Practice Second Midterm Exam
Instructions: You have 50 minutes to complete the test, every question
is worth one point, unless otherwise stated.
Conics
For #1-12, match the numbered quadratic equations in two variables with
their lettered sets of solutions. Worth point each. (Note: we will study 9
and 10 on Tuesday, the others you should know already).
1.)
2
= 1
4.)xy=l
2.) x
2 = 0
A
10.) y
2
—
y
0
—
2
5.)x
=
fri
=—1
2
7.)x
= 1
I
k
2
8.)y=x
J
3.)
1)
F
2+y
11.) x
2 = 1
E
2
2 = —1
+y
y
+0
2
6.)x
=
I
y
1
—
2
9.)x
=
C
12.)
= —1
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Trigonometry
13.) What is the distance between the points (3, —2) and (—4, 5)?
(3i)
(.2-5)q
14.) Find the length of the nnlabled side of the triangle below.
Z
7
32
N
3
15.) Find sin(8), cos(&), and tan(&) for the angle 9 given below. (3 points.)
g
‘5
2
16.) Find sin(O) for the angle & given below.
kUAJ
XiNNN
17.) Find cos(9) for the angle 0 given below.
/\\
6
Of
D
-36
-
18.) Find the length c shown below.
3
-
g
Cot,
19.) Write the vector (—3, 2) in polar coordinates. That is.
as a vector of the form r( cos(O), sin(O) ) where r 0.
write
(—3, 2)
Ii(-3,2)1. T
(c3L)
3
(
-3
—
/
—TI)
20.) Write the matrix that rotates the plane clockwise by an angle of
(Note: We’ll cover this on Tuesday).
I
1T
3
3
I3
27
3
3
)
1
4
Equations in Two Variables and Their Solutions
The Doub1e foliurn” is the set of solutions, S, of the polynomial equation
2+y
(x
.
2
) = 4xy
2
PoTS
21.) Give an equation for A(
,_l)(S), the Double folium shifted right 3 and
3
down 1.
-
)
3
A(
(
22.) Let D
by
( ).
(-3
A)
)
-
(x -3) (
i)
Give an equation for D(S), the Double folium scaled
in the x-coordinate and 4 in the y-coordinate.
(20
C
((‘x)
5
2.
2.
2.xf
2
************************************************
Planar Transformations
Shown below is a set S in the plane. (The x- and y-axes are not part of S.
They are just drawn for perspective.)
,i)(S)
2
23.) Draw A(_
F
:
24.) Draw
()
25.) Draw R(S)
(5)
-l
6
************************************************
Conics
For #26-28, Draw the set of solutions of the given equation in two variables.
(Label at least one point precisely in #26.)
26.) xy3
I.
28.) +4y21
27.) 2
+
x
=
16
y
4
4
1.
j
O)
.0)
vjuLwi
UA*ZAQJ (
(010)
************************************************
Trigonometric Functions
For #29-31, draw the graphs of the given functions
29.) sin(O)
31.) tan(O)
30.) cos()
I
/
4
IA!
iT/IT
a
—I
7
311
F/
************************************************
Equations in One Variable
The remailling questions are each worth 2 points. For #35-40, find the
so1utiois of the given equations. and show your work.
x —7)
log
(
32.) 2
x-i
4
D
X > 7
}
2
Lx=23)
3
2.? -7
33.)(2x_7)2=9
q (x
10
=
—4
[)
Q
8
-
A
i-I
—
Ix
2xL
2x=1O
34.) \/212
oR
-3
D
35.) 1og(x)+1og(x+4)=1og(4)
®
X >0
i x(x.4)\
-
X4x4
)
x
)
1
X(x+L
C
66
2
e
3
36.) (ex)
e
=
-.±
4
1
-2.zz.
3.4x+Z
3x+ x. 2.
(y
37.) =1
2
DH x
x,x-}
-
3x
(x +
4
—
-
X41
F
x.Z
2x
x
4
2.
L
.
(4ck9 e
X-3)(X4i)
- 2x
-3
************************************************
Extra credit
I will assign some (two or three) problems for extra credit. These will be
worth 3 points each, with no partial credit.
9
L .L.l
u
.1.
a1I1c.
---“--, ‘-
.
1.)
13.)
2.)
14.)
3.)
15.) sinO)
=
cos(8)=
4.)
tai(O)
5.)
16.)
6.)
7.)
17.)
8.)
18.)
19.)
9.)
10.)
20.)
11.)
12.)
10