Guys! Here's a very nice scan of the Math handout thingies for the perio 8D. It's very long =)). 25 pages. Good luck 8D.

1. I •
Practice Set 1 Parabola parts dlmgutierrez
OassID _ N~e _ Date _ SCore _
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ..
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Give the focus, directrix, and axis for the parabola. A)&e> ~Ird ~t P)'IMD'ro- CbCls I eq.Vll{"tilOV1. .'
1) x2 = 16y Ve"b'tes . etc. 1) _
A) (0,4), Y= -4, y-axis B) (4,0), x = 4, x-axis
C) (4,0), Y= 4, y-axis D) (0, -4), x = -4, x-axis
1
2) _--x2 =Y 2) :.
40
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A) (-20,0), x = 10, x-ct*is B) (0, -10), y = 10, y-axis
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A) o} x ;6' x-axis 6 ~,x-axj,
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1~ 4) y2 = -12x 4)
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.q A) (3, 0), x = -3, x-axis B) (-3,0), x = 3, x-axis
;~~ C) (0, -3), y= 3, y-axis D) (-3,0), Y= 3, y-axis
..
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5) (x + 2)2 = -28(y - 5) 5)
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A) (-2, -2), y= 12, x =5 B) (-2, -2), y = 12, x = -2
.: C) (-2, -2), y = 12, x = 6 D) (-9,-2), Y= 12, x = -2
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~., 6) (y - 5)2 = -4(x + 4)
A) (-5,4), x = -3, Y= 5
6)
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.• B) (-5,5), x = -3, Y= -4
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7) (y - 2)2 = 20(x - 3) 7)
A) (7,3), x = -3, Y= 3 B) (2, -2), x = -8, Y= -2
C) (8,2), x = -2, Y= 2 D) (-2,2), x = 8, Y= 2
8) (x + 4)2 = 4(y - 2) 8)
A) (2, -3), y= -5, x = 2 B) (4, -1), v= -3, x = 4
C) (-4,1), x = 3, Y= 2 D) (-4,3), Y= 1, x = -4
1

2. ··.
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Practice Set 2 Parabola equations dlmgutierrez
OassID _ Name _ Date _ SCore _
I.. ...
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MULTIPLECHOICE. Choose the one alternative that best completes the statement or answers the question.
Write an equation for the parabola with vertex at the origin.
"
1) Focus (5, 0) 1)
A) y2 = 5x B) y2 = 20x C) x2 = 20y D) x2 = 5y
2) Focus (0, 9) 2)
A) y2 =9x B) y2 = 36x D) x2 = 36y
3) Through (-7,7), opening to the left 3)
i
A) y2 = -7x ~ B) x = .ly2 C) x = -7y2 D) x2 = 7y
~' 7 1
4} Through (7,6), opening to the right 4)
36 36 49 36
A) y2 = - -x B) x = _y2 C) x 2 =-y D) y2=-x
7 7 6 7
5) Through (-J7, 7), opening upward 5) , .
A) y = 7x2 B) y = x2 C) x = -J7 y2 D) x = y2 I .
7 I
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6) Through (5, -10), opening downward 6) r,',
'2 _ 5
A) x = - _y2 B) x2 - - -y D) Y =lx2
5 2 5 I'.
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7) Through (6, -6~), symmetric with respect to the x-axis 7)
I::::'
A) x = 36y2 B) x = ~y2 C) y2 = 36x D) x2 =--J6y (:',
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8) Through (6,6), symmetric with respect to the y-axis 8) 1'-:
,.
A) x2 = 6y B) Y = 6x2 C) x= -6y2 D) y2 = 6x t ..
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I
Write an equation for the parabola.
9) vertex (4,10), focus (4, 12) 9) _
A) 2(y - 10) = (x - 4)2 B) (y - 10)2 = 8(x - 4)
I.
C) Y - 10 = 8(x - 4)2 D) 8(y - 10) = (x - 4)2
10) vertex (7, -9), focus (10, -9) 10) __
A) (x - 7)2 = 12(y + 9) B) x - 7 = 3(y + 9)2
C) (y + 9)2 = 12(x - 7) D) l(x - 7) = (y + 9)2
4
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1

3. I,
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11) vertex (-3,4), focus (-14,4)
11) I
A) x + 3 = -44(y- 4)2 B) x + 4 = -14(y - 3)2 !
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q -44(x - 3) =: (y + 4)2 D) (y - 4)2 = -44(x +3) I
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12) vertex (-5, -9), focus (-5, -13) ~. I
•• •• 12)
A) (x - 5)2 =: -52(y - 9) B) (x + 5)2 =: -16(y + 9)
q 16(y - 5) =: (x - 9)2 D) 16(y - 9) =: (x - 5)2 !
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13) vertex: (-4,4), directrix: y = 11 I
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13)
A) (x + 4)2 =: -28(y - 4) B) (y + 4)1 =: 8(x - 4)
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q (x + 4)2 =: -28(y + 4) D) (y + 4)2 = -28(x - 4)
14) vertex: (2, -4), directrix: x = 10
14)
A) (y - 2)2 =: -32(x + <U::t B) (x + 4)2 =: -32(y - 2)
q x2 =: -32(y - 2)",' D) (y + 4)2 =: -32(x - 2)
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4. Pfc]'cti~ Set .3 Ellipse and graphs
'. 'dassID Name _ Date, _ SCore _
----
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the ellipse. ,!
,
x2 v2 1) _
1)-+"'- =1
36 4
y
x
A) B)
y y
10 10
5 '
-10 -5 5 10 x -10 x
10
-5
-10 -10
C) D)
y y
50 50
-50 50 x x
-50 50
-50
1

5. '.
x2 v2 2) _
2)-+"'- '=1
16 25
y
x
A) B)
, y
10
50
5
-50 50 x -10 10 x
-5
-50
-10
C) D)
-50 50 x
-10 -5 5 10 x
-10
2

6. "
3) 4x2 + 64y2 = 256 3} _--:-_
y
10
5
-10 -5 5 10 x
-5
-10
A} B}
y y
I':
.~.
10 10
5
-10 -5 5 10 x -10 -5 5 10 x
-5
-10 -10
C} D)
y y
10 10
5
-10 10 x -10 10 x
-5
-10 -10
3

7. · '
4) 49x2 + 9y2 = 441 4)
-.
y
10
5
-10 -5 5 10 x
-5
-10
A) B)
~' y y
10 10
5
-10 10 x -10 -5 5 10 x
-5
-10 -10
C) D)
y y
10 10
-10 -5 5 10 x -10 -5 5 10 x
-10 -10
4

8. '. 5) (x + 1)2 + (y + 3)2 = i
4 9
5) _
y
10
5
-10 -5 5 10 x
-5
-10
A) ~ B)
y y
10 10
5
-10 -5 5 10 x -10 -5 5 10 x
-5
-10
C) D)
y y
10 10
5 5
-10 -5 5 10 x -10 -5 5 10 x
-5 -5
-10 -10
5

9. '"
(x + 1)2 (y - 1)2 =1
., 6)
16 + 9
6) _
y
10
5
••
-10 -5 5 10 x
-5
-10
A) B)
y
10
5
-10 5 10 x -10 -5 5 10 x
-5 -5
-10 -10
C) 0)
y y
10 10
5 5
-10 -5 10 x -10 -5 10 x
-5
-10 -10
6

10. Practice Set 4 Ellipse parts dlmgutierrez
OassID _ Name _ Date _ SCore _
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question .
••
c.: ',
Write an equation for the ellipse. .
....
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1) center at origin; length of major axis 10; y-intercepts ±4 1) _
x2 v2 x2 v2 x2 v2 x2 v2 1 I' ' :
A) - + ...£.- = 1 B) - + ...£.- = 1 C) - + ...£.- = 1 D) -+...£.-= I',
5 4 16 25 4 5 25 16
2) foci at (-2,6), (-2,0); major axis length of 10 2) _
(y - 3)2 (x - 2)2 1 (x - 3)2 (y - 2)2 _
A) 25 + 16 B) 16 + 25 - 1 r ....
C) (y - 3)2 + (x + 2)2 = t D)
(x - 3)2
25 +
(y - 2)2 _
16 - 1
r •
>
25 16', 1 " •
I"
: "
3) minor axis from (-5, -4) to (-1, -4); major axis from (-3, -8) to (-3,0) 3) _
I'
(x - 2)2 + (y - 4)2 _ (x - 3)2 (y - 4)2 _ r
A) 4 16 - 1 B) 4 + 16 - 1
C) (x + 4)2 (y + 3)2 = 1 D) (x + 3)2 (y + 4)2 = 1
4 + 16 4 + 16
4) eccentricity ~; foci at (3, 0), (-3,0) 4) _ ','
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x2 v2 x2 v2 x2 v2 x2 v2
A) -- + ..I.- = 1 B) -- + ..I.- = 1 C)-+..I.-=1 D) - +..1.-= 1 i..:
,.
9 16 16 9 16 25 25 16 I.'
5) foci at (0, 9), (0, -9), through the POin{I' 41~J 5) _
x2 v2
~+L- -
A) 1600 1681 1
B) - +..1.-= 1
40 41
x2 L x2 ..E.-
C) 1681 + 1600 = 1 D) 41 + 40 -1
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: -Practice Set) Hyperbola and graphs
Class ID _ Name _ Date _ Score _
'.;
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the hyperbola. ':"
x2 i!:.. !
'.
1) 25 -'4= 1 1)
I'
y
10
I
f'
5
I .
f:
i.'
-10 -5 5 '" 10 x
-5
-10
A) B) ' ..
r.·
y
10
t:
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r
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-10 -5 5 10 x
l",
t
r
C) D)
y y
10 10
5
-10 -10
,.
1
,
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12. ",
x2 v2
2) --...1..-= 1 2)
9 36
y
10
'.'
"
5
'.
-10 -5 5 10 lC
-5
-10
A) '~'.
B)
-10 ro x -10 10 x
<:;
",:'
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:':'1
~~
":,
~.~~
.. C) D)
y y
,..
, .~. 10 10
'~:..~
. . ,~
5
t::,'1
.: ':
x -10 -5 5 10 x
-10 -10
2

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3) (x - 3)2 _ (y + 2)2 = 1
3)
.:
25 36 ,
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y l,
10
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t,;
-10 -s S 10 l(
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-5 L
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l:
-10
r
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A) B) r
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y
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y I
10
I
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r.
f
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-10 10 x -10
-10
C) D) "
~
:
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5
t
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~ -10 -5 5 10 x
~
;:~ -5
~
1.
-10
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3

14. 4) (y + 3)2 _ (x - 2)2 1 4) _
25 49
r
y
10
5 ,
i
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·10 ·5 10 l(
I :.
·5
I':
r:
~:
:.::,'
·10
A) B)
y
':', '
10
·10 ·5 10 x
·5
·10
C) D)
y
10
5 5
·10 ·5 5 10 x ·10 ·5 5 10 x
·5
·10
','
4

15. .•
5) 4y2 - 25x2 = 100 5) _
y
10
5
••
·10 ·5 5 10 x
·5 I
.'
.10
.'
.-::
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A) B) I
y <r~ y
10 " 10
"
5 5
.'.
·10 ·5
·5 ·5
·10 ·10
C) D)
",
:.......
·10 ·5 10 .X ·10 10 x
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5
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16. I
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4.
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..
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6) 16x2 - 4y2 = 64 6)
y
10
I,
-,,:. I:
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1',
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..
1...
·
-10 -5 5 10 x
.. ;
-5
',": -10
A) B)
y
10
,
f
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-10 10 x x
-t
"
,.
-10
C) D)
y
10
-10 10 x -10 -5 10 x
-5
-10
6

17. Practice Set 6 Hyperbola parts dlmgutierrez
OassID _ Nmme _ Oate _ Score _
"
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
. :,,' Find the center, foci, and asymptotes of the hyperbola .
x2
1)9- 16 = 1
r.. 1) _
4
A) C: (0, 0); F: (0, -4), (0, 4); A: y = IX, Y = - x
3 3
B) C: (0,0); F: (0, -4), (0,4); A: y = "4x, y = -"4x
~ 4 4
C) C: (0,0); F: (-5,0,,:-<5,0); y
A: = IX, Y= -"3x
3 3
0) C: (0,0); F: (-5, 0), (5,0); A: Y = "4X, Y = -"4x
r.. ~-
2) 36 - 64 - 1 2) _
4 4
A) C: (0, 0); F: (-8, 0), (8, 0); A: Y = IX, Y = - IX
- 3 3
B) C: (0,0); F: (0,-10), (0, 10);A: y = "4x, y = -"4x
3 3
C) C: (0,0); F: (0, -8), (0,8); A: y = "4x, y = -"4x
4 4
D) C: (0,0); F: (-10, 0), (10,0); A: Y ="3x, Y = -"3x
3) (x + 3)2 _ (y + 3)2 = 1 3) _
9 16
3 3 3 21
A) C: (-3, -3); F: (-3, -8), (-3, 2); A: y = 4x - "4' Y = - "4x + T
4 4
B) C: (-3, -3); F: (-8, -3), (2; -3); A: y ="3x + 1, y = -"3x - 7
16 7 16 7
C) C: (-3, -3); F: (-7, -3), (1, -3); A: y = TX +"3' y = - TX +"3
16 1 16 7
D) C: (-3, -3); F: (-3, -7), (-3, 1); A: Y = TX -"3' y = - TX +"3
....
....
1

18. (y - 4)2 (x + 1)2 _ 1
4) 400 - 225 - 4) _
16 8 16 8
A) C: (-1, 4); F: (-11,4), (19,4); A: Y = 9x - 45' Y = - T" - 45
4 16 4 8
B) C: (-1, 4); F: (4, -21), (4, 29); A: Y=3"x -3' Y= - 3"x-3"
4 16 4 8
q C: (-1, 4); F: (-1, 29), (-1, -21); A: Y=3"x +3' Y = - 3"x +3"
16 16 16 8
D) C: (-1, 4); F: (4, -11), (4, 19); A: Y = 9x - 45' Y = - 9x - 45
5) x2 - y2 = 8 .'I"t 5) _
A) C: (2, 2); F: (4, 0), Ct- 0); A: Y = 2x, Y = - 2x
B) C: (0,0); F: (4,0), (..:..'4,0); Y = x, Y = - x .
A:
q C: (0,0); F: (4,0), (-4, 0); A: Y =2x, Y = - 2x
D) C: (0,0); F: (2,0), (-2,0); A: Y = x, Y = - x
2

19. Practice Set 7 Hyperbola equations dlrngutierrez
OassID _ Nmne _ Date _ Score _
..
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write an equation for the hyperbola.
1) vertices at (2, 0), (-2, 0); foci at (6, 0), (-6, 0) 1) _
x2 i!:... x2 i!:... x2
C)--..L-=l
v2 x2
D) __
2
v
..L-= 1
A) 36 - 4 = 1 B) 4 -36 = 1 32 4 4 32
2) vertices at (3, -5) and (9, -5), passing through the point (-6,9) 2) _
(x - 6)2 (y + 5)2 (x - 6)2 (y + 5)2 1
A) 9 - 196 ~l= 1 B) 9 - 331
- -
15 ~ 15
(x - 6)2 (y + 5)2 _ (x-6)2 (y+5)2
C) 331 - 9 - 1 D) 196 - 9 =1
15 15
3) vertices at (0, ±4), asymptotes at y = ± ~ x 3) _
A) v2
-L- __
x2 = 1 .E - ~- -1 .E_ x2 _ v2
D) ..L- __x2 = 1
144 16 B) 16 36 C) 16 144 - 1 36 4
4) vertices (-4, -5), (-4,9); eccentricity ~ 4) _
(y + 4)2 (x - 2)2 = 1 (y - 4)2 (x - 2)2 = 1
A) 9 - 49 B) 49 - 9
(y - 4)2 (x + 2)2 = 1 (y - 2)2 (x + 4)2 =1
C) 49 - 9 D) 49 - 9
.
:'
5) center at (6, -13); focus at (6 - yJiO, -13); eccentridty ~ 5)
,',
•.
.
"
A) (x + 6)2 _ (y -13)2
81 9
=1
B) (x - 6)2 _ (y + 13)2
9 .81
=1
C) (x + 6)2 _ (y -13)2 (x - 6)2 (y + 13)2
=1 D) 81 - 9 =1
9 81
1

20. ·.
Practice Set 11 Limits algebraic functions dlmgutierrez
Class ID _ Name _ Date _ Score _
•..
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the limit, if it exists.
1) lim x2 - 2x - 15 1)
x--5 x+3
A) -8 B) Does not exist C)5 D)O
x3 + 12x2 - 5x
2) lim 2)
x--O 5x
".
" " B) Does not exist
A)5 C) -1 D)O
3) lim x2 + 2x - 80 3)
x -- 8 x2 - 64
A)O
B) 2.. C)--
1
D) Does not exist
8 8
x4 -1
4) hm --
x-I
4) ,'.
x--l
,
A)2 B) 4 C) Does not exist D)O
2
5) Hm 5) _ . "
....
h--O ,J3h+4 + 2
A) 1/2 B) Does not exist C)2 D)1
7x + h
6) lim 6) _
h-» 0 x 3(x - h)
A)~ B) Does not exist C) 7x
x4
(x + h)3 - x3
7) !im 7) _
h--O h
A) 3x2 + 3xh + h2 B) a C) Does not exist D) 3x2
~-1
8) lim 8) _
x--O x
A) Does not exist B) 1/2 C) 1/4 D)O
(l+h)1/3- 1
9) lim 9)
h--O h
A) 1/3 B) 3 C)O D) Does not exist
1
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21. r., -:
1._
....
r·',:
Practice Set 12 One-sided limits: special pc-wise defined functions dlmgutierrez
f<
I.'.·,
i,
Class ID _ Name _ Date _ Score _ l',l' ,
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
A
Use the graph of the greatest integer function y = l J to find the limit.
x
1) lim lx J 1) _
x-2- x
2) lim lxJ 2) _ I'
x-2+ x i.:
3) Iim [ 3x 1
'r
3) _ i'
I,
x-0.5- r
" "
I,
4) lim [3x] 4) _
x-O.5+
,
5) lim lx/3 ] 5) _
"
,-"
x-0.5+
I>
i: '
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6) lim [x/3 ] 6) _ r
,'< ',',
x-0.5- 1
r'"
Find the limit.
;]
7) lim lzl 7) _
:4 x--'O+ x
J
8) Jim
lz.l 8) _
x
x-O-
9) lim h=1l 9) _
x--.2+ x-2
,
,
f '
10) Jim ~ 10) _
x-2- x-2 j".
f' ,
r',
11) lim ~
f"
11) _
2-x
x-2+
12) lim ~ 12) _
2-x
x-2-
13) lim CX-3{J::~lJ 13) _
x-+-1-

22. Practice Set 13 One-sided limits: concepts dlmgutierrez
Class ID _ Namc _ Oate _ Score _
"
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) Given lim f(x) = LI, lirn f(x) = Lr, and Ll '" Lr, which of the following statements is true? 1)
x-+O- x-+O+
1. lim f(x) = L)
X-+O
II. lim f(x) = Lr
x~O
III. lim f(x) does q.~t exist.
x~O .'.'
A) III B) none C)IJ 0)1
2) If lim f(x) = L, which of the following expressions are true? 2)
x~O
1. lim f(x) does not exist.
x~O-
II. lim f(x) does not exist.
x-+O+
III. lim f(x) = L
x~O-
IV. lim f(x) = L
x~O+
A) III and IV only B) I and IV only C) I and II only D) II and III only
3) If lim f(x) = 1 and f(x) is an odd function, which of the following statements are true? 3) _
x~O-
1. lim f(x) = 1
x~O
II. lim f(x)=-1
x~O+
III. lim f(x) does not exist.
x~O
A) II and III only B) I and III only C) I and II only D) 1, II, and III
4) If lim f(x) = 1, lim f(x) = -I, and f(x) is an even function, which of the following statements are 4)
x-+l- x~l+
true?
I. lim f(x) = -1
x~-I-
II. lim f(x) = -]
x~-l+
III. lim f(x) does not exist.
x~-l
A) I, II, and III B) I and III only C) I and II only D) II and III only
1

23. ..Practice Set 14
"
Infinite limits dlmgutierrez
Class ID _ Nrume _ Date _ Score _
..
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question .
..'.
Find the limit. Write the equation of the vertical asymptote/s, if any.
1
1) Hm 1)
x~-2+ x+2
'
A)-oo B) -1 C) 0 D) 00
':'".
4
2) hm 2 2)
x --->- x - 9
-3- 'rt
A) -00 B) 00 C)O D) -1
x2
3) lim --- 3)
x --->- 2
0+ x
A) 00 B)-oo C) Does not exist D)O
x2 - 5x + 4
4) lim 4)
x --->-
1- x3 - x
.~'.
:', 3
A)-oo B) 0 C)-- D) 00
2
I.
I
I
x2 - 3x + 2 I,
5) lim 5)
x--->-O x3 - x
I.
-I
I
A)2 B) 00 C) Does not exist D)-oo 1
!
6) lim [_1_ - 1
x __ 5- x4/5 (x - 5)4/5
J 6)
A)-oo B) a C)OO D) Does not exist
I
I
"
I
!,
1

24. :t;'
r:
.'
.'
Practice Set 15 Limits at infinity dlmgutierrez
"
"
,,'
'"
"
Class ID Name Date Score
i'
:1
-,., t
,~ .. I
r·,
:f.: ,
I
,:~I MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
~: Find the limit. Use the indicated limit to identify the equation of the horizontal and oblique asymptote/s, if any.
','
:!'
x2 + 8x + 6
"
1) Jim 1)
x~oo x3 - 9x2 + 5
.:"
-,'
"
1t.' A)O B)i C)1 0)00
5
-9x2 - 8x + 2 '1'
2) Urn 2)
x~-oo -3x2 + 3x + 16 "
B) 1..
A) 3 C)1 D) 00
8
5x3 + 3x2
3) Jim 3)
x~ - 00 x - 6x2
::'; 1
A)5 B)-oo C)-- 0)00
~,
2
~{
,.
r-,
~~:
1
.••·1
4) lim --2 4)
/ x~oo x
~'.-;
A) -1 B) -2 C)2 0) -3 I
"I
-5 + (2/x)
5) lim 5)
X~-oo 5 - (l/x2)
A)-oo B) - 1 C)OO 0)1
2
6) lim 6)
x~-oo 4 - (7/x2)
2 C)1..
A)-oo B) -- 0)2
3 2
49x2
7) Jim 7)
X---700 2 + 4x2
A) 49 B) 49 C)~ 0) does not exist
2 4 2
-3"Jx + x-I
8) lim 8)
x~oo 3x + 3
A) -1 B) 00 C)O 0)1
3
1

25. ·,"1
.
j
,
I
3
'$ - 5x + 7
9) lirn 9)
X--oo -7x + x2/3 + 2 ,
~
A)O B)~
q~ .. !
0)-00 :
7 5
10) lirn (4x - --j16x2 - 5x + 6) 10)
X-oo
A)O 8) -12 qi 0)-00
8
11) lirn --jx2 + 12x - x '1'-. 11)
x-co ~~~,
A)6 " B) 00 qo D) 12
12) lirn (--j3x2 + 7 - --j3x2 - 3) 12)
x-co
A)O B) 00 q 1 0)-j3
2~
13) lirn ~x2+2_x-~x2_7x 13)
x-co
5
A) -- B) 9 q~ D) does not exist
2 2
I'
i
2