Giveme45 Posted May 10, 2013 Report Share Posted May 10, 2013 Hey guys, we're allowed to discuss P1 now and P2 tomorrow!I loved the questions, they were brilliant, especially the complex numbers one in q.13. Initially, i must admit I didnT' really see how to answer them, but then it just struck me and BAM. Really high hopes on this paper, thinking about 113/120. (Got my stupid graph wrong because I forgot the minus at the second derivative. Jesus.)I found the question abotu the sequences werid, where you had to find r, which was only 6 marks. Because I felt it should have been more than 6 marks. Finding the pattern, simplifying, seeing that (r-1) is a factor of the 3rd degree polynomial, finding the other factor by identification, solving the quadratic, to give r=1, r= -1.67 and r=2/3, then seeingn that only the last is the actual value since it was a sum to infinity, seemed a bit much for a 6 marker.How did it go for you guys? Let's discuss some of the questions! Reply Link to post Share on other sites More sharing options...
Giveme45 Posted May 10, 2013 Author Report Share Posted May 10, 2013 I really enjoyed the paper tbh. The complex number questions were smart, but once you noticed the trick, the marks just came flying. I did a stupid mistake with the function sketching: I forgot the minus sign for the second derivative so the curvature of my graph is wrong, which will probably make me lose 4-6 marks.The third degreee gemoetric sequence question admittedly was far too hard for a 6 marker. The trick was that you had to see that (r-1) was a obvious factor. So you would have (r-1)(quadratic). The coefficients of the quadratic are then found by identification. Then you had to solve the quadratic by using the discriminant, giving r=1, r=-1.67, r=2/3. the only possible answer was r=2/3 because it was an infinite sum.I doubt the grade boundaries will be far lower than usual, probably around average. I found the paper relatively easy (expecting a 113/120), but most of my class did not, so who knows. But yeah, the graph sketching is annoying. I can't believe they gave so many marks for sketching graphs --- blunder. Reply Link to post Share on other sites More sharing options...
kinguncaged1 Posted May 10, 2013 Report Share Posted May 10, 2013 I loved the vectors question! I thought the part b complex number question a bit difficult, at least for the second half of it... Reply Link to post Share on other sites More sharing options...
Giveme45 Posted May 10, 2013 Author Report Share Posted May 10, 2013 I loved the vectors question! I thought the part b complex number question a bit difficult, at least for the second half of it... Yes the vectors question was a gift! Do you remember what values you got? I remember and some point i had lambda=-1/2, and D coordinates were something like 7/2 5/2 and stuff. Reply Link to post Share on other sites More sharing options...
kinguncaged1 Posted May 10, 2013 Report Share Posted May 10, 2013 Yah i got the same values for point D, like (7/2,5/2,1) or something like that... i don't remember the exact values :'( Reply Link to post Share on other sites More sharing options...
kinguncaged1 Posted May 10, 2013 Report Share Posted May 10, 2013 Can you guys remind me of the infinite geometric series question you mentioned on part a??! Reply Link to post Share on other sites More sharing options...
Giveme45 Posted May 10, 2013 Author Report Share Posted May 10, 2013 Can you guys remind me of the infinite geometric series question you mentioned on part a??!Two geometric sequences:First one has first term a, common ratio r, sum to infinity 36Second one has first term a, common ratio r^3, sum to infinity 76.Should've been a 9 marker. Reply Link to post Share on other sites More sharing options...
bomaha Posted May 10, 2013 Report Share Posted May 10, 2013 Can you guys remind me of the infinite geometric series question you mentioned on part a??!Two geometric sequences:First one has first term a, common ratio r, sum to infinity 36Second one has first term a, common ratio r^3, sum to infinity 76.Should've been a 9 marker.The question is wrong as written. The sum of infinity for the two sequences must be interchanged. Reply Link to post Share on other sites More sharing options...
Giveme45 Posted May 10, 2013 Author Report Share Posted May 10, 2013 (edited) Can you guys remind me of the infinite geometric series question you mentioned on part a??!Two geometric sequences:First one has first term a, common ratio r, sum to infinity 36Second one has first term a, common ratio r^3, sum to infinity 76.Should've been a 9 marker.The question is wrong as written. The sum of infinity for the two sequences must be interchanged. True, apologies. Edited May 10, 2013 by Giveme45 Reply Link to post Share on other sites More sharing options...
bomaha Posted May 10, 2013 Report Share Posted May 10, 2013 (edited) Can you guys remind me of the infinite geometric series question you mentioned on part a??!Two geometric sequences:First one has first term a, common ratio r, sum to infinity 36Second one has first term a, common ratio r^3, sum to infinity 76.Should've been a 9 marker.The question is wrong as written. The sum of infinity for the two sequences must be interchanged. No its right like this.I know for sure the answer was r=2/3So, how do you solve it? 36(1-r)=76(1-r^3) gives you no real solutions except 1. Edited May 10, 2013 by bomaha Reply Link to post Share on other sites More sharing options...
bomaha Posted May 10, 2013 Report Share Posted May 10, 2013 (edited) Note that in the exam, the question was written as you wrote it. So I think their was a mistype?! can anyone elaborate? Edited May 10, 2013 by bomaha Reply Link to post Share on other sites More sharing options...
Giveme45 Posted May 10, 2013 Author Report Share Posted May 10, 2013 Note that in the exam, the question was written as you wrote it. So I think their was a mistype?!I corrected earlir that you were right, I'm sorry. I just checked it. Reply Link to post Share on other sites More sharing options...
bomaha Posted May 10, 2013 Report Share Posted May 10, 2013 but wait, i remember it was written as you wrote it? Reply Link to post Share on other sites More sharing options...
Giveme45 Posted May 10, 2013 Author Report Share Posted May 10, 2013 but wait, i remember it was written as you wrote it?Im confused right now, let's check through it.Say i was right, then we have:a/(1-r)=36a/(1-r³)=76so we have a=(1-r)*36giving(1-r)/(1-r³)=76/36 i remember the coefficient was 36/76 though -> thus i must have exchanged the sum to infinities, and indeed you were right. So the real question was:First one has first term a, common ratio r, sum to infinity 76Second one has first term a, common ratio r^3, sum to infinity 36.Tada How did you do on the rest of the exam? Reply Link to post Share on other sites More sharing options...
bomaha Posted May 10, 2013 Report Share Posted May 10, 2013 I was confused with the sequence question because, I got a quadratic, then I used the quadratic formula but did not simplify!, so did not get 2/3. Got (-9+sqr(441))/18, which is essentially 2/3. So lost a mark there!The exam was fairly easy. Expecting about 110+/-, depending if arithmetic mistakes occurred. Reply Link to post Share on other sites More sharing options...
Giveme45 Posted May 10, 2013 Author Report Share Posted May 10, 2013 (edited) I was confused with the sequence question because, I got a quadratic, then I used the quadratic formula but did not simplify!, so did not get 2/3. Got (-9+sqr(441))/18, which is essentially 2/3. So lost a mark there!The exam was fairly easy. Expecting about 110+/-, depending if arithmetic mistakes occurred. I was also a bit baffled that the sequence question was only 6 marks, shoudl've been like 8 or 9 tbh.Agree, also expecting about that. I hope I did not do any silly mistakes. What value for the angle did you get in the complex numbers question (w+1)? I got pi/7.Also, the graph question was extremely annoying, because i forgot the minus for the second derivative, and therefore my curvature was wrong. I bet that will lose me at least one A1 mark for correct shape for all of the graphs we had to draw from there on, if not even more marks. What a blunder... Edited May 10, 2013 by Giveme45 Reply Link to post Share on other sites More sharing options...
bomaha Posted May 10, 2013 Report Share Posted May 10, 2013 (edited) rhombus, thus pi/7! what did you get for the minimum Iz1 + az2I? Edited May 10, 2013 by bomaha Reply Link to post Share on other sites More sharing options...
Zuler Posted May 10, 2013 Report Share Posted May 10, 2013 Did you guys actually manage a lot in the complex question?! I thought it was harder than the usual (that particular question): while most of it was standard, I thought the z1^3n + z2^3n = 2z3^3n proof was hard (though I figured it out right in the end that I had to separate the 2pi's, but didn't get enough time to write it down). Also, the last last question, god that was insane at first (the z^2 - 2z cos2pi/7 + 1 is a factor). I didn't write anything for it and didn't have a clue, but funny enough today in the shower I figured it out (God, what has IB done to me?!)For anyone who's curious, you had to realise the roots occur in conjugate pairs (a little unfair at first considering my 7 roots had positive arguments since the standard is to usually substitute for cis 2kpi/7 for positive k), so you would realise that two roots were cis 2pi/7 and cis -2pi/7. The sum of these roots are 2 cos 2pi/7 (-2c = -b/a) and the product of these roots were 1 (c^2 + d^2 = c/a). And then yeah, the other two factors were z^2 -2z cos4pi/7 + 1 and z^2 - 2z cos 6pi/7 + 1.I realised this in the shower and not in the exam, I seriously need to shut off my brain soon.I left these two (I did a bit of work in the proof one but didn't finish it as I said), and the sum to infinity one I reached the quadratic but was getting a negative discrimant by mistake so left it for time. I also didn't fully sketch my f(|x|) because of time. How many marks do you think I left out? (I was thinking 2 for the sum to infinity, 2 for the graph, 2 for the proof and 4 for the z^2 - 2z cos 2pi/7 + 1 thing)I think the boundaries for paper 1 will be 88+ or so, would you agree? Reply Link to post Share on other sites More sharing options...
Giveme45 Posted May 10, 2013 Author Report Share Posted May 10, 2013 rhombus, thus pi/7! what did you get for the minimum Iz1 + az2I?Wtf is rhombus hahahaI forgot tbh, i think i got sqrt(2), you? Reply Link to post Share on other sites More sharing options...
bomaha Posted May 10, 2013 Report Share Posted May 10, 2013 (edited) yep, same answer. but for the w+1 question, i drew a rhombus, and since the diagonal of a rhombus bisects the angle, arg(w+1)=pi/7. wait what was the question with the graph and second derivative? Edited May 10, 2013 by bomaha Reply Link to post Share on other sites More sharing options...
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