Practice First Midterm Exam
Instructions: You have 50 minutes to complete the test every question
is worth one point, 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.
1.) y+3x
=0
2
2.) x
=
5
2
3.)y=3x
4.)y=
.)y=—
5
1
2
6.) y=2(x—3)
y
+0
2
7.)x
=
2
= 0 (Hint: factor
8.) x
and ‘use union of solutions)
—
/
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*
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*
*
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*
)
biD
.
.—
0
j
0
0
bo
.
cc
‘1
cD
cc
-
i=
c.s1
16.) Find the product
(2
—3) (_2
17.) Give the determinait of
18.) Give the inverse of
(39
(
)
4)
)
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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 (1,5).
3
21.) Give the slope of the line that passes through the points (1, —3) and
(—4,2).
22.) Give an equation for the line that passes through the points (1, —3)
and (—4,2).
Equations in One Variable
23.) Give the implied domain of the equation 197x
2 + 2x + log(x)
70,000.
4
=
T +
e
For #24-26, find the solutions of the given equations, and explain your
answers. #24-26 are worth 2 points each.
2 _4ex 5
24.) (e’)
25.) xlog(2x —3)
26.) \/7x
—
5
=
=
=
0
x where >
—3
a
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Equations in two variables and their solutions
27.) Suppose p(x, y) = 4xy 3y
2
don’t have to simplify your answer.)
—
—
2x + 7. Find p
o
A(lS)(x, y). (You
#28-30 are worth 2 points each.
The “Standard singular cubic” is the set of solutions, S, of the polynomial
equation y
3+
2 x
28.) Give an equation for 3
,
2
A(
)
(S),
_ the Standard singular cubic shifted
right 2 and down 3. (You don’t have to simplify your answer.)
6
29.) Let D
=
(3
.
Give an equation for D(S), the Standard singular
cubic scaled by 3m the x-coordinate and
have to simplify your answer.)
in the y-coordinate. (You don’t
-
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.)
x=y
7
First Name:________________________ Last Name:
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