2012
Wed
7
Nov

GCE A Level 2012 Oct/Nov H2 Maths 9740 Paper 1 Suggested Answers & Solutions

(53)
Tuition given at 9:09 pm (Singapore time) by The Higher Council in H1/H2 (A Level) Maths Tutor

It’s my annual hello to all of you again.

While my sister has churned out her O Level A/E-Maths solutions with much fanfare, here’s my little contribution to all our A Level comrades this year.

Click the Like button and grab it here!

Latest version:

  • 1.1:

    Q6(iii) – amended working step n = lg1000/lg2 to compare 29 = 512 and 210 = 1024, in order to comply strictly with the “No Calculator” requirement in this question.
    Q11(i) – improved descriptions of the tangents (sorry couldn’t write straight that night *sigh*)

GCE A Level 2012 H2 Maths 9740 Paper 1 Solutions
Access it here if you’re having trouble accessing it on Facebook using your state-of-the-art smartphone :(

As usual, all yim yim jim jim scrutinizers please leave a gentle comment should you spot any mistake in this set of suggested solutions, which was produced well after my last class at the end of my tiring day *rubs eyes*

Now go revise your

  • AP/GP
  • Integration by parts/substitution/ Volume of revolutions
  • Summatioon (Method of Difference)
  • Complex Numbers (Argand diagram)

All the best for your Paper 2!

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Revision Exercise

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Comments & Reactions

48 Comments

  1. pheng's Avatar
    pheng says


    2012
    Nov
    7
    Wed
    9:33pm
     
    1

    just wondering, how difficult do you think this year's H2 paper was?

    • boo's Avatar
      boo replied to pheng’s comment


      2012
      Nov
      8
      Thu
      9:47am
       
      1.1

      @pheng: wa tis year's paper too easy.. RJC's tcher said to get A yall hav to score above 87 at least

      • x's Avatar
        x replied to boo’s comment


        2012
        Nov
        9
        Fri
        6:15pm
         

        @boo: Which "RJC's teacher" said that, may I ask? I'm from RJC myself, and if it's true that the grade boundary is 87, then even this school will have a ridiculously low distinction rate. Look at my below comment, and that of Carol.

  2. Michelle Lee's Avatar
    Michelle Lee says


    2012
    Nov
    7
    Wed
    9:35pm
     
    2

    Hi hi, are you gonna share the solutions for H1 Math too?

  3. ck's Avatar
    ck says


    2012
    Nov
    7
    Wed
    9:41pm
     
    3

    Hi sir, just a few qns. for qn ten my method was correct of substituting h equals to something k, but the substitution was wrong. approximately how many marks for method will i get? additionally for the mi qn i put n is z and not z plus, is that ok,like will minus mark? and erm for the definite integral i just put =answer(in 3dp) without the longer answer than the curly equal sign, is that ok, like will minus mark? and uhm for the vectors qn 9 i got first aprt correct but cos of calculation error second and third aprt wrong but emthod correct, approx how many method marks? similarly for the intial vector qn ihad a calculation error at the final step the square root u etc last step, is that enuff for two method marks? and for the integration qn i didnt say c is a constant is that ok? and finally do u hv any duiea whats the grade range for a? any help would be sincerely appreciated thanks

  4. ck's Avatar
    ck says


    2012
    Nov
    7
    Wed
    9:45pm
     
    4

    and sorry one last one. for qn 8 i just said since the sign is negatiove its always less than zero. but i accidentally put min point. will is till get 1method mark? thank you

  5. j's Avatar
    j says


    2012
    Nov
    7
    Wed
    9:49pm
     
    5

    hi sir can u approximate the a for this year?

  6. angstzx's Avatar
    angstzx says


    2012
    Nov
    7
    Wed
    9:53pm
     
    6

    hello

    for qn 9 (ii) is it possible to find the ratio of the lengths AN:NB using this method? or why is it not acceptable?

    AN = ON - OA
    NB = OB - ON

    proceed to mod AN and NB, then compare the lengths? my answer was 1:5 if i didn't forget.. :/

  7. gr's Avatar
    gr says


    2012
    Nov
    7
    Wed
    9:59pm
     
    7

    i think the difficulty of p1 for this year as compared to last year was eazier

  8. Ang's Avatar
    Ang says


    2012
    Nov
    7
    Wed
    10:53pm
     
    8

    Hi I think qn 11iii) has a mistake, the limits weren't changed from x to teter?

  9. Wesley's Avatar
    Wesley says


    2012
    Nov
    7
    Wed
    11:18pm
     
    9

    Hi, I would like to ask if there's likely to be ECF for QN 11, as I did not include the base surface area.

    Thanks!

  10. x's Avatar
    x says


    2012
    Nov
    7
    Wed
    11:26pm
     
    10

    Here we go again, people asking about the grade boundary to get an A, as with every year. There is really no way anyone can give a good approximate, because SEAB is very opaque when it comes to their moderation procedure, so we can't really know. The worst thing anyone can do now is to give a high estimate (e.g. 85) since this was an 'easy' paper, then everyone who did NOT get that grade will start fearing, and have decreased morale.

  11. cheryl's Avatar
    cheryl says


    2012
    Nov
    7
    Wed
    11:38pm
     
    11

    Hello! May I ask what is the estimated mark for an A this year?:)

  12. Jud's Avatar
    Jud says


    2012
    Nov
    8
    Thu
    12:05am
     
    12

    For question 9(i),

    Why shouldn't the solution be:

    Vector equation of the line AB:
    r = (7,8,9) + λ[ -(7,8,9) + (-1,-8,-1)]
    = (7,8,9) + λ(-8,-16,-8) , where λ is a parameter.
    (Can this be left as the final answer?)

  13. daniel zeng's Avatar
    daniel zeng says


    2012
    Nov
    8
    Thu
    2:20am
     
    13

    is 75 safe? can any1 estimate for me pls

  14. T's Avatar
    T says


    2012
    Nov
    8
    Thu
    7:39am
     
    14

    Hi, I would like to ask if answers that are not simplified will be accepted or penalized. For eg Q9iii, I didn't simplify my answer and left the Cartesian equation as over 2, -8 and 2 for the x y and z respectively. And for Q6iii also I left it as -10pie /3.

    Thanks



    • 2012
      Nov
      9
      Fri
      1:04am
       
      14.1

      @T: For Q9(iii), you mean you left your equation of the line as a column vector? If this is the case then it's not in cartesian equation form leh.

      For Q6(iii), generally it's a good idea to express your final answers for arguments as the principle argument but you may get away with leaving it as −10π/3 since the question did not specify requirement for the argument of zn to be between −π and π in this case.

  15. curious's Avatar
    curious says


    2012
    Nov
    8
    Thu
    8:09am
     
    15

    Hi may I ask if they asked you not to use a calculator in question 6 and you used lg1000/lg2 to compute n which is also stated in your solutions provided, what will happen?

  16. meme's Avatar
    meme says


    2012
    Nov
    8
    Thu
    1:17pm
     
    16

    I could guarentee 85 - 88 marks. Isit safe for an A ?

  17. Carol's Avatar
    Carol says


    2012
    Nov
    8
    Thu
    6:55pm
     
    17

    hi to all who asked about mark gauges..
    i would like to paraphrase a quote from a previous forum, and the quote was from the cambridge examiners themselves: the grading for a levels is comparable to judging a student's ability to swim 100 metres. if you're able to clear the 100 metres, you'll get the A regardless of the number of people who are able to swim around the world. so i guess don't worry if you aren't able to hit a high score, just aim for as high as possible for tmr's paper!

    if you really want a gauge.. i think the RJ comment is not representative of wat is going on in SG la. over here at where i am the consensus is "ok but damn tedious", My estimate for my own score is 82 (provided got ecf..), but i've also seen ppl who couldn't do all the last three qns. so i guess this year the threshold will be lower..

    • meme's Avatar
      meme replied to Carol’s comment


      2012
      Nov
      8
      Thu
      7:23pm
       
      17.1

      @Carol: True. If its 87 for an A, all the people taking h2 math in rj and hci sure A then people of yjc and mi get D? Lol



    • 2012
      Nov
      9
      Fri
      12:00am
       
      17.2

      @Carol: LIKE!

      This quote really brings back memories of that long list of comments in 2010!

      • Carol's Avatar
        Carol replied to Mr Loi’s comment


        2012
        Nov
        9
        Fri
        3:18pm
         

        @Mr Loi: oh yes Mr Loi, just some question to ask: will there be method marks and ecf for question 10 if i forgot to include the base area. because i did everything else the same way and got an answer for r that differs by a digit..

        and for question 11 i used parametric integration (the one where you differentiate y in terms of t and leave x as it is, then integrate in terms of t), and got 3pi (though with a negative sign so i took absolute value). would that be fine as well?



        • 2012
          Nov
          13
          Tue
          12:29am
           

          @Carol: As mentioned here, method marks and ECF are determined by the mark scheme, and that they are given when it was only the substitution of a wrong value in your appropriate steps that led to the wrong answer.

          While I think there's a good chance they're allocated here with [7] & [5] marks in parts (i) & (ii), I'm really hoping they'll be lenient in your case since omitting the base area would have affected the expressions for the surface area, its derivative, r and h. (unless you've gotten some of the above right?)

          For Q11, you seem to have done it the same way as me. If so, you shouldn't get −3π. Have you gotten your limits the other way round in the definite integral?

          • Carol's Avatar
            Carol replied to Mr Loi’s comment


            2012
            Nov
            13
            Tue
            7:11pm
             

            @Mr Loi: Sorry for the long hiatus. I found h in terms of r using the volume expression, so that part would be the same as the answer scheme. Yeah I do hope method marks will be given, since there is really no difference in the method other than the base area, and quite a lot of people from my school had left out the base area when calculating as well..

            As for question 11, I realised I had unwittingly integrated x in terms of y, and it so happened that the answer was the same in magnitude. So I suppose I will lose the method marks and hopefully get one mark for the right answer...

            Luckily paper 2 managed to pull me up, despite being a harder paper.

  18. Adeline's Avatar
    Adeline says


    2012
    Nov
    8
    Thu
    9:59pm
     
    18

    Hi, will there be solutions for the Math H1 paper as well?

  19. amos's Avatar
    amos says


    2012
    Nov
    9
    Fri
    5:49pm
     
    19

    Will it be penalised if l = -1/3 is found using GP method instead of the usual way?

  20. Ang's Avatar
    Ang says


    2012
    Nov
    9
    Fri
    6:55pm
     
    20

    Hi Sir, may I know if today maths paper 2 solutions will be up?

  21. Jess's Avatar
    Jess says


    2012
    Nov
    10
    Sat
    1:08pm
     
    21

    Hi, for the question that needs us to show that dy/dx = cot 0.5θ, could we do it this way?
    dy/dx=...
    = (sin θ)/(1-cosθ)
    = (sin 0.5θ+0.5θ) / ( 1- cos(0.5θ+0.5θ))
    then we go on to solving the equation using these 2 formulas:
    sin( A+B) = sinAcosB+cosAsinB and
    cos(A+B)= cosAsinB-sinAcosB
    if not, then why is it wrong?

    thanks :)



    • 2012
      Nov
      13
      Tue
      12:41am
       
      21.1

      @Jess: Q11(i) Using Additional Formulae is perfectly fine, though it looks a bit tedious ;)

      • Jess's Avatar
        Jess replied to Mr Loi’s comment


        2012
        Nov
        13
        Tue
        2:19pm
         

        @Mr Loi: Hi Sir, but the problem is that when I continued to solve it using the additional formula, the final answer I get is 2 sin 0.5θ cos0.5θ. I am unable to get cot 0.5θ.

        thanks!



        • 2012
          Nov
          14
          Wed
          12:09am
           

          @Jess: Hmmm ...

          \frac{\sin (\frac{\theta}{2}+\frac{\theta}{2})}{1-\cos (\frac{\theta}{2}+\frac{\theta}{2})}

          =\frac{\sin (\frac{\theta}{2}) \cos(\frac{\theta}{2})+\sin (\frac{\theta}{2}) \cos(\frac{\theta}{2})}{1-[\cos (\frac{\theta}{2})\cos (\frac{\theta}{2})-\sin(\frac{\theta}{2})\sin(\frac{\theta}{2})]}

          =\frac{2\sin (\frac{\theta}{2}) \cos(\frac{\theta}{2})}{1-\cos^2 (\frac{\theta}{2})+\sin^2(\frac{\theta}{2})}

          =\frac{2\sin (\frac{\theta}{2}) \cos(\frac{\theta}{2})}{\sin^2 (\frac{\theta}{2})+\sin^2(\frac{\theta}{2})}

          =\frac{2\sin (\frac{\theta}{2}) \cos(\frac{\theta}{2})}{2\sin^2 (\frac{\theta}{2})}

          =\frac{ \cos(\frac{\theta}{2})}{\sin (\frac{\theta}{2})}

          = \cot (\frac{\theta}{2}) (shown)

          Did you steps tally?

  22. Yak's Avatar
    Yak says


    2012
    Nov
    15
    Thu
    10:44pm
     
    22

    Are we really expected to do 2^10 without calculators? =\

  23. Dudeail's Avatar
    Dudeail says


    2012
    Dec
    3
    Mon
    10:26pm
     
    23

    Hi ,I know it's kind of late haha but my friend wanna ask whether can switch step1 with step 3 for qn7:)

  24. Drea's Avatar
    Drea says


    2013
    Nov
    18
    Mon
    10:43am
     
    24

    Hi Miss Loi, I know this is not the 2013 thread but I can't find it so can I ask you a general question regarding the grading system?

    Does Cambridge give us our marks (based on score and/or ability) or do they simply write down our scores and give them to MOE who will moderate them and create the bell curve?

    I am asking this because I am afraid I am scoring a low 70s due to a lot of careless mistakes :(

    Thanks!

5 Reactions

  1. Tweetback
    Miss Loi tweeted


    2012
    Nov
    7
    Wed
    1:16pm
     
    25

    #alevel #H2 Maths suggested answers & solutions done on a really quiet night: http://t.co/dL0j7RWj (no twang twang twang this time) #math

  2. Tweetback
    yen tweeted


    2012
    Nov
    7
    Wed
    1:26pm
     
    26

    #alevel #H2 Maths suggested answers & solutions done on a really quiet night: http://t.co/dL0j7RWj (no twang twang twang this time) #math

  3. Tweetback
    Wee Keat tweeted


    2012
    Nov
    7
    Wed
    1:49pm
     
    27

    #alevel #H2 Maths suggested answers & solutions done on a really quiet night: http://t.co/dL0j7RWj (no twang twang twang this time) #math

  4. Tweetback
    Lau Hui Ru tweeted


    2012
    Nov
    7
    Wed
    2:40pm
     
    28

    #alevel #H2 Maths suggested answers & solutions done on a really quiet night: http://t.co/dL0j7RWj (no twang twang twang this time) #math

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