First Midterm Exam
Instructions: You have 50 minutes to complete the test, every question
is worth oe oint, unless otherwise stated.
Equations in two variables
For #1-8, match the numbered equations (linear or quadratic) in two vari
ables with their lettered sets of solutions.
=
®
—
3.)x
=
2
0
y
4.)x=5
(
D
5.)y=
6.) y=2(x—3)
7.)y=—2x
I
I-i
B
F.
+0
8)x
=
2
y
(j
•
S
*
*
*
*
*
*
*
C
I—
C
*
*
Cl)
*
*
*
*
*
*
*
*
*
*
*
)
C
d
_-
bJD
C
C-;
i
—
cL
*
biJ
*
*
—
Ct
*
*
*
*
*
—
—
Li)
—
LCD
LI’
C
LCD
—
16.) Find the product
(3
+. Z
)( )
2-HO
-.7
2
17.) Give the determinant of
18.) Give t:e inverse of
(
4)
3
=
IS
(24
Lines
19.) Give an equation for a line in the plane that has slope 3 and passes
through the point (0, 0).
3x
20.) Give an equation for a line in the plane that has slope 4 and passes
through the point (—1, 45).
(I)
21.) Give the slope of the line that passes through the points (1, 3) and
(4, —1).
-
22.) Give an equation for the line that passes through the points (1, 3) and
(4, —1).
3
j-.
-(x.-i)
Equations in One Variable
23.) Give the implied domain of the equation 7x
2 + 2x +
[o nc)
J ot
/
4
cJ)
=
Lo, c)
_5ex + 4.
cvJ
For #24-26, find the solutions of the given equations, and explain your
answers. #24-26 are worth 2 points each.
_ex_6=O
2
24.) (ex)
±
e
25.) xloge(4x —5)
=
x where x>
x
-
40
e
S
26.)
i/3x
+5
=
—2
0
/
4
()
0
************************************************
Equations in two variables and their solutions
27.) Suppose p(x, y)
1oii’t ivc to simplify
=
2
xy 3y
answer.)
—
wiir
—
—
2x +7. Find po A(_i,
)(x, y). (You
3
2.
2,(x-D4
—
#28-30 are worth 2 points each.
9
The “Tacnode” is the set of solutions, S, of the polynomial equation
4
4
= x
+ y.
—1: : ::
28.) Give an equation for A(l,_
)(S), which is the Tacnode shifted right 1
2
aild down 2. (You don’t have to simplify your answer.)
o
:
2
(X—i)
6
pc-.
L)’
29.) Let D
=
( ).
Give an equation for D(S), the Tacnode scaled by
in the x-coordinate and 2 in the y-coordinate. (You don’t have to simplify
your answer.)
(51(3
(‘
r
4
(3X)
(x)
4
2..
30.) Give an equation whose set of solutions is the union of the Tacnode
= x
4 +y
4 and the horizontal line y = 0. (You don’t have to simplify your
answer.)
o
oc
j-
• (x
7
x-)
))