Name: __________________________________________________________ Date: _______________ Block: _____
Chapter 10: Conic Sections
Classifying Conics from Equations
Parabolas
These equations have a single squared term x2 or
y2, but not both.
y  a ( x  h) 2  k
Circles
These equations have two squared terms x2 and
y2. The squared terms are added. The
denominators in the equation are the same.
x  a( y  k ) 2  h
or
( x  h) 2  ( y  k ) 2  r 2
Ellipses
These equations have two squared terms x2 and
y2. The squared terms are added. The
denominators in the equation are different.
Hyperbolas
These equations have two squared terms x2 and
y2. The squared terms are subtracted.
( x  h) 2 ( y  k ) 2
( x  h) 2 ( y  k ) 2
or

1


1
b2
a2
a2
b2
( y  k ) 2 ( x  h) 2
( x  h) 2 ( y  k ) 2
or

1


1
a2
b2
a2
b2
Determine the type of conic from the equation:
1.
x2 + y2 – 2x – 31 = 0
4.
x2 y2

1
25 144
2.
x2 + 4y2 – 6x + 16y + 21 = 0
5. x  ( y  4) 2  2
3.
16x2 – 9y2 = 144
6.
( x  2) 2 y 2

1
36
144
Match the equation to the graph:
1. 9 x 2  4 y 2  36
2. y 2  x  1
3. ( x  2) 2  ( y  1) 2  9
4.
x2 y2

1
9 16
Name: __________________________________________________________ Date: _______________ Block: _____
Changing Conics from Standard to Vertex Form
1. Group the (x terms) and (y terms) and move the constant to the other side of the equation
2. Pull out a GCF from each group, if possible.
3.
2
Complete the square twice.  b  Remember to add terms to both sides of the equations
2
and if necessary, multiply by the GCF when adding to the other side.
4. Write trinomials as binomial factors
5. Divide each side by the constant and simplify
Change the equations to vertex form:
1. x 2  y 2  x  3 y  4
3. x 2  4 y 2  2 x  8 y  11
2. 3x 2  3 y 2  6 x  12 y  36
4. y 2  9 x 2  18 x  6 y  9
Name: __________________________________________________________ Date: _______________ Block: _____
Chapter 11: Sequences and Series
Finding the nth Term of a Sequence
Arithmetic
an  a1  (n  1)d
a1 - first term n - number of term
d - common difference
Geometric
an  a1  r ( n1)
a1 - first term n - number of term
r - common ratio
Find the 14th term for each sequence.
1. 34, 37, 40, 43...
2. 23, 30, 37, 44....
3. 9, 4, -1, -6, -11...
4. 3, 12, 48, 192...
5. 2, -6, 18, -54...
6. 2048, 1024, 512, 256...
Find the first five terms in each sequence using the given information.
1. a1 = 3 and d =10
2. a1 =26 and d  4
3. a1 =100 and d  25
4. a1  4 and r  3
5. a1  1 and r  5
6. a1  200 and r 
Finding the Sum of a Finite Series
Arithmetic
n
S n  (a1  an )
2
a1 - first term n - number of terms
a n - nth term (can be found using nth term
formula)
Geometric
a (1  r n )
Sn  1
(1  r )
a1 - first term n - number of terms
r - common ratio
1
2
Name: __________________________________________________________ Date: _______________ Block: _____
Find the sum of the first 10 terms of each series.
1. 1 + 2 + 4 + 6 + 8 +....
2. 2.3 + 4.6 + 6.9 + 9.2 + ...
3. 2 + 4 + 8 + 16 + 32 +...
4. 7 - 35 + 175 - ...
Finding the Sum of a Infinite Geometric Series
An infinite geometric series with r  1 converges
to the sum:
a1
S
(1  r )
where a1 - first term r - common ratio
Find the sum of the infinite series.
1. 1 
1 1
  ...
4 16
2. 1 
1 1

 ...
5 25
Evaluating Using Summation Notation
1. Find n
2. Find a1 by substituting the lower limit into the explicit
formula
3. Find a n by substituting the upper limit into the explicit
formula
4. Find the sum using S n 
1. Find n , a1 , and r (remember a1  r ( n1) )
2. Find the sum using Sn 
n
(a1  an )
2
Arithmetic
Geometric
3
3
Ex.
a1 (1  r n )
(1  r )
 (5n  1)
Ex.
n 1
n 1
n 1
n3
a1  (5 1  1)  6
an  (5  3  1)  16
 5(2)
n3
a1  5
r2
5(1  23 ) 5(1  8) 5(7)  35
Sn 



 35
(1  2)
(1)
(1)
1
3
S n  (6  16)  33
2
Evaluate.
5
1.
 (2n  1)
n 1
4
8
2.
 (7  n )
n 1
3.
 7 ( 2)
n 1
5
n
4.
 6(1)
n 1
n 1