Practice First Midterm Exam
Conies
For #1-8, match the numbered quadratic equations in two variables with
their lettered sets of solutions.
=—1
2
1.)x
=O
2
2.)x
2
3.) x
=
1
4.) xy
=
1
5.) y
A
D
C
=
6.) x
2+y
2
=
—1
7.) x
2+y
2
=
üç
— y2
=
0
8.) x
2
:
:)
E
1
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
C)
o
—i
*
*
*I.
C
-
C)
C
cc:3
C)
C
C)
-
-‘
—
5.—.—-
+
Ifi
I.
5
‘—
j
LD
I
C
.—
bC
-‘
LCD
d
:1:1:
C
I
I
I
I
÷
-o;
— o
S.—,
°
—‘
0
•O
—4
,.
—
Li
II
aD’
‘—S.’
I
‘—5--’
‘I
‘.5.—’
0
VI
0
-
7
I
--..?)
—
—
—
‘—S.--’
CDD
“-.—‘
‘I
‘S.5-’
0
0
I
I
-
—
-.__i_c-I
-._../
I
-6
I
+.
4.
5
-• 0
—
ii
0
0
‘
$
—S.-’
ii
—
,_—
‘—4
‘1-
vii
‘I’
0
a
l4
-
H
c-I
,z.
ii
—2’
______%
-
ø
<
,______5_S.
I
‘—.‘
-
+
\Q
1.
—5-
—S.
‘J’
-
jI1
I
I
I
—.4
LCD
(- z
16.) Find the product
(i)(5) + (3)(-z)
(-z’)(i)
Jo
(z)(3)
—
((7
18.) Give the inverse of
I e+rw vcvt
()
/3
—
c_u
-5o
8
—20
i5
1
-O+72 =12.
/-20
-8
—2.0
3
q
,oiI
i
Lines
19.) Give an equation for a line in the plane that has slope —6 and passes
through the point (0,0)
20.) Give an equation for a line in the plane that has slope 3 and passes
through the point (4, 8).
(-8)
3
(Lf)(3)
O)(’)+ (3)(3)
-212
17.) Give the determinant of
+
21.) Give the slope of the line that passes through the points (2, —4) and
(—3,2).
22.) Give an equation for the line that passes through the points (2, —4)
efYt ooa a15vJYS Iwxe. Y
’L
0
and (—3,2). Tlee ace two
a(- -o i’j€. oye. O
QUs-
pot (z,-
(-€(x-z’)
(+)-g(x—2)
-[e
?0
(-a)= -g(-C-3)
(-3,2.’)
‘s
************************************************
Equations in One Variable
23.) Give the implied domain of the equation 48x
2 + 3x +
ovy
it’s
s
yo-t
uace root
to
ney-l-we. 7i&s, -l- I?\;d
[o,oo’).
4
=
eX + 7.
o.
cIowaei
For #24-26, find the solutions of the given equations, and explain your
answers. #24-26 are worth 2 poillts each.
2 +
24.) (ex)
an
2ex
—
©T
3= 0
1
irpIie.& aowia’w is
becas
aV%y flAWilo(V
I e—3,
-en
ace no oLcton
use e.” can Ony
Ci
placcJ iv aepontit
uatioY in ?,
9
or
.
oc +Iie. 4wi a-(e’)
+ b(ei+c Q.
2
oL,ba,a’4 c—3. Tlie 0
yi3
d;
w
;
E.7cLton
1
J-I€e..
Since i
x
-roi e
iS
are -two
e?’ -a-Ji
-
I.
SOh.ttioYS
-2-
-
—
is
posH-k.
2
-2+
a
z= Ia e(’)
Tkcecore, x=O
-ile onI o ufon
(e)+ z() —3 0
Z
eXr
()Z
1
X
E.c
k
0Y_
—
—
be postiie.
3
—)
no soLtor,
2(ez)O
eI
25.) xlog(3x
—
2) =
x
where x>
Sce
know
v.Ie can
x0.
Na-tc..
dnJ€
syct
Joe2
0..
Is
e’e
3)+2
dr2
I
A
sce yôok
c.onwt ,e
So1wth9j.
Tececo’rL,
+Iie.
ho%’Je to
y’
2+
Sovie
&c1L.4cL
xaw,
y€-t-ie.
yu wIc(nj-
Zrft so niiack
2S, 6u.1- y .woi.a.1cI n€ea
ecp\ovia+’on. 7l.e asvu.cs a-e bo€cJ.
5
ceJ..
s
5.Cton
okd1oy.
) ?
26.) /3x+2=—1
—
e”cD,
uaHon.
3z-Z
e+2
1hot
It’s
1b
{
-l-i€
1
e+i
Equations in two variables and their solutions
27.) Suppose p(x,y) = 2xy 5y
2
don’t have to simplify your answer.)
—
)
3
p oA(
—
x + 11. Find po 3
,
2
A(
)
(x,y).
_ (You
(x+2,-3)
2 (-* 2 ( —3) -5 ( -s) - (x+ 2) ÷ I I
#28-30 are worth 2 points each.
The “Folium of Descartes” is the set of solutions, S, of the polynomial
equation x
3+y
3 = zy.
S
28.) Give an equation for A(
,_l)(S), the Folium of Descartes shifted right
3
3 and down 1. (You don’t have to simplify your answer.)
‘-
)(s)
3
A
11
S
,A(
3
)(s)
34 3
A(
A
,
g)
(t3)(x3(r)
6
29.) Let D
=
( ).
Give an equation for D(S), the Folium of Descartes
scaled by in the x-coordinate and 4 in the y-coordinate. (You don’t have
to simplify your answer.)
9
5
D(s)
_fz o\
-o }
D(5)
;3
()÷ ()= (2x’Xt)
30.) Give an equation whose set of solutions is the union of the parabola
2 and the line x = y. (You don’t have to simplify your answer.)
y=x
is
e.juva(evt
-10
is
eiaeyk
0
/
c
!ot€’.
axe
(j. -xi’) x
-Fe
(Z)()j
o.\so
1AvOfl
O
-
y’) =
s
4€
n
avid
- Ine.
(_z?rx)o, ayd
30. ‘(ou
as’J5
ov a ac.-t7
u.c1-
oye
First Name:
Last Name:
1.)
14.)
(—3, 12’)
15.)
(
2.)
A
3.)
0
4.)
C
16.)
5.)
13
17.)
F
18.)
ii,zf)
—50
6.)
7.)
8.)
19.)
9.)
(i, -i)
20.)
10.)
(—L,
21.)
(8)=3(x-f)
—
(‘t)-€.g.(x-2)
11.)
(-3,
/‘2.)
12.)
(-s,z’)
(
13.)
(tj.,3)
/
or
(‘.-z) (x÷3)
[,oo)
23.)
o decent
422.
There
I3o1i a’Ce jct+e oo’Je.
Ov
+\le
us*
actua
jyte.
excw,
oe
o
yd
+1w