2015 A-level H2 Mathematics (9740) Suggested Solutions

All solutions here are SUGGESTED. KS will hold no liability for any errors. Comments are entirely personal opinions.

Paper 1

Numerical Answers (click the questions for workings/explanation)

Question 1: a = -3.593, b = -5.187, c = 7.303;~x=-0.589;~y=5.19x + 7.30
Question 2: -1.73 < x < 0.414 \text{~and~} x >1.73
Question 3: \frac{3}{4}
Question 4: \frac{1}{32}
Question 5:
Question 6: 2x - 2x^2 + \frac{8}{3}x^3;~ a=2, b = \frac{5}{3}, c = - \frac{3}{5};~- \frac{104}{27}
Question 7: \frac{5}{11} \textbf{b};~ l_{BC}: \textbf{r} = \frac{3}{5}\lambda \textbf{a} + (1 - \lambda) \textbf{b};~ l_{AD}: \textbf{r} = \frac{5}{11} \mu \textbf{b} + (1 - \mu) \textbf{a};~11: 9
Question 8: \{ T: T \in \mathbb{R}, 59 \le T \le 77 \};~\{ t: t \in \mathbb{R}, 63.9 \le t \le 74.4 \};~11
Question 9: w = a \pm \frac{a}{\sqrt{3}}i;~\vert z \vert = 2, -\frac{\pi}{10}, -\frac{\pi}{2}, -\frac{9 \pi}{10}, \frac{3. \pi}{10}, \frac{7 \pi}{10};~4 \sin(\frac{\pi}{5})
Question 10: \sqrt{2};~a = 0, b = \frac{\pi}{4};~\pi ( \frac{\sqrt{2} \pi ²}{32} + \frac{\sqrt{2}\pi}{4} - \sqrt{2} )
Question 11: \frac{dy}{dx} = 2 \text{cot} \theta - \text{tan} \theta;~ k = 2;~ ( \frac{2 \sqrt{6}}{9}, \frac{2\sqrt{3}}{3} );~ 0.884;~a = \frac{3 \sqrt{2}}{2}

Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11

Paper 2

Numerical Answers (click the questions for workings/explanation)

Question 1: h = 32;~t = 46.9
Question 2: 73.4^{\circ};~\vec{ON} = \frac{1}{7} \begin{pmatrix}17\\1\\-58 \end{pmatrix};~ 36x - 2y +11z = -4
Question 3: D_{f^{-1}} = \{ x: x \in \mathbb{R}, x < 0\};~R_g = ( - \infty, 1 - \frac{3}{2}] \cup [ 1 + \frac{3}{2} , \infty)
Question 4: A = 1, B = -1;~ \frac{1}{3} - \frac{1}{2n+3};~ 499
Question 5:
Question 6: 0.224;~0.149;~0.825
Question 7: 0.165;~n = 4
Question 8: 0.265
Question 9: 0.4;~0.185;~0.33;~0.165 \le \text{P}(A' \cap B' \cap C' ) \le 0.33
Question 10: -0.9807,- 0.9748, -0.9986;~P = - 0.147 \sqrt{h} + 34.8;~ P = -0.266 \sqrt{h} + 34.8
Question 11: 10080;~ 10079;~ 720;~ 5760
Question 12: 0.0127;~0.0524;~0.742

Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12

Relevant materials

MF15

KSΒ Comments

Showing 241 comments
  • Student a
    Reply

    Hi what do you think is the A range for this paper? I lost about 30 marks do you still think it’s possible for me to get my A?

    • KS Teng
      Reply

      Hi, its too early to say, probably >80 is safe. You still have Paper 2 which is equal weightage as Paper 1, so yes it is definitely possible still.

      • Student a
        Reply

        Was this paper considered easy? Because I found it not in the least easy ):

        • KS Teng
          Reply

          hmm, i feel that several questions were from the previous past year papers and was modified. This paper was rather tricky in my opinion, quite easy to overlook a few things and fall for the trap. It is tedious due to all the graphs you need to draw. But if you foundations are strong, the paper is manageable as you just have to be meticulous in your workings and presentations.

        • student b
          Reply

          what school are you from? how did your peers do? did they lose as many marks as you? or do you seem to be the only one

  • Student 97
    Reply

    So far I think I lost about +/- 10 marks, how much do you think I need for paper 2 to get A?

    • KS Teng
      Reply

      like on the dot for an A? hmm 25~30. I can tell you that 170/200 is a safe A. πŸ™‚ Hope it helps.

  • Student B
    Reply

    Question 8. shouldnt 63.84 approximate to 63.8

    • KS Teng
      Reply

      nope, you must round up, else the you will include 63.8 which will result in B reaching earlier that 1.5H. Its quite tricky

    • :(
      Reply

      Can I get C with 50+

  • Anonymous
    Reply

    This was definitely one of the hardest Alevel papers.

    • kahwee
      Reply

      I hope you fare well!

  • Bob
    Reply

    How much do you reckon is needed to get a B or C

    • KS Teng
      Reply

      hard to say. a lot depends on Paper 2 too, same weightage after all πŸ™‚

      • Bob
        Reply

        Will bell curve help the weaker students

        • KS Teng
          Reply

          Bell curve is meant to even out the distribution for marks. So yes, it should help a bit

  • student
    Reply

    For questions 9a, arg( w^2/w*) can go above pi and below -pi.
    So there’s 2 more solutions of negative a

    • KS Teng
      Reply

      How so? I didn’t use argument here. Furthermore, a is a real number

  • jen
    Reply

    Hi, for question 4, i equated the total length wrongly to d, i misread that x is the diameter. But the method of doing is correct, how many marks do u think i will get?

    • KS Teng
      Reply

      You should still get method marks. Let’s be optimistic and say 3.

  • Random
    Reply

    I made so much careless mistakes and I dont even dare to count my marks… Is there ecf or method marks for math? ): Will paper 2 help to pull me up if I do well for paper 2?

    • KS Teng
      Reply

      definitely! dont give up. πŸ™‚ yes this paper is really tricky in my opinion. :/

      • Random
        Reply

        Sigh..and I practiced alot for paper 1 too.. Thanks anyway.. (:

        • KS Teng
          Reply

          Don’t worry so much. There is still a Paper 2 which is equal weightage. πŸ™‚

  • lim
    Reply

    For the integration of volume question 10, if i made careless mistakes in the last few steps, will minus how many marks?

    For question 1, can i write the asymtope as y=bx+c?

    For question 9bii, do i get any marks stating what is z1 and z2? And for 9a, i could get the fraction but couldnt divide to find the real and im parts, how many marks will i get?

    • KS Teng
      Reply

      1. i think that should be fine too, since its used in the question. There should be benefit of doubt should (i) is wrong.
      9. (a) depends on your accuracy, but i’ll say 1. (bii), i don’t think since the question is only 4 marks.

    • KS Teng
      Reply

      for 10, it depends on where your mistake is. at the end of the day, we could’ve check answer with the GC too. :/

      • student
        Reply

        My first two terms are correct, but my last term is wrong

  • student
    Reply

    For question 5, why isnt the graph stretched horizontally when x becomes 0.5x?

    • KS Teng
      Reply

      because for x from 3 to 4, the equation become f(x) = 1 (after translating 1 unit in positive y direction), and is independent of x still. the “curve” part of the graph is only from x=1 to x=4, And yes it stretches parallel to the x axis, so the y values will alternate according too and the respective x values, and we still must translate it in positive y direction.

      To be fair, this question is really difficult. It has too many pitfalls for us to commit a carless mistake.

      • another student
        Reply

        When you sub in x/2, why doesn’t the part of the graph that corresponds to the curve become 1<x/2<=3 (i.e. 2<x<=6) as per the rule of the function?

        • KS Teng
          Reply

          oh my, you’re right. careless on my part. I forgot to convert the domains too. Thanks for pointing that out! πŸ™‚ I’ve changed the curve. Thanks again

  • Stranger
    Reply

    Hi! Eagerly awaiting H1 Math solutions… (-: Thanks!

    • KS Teng
      Reply

      haha i have lessons from 5pm today, so it should be done by tomorrow 9am.

      • Eileen
        Reply

        any indication of how many marks every year on average must be attained in order to score an A for H1 math , after bell curve ? 😊

        • KS Teng
          Reply

          I can only say that scoring 170 every year, will be a safe A, based on the nature of the distribution curve. I think there is a reason why they only give letter grades to avoid discrepancies in grading too. if you’re looking at minimum A, probably 155, but thats about the lowest it can go.

          • Eileen

            H1 math is upon 95 marks tho ! πŸ˜… would 73/95 be a safe bet ?

          • KS Teng

            you’re h1? oh haha i haven’t seen the h1 paper actually. but in general, i think 75 is safe

  • Student Sadness
    Reply

    For 10(iii) I started out correctly and executed everything correctly but I carelessly forgot to include the pi at the front somewhere along the workings. So in the end my final answer looked like the second last statement without the pi. Oh dear. Do you think there will be method marks given? If have, around how much? Agar agar can already! πŸ™‚

    • KS Teng
      Reply

      haha i think you will lose 1 mark only. it is very minor & common mistake actually.

      • Student Sadness
        Reply

        That’s nice to hear!!! Thanks!! πŸ™‚

  • Bro
    Reply

    How much do you think is a safe B for overall /200?

    • KS Teng
      Reply

      k bro, I’ll say >131

  • :(
    Reply

    I got about 73 marks. Is this enough to A? πŸ™

    • KS Teng
      Reply

      There is still a paper 2! πŸ™‚

      • :(
        Reply

        What score should I aim for paper 2? Is 80 enough?

        • KS Teng
          Reply

          sounds good. πŸ™‚ but why limit yourself

  • Student
    Reply

    Do you know what’s the usual mark to score B

    • KS Teng
      Reply

      i’ll reckon > 131.

  • john
    Reply

    i think i lost around 25 marks for this paper is that still within the A range taking into consideration the difficulty of this paper? also for the APGP question i did (ii) wrongly with all the correct working just that i used 1.02^49 instead of 50 and same for (iii) how many working marks will i get for both parts?

    • KS Teng
      Reply

      you should still retain the method mark, but lose the answer marks for t. but dont worry, i forsee quite a long of them rounding off the set of t to 3SF wrongly too.
      There is still a paper 2 pending, so it is really too early. But I can say that 170/200 is a very safe A. πŸ™‚

      • john
        Reply

        would ~155/200 be an A usually? 95/100 a bit unrealistic for paper 2 haha

        • KS Teng
          Reply

          haha perhaps. have to really see the difficulty of paper 2, i’ll say.

  • Studentr
    Reply

    For qn8, can 63.8<t<74.5 be accepted? Strictly < without equal sign

    • KS Teng
      Reply

      then you will accept 63.81 which will cause B to reach earlier, same consideration for 74.49. :/

  • student
    Reply

    Hi do think this is harder than 2013?

    • KS Teng
      Reply

      slightly. cause this paper is actually really really tricky. full of pitfalls here and there. haha

    • Student
      Reply

      Yea definitely harder
      The first few qns were difficult

      • KS Teng
        Reply

        all the graphs. very tedious. haha

  • Sigh
    Reply

    For question 3ii, if i did (1/x)^1Γ·3 instead will there be 1 method mark?

    • KS Teng
      Reply

      oh, but thats a different curve alr. :/

  • Rys
    Reply

    Hi, when will you be posting 2015 h1 maths? Thank you

    • KS Teng
      Reply

      probably tomorrow haha cos i have lessons at 5pm

  • student
    Reply

    hello! for 10 iii i got the limit right but the first by parts wrong, how many marks would i get out 6? and for 6ii i missed out the a in front of the third term when calculating b and c so my b and c are wrong… How much would i get for that?

    • KS Teng
      Reply

      that should affect your (iii), but if you show the correct formula for the coefficient, should still get a method mark.
      I think if first by parts wrong, its wrong for the subsequent alr. the shown part should be 2 marks.

  • student
    Reply

    For Q1, all my working is correct except the final answer is wrong. How much ecf can I get for part 2 and 3???

    • KS Teng
      Reply

      it depends on how you solved (ii), if you used GC, there isn’t much method per se. The last part, I think you should still get the marks if you identify the correct bx+c

    • KS Teng
      Reply

      if equations all correct, just copy GC wrongly then that should cost your answer mark

      • Student
        Reply

        I made c the subject in part i and made a careless mistake somewhere along the way bcos my three equations were correct. for part ii subbed in the answer and part iii I got bx+c, so how many marks will I lose??

  • Student JR
    Reply

    My Q1 if one of the simultaneous equations I write wrong what will happen to my (i) 4 marks (ii) 2 marks and (iii) 1 mark ah? πŸ™

    • KS Teng
      Reply

      probably 1 mark. :/

  • Jackie Ng
    Reply

    Hello Sir, what topics do you think would be best to prepare for paper 2? And does A level marking tend to be more lenient ? Do I have still have hope for at Least a B if I score maybe 60 plus :/ thanks

    • KS Teng
      Reply

      DE, Vectors Planes & Lines, Complex Loci, MI + S&S, Functions. For pure math. These didnt come out la.
      That depends on how to define leniency. Like set notations, etc are quite important since they mandate these as part of the answers and should determine answer mark.
      Definitely, work hard for paper 2! they have equal weightage after all πŸ™‚

  • student
    Reply

    What do u think are the probable topics for pure maths paper 1?

    • KS Teng
      Reply

      you mean paper 2?
      DE, Vectors Planes & Lines, Complex Loci, MI + S&S, Functions.

  • student u
    Reply

    aiya i lose 50+ mark already… can pass or not i very sad πŸ™ if cannot then can chope slot next year? tq

  • f
    Reply

    Hello!! πŸ™‚ I got the limits and substitution correct but the rest wrong. How many marks would I get?

    • KS Teng
      Reply

      you mean for 10iii? 2 marks since the integration requires you to do integration by parts twice.

  • HARDESTMATHPAPERTHUSFAR
    Reply

    hey for 10iii, coefficeients for all the ‘pi’s are right just that infront of the pi^2 i put a negative instead of positive…. minus how many? And is it safe to say that since it was considerably a harder paper, that the marks for an A could be lower? (or maybe thats just me being hopeful la ya? i dont plan on scoring 95/100 for paper 2 anytime soon hahah)

    • KS Teng
      Reply

      tbh, i dont’t think this is that hard, it is definitely not an easy paper. It is very very tricky compared to other years, but much less conceptual than 2014 paper. if you have good stamina for the paper, you should do fine. Just do your best for Paper 2. They are equal weightage after all.

  • student
    Reply

    Hi! How many marks will i get for 10iii, if i got the first term correct, but last 2 terms wrong cos i forget to times the 2 outside the bracket?

    • KS Teng
      Reply

      assuming your proved correct, max minus 2 depending if you put the 2 there after integrating

  • student m
    Reply

    hi. for the APGP question, i accidentally calculated the answer wrongly for the first part because i wrote the sum as (n/2)(2a – (n-1)d). hence, i got a really huge number and my part 3 was affected. how many marks do you think i could get from it? thanks!!

  • anon
    Reply

    For 11i, if i get sintheta and costheta value correctly, but i substitute wrongly for the coordinates,how many marks will i get?

    And for 11iii, if i write 0.883 instead of 0.884, will it be accepted?

    • KS Teng
      Reply

      that rounding off error, dont think can. Its a precision problem alr. :/

  • J
    Reply

    Hello! I got around 70 marks… Does that mean I stand a low chance of getting an A provided that paper 2 has a similar level of difficulty? :/

    • KS Teng
      Reply

      yes, i think a similar stamina consuming paper, which is manageable like p1. the h1 math paper had 13 questions

  • X
    Reply

    Hi will I still get credit if Affer solving k is 2 I did the rest of the parts with k? like I forgot to sub in 2 for max point thanks

  • Student
    Reply

    The paper was really difficult πŸ™
    Just hoping for a B now.
    What do u think is the bell curve range for just this paper itself?

  • dannyfentun
    Reply

    I study so hard still fail 😞😞😞

  • Dianne
    Reply

    For qn 1i, I saw the eqn at ax^2 instead of a/x^2. So the resulting equations that I key into the gc will be different and answers are different for part I and ii as a result. How many marks will I get?

  • Anxious
    Reply

    Hi teacher, I had a panic attack midway through the paper and couldn’t think, I am still very scared now. I’m looking at only about 35-40 marks for this paper. What is your predicted range out of 200 for C and D? I am a private candidate, is it true that private candidates are not grades on the same bell curve as the general cohort? Thanks

    • KS Teng
      Reply

      I’m sorry to hear that and hope you’re better
      I don’t really know if they are on different curves in reality, but I believe not. It will create Bias. And they should not be able to differentiate since its based on the same subject code and school code.
      As for the range, I explained a bit on bell curve and you can read more here. So it highly depends on how the others did.

  • Students
    Reply

    Hi, qn 1i, I made a careless mistake in one of the simultaneous equations. I wrote coefficient of c wrongly in one of them but the other two eqns are right. how many marks will I get for part i? Will there be ECF for part ii?

  • Amanda
    Reply

    Hi for the qn 2 I left out one of the range so I just got the a<x<b part will it be totally wrong

  • Amanda
    Reply

    Sorry for one more the apgp part I managed to get the T and t values but forgot the u50 for each can I still get ethos marks

  • A for Math
    Reply

    Hi(: Do you think I can get an A if I score around 75-80 for this paper?
    And do you think that this year’s marks for A will be lower because this paper is slightly harder?
    Thanks(:

    • KS Teng
      Reply

      Yup, I think you can put it that way. I explained a bit on bell curve and you can read more here.
      I think its more tricky paper. Well you still have a paper 2 which is equal weightage!

  • Student A
    Reply

    Hi, I would just like to point out that there seems to be a mistake with the computation of the 2nd derivative for Question 11).

    Since we are differentiating dy/dx with respect to theta, shouldn’t the 2nd derivative be computed based on this formula?

    d^2y/dx^2 = d(dy/dx)/d(theta) * d(theta)/dx

    • KS Teng
      Reply

      Yes, thank you so much for pointing that out! I was too careless! Thanks again!

  • J
    Reply

    Hi! I think I scored around 70 marks for P1.. Does it mean that I stand a low chance of getting an A, assuming that P2 follows a similar level of difficulty? Thank you! πŸ™‚

    • KS Teng
      Reply

      haha paper 2 must wait till paper 2 comes out. But the pure math topics left in paper 2 aren’t easy. Mostly quite tedious. From paper 1, it seems that this year they are concerned about your precision and accuracy given that you have good speed. Which means your stamina is really important here.

  • Student :)
    Reply

    Hello! I am really grateful for all these answers! πŸ™‚ For qn 3, I integrated x^(2/3) out of carelessness and for qn 8i and ii, my working is the same as yours but somehow I got the wrong ans, probably because I keyed wrongly into the calculator? πŸ™ This resulted in my 8iii ans to be wrong as well. How many method marks do you think I will get for these two qn? Thanks for looking through my qn!

    • KS Teng
      Reply

      Ah human error is quite common, dont be too hard on yourself. If you suggested the correct function to integrate, then you should get 1.
      If you use the correct method to find the time taken, you should be awarded your method marks. And dont worry, I think many students lost the answer mark in 8iii as they might round off too carelessly.

      • Student :)
        Reply

        Alright! Thanks for the reassurance 😊

  • Student c
    Reply

    Hi for example if Q4 i didnt times 1/2 to the area of circle to find area of semicircle but my workings are correct and i manage to prove minimum, will i get method marks?

  • Student c
    Reply

    Sorry maximum*

  • Student c
    Reply

    What if my area for Q4 i didnt times 1/2 but i manage to prove maximum and workings are right? how much will i get for method marks roughly?

  • stewdunt
    Reply

    hello sir!! for 9a) can I do the longer method by finding the mod and argument for w2/w* and form the r([email protected] + [email protected]) and equate the real part to 0 and solve using trigo? I know this is lengthy and rather washy @[email protected]

    • KS Teng
      Reply

      I suppose its fine. but how do you find the argument since we dont know which quadrant the complex is in. :/

      • stewdunt
        Reply

        I was stuck for quite a while there too. only got my short sightedness to blame for not being able to see the bigger picture πŸ™ basically cos (tan^-1 [email protected])=0. and tan^-1 @ = pi/6, 5pi/6 and so on.. and these values give either 1/sqrt3 and -1/sqrt3. and @ = b/a. took one Long page of working :/ can it be accepted? thank you!

        • KS Teng
          Reply

          right, so you worked out \theta? Think thats fine. But its really long eh. you’re patient haha

  • Student A
    Reply

    Hi may I know for qn 1, I did a really stupid careless mistake while typing into GC , but all eqns are correct, may I know how many marks will I lose?

  • Vanessa
    Reply

    Hello, if my final ans i didnt rationalise, will i be penalised?

    • KS Teng
      Reply

      I think its fine. They are not that particular and no specific mention there too.

  • S
    Reply

    For AP/GP, I subbed 20 instead of 50 for n, what is the possible marks I can attain by method marks assuming my methods are right?
    Also, for the complex roots qn, I carelessly subbed Pi/4 instead of Pi/2. How many marks will I be able to get if any at all…
    For Qn 3i, i drew the bar graph but instead of leaving the centre blank indicating a unknown number of bars, I drew a random number of bars writing “1/n, 2/n … n/n” on the x-axis. Will I still get the marks?
    Asuming I lost 20+ marks in P1, at least how many marks should I get for P2 if I were to aim for an A?

  • Janel
    Reply

    Is there ecf for math?

    • KS Teng
      Reply

      no, but its based on Method Marks. You will still lose the answer mark

  • student x
    Reply

    i thought it was an extremely easy paper, frankly disappointed by what cambridge thinks of us

    • KS Teng
      Reply

      Haha thats good to hear. πŸ™‚

  • Student T
    Reply

    Hi, for my qn 1 i got a and b write but c wrong so how many marks will I get for qn 1? And for part (ii) and (iii) . And qn ,6(ii) my a b c are correct but not the coefficient of x^4 so how many marks will I get?

  • Student
    Reply

    I got about 60marks, will I still be able to get at least a B? How many marks should I score for p2

  • Student
    Reply

    For qn 1 i got a and b right but not c so how many marks will I get for (i) and will there be e.c.f for (ii) and (iii)?
    Qn 6(ii) I got a b c right but not the coefficient of x^4 so how many marks will I get out of the 6

  • Student
    Reply

    Whats usually the range for C and D? Thanks sir!

  • Ting
    Reply

    Hello, will there be any suggested solutions for h1 math? πŸ™‚

    • KS Teng
      Reply

      I’m doing it after my lessons only.

    • KS Teng
      Reply

      I’m in the midst of doing it. But laptop dying and wifi is really bad here haha

  • student
    Reply

    Hi, if q4 I forgot the 2x for the perimeter of the semicircle, how many marks do you think I can get for the rest of the question? Because all my working is correct but my mistake is on the first line πŸ™ πŸ™

    Also, for 10ii, if I wrote t(1.02^49 -1) instead of 50, will I get any method marks? And is there ecf for 10iii?

  • Noelle
    Reply

    Hi! Do you think the paper 2 will be as hard or easier??

    • KS Teng
      Reply

      I honestly think that this paper wasn’t crazy hard, its just very tricky with many pitfalls. If you really consider yourself doing 2013 or 2014 under exam conditions, you might not think this year is that hard. The pure Math topics left for Paper 2 are particular big topics and hard questions can come out. I don’t forsee the pure math in paper 2 to be easy. :/

      • Ex A level Student
        Reply

        I agree with you Sir. Did my A levels in 2013 and was quite satisfied with all the creativity put in by the Cambridge setters which differentiates the standard per say… My advice would be practicing “nasty” questions like the MI qn on trigonometry cos i practiced liked mad and was hoping to come out! πŸ™‚ Enjoy the Paper ahead haha πŸ™‚

        • KS Teng
          Reply

          haha yea, wow you’re enthusiastic to revisit A-levels. Yes, I thought the piecewise coming back was interesting, and this paper should rob many people of answer mark as they probably made a few round off error here, quite sneaky in my opinion. But conceptually, I think 2013 and 2014 was harder. While their focus this time seem to be on precision. πŸ™‚
          As for paper 2, the topics left are mostly large topics, we anything other the sun can be tested.

  • Noelle
    Reply

    Hi! Do you think the paper 2 will be as hard or easier?? Sorry and do you mind explaining how the bell curve works? Usual A is 70 but now bc of the bell curve it’s pushed up to 80+??

    • abc
      Reply

      80++?? So high? πŸ™ I thought this year’s paper was quite difficult πŸ™

    • KS Teng
      Reply

      I explained a bit on bell curve and you can read more here.
      This is general treatment of bell curve. So you need to actually hope that some schools don’t over perform

  • Student
    Reply

    Question 10iii, my first 2 terms are correct but last term is same also but i put in plus sign… may i know whether i can get 5 marks?

  • Student c
    Reply

    Hi if for Q4 my area equation is wrong but i managed to prove that it’s maximum and differentiate correctly and find a value of X which i put into A to get the answer, how much method marks will i get?

  • Student
    Reply

    Question 11ii, i left my turning pt coordinates in ((sin(taninverseroot2))^3 and same for y, how much marks i will be penalised? Thank you

    • KS Teng
      Reply

      I think you might lose max 2 marks since they did ask for non-trigo form

  • Student c
    Reply

    And also for question 2i, if i didnt label the axes points but i just labelled the asymptotes as they requested, will i be penalised?

    • KS Teng
      Reply

      of course thats fine. haha I just out of habit did it.

  • A Student
    Reply

    For the question asking for modulus and argument of z, i just listed them in exponential form… How much marks will i be penalised?

    • KS Teng
      Reply

      i think if lenient, it should be a forgivable mistake, after all your found everything. If they are indeed particular, might lose the answer marks.

      • A Student
        Reply

        Thank you very much for replying to all your comments!

  • Corn-cerned
    Reply

    sigh math

  • Screwed
    Reply

    Hello for the complex number question I forgot to add the negative sign for the modulus and my subsequent parts are wrong. Do you think there will be still method marks or will I get a 0?

    • Screwed
      Reply

      I mean the argument sorry I wrote pie/2 instead of -pie/2

    • KS Teng
      Reply

      yes, there will be method marks too. πŸ™‚

  • hi
    Reply

    for question 2, if I write square root 3 instead of 1.73 will I get marked down?

    • KS Teng
      Reply

      eh, but the actual value is not \sqrt{3} right? :/ It did cross my mind haha but I recall its to be 1.73214, and the given value from GC wasn’t if I recall correctly.

      • ROOOOT 3
        Reply

        Nope it’s 1.732051! Which is equal to root 3 hahaha, I made sure to try a few times

        • KS Teng
          Reply

          oh then okay la. haha they didnt say anything about 3sf or exact etc. so all should be fine.

  • student m
    Reply

    hi. for the APGP question, i accidentally calculated the answer wrongly for the first part because i wrote the sum as (n/2)(2a – (n-1)d). hence, i got a really huge number and my part 3 was affected. how many marks do you think i could get from it? thanks!!

  • Anon
    Reply

    Hi! Will Cambridge give method marks? And for the apgp question I wrote > and < instead of lessor or equal to and etc

    • KS Teng
      Reply

      yup, there are always method marks πŸ™‚

  • D
    Reply

    hello!! just really curious, what do you think is the average mark for paper

  • D
    Reply

    hello!! just really curious, what do you think is the average mark for paper 1 based on what you have observed?

    • KS Teng
      Reply

      by average mark, you refer to the 50th percentile mark? It seems like is 62, from what i gather from my students. The highest that have told me is 98.

      • ooh
        Reply

        so it is possible that those as long u get above 62 still stand chance of getting A? since national distinction rate 50%?

        • KS Teng
          Reply

          yes, provided you’re 50th percentile. National Distinction rate hovers around there. But for example, RIJC has >70% distinction rate in 2014 and they had about 1200 students. Thats just RIJC, the list goes down. So its really dependent on how well the rest did. πŸ™‚

  • Pizzalover
    Reply

    Hi, for 10 part iii, how many marks would I get if I proved the statement as well as got the correct limits?

    For 11 part ii, I got square root 2 and second derivative correct, how many marks do you think i can get?

    for part iv, I got 3/a, but did not proceed to get final ans, how many marks does that warrant?

  • J
    Reply

    Hi will I still get method marks if I found my max point in terms of K but did not sub in K is 2? thanks!

  • Pizzalover
    Reply

    last year math distinction rate is how much??

  • Shawn
    Reply

    Is 96 a good score?

    • KS Teng
      Reply

      Yes Shawn. Good job!

    • ?????
      Reply

      U fokin wot m8??!?!?

    • student
      Reply

      Shawn, my condolences.
      As a fellow candidate, I honestly cannot help but feel sorry for your under-performance. Seriously though, did you even study for this paper? Getting 96 is, to say the least, nothing short of dismal – I suggest that you start putting some conscientious effort into studying Math. Please reflect.

  • help me pls!
    Reply

    sir… is my chances of getting a B slim if i obtained about 52-55 marks for this paper..? i’m really careless in the paper and have lost alot of unnecessary marks, how much must i score for paper 2 to secure at least a B? thank you so much!

    • KS Teng
      Reply

      Just do your best for paper 2 πŸ™‚

  • AimingHighINeedSelfEsteem
    Reply

    Hi sir, I have very high expectations of myself and am quite stressed out although I don’t show it much. Any tips on how to maintain stamina?
    1. For Q3.i), I drew the diagram with the rectangles’ corners touching the underside of the curve. I wrote that the width of each rectangle is (1/n) and the height is the “x coordinate value where the rectangle’s corner touches the curve is subbed into f(x).” How many marks will I get?
    2. 5.iii) how many marks will i get if I didn’t draw the “-1<x<0" part of the curve? The rest of the curve is correct.
    3. 8iii) will cambridge also accept 12 seconds? Since the 2dp ans is 11.46 I thought it could round up to 11.5, then to 12
    4. 9b)ii) How many marks will I get if I identified only Z1 correctly? Subsequent ans affected
    5. 11.ii) How many marks will I get if my method is correct but my k is wrong? I used the cosine double angle formula when solving dy/dx = 0 and got k=1 πŸ™ and I also wrote that second derivative < 0 hence it is a maximum but I didn't show working. Since my k is wrong, it affected my ans for 11.iv) but my method for the whole of question 11 is correct.
    I calculated a tentative of 88 marks for math paper 1. How much should I aim for paper 2 to get an A? Also, how much time should I spend on the pure math section for paper 2? Thank you!

    • KS Teng
      Reply

      hi, don’t be so stressed :/ Last thing you want is blank out or panic attack now. haha
      1. its fine if you touch the underside, meaning I took the right side of rectangle, while you took the left. but in this case, your height will be slight different actually. your first height will be f(o) while the second height will be f(1/n). So you summation needs to be properly justified. Slightly more tedious in my opinion. But it should not be much of a problem should you be precise. If you’re concerned about presentation, google Riemann Integral or Riemann Summation. πŸ™‚
      2. You probably just lose 1 mark. You aren’t alone I think so don’t worry bout this.
      3. But that’s not really how we are taught to round off decimals actually. :/
      4. So you attempted the rest of the parts, but with a mistaken Z2? You should still get method marks if your approach is correct.
      5. Then you will lose the answer marks and get the method marks if everything else if correct and well presented.

      88 marks is very good. πŸ™‚ Just maintain the same standard for Paper 2. I can tell you that 170/200 is a very very safe A. Not a sufficient grade. My close students will know why I can say that safely haha.

      Well, my take, judging from Paper 1 (contrary to how people say its hard, I think its very very tricky and tedious but not conceptually challenging), Paper 2 is left with really big topics. I’ll give an hour or even 10 minutes more for the Pure Math as I do anticipate it to be rather tedious, that said, there should be many pitfalls for careless mistakes. So I will actually spend a bit more effort to be really careful with my workings and make sure I’m precise. πŸ™‚ As for paper 2, just don’t copy wrong values of GC. πŸ™‚

  • ooh
    Reply

    sorry can you answer this I’m pretty worried!!!
    Hi, for 10 part iii, how many marks would I get if I proved the statement as well as got the correct limits?

    For 11 part ii, I got square root 2 and second derivative correct, how many marks do you think i can get?

    for part iv, I got 3/a, but did not proceed to get final ans, how many marks does that warrant?

    Thank you!!!:)

    • ooh
      Reply

      for whatever that’s stated above I didn’t proceed to get the final answers..

    • KS Teng
      Reply

      I think the prove is 2 marks, cos what follows is integration by parts twice.
      So you didnt find the coordinates only, would say 4.
      You probably lose 1 mark for not equation the tan back.
      Sorry bout not replying earlier, got classes on, and also overlook some comments. :/

  • ooh
    Reply

    and what is the lowest mark you’ve heard of so far??

    • Pi bond
      Reply

      From what i heard from others, 75~90

  • aaa
    Reply

    um so sorry to disturb.. did you find more people complaining that this paper was hard vs the past few yrs?? and what was the mark to get grade A in 2014, 2013 and 2012 ( I know can’t be exactly accurate but an estimation will do πŸ™‚ )

    • KS Teng
      Reply

      Yes, more were complaining that its is hard this year compared to last. But some do find this paper generally easier too. I think its how you’re trained.
      I dont know the minimum grade to get A. Sorry, and I don’t have sufficient information to run it too, even if I can code. But I can only say that 170/200 is a very very safe A.

  • diego
    Reply

    Hi, appreciate the answers you have provided. Just calculated my score and got about 75-80 for Paper 1. I know there’s still paper 2 and all. Based on the feedback you have received from all the students and assuming the difficulty of Paper 2 remains the same as previous years, what would you say the range for an A would be?

  • diego
    Reply

    And in your explanation of the bell curve, you mentioned that 25% would of the population would normally score an A, how is this possible when the national average for distinction is at about the 50% range?

    • KS Teng
      Reply

      Yes, cos I didn’t go further to explain skewed distribution curves. I think it will not help the morale. But if you are really keen, you can go google more on skewed normal distribution. Yes, I mentioned that according to a nice normal distribution curve. But we never get that in reality.

      I’ve updated the post to include a curve with skewed distribution.

      At the end of the day, Statisticians, we love the symmetrical normal distribution curve, it also means I set a good paper that had assessed my candidates well. But what I can’t pre-empt is students all doing too well. And since the max{marks} = 100, it gets pushed to the right, resulting in skewness. The median and mode deviating from the mean (which is perfectly normal), also encourage the curve to shift accordingly.

      Consider this really basic scenario, where my median score is 70 and my curves is skewed to the right. This implies that many students had scores close to 70 (can be higher or lower) but a few students scored much higher.

      • diego
        Reply

        okay thank you so much. also if you don’t mind, can you answer my previous question before this on what you think will be sufficient for an A (over 200 marks) based on the feedback you’ve received from the paper so far and assuming Paper 2’s difficulty remains the same as previous years

        • KS Teng
          Reply

          I can’t suggest a sufficient mark here. But a necessary mark is above 70. I feel that 170/200 will be super safe. πŸ™‚

  • squirrel
    Reply

    hi sir, how many marks will i lose if i didnt write set notation for both Q8i and ii? and will they deduct marks for not explicitly writing k=1/32 for Q4 even tho i derived at the ans in the form they wanted? also, do they deduct marks for giving the wrong units even tho the value of the ans is correct (such as in qn4)? thank you!!

    • KS Teng
      Reply

      the k part, should be okay. just presenting nicely. haha.
      units might not matter that much honestly, just a presentation too. Its more of the SF that matters I reckon and the form they request for the answer marks. So yes, if they want set, I think you should need to give in set.

  • Ecfpls
    Reply

    hii sir!! if i copied the -32i in qn 9 wrongly to be 32, would they still give method marks for subsequent parts?? and also if i didn’t have time to finish the differentiation question, i only wrote out eqns for perimeter, would i still get method marks? also for the maclaurin question, my ans for b and c were swapped, but would i also get method marks? is a tentative score of 72 good enough for an A? (lol i dont think i can get 98/100 for p2)

    • KS Teng
      Reply

      i think you will still get method marks, |z| should be correct after all. There might be method marks for the perimeter, this question quite generous, though having rearranged it to find y would’ve been better.

      oh man, the b & c haha, one of my JC1 did that same careless this morning. When I say 170/200, I do mean by very very safe A and is not a sufficient mark. Necessary mark will be more than 70/100. As for a sufficient mark for A, I can’t say much.

  • student
    Reply

    Hi sir, firstly, thank you for answering all these questions from students meticulously, it most definitely is no easy task and we appreciate it a lot πŸ™‚
    Was just scrolling through these comments and one thing that alarmed me was the “A-range”.
    According to my teacher (I’m a student in RJ and my math teacher is a highly respected teacher with at least 10 years of experience), on normal years, getting 74~76% is enough to secure an A grade. Given that this year’s paper was rather challenging (as many students from our school felt), I was thinking that the cutoff would me much lower.
    Just to give you an idea of how my schoolmates did, the median stands at about 75 (I feel, based on what my friends tell me, sample size < 50 unfortunately). Given that, based on our school's records, approximately 75% of our school gets an A grade for math, hearing that 155 is as lowest as A grade goes is rather alarming.
    Also, I feel that "170 for a safe A" is really a gross overestimation even based on normal years (I'm just taking my teacher's word on this, while you definitely have your fair share of experience), much so for this year. Sure, it is safe, but I feel as though 160 should be more than enough for a safe A, assuming Paper 2 is of normal difficulty.
    I really respect your opinion and such, and I really trust in your judgment, and I would just love to hear your thoughts πŸ™‚

    • KS Teng
      Reply

      Hi, I said 170 is a very very safe A, like I’m sure it gives an A. I do not know the exact bound as a lot depends on how well the others. Personally, I do not dare to give a broader range as it is out of my confidence interval. So take that with a pinch of salt, as I don’t have a good data. And yes, 75% of your school get an A and 80% of HCI get an A, if we reverse engineer this data based on the population, we realise that there are lesser A’s left than proportion. And we can continue to skim the number number, and some schools do end up as collateral by being on the left tailed of the curve. And I don’t want to give any number that I’m not confident of giving. I can say that 85 is definitely an A.

      Personally, I feel that the year paper seems to be more of testing students on precision and consistency. You just need a lot of stamina and tenacity haha. If the difficulty is same, I’ll say paper two will just be tricky.

      Having the median is helpful, but we sill need mean and standard deviation haha. but that should be a healthy benchmark for A. Maybe next year, I’ll write an algorithm just for students to input their guessed marks and curve it out haha.

      • student
        Reply

        Hahaha…. thank you πŸ™‚

    • aaa
      Reply

      wow ur teacher said 75 only??

      • student
        Reply

        Yeah he did… maybe it’s not completely accurate, don’t take my word for it. All the best. πŸ™‚

        • aaa
          Reply

          haha but for sure your peers thought it was a challenging paper and most of them got around 75? It would be comforting to hear.. but sounds too good to be true that I’m not that far off..

          • student

            How much my peers got depends on their individual capacity as a candidate – of course there are a few who have gotten everything right and a few who dropped more marks than they would have wished to, but the general opinion I got after speaking to many of my friends was that they dropped about 20-30 marks… I cannot confirm if it indeed is representative of our cohort.
            Haha cmon dude we are all really normal people not result-producing machines calibrated to solve math questions haha have more faith in yourself man

          • Student U

            Really? My classmates however felt it was an manageable paper. I got 82 marks (inclusive of the loss of marks due to careless mistakes).

          • KS Teng

            thats good! hopefully paper 2 will be better!

          • Student U

            And i dont think that over 170 marks is an overestimate.

          • KS Teng

            I should clarify that 170 isn’t a sufficient nor necessary estimate. It is a very very safe A.

          • Almighty

            Hi, I am also from RJ, but I doubt the average score is 75. Really sorry but from what i gathered from my classmates and friends it is actually way higher than that. I am also from an average class btw.

          • Lazystudent

            Hey guys, there are still other subjects left. If you are unable to get A for math there are still other subjects for you to score that A. And also A levels is not everything in life.

          • DJmax

            From what i have gathered, A grade this year should be around 160 – 170…

        • PleasegivemeAforMath
          Reply

          u from which class in RJ?? How come My feel is so different from urs? Your friends usually score well or not?

          • PleasegivemeAforMath

            just trying to estimate the accuracy of ur statement btw… no offence!!!

          • student

            I’m from a Physics class πŸ™‚ You mean your friends found it easy? Like, I know our school streams classes to a certain extent, but I think my class is pretty average.
            What is the range that your friends give? Mine is about 70-85 (not just my class). I got ~84.

          • Student

            After asking around, I got the sentiment that most people in the top 50 percentile scored 70+, and those in bottom 50 percentile scored around 60+? There has been quite a lot of people saying the A grade this round should be at most 70..not too sure how accurate this is though, but I sure am hoping it is true! (Scored 70+ myself ><)

  • Mango Ice blend
    Reply

    Demoralising paper…. I think it is difficult to get A as people from the top tier JCs may find this paper easy…. πŸ™

  • Student A
    Reply

    Thanks for the worked solutions, Lol i got 82 marks (inclusive of loss of marks due to careless mistakes). However, my other classmates scores were higher than me and they said the paper was manageable.

    • KS Teng
      Reply

      Yea, in general there is a proportion of students that did quite well too haha Like I said, 170/200 is my gauge of a very very safe A, and not a sufficient mark.

      And thats great! keep up the good work with Paper 2. πŸ™‚

  • J
    Reply

    Hi Can you find equation of tangent and equate it to ax?

    • KS Teng
      Reply

      I’m not really sure how it works, cos you still have an unknown x right?

  • Student g
    Reply

    For qn9bii, will I get some marks by doing by this mtd : find z1 – z2, then take the sq of the coefficient of real root + sq of coeff of imaginary roots, then sq root ?
    Now that I think about it, it’s very weird but somehow I manage to prove

    • KS Teng
      Reply

      yes definitely. you’re doing by the definition of modulus actually. πŸ™‚ They didn’t ask for any specific method like aground diagram, etc. So that’s perfectly fine.

  • Student
    Reply

    For 9bi, I stupidly made a careless mistake so my |z| is wrong, but the roots and methods subsequently are are correct. How many marks would this cause me? Thanks!

  • Former A-level student who survived and got my A
    Reply

    As a former HCI student who took the test last year, I would like to share some of my personal understanding and also those from my teachers regarding the minimum benchmark required to get your shiny A for Math. I can totally understand how some (or most) of you are going through right now since at this point of time last year, I was desperately trying to gather as much information as possible regarding my chances of getting an A for math, after my less-than satisfactory performance during the very test.

    My information coincides with those given by the RJ candidate who shared his thoughts in the comment sections as well. My math teacher (whom I respect tremendously) who taught math for the past 30 years of her life said that the cut-off point for an A grade is probably a “high 70 (exact phrasing)”, which would be around 155/200, or the bare-minimum estimated by Mr Teng himself. Given that the trend of difficulty in A-level is increasing by year, it is reasonable to think that a 160 would probably land yourself in the safe zone this year.
    As for myself, I must said I performed extremely poorly that year, committing mistakes in literally every single questions. I scored around ~75 for paper 1 and ~80 for paper 2 (of course, I am abit harsh on myself and did not grant myself with generous method marks). I was really crestfallen then and it affected me even in the science papers. Eventually though, I still got my A for math, which made me really happy (lol).
    What I want to say is, don’t lose faith in yourself. Sometimes the A is really easier to obtain than what you have thought. Just keep calm and carry on, and you will get what you deserve.

    • aaa
      Reply

      don’t mind me asking: which year did u graduate? πŸ™‚

      • DJmax
        Reply

        Dude read, he said last year…

      • Former A-level student who survived and got my A
        Reply

        Last year? I said in the post lol

        • aaa
          Reply

          oops sorry blur. how much dou think u got including method marks?

          • Former A-level student who survived and got my A

            I am not sure how lenient the markers will be when they give out method marks. I do remember that the range of scores I gave myself by calculating the so called “best and worst scenarios” was 150-165. So I guess if my estimation was correct, I should have scored in the high 150s.

  • Student
    Reply

    For qn 1i, I made a careless mistake in one of the simultaneous equations. I wrote coefficient of c wrongly in one of them but the other two eqns are right. how many marks will I get for part i? Will there be ECF for part ii?

  • Student x
    Reply

    Hi!Paper 1 I scored 82, paper 2 71! Is there sympathy mark if the product correlation is given in 3sf but calculated correctly?
    153 sufficient to get an A?

    • KS Teng
      Reply

      i think since its not like 1 mark individually, they give 3 marks for the whole mark. they won’t minus all 3 cos you didn’t round to 4 dp haha. there should be method mark. haha i’m not sure if its sufficient, but it should be necessary. πŸ™‚

  • late
    Reply

    Hi I know its kinda late but I thought I should just try asking. For Q4 my initial area equation was correct but my d equation was wrong so I substituted and differentiated the wrong equation. Therefore couldnt prove it was a maximum by differentiating the differential. However I did all the right steps. Do I get any sort of method marks?

    • KS Teng
      Reply

      you might get 2-4 marks. πŸ™‚ Dont worry and good luck for the remaining papers

  • Student
    Reply

    Hi!For the APGP question I carelessly put my n=20 instead of 50 but the rest of the method is correct.Would I still be awarded the method marks for it and how much marks do u think I would get for the question out of 11?

  • approximation
    Reply

    for question 9(ii), I carelessly wrote e to the power of ipi/2 and forgot the negative sign. however the rest of my working is correct. Will I be able to get 2/3 marks?

    • KS Teng
      Reply

      i assume you refer to 9bii. it should be 2 marks each, and you were not required to write out what z_1 and z_2 are explicitly. And I believe the answers will be the same, so long as you take a pair of z’s that are next to each other actually. You might lose 1 mark for the method, for overlooking the angle.

  • aabcde
    Reply

    Hi KS just curious, what do you base your estimates for the min. number of marks to get A on? πŸ™‚

  • lol
    Reply

    hi! i am a student from hci. guys please relax and jiayou for the papers ahead !! a lot of my peers and i in fact, found the paper quite tough tbh!! more difficult than the past year papers and this year’s paper 2 pure math was definitely more challenging πŸ™‚ point is, there really isn’t any use in knowing where you stand/ whether you can get your a for math i guess. because no one knows how the entire cohort is going to fare right πŸ™‚ let’s just jiayou and focus on the remaining papers!!! and continue to have faith!!!

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