<p>So it turns out everybody had the punctuation and pencil dual passages, both of which were pretty hard. </p>
<p>Pencil: Tribute or uncommon preference? Fundamental character or primitive condition? Crude expression or messy process?
Punctuation: Anything about pervasiveness or dynamic? </p>
<p>Do you guys remember any other questions from those passages?</p>
<p>for the question (punctuation passage) that asked for which thing the two authors most disagreed on, did you guys say consequence of punctuating or something like that?</p>
<p>Point B is reflected across what line? I got x=-1</p>
<p>There was also a math question where it’s like "these 4 points form a square, what is the value of k? and since the height of the square was 6, and one of the points was at (-2,-1), k=4 (k being the x-value)</p>
<p>If I got one math question wrong and one omitted, do you guys think I could still do better than a 700? I honestly have no idea how these things are curved and that math felt much easier than most SAT math.</p>
<p>II: Develop the first few terms to determine the formula for the nth term
n a(n)
1 2^2-1
2 2(2^2-1)-1=2^3-2^1-1
3 2(2^3-2^1-1)-1=2^4-2^2-2^1-1
4 2(2^4-2^2-2^1-1)-1=2^5- 2^3-2^2-2^1-1
n 2^(n+1)-2^(n-1)-2^(n-2)…2^2-2^1-1
n+1 2^(n+2)-2^n-2^(n-1)-2^(n-2)-…-2^2-2^1-1</p>
<p>u(n+1)-u(n): all the terms from 2^(n-1) onwards are the same, so we are left with
2^(n+2)-2^n-2^(n+1)=2^n(2^2-1-2^1)=2^n(4-1-2)=2^n True.</p>
<p>III u(n)=2^(n+1)-2^(n-1)-2^(n-2)…2^2-2^1-1
separate out all the term except the first and last:
-2^(n-1)-2^(n-2)-2^(n-3)…-2^3-2^2-2^1: This is the negative of a geometric series with u(1)=2 and r=2</p>
<p>We can calculate this sum with the sigma function of the TI-Nspire CX CAS or with the geometric series formula
u(1)(1-r^n)/(1-r)=- 2(1-2^(n-1)/(1-2)=2(1-2^(n-1))=2-2^n
Now we add this result to the remaining two terms: 2^(n+1)-1+2-2^n=2^(n+1)-2^n+1=2^n(2^1-1)+1=2^n+1 True.
Of course, picking numbers is faster.</p>
<p>Guys for the paint bucket one I got 45, because if you inverted the fraction 2/9 to 9/2 and multiplied 10 to the 9/2 you get 45. 22.5 is the least number of gallons.</p>