Math 1060
March 27, 2015
Exam 2
Answer all questions below. All questions are worth 1 point except where
otherwise noted. No cell phones, calculators, or notes are allowed (luring the
exam. If you are stuck on a problem, skip it and come back to it later.
UID:
Name:
Write your answers to 01-24 on tire answer sheet provided.
Conics
For #1—12 match tire numbered quadratic equations
of solutions. Worth point each.
1. y
2 .x
5.
=
9
9
—
y-
=
y
+1
2
x
=
6. 2
y
+0
:r
=
0
0
0
3
2
4.
zej =
7. r + y-
=
‘Hint:
9
8.2-
1
2
r
—
2 =
I
(z + y)Qr
—
y)
=
=
—1
—1
iii
two variables with their lettered sets
—i
2
9. x
10. y
2
1L
12.
=
1
Lines
13. Give an equation for a line, in the plane that bus slope 4 and passes through the point
(0,0).
14. Give an equation for the line in the plane that has slope —7 and passes through the
point (—2,5).
15. Give tile slope of the line that passes throngh the points (—3,6) and (4.2).
16. Give an equation for the line that passes through the points (—3,6) and (4,2).
Page 2
Trigonometry
17. What
is
the distance between the
points
(4, —1) and (—3, 5)?
18. Find the length of the unlabeled side of the triangle below.
3
19. Find tile length of the unlabeled side of the triangle below.
a2.
20. Find the angle 8 labelled
below.
Page 3
For #21-24, find wind(8) for tile given angles. You may use the pictures of the unit circle
that are attached to your answer sheet.
21. Find wind()
22. Find wind(t)
23. Find wind(—)
24. Find wind()
Page 4
Transformations of Solutions of Equations in Two Variables
The remaining questions are worth 2 points. The Folium of Descartes is the set of solutions,
S, of the polynomial equation
+ 3 = xy.
S
,_l)(S), the Folium of Descartes shifted right 3 and down 1.
3
25. Give an equation for A(
) (s)
3
A(
/1/2 oN
Give an equation for D(S), the Folium of Descartes scaled by
4
0
in the x-coordinate and 4 in the y-coordinate.
26. Let D
=
).
IL
\0
Page 5
Equations in One Variable
Find the solutions of the given equations and show your work. If an equation has no solution,
explain why. You do not need to simplify your answers.
(z
3
27. iog
—
28. (2x —5)
7)
=
=
16
4
Page 6
29.
30.
v’3x2
—
=
2
=
1
Page 7
UID:
Name:
14.
1.
2.
15.
3.
16.
1.
17.
5.
18.
6.
19.
7.
20.
21.
8.
9.
22.
10.
23.
21.
11.
25.
12.
26.
13.
Page 8
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