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The calculation is 4 times 13C3 / 52C3 ie. pick the suit, then pick 3 cards from 13 in that suit The reason your answer is wrong is that you are triple counting. You will choose each hand 3 times. eg. if the hand is 2H, 3H, 4H ... you will get that hand by first picking 2H then the other two...

Re: HSC 2015 4U Marathon - Advanced Level Hmmm .... are you sure about this question? Just for starters, are there restrictions on the pronumerals? And ... do you really mean to have a power inside the cis? Don't get me wrong ... I'm not yet prepared to say it is all wrong .... but it...

Where is Huntsville?

If a=b then equating vector components: z=1 x+y = 3y+2 x=2y+2 2x+y=5x-3 y=3x-3 Solving the last two simultaneously: y=-3/5, x=4/5, (z=1) | 1.25xi +5yj +6zk | = | i - 3j +6k | = sqrt (1^2 + 3^2 +6^2) = sqrt 46

Just a couple of question for the expert: Although I talk of Strong Induction, I haven't seen a question that requires an assumption involving more than 2 or three values. SO: (1) Is there a name for that other than something like "a weakened form of strong induction"? (2) Do you know of...

Re: HSC 2015 4U Marathon (a) Not sure ... is it 343 ? (EDIT : no, I'm double counting, aren't I)

TOTAL number of arrangements = 7!/2! = 2520. (a) Ignoring the other letters, the only arrangements for the G, E, E are: GEE, EGE, EEG So one third of all arrangements have the G between the Es, ie. 840 (b) Number of 'words' using MUEE is 4!/2! = 12. We want MEUE - ONE of the 12...

Re: HSC 2015 4U Marathon Your expressions include an 'n' representing the number of terms. So they can't possibly be limiting (ie. infinite) sums. You have to find limits as n->infinity, and these limits do not exist. Try x=pi/2: cisx=i cisx+cis2x = i - 1 cisx+cis2x+cis3x = i - 1 - i = -1...

Re: HSC 2015 4U Marathon The restriction for the limiting sum of a GP is r must lie between -1 and 1. That is ... r must be REAL (To use that formula anyway) This has no limiting sum. If x is a rational multiple of pi, the partial sums follow a cyclically repeating pattern. If x is a...

Re: HSC 2015 4U Marathon Surely this won't have a limiting sum.

Re: HSC 2015 4U Marathon Just checking - is the answer is 30? (No working, so that someone else can give it a go)

Re: HSC 2015 4U Marathon If this were an HSC question, working would not be expected. In fact, they would probably ONLY ask for a sketch.

There is no issue with limits actually being reached. For example, lim(x->1) x is a valid question. But for the limiting sum of a GP, it really is a degenerate case.

Of course there are exceptions (I did say 'typical'). But generically what I am saying is true - I'm speaking from experience.

You would be surprised.

You are speaking from the point of view of someone who understands maths. You wouldn't believe how hard it is to explain the simplest mathematical concept to a typical English teacher. And then there are the Art teachers ....

Let me guess ... she taught one of the 'less equal' subjects ?

Re: HSC 2015 4U Marathon Since you didn't specifically ask for a polynomial equation, couldn't we just say: y = | x |³ + 2x² + 3 | x | + 3

Re: MX2 2015 Integration Marathon That reminds me ... time to see a dentist.

Using calculus, it it perfectly legitimate in 2U to ask for the turning points of functions which are linear combinations of sin and cos. The resulting equation for finding turning pts is a simple tanx = c. In the 1998 2U HSC, whilst they didn't ask for a sketch, they asked for the max and...