FirstFirst
Midterm
Exam
Practice
Midterm
Exam
C onics
Conics
: :
thenumbered
matchthe
For#1-8,
numberedquadratic
quadraticequations
twovariables
with
equationsinintwo
variableswith
#1-8,match
For
theirlettered
solutions. Worth point each.
letteredsets
setsofofsolutions.
their
1.)x2=_1
1.) x2 =
1
2
2.)x2 ==0
2.)
2==1 1
3.)x2x
3.)
4.)xyxy==1 1
4.)
=
5.)y y= x2
5.)
6.)x22
+
x
=
y
6.)
+ —1
y2 =
1
7.)x22
+
x
=
y
7.)
+ y 2O
=0
9
2
8.)x—y
8.)
x2 y 2 ==0
0
fi
1 1
•
************************************************
Linear algebra
For #9-15, give the vector, written as a ROW vector.
9.) A(−2,4) (3, −5)
1 0
0 1
−1 0
0 1
3
4
1 0
0 −1
−5
−2
0 1
1 0
3
4
3 0
0 2
−1
6
2 −4
−3 6
10.)
11.)
12.)
13.)
14.)
15.)
−1
8
3
−2
2
−2 4
−5 1
16.) Find the product
1 3
−2 3
2 8
17.) Give the determinant of
7 3
18.) Give the inverse of
3
8
−9 −20
************************************************
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).
3
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)
and (−3, 2).
************************************************
Equations in One Variable
23.) Give the implied domain of the equation 48x2 + 3x +
4
√
x = ex + 7.
For #24-26, find the solutions of the given equations, and explain your
answers. #24-26 are worth 2 points each.
24.) (ex )2 + 2ex − 3 = 0
25.) x loge (3x − 2) = x where x >
26.)
√
2
3
3x + 2 = −1
5
************************************************
Equations in two variables and their solutions
27.) Suppose p(x, y) = 2xy 5y 2
don’t have to simplify your answer.)
x + 11. Find p
A(2,
3) (x, y).
(You
#28-30 are worth 2 points each.
The “Folium of Descartes” is the set of solutions, S, of the polynomial
equation x3 + y 3 = xy.
9
9
S
28.) Give an equation for A(3, 1) (S), the Folium of Descartes shifted right
3 and down 1. (You don’t have to simplify your answer.)
/
6
7
✓1
◆
0
29.) Let D = 2
. Give an equation for D(S), the Folium of Descartes
0 4
scaled by 12 in the x-coordinate and 4 in the y-coordinate. (You don’t have
to simplify your answer.)
9
9
9
9
) (5)
3
A(
) (5)
3
A(
30.) Give an equation whose set of solutions is the union of the parabola
y = x2 and the line x = y. (You don’t have to simplify your answer.)
/
77
/
7
First Name:
Last Name:
1.)
14.)
First Midterm
Midterm
Exam
First
15.) Exam
2.)
C onics
Conics
3.)For
thenumbered
matchthe
numberedquadratic
quadraticequations
twovariables
with
equationsinintwo
variableswith
#1-8, match
For #1-8,
theirlettered
solutions. Worth
letteredsets
setsofofsolutions.
pointeach.
each.
Worth1 point
their
2
4.)1.)x2=_1
16.)
1.) x2 = 1
2
2.) x2 ==0
2.)
5.)
2 = 1
2
3.) xx
3.)
=1
6.)4.) xy = 1
4.) xy = 1
=
5.) yy= x2
5.)
7.)
2 —1
6.) x2
+
x
=
y
6.)
+ y2 =
1
2
2y
7.) x2
+
x
=
8.)
7.)
+ yO
=0
9
2
8.)x—y
8.)
x2 y 2 ==0
0
9.)
: :
17.)
18.)
19.)
20.)
10.)
21.)
11.)
22.)
12.)
23.)
13.)
8
fi
•