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Mathematics HL paper 3 Calculus


Yuki Kuran

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Omg, people, that was just too easy. Honestly, I didn't even prepare for exams but was worried about paper 3, since I knew only the ratio test (hate memorizing, I like problems that are solved using logic). However... THIS WAS JUST SUPER EASY.

Do you think that boundaries for this year will be higher?

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Haha Yuki, I swear. The only question I found weird was the last one, sub part b, the one to be proved using Rolle's theorem. What did you do for that? I found it weird that it was a 9 marker. The first part, regarding proving that the function was constant in that interval was simple. But the second part, all I could think of was substituting the value of x in the equation ( 0 and 1 ) and both times I got pi. And I said that since the function is constant in the interval, all values between 0 and 1 (inclusive) have a y value of pi. I didn't see the "9 marks" in that, what do you feel? 

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Haha Yuki, I swear. The only question I found weird was the last one, sub part b, the one to be proved using Rolle's theorem. What did you do for that? I found it weird that it was a 9 marker. The first part, regarding proving that the function was constant in that interval was simple. But the second part, all I could think of was substituting the value of x in the equation ( 0 and 1 ) and both times I got pi. And I said that since the function is constant in the interval, all values between 0 and 1 (inclusive) have a y value of pi. I didn't see the "9 marks" in that, what do you feel?

It could be like that:

3 points for proving the continuity of the function. (Limits)

3 points for finding that the derivative of the function is always 0.

1 point for saying that the function is always differentiable for X € R

1 point for stating that the function is constant using the expression from 5 b.

1 point for finding the value of f(x) at a random x.

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I see not reason to prove continuity if the function is not piecewise or absolute value. (and arctan is continuous).
Im guessing 1 mark for continuity, 1 mark for use of Rolle's Theorem, 4 marks for proving f'(x) = 0.and everything else agree with Yuki Kuran.

Hmm the November 2014 Calculus paper 3 did seem to be A LOT harder than this one. But the difference is that for us the marks are pretty large and less broken down (eg find that improper integral was also heavily weighted, also finding the first term of the McLaurin expansion), but the November one is slightly more bread crumbed. 

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