o
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).
2.) x
=
0 2 + y
=
—1 1.) x
=
1
4.)xy=1
7.) x
11.) x
9.) x
12.) xy=—l
6) N.
1

************************************************
Trigonometry
13.) What is the distance between the points (3, —2) and (—4, 5)?
14.) Find the length of the unlabled side of the triangle below.
3
15.) Find sin(8), cos(9), and tan(s) for the angle 0 given below. (3 points.)
8
15
2

16.) Find sin(9) for the angle 0 given below.
17.) Find cos(9) for the angle 9 given below.
S
18.) Find the length c shown below.
4
2
C
3

19.) \‘Vrite the vector (—3, 2) in polar coordinates. That is, as a vector of the form r( cos(&), sin(O)) where r > 0.
write (—3, 2)
20.) Write the matrix that rotates the plane clockwise by an angle of
(Note: We’ll cover this on Tuesday).
4

************************************************
Equations in Two Variables and Their Solutions
The LDoub1e folium” is the set of solutions, S, of the polynomial equation
22
21.) Give clowil 1.
an equation for A( Double folium shifted right 3 and
22.) Let D
=
( ).
Give an equation for D(S), the Double folium scaled by in the x-coordinate and 4 in the y-coordinate.
5

Planar Transformations
Shown below is a set S ill the plane. (The x- and y-axes are not part of S.
They are just drawn for perspective.)
24.)
Draw
( )
(S) 25.) Draw R(S)
I
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.) xy=3
28.) +4y2
1
I t —t———————4————+————
I
‘ I
I
-
************************************************
Trigonometric Functions
For #29-31, draw the graphs of the given functions
29.) sin(O) 30.) cos(8)
‘1
I iT
I I z..
I
-ii
I
!
31.) tan(O)
‘7,
I I I

Equations in One Variable
The remaiuiig questions are each worth 2 points.
For #35-40, find the solutions of the given equations, and show your work.
—
7)
=
4
33.) (2x
—
7)2
=
9
—
10
=
—4
8

35.) 1og(x) + 1og(x + 4)
= log(4)
36.) 2 =
4
37.)
=
1
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