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Ok, I understand it's customary to post a problem. Might be a little old but it's a good 'un.

ABC is isosceles.

AB=BC

AB= \sqrt 5

AC=2

Find a way to cut the triangle into 4 pieces so that they can be constructed to form a regular square.

Reply 1221

The Muon

Had to post this somewhere and I thought, I spend all my time in f38 so why not here:

Post 1000!!!!!!! :woo:

Reply 1222

Square

Ekpyrotic

Ok, I understand it's customary to post a problem. Might be a little old but it's a good 'un.

ABC is isosceles.

AB=BC

AB= \sqrt 5

AC=2

Find a way to cut the triangle into 4 pieces so that they can be constructed to form a regular square.

Spoiler

Reply 1223

username165864

The Muon

Had to post this somewhere and I thought, I spend all my time in f38 so why not here:

Post 1000!!!!!!! :woo:

...

Just joking. Congratulations, I think. :eyeball:

Reply 1224

Glutamic Acid

Ah, here's one: Factorize x^8 + x^4 + 1 into four quadratic factors each with real coefficients.

Reply 1225

Dadeyemi

The Muon

Had to post this somewhere and I thought, I spend all my time in f38 so why not here:

Post 1000!!!!!!! :woo:

When you get to this point you start to realize just how much of your life has been wasted on TSR

Reply 1226

SimonM

Glutamic Acid

Ah, here's one: Factorize x^8 + x^4 + 1 into four quadratic factors each with real coefficients.

Nice question (a little easy though :p:

)

Spoiler

Reply 1227

Kevin_B

Find the sum of the infinite series

\displaystyle \frac{a}{b} + \frac{a+c}{bd} + \frac{a+2c}{bd^2} + \frac{a+3c}{bd^3} + \cdots

Reply 1228

SimonM

Kevin_B

Find the sum of the infinite series

\displaystyle \frac{a}{b} + \frac{a+c}{bd} + \frac{a+2c}{bd^2} + \frac{a+3c}{bd^3} + \cdots

A little easy again

Spoiler

Nice

Kevin_B

Nice

Yeah, those identities are pretty much STEP II unofficial syllabus rule number 1 (from my experience)

Reply 1231

Horizontal 8

One my teacher set us last week. It's relatively easy but fun nevertheless...

Evaluate:

\displaystyle\int^{\frac{\pi}{2}}_0 \, \frac{x}{sinx + cosx}dx

Spoiler

Reply 1232

sonofdot

8 Horizontal

One my teacher set us last week. It's relatively easy but fun nevertheless...

Evaluate:

\displaystyle\int^{\frac{\pi}{2}}_0 \, \frac{x}{sinx + cosx}dx

Spoiler

Too tired/tipsy too work it all out properly now, but:

Spoiler

Reply 1233

Swayum

sonofdot

Too tired/tipsy too work it all out properly now, but:

Spoiler

Yes, that works. Now what does 1/sinx equal?

Reply 1234

Horizontal 8

sonofdot

Too tired/tipsy too work it all out properly now, but:

Spoiler

Is this a real question or rhetorical?

assuming its a genuine question..

Spoiler

Reply 1235

sonofdot

Swayum

Yes, that works. Now what does 1/sinx equal?

so then I would get xcosecx which I could do by parts, but I can't be bothered to do that now :p:

Reply 1236

SimonM

Hmm... I think this is one of that

\displaystyle \int_0^a f(x) dx = \int_0^a f(a-x) dx

jobs

sonofdot

so then I would get xcosecx which I could do by parts, but I can't be bothered to do that now :p:

Kinda tough integral though, doesn't evaluate in elementary functions

Reply 1237

Zhen Lin

SimonM

A little easy again

Spoiler

Random trivia:

\begin{pmatrix} a \\ b \end{pmatrix}

is not the same thing as

\displaystyle \left( \frac{a}{b} \right)

. The latter is something called the Jacobi symbol.

Reply 1238

The Bachelor

Zhen Lin

Random trivia:

\begin{pmatrix} a \\ b \end{pmatrix}

is not the same thing as

\displaystyle \left( \frac{a}{b} \right)

Doh

Reply 1239

Horizontal 8

SimonM

Hmm... I think this is one of that

\displaystyle \int_0^a f(x) dx = \int_0^a f(a-x) dx

jobs

Kinda tough integral though, doesn't evaluate in elementary functions

Yep that's the way forward (that's how the teacher expected us to do it atleast)

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