Practice First Midterm Exam
Instructions: You have 50 minutes to complete the test, every question
is worth one point, unless otherwise st.ated.
Equations in two variables
For #1-8, match the numbered equations (linear or quadratic) in two vari
ables with their lettered sets of solutions.
H
1.)y+3x
=
2
0
2.)x=5
3.) y
=
0
2
3x
&
7
I
‘A
I-k
.)y=—
5
1
2
C.
6.) y=2(x—3)
+0
2
7.)x
=
y
B
2 y
8.) x
2 = 0 (Hint: factor
and use union of solutions)
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21.) Give the slope of the line that passes through the points (1, —3) and
(—4,2).
-3
-
I
-(-)
22.) Give an equation for the line that passes through the points (1, —3)
and (—4,2).
-() -1(x-r)
- (x-)
************************************************
Equations in One Variable
23.) Give the implied domain of the equation 197x
2 + 2x + log(x)
70,000.
=
t +
e
R
(
4
000
L)
(o,oo
(
o
(x
)).
0
-d
0
)
—
Q
-
0+
&J
—
0
o
cD
—
-
co
c”1c1
0
,
)o
Th
0
x’J
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a
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t
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x
c.L
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c:)
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0
Equations in two variables and their solutions
27.) Suppose p(x, y)
4xy
2
3y
A(i— dont have to simplify your answer.)
—
—
2x + 7. Find p
o
A(L_3)(x, y). (You
T
+
#28-30 are worth 2 points each.
The “StndarLsiugu1ar cubic” is the set of solutions, S, of the polynomial
equation
3 +
x
(S),
_ the Standard singular cubic shifted
28.) Give an equation for 3
,
2
A(
)
right 2 aild down 3. (You don’t have to simplify your answer.)
S
y),)
*
-
,
0
S
X—)x--Z
T
->
A (L- 3) S
‘
)-
29.) Let D
=
( ).
Give an equation for D(S), the Standard singular
cubic scaled by 3 in the i-coordinate and
have to simplify your answer.)
in the y-coordinate. (You don’t
‘1
[(,
3
poD x,y)
)
P
(rve 0
(
3
rt
(2
()3
(
30.) Give an equation whose set of solutions is the union of the concave
down parabola y = —x
2 and the line x = y. (You don’t have to simplify your
answer.)
Q
x=y
4X
Aa
04
D
0
7
bMA.
Qf(LQCAJVUJ
First Name:_______________________ Last Name:
14.)
1.)
15.)
2.)
3.)
16.)
4.)
17.)
5.)
6.)
7.)
18.)
8.)
19.)
9.)
20.)
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21.)
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22.)
12.)
23.)
13.)
8