The District Tests

[LeoG]

Once the district tests are posted, everyone check out a story problem on district test one on page two I believe. It is about two sheets of paper. It was a very very tricky problem, and nobody in my district got it right lol.

[Celsion]

Yeah got that wrong too, most people would think just area, but didn't take in the shape. What is the largest number of 8.5 in by 11 in rectangular pieces that may be cut from a 2 ft by 3 ft sheet of poster board?
So most people would put 9 because (24 in * 36 in)/(8.5 in * 11 in)=9.24. But I think the answer is really 8, enough room for 2 on the width and 4 on the length. Haven't seen the answer key so not sure.

Edit: Whoops, I see 8 now, thanks for the correction.

[LeoG]

na..the answer is 8..i put 9 but then my coach explained it to me and the answer came out to 8

[bradp]

yeah i missed that too.. i put 9 yay me.

Even though I put the fez thing in my sig i never actually bothered to figure out how to do the problem. I saw that problem and wanted to kick myself.That was seven more points...

Did anyone get #38 right? I got 150 using 95*.947 = a .... a/.6 = 150 which makes sense to me but what is the actual way to do it?

[Kurt]

Hmm, I think I got the paper one right. However they took up my test after verification, and I can't really remember. They'll mail it later, apparently.

What problem is #38?

[bradp]

the question about drying a block of wood


also - how about #40 ? i still can't figure it out :(

[Kurt]

Ah, don't know - I couldn't make it to verification, and I can't remember exactly what the question was asking, lol.

[stupidityismygam]

[LeoG]

lol stupid fez problem..it goes like this...

use the area of a circle to find your radius with the area they give you which is R1

R1 - sin(angle/2)*slant = R2

then find the area of the circle using R2

[Celsion]

How would you go about solving the geometry problem number 60?

[bradp]

call the top vertex point D

find CD using law of sines (angle DCA is (180-35.9)/2)

with CD, use law of sines again to find BC (find angles using isosceles and 180 stuff again)

BC and AC are two legs of a rt triangle ---> pyth theorem --> AB

[AuSmith]

This is probably too late, but for the sake of completeness...

38) That's what I did

40) In a circle of diameter [unparseable or potentially dangerous latex formula], an inscribed angle of measure [unparseable or potentially dangerous latex formula] intercepts an arc with chord of length [unparseable or potentially dangerous latex formula]. Therefore, if the apex of the isosceles triangle has measure [unparseable or potentially dangerous latex formula],

[unparseable or potentially dangerous latex formula]

Solve for [unparseable or potentially dangerous latex formula], the measure of the base angles,

[unparseable or potentially dangerous latex formula]

Apply the same formula,

[unparseable or potentially dangerous latex formula]

[bradp]

How about 07G-57?

[AuSmith]

[PatriotAlanis]

both on district 2

07G-36- Kaitlyn makes four equal annual payments to a bank that pays 6% annual interest. At the end of the fourth year, she has earned $500. How much was one of the four payments?

Answer- $784.81

07G-38- A screen transmits 35% of the incident light. What fraction of incident light passes through two screens stacked together?

Answer- 21.2

[bradp]

07G-36 - These are annual installment payments... so the first one gets four years of 6% annually compounded interest, the second three years... etc.

each acct gets X dollars
using the compound interest formula and the fact that the resulting balance will be the amt of money put in (4X) plus the interest (500):

X(1.06)^4 + X(1.06)^3 + X(1.06)^2 + X(1.06) = 4X + 500

set it equal to 0 and put in calculator.. or you could solve by hand but i wouldn't (it is a calculator test after all)

07G-38

when i first did this problem i thought... 35% goes through the first and 35% of that goes through the second ---> 12.25%

but when the first 35% hits the second screen, part is reflected back to the first screen which then reflects some back to the second screen....
what it turns into is..

(.35)(.35) + (.35)(.65)(.65)(.35) + (.35)(.65)^4(.35) + (.35)(.65)^6(.35)...

infinite geometric series = a/(1-r) = (.1225) / (1- (.65)^2) = 21.2%

[PatriotAlanis]

nifty (yes I used the word nifty) or should I use uber haha

[indianpapu]

Problem # 60 on District 2
Regular Hexagon
Distance from the circumscribing radius (to) apothem given
asking for side

answer: 22.0
I keep getting 23.6
I made a right triangle and solved for side
I don't get how they got 22.0 and I missed verification
so...

[bradp]

yeah... the circumradius (which is equal to the sidelength) is x... the inradius (aka apothem) is xsin(60) and the included angle between the two is 150. Using the law of cosines

0 = sqrt( x^2 + (xsin60)^2 - (2)(x)(xsin60)(cos150) ) - 42.5

x = 23.6
i could be wrong

[AuSmith]

It looks like 22.0 is the answer if you find one of the legs of an isosceles triangle with base of length 42.5 and apex angle 150 degrees. So, this is not isosceles, and y'all have the correct answer...

Alternate solution: ignore the radii and the center. It's just a right triangle.

[unparseable or potentially dangerous latex formula]

[Kurt]

Yeah I got 23.6 as well when I just took it. It's not exactly a tricky question, so I doubt this many people were doing something wrong. ;)

[ZachB]

How do you do the question about the drying block of wood from District 1? I played with the figures for a while but I just can't get to the answer on the key.

[AuSmith]

[Kurt]

[bradp]

it says 'by weight' on the test