Math Analysis Honors MATH Sheet
M = Modeling
A = Again T = Today’s Topic H = Homework
#58 Monday 12/1_____________________________________
M
n 1
.
n
n 1  2 
Ex. 2 Write the first six terms of the following sequence: an   1   .
n
Ex. 1 Write down the first six terms of the following sequence: an 
Ex. 3 Determine the sequence from the given pattern: a) e,
6
Ex. 4 Write out each sum: a)
1
k
k1
e2 e 3 e 4
, , ,... b) 1, 3, 5, 7,...
2 3 4
5
b)
  3k  1
k 1
Ex. 5 Express each sum using summation notation: a) 12  22  32    92
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c) 1, 4, 9, 16, 25,...
b) 1
1 1 1
1
    
2 4 8
128
None
Sequences
Worksheet 47
#59 Tuesday 12/2____________________________________
M
Ex. 1 Find the explicit and recursive rule of the given arithmetic sequence, then find a13 : 2, 6, 10, 14, 18,...
Ex. 2 Find the explicit and recursive rule of the given arithmetic sequence, then find a19 : 5, 2, 1, 4,...
Ex. 3 Find the explicit rule of the given arithmetic sequence: 8th term is 8; 20th term is 44.
Ex. 4 Find the explicit rule of the given arithmetic sequence: 4th term is 3; 20th term is 35.
7
A
1) Find the sum:
  2n  1
4
2) Find the sum:
n 1
  3n  5
n 1
T
Arithmetic Sequences: Explicit Rule: an  a1  n 1d Recursive rule: Define a1 ; an  an 1  d
H
Worksheet 48
#60 Wednesday 12/3_____________________________________
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Ex. 1 Evaluate S8 for an  3n  5 .
Ex. 2 Find the sum of the first 20 terms of the sequence an  9n  11 .
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Ex. 3 A ceramic tile floor is designed in the shape of a trapezoid 20 feet wide at the base and 10 feet wide at the
top. The tiles, 12 inches by 12 inches, are to be placed so that each successive row contains one less than the
preceding row. How many tiles will be required?
Ex. 4 The Drury Lane Theater has 25 seats in the first row and 30 rows in all. Each successive row has two
additional seats. How many seats are in the theater?
Solve 3x2  4x  5  4
n
Arithmetic Series: Sn   a1  an 
2
Worksheet 49
#61 Thursday 12/4__________________________________
M
Ex. 1 Find the explicit and recursive rule for the geometric sequence: a1  2; r  3 .. Find a9 .
Ex. 2 Find the explicit and recursive rule for the geometric sequence: 8, 4, 2, ... . Find a7 .
Ex. 3 Find the explicit and recursive rule for the geometric sequence:
A
Find S20 for an  7n  11
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Geometric Sequences: an  a1r n1 , r  0
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Worksheet 50
1 1
, , 1,... Find a7 .
25 5
#62 Friday 12/5___________________________________
M
Ex. 1 Find the sum of the first 15 terms for Sn  4 3 .
A
1 1
Ex. 3 Find the sum: 1   
3 9
None
T
H

1
Ex. 4 Find the sum:  5  
k 1  4 
1 rn 
Geometric Series: Finite: Sn  a1 

 1 r 
Worksheet 51
n
2
Ex. 2 Find the sum    .
n1  3 
8
n1
Infinite: S 
k 1
a1
, where r  1 (divergent series only)
1 r
#63 Monday 12/8______________________________________
M
None
A
None
T
Sequences and Series Review
H
Worksheet 52
#64 Tuesday 12/9______________________________________
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None
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None
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Sequences and Series Test #9
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None
#65 Wednesday 12/10__________________________________
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Handout
A
Find the product mentally (do not write anything down except the answer):
1.  3x  2  2 x  5
2.  2 x  3 x  7 
3.  3x  5 4 x  1
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H
Solve Counting Problems Using the Multiplication Principle/Permutations
Worksheet 53
#66 Thursday 12/11___________________________________
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Handout
A
Find the product mentally (do not write anything down except the answer):
1.  2 x  1 3x  8
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2.  x  7  x  3
Combinations
Worksheet 54
#67 Friday 12/12____________________________________
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None
1

3.  2 x  1  x  5 
3

A
T
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Factor the binomial mentally (do not write anything down except the answer):
1. x2  12 x  32
2. x2  8x  12
Counting Principles Review/Calculator
Worksheet 55
3. x 2  5 x  36
#68 Monday 12/15_________________________________
M
Ex. 1 Expand  a  b  , using a calculator to compute the binomial coefficients.
5
Ex. 2 Expand 3x  2 , using a calculator to compute the binomial coefficients.
4
Ex. 3 Find the coefficient of x10 in the expansion of  x  2 .
15
Ex. 4 Find the coefficient of x6 in the expansion of  x  3 .
10
A
T
H
Factor the binomial mentally (do not write anything down except the answer):
1. 2 x2  5x  12
2. 3x2  16 x  5
The Binomial Theorem
Worksheet 56
3. 4 x2  33x  8
#69 Tuesday 12/16_________________________________
M
Ex. 1 Find the probability of each of the following events.
a) Tossing a head on one toss of a fair coin.
b) Drawing a queen from a standard deck of 52 cards.
c) Guessing all 6 numbers in a lottery that requires you to pick 6 numbers between 1 and 46, inclusive.
Ex. 2 Find the probability of rolling a sum divisible by 3 on a single roll of two fair dice.
Ex. 3 Find the probability of rolling a sum that is prime on a single roll of two fair dice.
A
3x 2  1,
For f  x   
2 x  5,
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Probability
Worksheet 57
x  1
, find a) f  3
x  1
b) f  1
c) f  4 
#70 Wednesday 12/17________________________________
M
None
A
Write the equation of the line perpendicular to y  3x  2 that passes through 6, 2 
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H
Combinatorics Review
Worksheet 58
#71 Thursday 12/18___________________________________
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None
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None
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Combinatorics Test #10
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None
#72 Friday 12/19_____________________________________
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There will be a worksheet posted at the beginning of each week during Christmas break. DO NOT wait until
your break is over to complete the Worksheets. STAY SHARP!!
A
Enjoy your day today!
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None
H
Enjoy your Christmas Break and Happy New Year!! See you in 2015!