line that passes through the points (3. 7) and
(5,1).
3-5
3
L
-z
-
22.) Give an equation for the line that passes through the points (3, 7) and
(5,1).
av5’(S:
3(3)
************************************************
Equations in One Variable
23.) Give the implied domain of the equation
(o,ac)
/
b€..ccws
rts
j’J€.
rosrhI.
4
2
1og(z)
—
3log (x) + 2
=
0.
1M
4
loja(ii
For #24-26, find the solutions of the given equations, and explain your
answers. #24-26 are worth 2 points each.
24.)
2
Iog(X)
3loge(x) + 2
—
0
jo(*)3+4
oyavi
--t-
-tov
tkeri
P Io()
;hi
/r# a b-3, c=2
3±JJ()(z)1
5o
1
I
,
3±J I
j
2(g)
3+j
L2’
6o-ik solu-t-iis.
-j4,,
37
a
—i ze
25.) (4x
—
5)2
=
3
v soi
cc €e’(
26.)
i(x+2)
x
=
b cause
a suar
€
2
ôt
bCcjiJS€
.ie ca
0.
i€(
1 kOY1lO)V1
mo
x(z÷i’)
,
soIwtor
LA.tior.
(x+z)2
5
50
so-f
iS
#kas
************************************************
Equations in two variables and their solutions
27.) Suppose p(x, y) = 3x
2 2xy + y —3. Find p o A(_l,
)(x, y). (You don’t
4
have to simplify your answer.)
—
-3
3(x--2(XI
#28-30 are worth 2 points each.
The “Cissoid of Diodes” is the set of solutions, S, of the polynomial equa
tion x
3 + xy
2 =y
.
2
28.) Give an equation for A(l,
)(S), the Cissoid of Diodes shifted right 1
2
and up 2. (You don’t have to simplify your answer.)
í7’ A,
21 (.s)
)
11
A(
S
I,
___________
6
+
D
-F
1
2
I)
z
c
l.A
/
.
0
;
—.
L
—
,<
I
‘I
cD
/4
C
0
ii
I
CD
—
CD
.
0
DQ
.
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CL)
CDCI)
CD
o
,—
.
lCD
c
lj
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T
+
0
o
CD
Cl)
CD
—
CD
Z
0
0
CD
0
CD
)
cc
Cl)
CD
0
—.
0
0
a
CD
,
0
.
-
CD
I
II
cc
—