some questions from tmsca 11 and misc.

[B3ndythumbs]

47. if a^0.75 x a^.8 equals a^(k/n), where n and k are rel prime, then n=?? I always miss this one...am i overlooking something? i put 15.

56. arc length of sector of a circle with radius 4 and central angle of 2.7 rad is ??? inches. how do u do area of a sector also?

64. shortest distance between the origin and line x-2y+8=0 is k*sqrt5. Find k.

40. 833x126=? I used the rounding then mulitplication tech, but i noticed 833 is 5000/6. so should i mulitply 126 by 5/6, then add 3 zeros?

MISC:

25^3-24^3? I hated this. i think i'm supposed to memorize cubes up to 25? or do you use the diff of cubes formula.

43^2+44^2. for this one, i evaluated the lower square, multiplied by 2, then added 2(43)+1. good way?

[Englandude]

47) [unparseable or potentially dangerous latex formula] So now you just add your exponents and you get [unparseable or potentially dangerous latex formula] so n=20

40) [unparseable or potentially dangerous latex formula] Your way is good, but i probably would have done the 125's trick. [unparseable or potentially dangerous latex formula]

[sexyasiangirl]

56. arc length = angle x radius, area of sector = (1/2) angle x radius^2

64. shortest distance between a line and a point is abs(Ax+By+C) / sqrt.(A^2 + B^2). the x and y of the origin are (0,0), so plug it in and you get 8/sqrt.(5), which is same as 8sqrt.(5)/5, so the answer is 8/5.

40. I think the 5/6 way is easier, but Englandude's works also.

If anyone can answer his MISC, I'm interested also.

[SumitG]

25^3-24^3=1801
We see through some factoring and because the difference between 25 and 24 is 1 that the answer will just be 3x(25x24)+1. This works for any two numbers differing by 1 x and y. For example, 6^3-5^3=3x(6x5)+1=91.

44^2+43^2
You had the right kind of concept I think. Some better factoring would give us that the sum of two squares which differ by 1 is merely 2xy+1, where x and y are the two numbers being squared which differ by 1. So you say that 44^2+43^2=2(43)(44)+1=3785.

[AuSmith]

47. I like converting [unparseable or potentially dangerous latex formula] to fraction better.

56. I like to define the radian measure of an angle [unparseable or potentially dangerous latex formula] as the arc length of a sector with radius [unparseable or potentially dangerous latex formula] and central angle [unparseable or potentially dangerous latex formula]. Arc length [unparseable or potentially dangerous latex formula]. You only need multiply the two together ([unparseable or potentially dangerous latex formula] in radians). The area is [unparseable or potentially dangerous latex formula].

64. The shortest distance between the point [unparseable or potentially dangerous latex formula] and the line [unparseable or potentially dangerous latex formula] is [unparseable or potentially dangerous latex formula].


Multiply [unparseable or potentially dangerous latex formula] by the product of the two numbers and add [unparseable or potentially dangerous latex formula]. It only works when they're [unparseable or potentially dangerous latex formula] apart. [unparseable or potentially dangerous latex formula].


Add [unparseable or potentially dangerous latex formula] to twice the product. [unparseable or potentially dangerous latex formula].

[Roel]

56.
[unparseable or potentially dangerous latex formula]
A sector is a piece of the circle with a given angle [unparseable or potentially dangerous latex formula](radians)
[unparseable or potentially dangerous latex formula]
Plug in numbers and get [unparseable or potentially dangerous latex formula]

64.
Distance Formula for a line, [unparseable or potentially dangerous latex formula], and a point [unparseable or potentially dangerous latex formula]:
[unparseable or potentially dangerous latex formula]
Plugging in numbers we get [unparseable or potentially dangerous latex formula]

MISC.
1.
Yeah, difference of cubes is the easiest way i can think of.
[unparseable or potentially dangerous latex formula]
We can see that the[unparseable or potentially dangerous latex formula] term disappears and [unparseable or potentially dangerous latex formula].
[unparseable or potentially dangerous latex formula]
I think this is still to long for NS so there might be a shorter way.

EDIT: See the other methods mentioned before, this one is too long.

2. Your way sounds good, or you could do what I did in HS and memorize the squares up to like 60 or something like that, I dont think i've seen problems with squares larger than that. Except for those problems like [unparseable or potentially dangerous latex formula], or [unparseable or potentially dangerous latex formula], but those are a different story.

[B3ndythumbs]

64. Wow I am an idiot...forgot to rationlize the denominator -.- okay, ty for all yo's help! i got the answerz.

Roel: You're only supposed to memorize up to 40, becuase there are tricks for 40-60. I think 667^2 had some weird property, so u had to memorize it specifically.

[AuSmith]

[unparseable or potentially dangerous latex formula]

[B3ndythumbs]

lol nice :P umm if u have something like sin (45) degs, should right it as 1/sqrt(2) or sqrt(2)/2?

also if they ask for nth term of bio exp, how do u do that?

[AuSmith]

I'm not sure I've ever seen a number sense answer with a radical. It may not even be covered in the directions.

you mean a binomial expansion [unparseable or potentially dangerous latex formula]?

Then, the [unparseable or potentially dangerous latex formula]th term has a [unparseable or potentially dangerous latex formula] factor (starts at [unparseable or potentially dangerous latex formula]). There are several parts... treat [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] as entities, then pull out [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] at the end.

1) Binomial coefficient [unparseable or potentially dangerous latex formula]

2) Inside parts [unparseable or potentially dangerous latex formula].

Multiply 1) and 2).

[B3ndythumbs]

yess they do. if u look at TSMCA 06 number 8, 62. it says sin(225)=?

[stupidityismygam]

UIL does not have radicals and never will. Test writers who try to copy UIL do because they don't understand the rules

[Roel]

[anthony newbs]

It's not technically against the rules to have radicals or have you write an answer as pi (well the symbol), but Larry White has chose not to write it that way. A lot of the old Don Skow tests did have them. I personally don't know why they went away from it.

[jahu]

i believe he said there would be no "symbols" on the uil number sense tests last year, so i think that means radicals, pi, and those things. if they show up, they probably will have answer under a radical, or the powers, or estimate