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Suggested Answers to 2014 A Level H2 Math 9740 PAPER 2

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The following is a suggested solution by our H2 and H1 Math Tutor, Mr. Teng. Please note that it is a suggested solutions and was rushed out. Mr. Teng omitted several presentation steps out of convenience. There might be alternative solutions at times too. Feel free to comment and discuss. Please let us know if there are mistakes too. Thanks in advance.

PLEASE NOTE THAT STUDENTS ARE EXPECTED TO WRITE STATE YOUR DISTRIBUTIONS CLEARLY. We omitted for convenience.

Disclaimer: This suggested solutions is provided free by Mr. Teng & Singapore Learner. Both parties do not profit from this. We simply believe that this will help current students and future students to learn from the mistakes of others. Thanks.

ERRATA & Remarks:

6(ii) I miscounted and was careless.

Case 1: A plays midfield, B sits out of attacker =>3c1 x 8c4 x 4c1 x 5c4

Case 2: A sits out midfield, B plays attacker => 3c1 x 8c4 x 4c2 x 5c3

Case 1 + Case 2 =1 6800

(iii) I doubled counted indeed. Thanks for pointing out. Should be

Case 1: Midfielder A plays midfield => 8c4 x 3c1

Case 2: Midfielder A plays defender => 8c3 x 3c2

Case 3: Midfielder A sits out => 8c4 x 3c2

3c1 x 5c4 x (8c4 x 3c1 + 8c3 x 3c2 + 8c4 x 3c2) = 8820

8ai. I drew the left side of the quadratic. It should be the right side. my bad.

9. I initially used Z-Test for this question. But T-test is definitely more appropriate as we are given as unknown population variance. I changed it to T-test in the following solutions, but understand that some teachers consider Z-Test to be acceptable too. I should highlight that nobody has access to the actual answer scheme; we only see the marker’s report.

(ii), (iii) Set notations should be used. {t>3.48} and {0<k^2<0.423}

11. Please take note that I used CLT here, so cc is not required.

– I understand some students misunderstand that CLT is used to find the mean of any distribution. This is a terrible misconception. CLT is a limiting theorem, and we apply it to approximate a non-normal distribution to a normal distribution, given n is sufficient. And they can be sum of independent random variables, sample sum, or sample mean. You can read more from the link below.

Click to access 408clt.pdf

– Why I used CLT approximation instead of poisson approximation (Poisson approximation is not incorrect either): I used continuity correction in qn 7 alr, so given examiner psychology, I would think they want to be impressed with something different. That’s why I picked CLT approximation. Do note that this does not mean that doing poisson approximation is wrong; so long as you perform cc precisely.

I do hope this clarifies, and I’m sorry it came late as I was ill and had jc1 classes yesterday too.

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518 thoughts on “Suggested Answers to 2014 A Level H2 Math 9740 PAPER 2”

  2. Hi, i think for the hypothesis question, it’s supposed to be a t-test, but i did a z test too:( will it have method marks? And for qn 2, i got the splitting of partial fractions wrong, can you give an estimate of how much marks will they give? Thanks’

    2. I corrected it thanks. My bad for the confusion
      You should still get credit if you used the correct integrals.

    1. To be honest, its just Alevels. Life is much more than that. 🙂 Furthermore, you still have many more papers to go. Don’t let math beat you down

  4. Hi, shouldnt Qn9 be done using T test since population variance is unknown and sample size=10 is small?

  6. For question 9, shouldnt it be t test instead? Since population variance unknown and sample size is small

  7. For 11 (iii), is it possible to do it like this? X~Po(11×52) –> Approximate to normal distribution?

    1. Also, for q9 is it a z test or t test and are we supposed to use inverse t or inverse norm for q9. I never heard of inverse t until today lol

      1. I understand that. That’s one of the reasons why I did not do T Test cos invT isn’t supposed to be tested. Haha. But that will leave us with the T-Table at the back of MF15. T Test was the better fit definitely, but due to syllabus constraints I did Z. But I’ve changed to T Test Statistic

  11. For hypothesis testing qn if i didnt calculated population variance and used sample variance will they penalize my whole thing?

  14. Q9 should be a T test since n=10 is small and the question gives a sample variance, which requires an unbiased estimator of the population variance s^2 (which you did) hence it cannot be a Z test? Am I wrong??

  16. Last question the ans should use continuity correction
    And I think for the hypothesis test should use T test and inv T

  18. Thanks a lot teacher!!

    I got 92 marks for this and 65 for the paper 1.. do i have a chance of getting A?

      1. Yes. I believe both are sound. There are a few reasons why i picked CLT to solve this question, primarily because cc was performed previously so I see that I should vary my approach with CLT approximation.

  20. Hi sir,
    Thanks so much for your help these few days : ) could I clarify if 6iii is meant to be 3 cases instead ie 1. The player isn’t in the team, 2. He is definitely selected as midfielder 3. He’s definitely selected as defender? It seems to me for the 2-case approach there might be overlap if he’s not selected to be on team but is considered for the position.
    Many thanks!

  21. for q9, don’t you have to do the s^2=(n/(n-1))(sample variance) since what you have is sample variance and not s^2?

  24. for 6ii, shouldnt it be 5C3 instead of 6C3 if you consider that the attacker brother is on the team?

  25. 11(iii)
    Is it possible to use Poisson approx to Normal instead of CLT? Since they didn’t ask for average.

      2. Then in that case if c.c was applied when approximating from poisson to normal, will that be marked wrong?

        1. no. if you had done poisson to normal via approx, since lamda>10, you need to do cc. only if you state CLT, then no need cc.

          1. But the answer for 11iii if you use clt and if you use poisson to normal approximation will be different so does that mean cambridge will accept 2 answers?

  26. part iii sorry (for q9, don’t you have to do the s^2=(n/(n-1))(sample variance) since what you have is sample variance and not s^2?)

    1. Hi, yes thanks for pointing out. did changed to T test. I used Z test initially as I understood that invT was not in syllabus.

  29. For 6iii)
    What is wrong with this?
    Case 1 status quo : 3C1 x 8C4 x 4C2 x 5C4 = 6300
    Case 2 one dude becomes defender: 4(3C1 x 9C4 x 3C2 x 5C4) = 22680

    Shouldnt’ we x4 for case 2 cos we can pick any 4 of the remaining members to be a defender

      1. But alternative method is to approximate poisson as normal since lubdar is more than 10 then do cc right?

      2. approximation of Po to N is not by CLT if i remember correctly, CLT is only in hypo testing no?

        1. CLT is also a form of approximation. So long as n is sufficiently large and distribution is non-normal, CLT can be applied. And its not only in hypo testing.

          1. Hi why can CLT? whats the n exactly? and why is there sample sum in iii? isnt poisson to norm the only way??

  31. Whats an ok grade for this yr p1 and p2 ? Also , how many percent gets A for math yearly? What do u think we need for an A this yr

  32. Also, for 9(ii) & (iii), the question wants set of values instead of range, so the answer should be expressed with {} instead?

  33. Scatter sketching diagram wrong and so is the explanation

    Z and T test

    CC
    … Thanks anyways

    1. Hi, thanks. I guess explanation could be much clearer and better. Maybe if you have time, help suggest it. Thanks.
      As for the Z, T Test, I corrected it thanks. My bad for the confusion
      CC was not required for 11 as I did via CLT. If you used standard approximations, you will cc.

  37. Pls check 6iii. 9C5 is definitely wrong because only 4 defenders were chosen. I think you need to include a third case where the midfielder/defender isn’t chosen.

    Pls check 8ai as well. It’s y=ax^2+b where a and b are positive. Graph should be rising

  39. For the last question, qn 11(iii) isn’t there continuity correction when we approximate the poisson to a normal distribution?

  40. For Q3, will i be penalized if i forgot to include the units?
    For Q6 iii), I think there is a mistake, how to get 8C4 and 9C5?
    For Q11 iii) will it be wrong if i did not use CLT but c.c instead?
    For Q9, shouldn’t it be t-test since n<30 ?

    1. I think units is a rather minor issue. 🙂 As for qn6, I corrected it thanks. My bad for the confusion. For qn 9, yes, I changed to T-test. My bad too. qn 11, I did CLT, you’re find with normal approximations w/ cc too.

  41. Hi. For qn 6(iii) since they say one of the remaining midfielders can play as a defender, shouldnt you times 4C1 for the case whereby the midfielder becomes a defender because any one of the four midfielder can become a defender.

  43. Regarding Question 6(iii)– wouldn’t the answer be the sum of P(subject is a midfielder) + P(subject is a defender) + P(subject is not on the team)?

  46. 6iii

    don’t you need to consider the 3 cases where
    1. the dual player is not on the team
    2. dual as defender
    3. dual as midfielder?

    also, when the “dual” player is put into the team as either one of the roles, he would not be considered for the other role? hence the need to reduce one person from the pool of choice?

  49. how did u find the 2 papers generally and will the bell curve be high? to me it was kind of difficult this year:/

    1. I think they were easier than last year actually. I have students who retook and they found it comfortable actually. 🙂

  50. Hi for 3ii can we use the n value gotten like 10.281… Then we take 0.281* a11 of the distance? Cuz it will give u 2k+m and if u take 1891/u11 you will only get .22something instead of .28

    1. hi, yea you need to find the a10 distance and minus off. Else, like you mention, there is underestimation

  51. It’s t test! Need to convert sample variance to population variance using n/n-1 x sample variance. Also, if I said if I accidentally saw wrongly the point to use for the perpendicular bisector and ended up with a wrong equation, how many marks will I lose?? Also for 6iii, he decides that one of the remaining midfielders can play as either a midfielder or defender. I assumed that that one could be any of the 4 remaining midfielders, so I had a x4. Will they give me marks for misinterpreting?

    1. Yes I changed to T-Test. I did the s^2 thing, maybe I wrote too briefly.
      Yes your bisector is wrong, its quite costly. the points will be mistaken too.
      I changed my PnC alr. haha.

      1. Oh, because i was aware that t test was the more suitable test, but didnt know of invt, so ended up using inv norm to find critical t value :/ do you think that they will consider the fact that it isn’t in our syllabus, and maybe give chance haha, thanks anyway for ur reply !

        1. Yes, if you read thru the comments etc. haha I do think that T test is more appropriate and simply used Z cos of the syllabus. haha but I guess certain school do teach it. 🙂 Furthermore, we don’t need invT to find the t critical. they do provide you with a T-table in the MF15…

          1. I see.. thanks 🙂 bt if our critical t value in wrong in part ii(cos of using invnorm and not invt), do we still get any marks? Also since part iii requires the same critical value as well, will there be method mark for part iii?
            For the complex qn, finding the possible values of z: i did it by finding the two equations of the loci, followed by finding the intersection by solving them simultaneously. However, j made a careless mistake halfway when transferring values across workings, hence had the wrong x values and corresponding y values. Isit a gonecase/ costly mistake for the 4 marks qn?
            Sorry, i know you are busy entertaining the many many questions, so do take ur time answering and ty !

  53. hi for the regression qn isit possible to leave price in cents? they didn’t ask to leave to anything so I though price in maths is dollars and cents

  54. Q6iii) Should it be 3c1 x 8c4 x 4c2 x 5c4 + 3c1 x 9c4 x 3c2 x 5c4 x 4c1? Because we need to choose 1 out of the 4 remaining midfielders?

  56. Hi can you explain your working in 6iii)? I’ve got 8820 and id considered 3 cases: 1) He’s playing midfield. 2) He’s playing defence 3) He’s not playing at all.

  57. can I leave my answer for the price for regression question I n dollars and cents since they ask for price?

  58. Furthermore there’s the question on hypo shouldn’t it b t-test? And finding k^2 shouldn s^2 b used?

    1. I corrected it thanks. My bad for the confusion
      yes I used s^2 actually. but some steps were skipped

  61. hello, for 6ii why did you only choose 1 midfielder instead of 2? similarly for the attackers, why did you only choose 3 instead of 4 of them? i got 29400.

  63. Qns 8(a)(i) shouldn’t the graph be sloping upwards?
    Qns 9(ii) Why is it a z-test instead of a t-test??
    11(iii) Continuity correction?

    Thank you!!

    1. yes, I actually did the left side of the curve. it should be sloping upwards. my bad.
      as for qn9, I corrected it thanks. My bad for the confusion
      qn11, I did CLT. So cc isn’t required.

  64. Hi Sir, may I know if we will be fully penalized for using Z-test? Since the first part is 4 marks and the second part is 3, does that mean we loss a total of 7 marks when Z test is used? Thank You!

  67. For the hypo ques, if we never use k^2 to find pop variance, but did everything else correctly, is there marks?

    1. Yes, but I treat like jackpot machine. so set 1 will be the first space, set 2 the second. so there is still quite a few variations.

  69. hello!
    for 6(iii) I think your answer is wrong as you double counted the number of ways that player is not playing (when you 8C4x 4C2, that player may not be chosen, and 9C4 x 3C2, the player may not be chosen again)

  70. Hi after seeing both papers , what do you think is the rough rough grade needed to score an A? Also, how many percent of SG usually gets an A? I think I did pretty badly for this paper I’m just hoping the bell curve helps. Also is there method marks for P&C questions? If I forgot to multiply by 2 will I still get a mark for it?

      1. Hi, I’m sorry. I don’t think its good to estimate a grade. 🙂 Many papers more to go. In any case, its over and you should not focus on ace-ing the other subjects.:)

          1. yes. sorry. haha too many comments. and Im like trying to answer all. plus fix my mistakes. haha

        1. Not possible to be 90. I am 99percentile in maths for all internal exams in my school and i only predict around high 70s for combined although i indeed screw up hard for paper 1. I guess it will be 70 this year as they would probably not moderate as long as the distinction rate is not too high.

          1. for all those wondering, my tuition teacher said anything 80 and above or the upper 75 range should be guaranteed A, but if you are in the lower range 70s its a bit risky (but don’t be discouraged maybe you will have method marks!!) Anyway, just work hard for the next few papers, we are all in this tgt 🙂 and it is highly unlikely that A will be cut off at 90, usually you only see that for o level math papers in singapore. Hope this helps!! 🙂

          2. yup. that’s true. But I tend not to say it since most students still having exams. but that’s the general range. you wont go 90.

        2. Are you for real? A 90 is ludicrous if you considered the difficulty of yesterday’s paper. It was likened to some of the top schools’ internal exam questions.

  71. hi, if you used z test for both, would there be ecf for solving the inequality? also, what do you estimate as the benchmark for A? thank you!

    1. I don’t think I can comment on the grade. You still have many more papers to go.
      I felt that both papers were easier than last year.

  75. Shouldn’t the bisector line not be drawn? If not the marker will think its the locus too…
    Also, the scatter plot A should be U shape with the positive side drawn?

    2. yes. the bisector is my bad I drew with pen and overlooked. :/
      Yea, both works so long as its the U-shaped

  77. Hi for Q9ii why isn’t it divided by square root 3.2/10 divided by root 10. U wrote 32 and 9?

    1. From my understanding, its not. Not all school teach it actually, which is why I used Z-Test. But you can obtain t critical via the T table in MF15

  83. Hi for question 6(iii), do we have to consider the fact that any of the midfielder can be picked to be a defender such that u will have to do a 3C1 x 4C1 x 9C4 x 3C2 x 5C4? Please reply

    1. haha but this is an art dealer, and I guess there are quite a few artists around. :/ I guess if you substantiate it well. should be ok.

      1. Will it be okay if I substantiate it as because the artist died, that’s why his art pieces become priceless so there’s an increase in demand for them?

        Also, is it alright to draw the scatter plot for 8ib such that the x values goes from positive y axis to negatove y axis?

  86. Hi, if we used z-test in q9, is it all marks gone?

    for q11ii, what if we did x~po(2n) , p(x<3) <0.01 , and showed the gc table?

      1. No you wont, so long as you state and explain the direction, etc. After all you did figure stage 11 out.

    2. No, I think z-test can still be used actually. since its already normally distributed. But T test seems to be appropriate since population variance is unknown. You should still get marks stating the rejection region, etc.
      They request for an inequality in n. so I think using the formula will be needed.

  87. For 6(iii) I think you have to multiply your answer by 4 for question 6 – Because they didn’t mention that a particular midfielder to be selected so either one of the four can be choosen.

  89. Hi sir,

    For 6 (ii) do you have to minus away the case where neither are selected from your answer? For your method i think there may be the case where neither are selected

      1. Thanks sir. Um i think 6 (ii) and (iii) both works on the same method. Could you clarify the answer for 6 (ii) too! Thanks alot! 🙂

  90. Hi, for Qn9 ii and iii, is it a must to use invT? Since we didn’t learn it.. or is it okay to use a T-test, and then standardise to Z and find InvZ?

    1. Nope, they are different curves which only coincide when n>30. So the values should differ. You can use the T Table provided in MF15 should you not do invT before.

  96. Aren’t we supposed to find 4aii by Cartesian equations of both loci?? Isn’t the answer completely wrong…??

    1. hi if you do by Cartesian equations. you should still get the same thing.
      you bisector should be y=-x-4.

  98. Thanks for the suggested answers for us to check against! The questions were really unusual, like the counting of symbols, wanting us to count stars until we see stars. 🙂

    1. yes, I saw many stars honestly. Pleasure, I needed you guys to help me check too. Cos I make too many mistakes haha

  100. Hi, Shouldn’t 8ai. curve be sloping upwards? Since it is a transformation of partial U shape curve upwards only , not left/rightwards.
    And I thought t-test was in syllabus? [Section 8.2. Include : -use of t-test]

    1. yes I changed it. t-test is in syllabus, but not invT actually. Some schools don’t teach it.

  102. Will I get penalize heavily if I forgot to do n/n-1 ? I got INVT, did t test and my set notation is correct 0<k^2<(some value close to answer since I forgot n/n-1)

  103. For question 6ii) and iii) will I get the method marks if I did the workings u did initially ?

  105. I think your answer to Q8 Part (i) is wrong – how come you can use the left side of the quadratic curve when the equation is y = px^2 + t ? the maximum or minimum of the curve should always be at x = 0

  106. I misread the question for the hypothesis one & wrote H1, more than 4.3. I will lose the marks for the rest of the question rigjt? :(( even if I used the T test & InvT correctly…

    1. I think you still get credit for doing the rejection etc. 🙂 don’t worry. all the best for the rest of your papers

    1. haha. that’s harsh. Well, I think you must consider paper 1 too. In any case, more papers to come 🙂

  109. i said that the paintings were like a jigsaw puzzle so that the event of huying one is dependent of abother. is it acceptable as an assumption?

    1. that’s really creative.. stretching it a little but I don’t see why its not valid since I know some art pieces are like these.

  110. For Qn 6 part 3, i feel your answer is wrong. Dont you need to account for the possible midfield players who can go to defense too? isnt this calculation based on the fact that you already pick out a specific individual to go to defense when the question did not have such a requirement?

    1. I think the team positions are meant to be filled according to question requirements. There is only one such midfielder present
      And my workings are wrong. refer to my errata pls. Thanks.

  111. Hi for qn 8(iii) i think u need to divide by 10 since it say price of a car and P is ten used car in context if i am not wrong

    1. Oh dear. You’re certainly right. Wow that’s terrible! I thought they were Singapore car prices.

      1. for 8biii Why need divide by 10? Because they are taking from sample of 10 cars but not taking the total price? Isn’t it like akin to telling you he use 10 cars as a basis to get the “mean” ?

          1. Wow. I still think the given data is one car, but just taken via averaging 10 cars lol, and dividing by 10 wouldn’t the Qn have more marks 🙁

  113. hi,
    for qn 1 ii, after getting the 3/2 p^2 and 9/2 p as the coordinates, i got the gradient of normal and left my ans in the form y-y1=-1/m(x-x1), thats an alternative right?

    for 4bii i stopped my workings at where -5 and 1 are the coordinates of the midpoint. will i get at least a mark for that

    for qn 10 ii, i went 1 step after the fraction and left by answer in 3 sig fig, shouldn’t be penalised for that right?

    thanks a lot for your help

    1. 1. but your equation must be rid of p.
      4. I think it depends on the extent of your workings.
      10. well by right, instructions are to only round off non exact answers to 3sf. that really depends on their leniency.

  114. Actually, what’s the maximum mark that we can get out of 4 if we forget to remove the -ve sign on pie for Qn 4(b)(i)?

  115. for 6(ii), i did the complement method: (Unrestricted) – (two brothers tgt)
    however i did not get the ans..31500 – (3c1 x 8c4 x 4c1 x 5c3 ). may i know where did i go wrong?

      1. thats very true, didnt come across my mind oops. so it should be (Unrestricted) – (2 bros tgt) – (none of bros tgt)

          1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

            Thanks for helping in the clarification!
            all the best for all your papers 🙂

  117. Based on your amended working:

    6 (iii) 3c1 x 5c4 x (8c4 x 3c1 + 8c3 x 3c2 + 8c4 x 3c2) = 8820

    There wasn’t a 4C1 anywhere so we take it that “one of the remaining midfielders” refers to a particular person and is not for us to choose right? Felt that Cambridge could have made it clearer.

    1. hmm. in a way, its one particular midfielder. putting 4c1 allows that midfielder to be different. I think “one of the remaining” informs us that this talented player is unique.

      1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

        as its “one of the remaining midfielders”, i understand it as just ONE object out of 4 and this object will be unique. so doing 4c1 allows the object to change.

  119. hi 6(iii) wont that method result in double counting in cases where that flexible player isnt chosen at all?

  120. For 11(iii) I did CC! Is it wrong? And for q2 I didn’t reduce my c! I got 24/9 which is 8/3 when reduced! Will they mark me down for that?

    1. no. its fine actually. so long as you cc.
      hmm That depends on the leniency of the markers 🙂
      Don’t worry and all the best for other papers!

  121. I forgot to change the range of the angle for 4bi and ii, end up I get 64e^-ipi and 1,7,13, will there be method marks??

    and 11 iii using poisson to normal instead the answer would not be the same right?

  122. Can I ask for 1(ii) I got the mid point but failed to obtain the equation. And for 3(b)ii I managed to get the question but when I found out I cannot get a nice number for n is stop halfway.
    For 4)aii) I use a line and circle to solve but wrong answer and for bi I forgot to change to positive pie
    6iii) is there another case that they player who can played as either midfielder and defender was not chosen to the teAm?
    9ii and iii if I use sample variance will I get 0
    I committed so many mistakes. Hopefully bell curve pull me up

    1. 4. you just lose answer mark without -pi
      6 I corrected it thanks. My bad for the confusion
      9 you should still get method marks.
      don’t worry. more papers to come!

        1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.
          qn1 half of it seems to be down, since you’re short of stating new parametric and substituting.
          3. then you probably just get like 2-3m, for that expression if correct and substitution and solving.

    1. no, it seems like some school teachers suggest Z test can be used too. Since its alr normally distributed. In any case, you should still be get marks for the subsequent portions.

  127. I believe the “10 cars” in Q8 refers to 10 different cars of the same model. These 10 cars correspond to 10 sets of data points given. So, if I’m not wrong, I don’t think there is a need to divide the “P” obtained by 10. =)
    I’m not sure but that’s how I interpreted “10 cars”. =)

    2. I highly doubt so as the phrasing is prices in dollars of a random sample of ten used cars of a certain model. It is unlikely that they mean ten cars all of same price since if that is the case they would gave add the word “average” to avoid confusion.

      1. I think they meant as 10 cars of the same model all of different months. Thus, there were 10 sets of values given.

          1. ya. i thought for 1m, they are really asking too much. but i’ve suffered a fair amount of torment to their english. So I think you guys can decide better 🙂
            Thanks

  129. I got 60% combined… Is that equivalent to a C or B based on the difficulty of both papers and the bell curve?

      1. Hi, i don’t like to comment on the grades since you still have more papers ahead and this might affect you. But i’ll say you need >80 for an A.

  130. Hi sir,

    For 6 (ii) dont you have to subtract the case which both of them are not selected? The method you used has double counting

  132. 4aii, i square both sides to get answer, but ended up with diff ans. however when i sub back the ans its correct. Is it mathematically right ?

        1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

          I see. You can’t square to remove the modulus. the modulus here for the complex number is to find the magnitude, and not the absolute function. you will need to apply the magnitude formula before squaring both sides

  133. Hi for question 2 after you integrate and sub in the values shouldnt the fourth term be 3/2 ln (-5) since it’s 2x – 5 and x equals 0?

  134. Is it assumed that the sample variance k^2 is biased for Qn 9(ii) and (iii)? Or do we take it as a biased estimate of sample variance because it’s a t-test? I assumed it as an unbiased estimate and my answer’s all different T_T my answers were t>3.58 and 0<k^2<0.548

    And also why do we need to put the answers in set notations?

    Thanks in advanced!

    2. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

      You should still get credit for stating the rejection region statements precisely.
      Cos they asked for sets, it will be more complete to give them in set notations. I overlooked it as i was rushing.

    1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.
      s^2=10(k^2)/9
      s^2/n= k^2/9
      I skipped a step as I used Bessel’s corrections instead

    2. Many people got confused cause he skipped out a step actual denominator is root(s^2/10) which will be root [ (10k^2/9) / 10] and because the 2 10s cancel out each other, thus it’s just root(k^2/9) (The 10 at the bottom is n)

      1. yup thanks for clarifying 🙂
        There are other formulas that are easier and I guess i conveniently used it hah

  136. For qns 2, I somehow derived the partial fraction wrongly, but got some of the values right in the end. How many marks should I get out of nine for the question?

    1. yup you should get marks there. 2-3? and the integration, probably another 1-2m if you did some parts correctly.

  137. Hi, may I ask for qns 9, why isn’t it z test since qns states it follows normal distribution?

    1. Because the sample is small and POPULATION variance (sigma square is unknown)! Just because its normal doesn’t mean it’ll be z test I think cause when you do t test you have to state ‘assuming x/variable follows a normal distribution’ If it isn’t normal.

      Situations you use z test: population variance known doesn’t matter if sample is large or small if large, clt applies.
      Large, but population variance unknown. Clt applies.

      1. yup. thanks for clarifying for me. and yea congrats on no more math 🙂 All the best for the rest of your papers

    2. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

      cos the population variance is unknown. T-Test would be better.

  138. Hi sir,

    For 6ii the method you used did not even choose 11 players as required by the question

          1. Yeah i saw it! But his method did not choose 11 players. He only chose 10! I got 23100 which i think is right!

        2. i got this ans too! but i got it using the complement method. awaiting his reply..finally someone with the same ans as me :))

        3. Sorry but 16800 should be correct even if you use a complementary method to exclude the case of both chosen and both not chosen that answer is obtained as well. In his solution he only chose 10 as in one case he already fixed one brother to be a midfielder and in the other case the other brother was fixed thus only 10 other members need to be chosen!

          1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

            Thanks for helping me clarify. 🙂

  139. Just a few question:
    Qn 2, does it matter if i leave my answer for c as proper or improper fractions?
    Qn 4a(ii): Is the locus of z required to be drawn, can I simply solve it algebrically?(i.e.find gradient of the 2 point, find normal, get equation, and solve with part 1 circle)
    Qn7iii: I retardedly did P(Y<=8)-P(Y<=3) instead of 4. What do you suggest is the marks I may score?
    Qn 8biii:@#$%%^&^%

      1. If I didn’t remenber wrongly the question stated that b was positive as well! Thus it’ll be a U shape curve that cuts the positive y axis. (But only draw positive x)

    2. qn2. by definitions, a rational number is expressed as a fraction, p/q where by p & q must be integers and q is non-zero. You can check this with wiki. You just can’t write mixed fractions.
      qn4. the locus is not required. algebra works fine.

  140. hi, for 4bii, if i forgot to change my -pi to postive in 4bi and used it for 4bii, will i get penalized again? i derived the ans correctly. my working is exactly the same as yours! thank you!

    1. Part 2 wrong. You will minus a few marks since the question explicitly asked for 0-2pi. But there is no reason why part 3 will be wrong.

      1. oh thanks! btw, by part 3 you meant part 2 right? since there are only 2 parts to part b of the question

        1. yup, sorry for the typo. But i had the same mistake as you. Sneeky cambridge decided to change the domain to 0<=x<2pi

  141. Hi, for qns 2, I somehow derived the partial fraction wrongly, but got some of the values right in the end. How many marks should I get out of nine for the question?

    And for 4ii, does sketching the line give any marks? Cause I noticed they didn’t ask for it

    1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

      qn2. you should get marks for integrating.
      qn4. no the line does not need to be drawn.

    1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

      thats the instructions given at the start. So you might be penalised for answers.

    1. lol? pretty insensitive of you to say that. 83 and you’re on the edge what about those that did worse

          1. yeah. the benchmark is not so high. its probably about 75-80 and i think most are in the 70-80 zone

          2. hahaha my teacher actually said the papers were very standard so based on their prediction , >85 then will gurantee an A

    5. tbh, its never about how well you as an individual do, more of the entire h2 math cohort. I’ll say >80 is okay for an A actually. Given the full 3hs, i know some students who are capable of getting full marks. 🙂
      In any case, its over and I think you should move on and look to finish the rest of your papers.

    2. complement method:

      # of ways w/o restrictions – both brothers in the team – no brothers in the team
      = 31500 – 3c1 x 8c4 x (4c1 x 5c3 + 4c2 x 5c4) = 16800

      2. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

        Thanks for helping!

  145. Hello, just to ask for q9, shouldn’t it be the case where part II, is used z test since variance is now known?
    while for iii, variance not known and population size small then use t test?

    1. the entire questions, population variance is unknown. we only have the sample variance which can be used to find the unbiased estimate of population variance.

  146. 8 (iii) No I don’t think you got tricked, 10 cars as in 10 data included in the table, not that each price is for 10cars

  147. for the hypo ques, i did inverse T correctly except for the sign wrong. does this means i get 0 for whole ques?

  148. Hi sir,

    if we used Z test for the hypothesis question instead of t-test? would we still get method marks and if so, at least half of the marks awarded for the question? or just like 1 mark..?

    1. hi, you should still get credit for stating the correct conditions for h0 to be rejected, etc. 🙂

  149. For 8 (iii) I rounded off to whole no instead of 3sf, is it acceptable?

    For 4 (b)(ii) I simplify w* to a real number before solving w^n/W* will it get the same answer?

    And for Qn 9, both test use t test? How can I get pop Var from sample var?

    2. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

      qn8. i think instructions at the front is clear that all non-exact answers are to be in 3sf.
      qn4. w* shouldn’t be a real number since w is a complex number. If w* is a real number, then w is a real number => w*=w
      qn9. s^2 =n/(n-1) (sample variance)

      hope it helps. all the best for the rest of A’s

  150. Hi, for question 8iii, need to /10 meh? I thought the 10 in the question just meant ’10 sets of data of cars which accounts nicely for the 10 sets of data?

    1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.
      No need. But I’m just bad with english. so . yea, i had to read a few times.

  153. Hey for hypo testing I did the t test everything exactly but the sign wrong will I still get some marks

    1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

      should have marks for correct rejections statements. those methods, if correct.

  154. For the last qn last part, besides the independent assumption, the other assumption is it: different weeks have different mean number OR within a week different days have different mean number? Thanks!

    1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

      those works too. so long as you consider how to violate the poisson assumptions. anything that is logical should be okay.

  156. If for question 2, somehow i got the wrong A,B,C values after using GC.
    But method was all correct and got the correct answer for a and d. How many marks will i be able to salvage?

    1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

      You should get marks for the system of linear equations if they are right, and the integration methods.

    1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

      you should still get credit writing correct statements for the rejections portion in subsequent parts. answer marks will be gone.
      all the best for other papers!

  158. Hi. I wanted to ask for the hypo qn, if i used Z test and confuse sample variance with population variance, will I get straight zero?

    1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

      you should still get credit writing correct statements for the rejections portion in subsequent parts. all the best for other papers!

    1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

      I skipped a step and applied bessel’s corrections.
      s^2 = 10(k^2)/9
      s^2/n = k^2/9 since n=10

  162. Hi Mr Teng, I appreciate that you put up the answers so quickly. I just want to clarify how are the method marks being determined and given to a candidate? It has been bugging me because I don’t know how much workings is exactly worthy of a mark even when looking at marks allocation in each question.

    For example if I get the shape of the graph correct is that one mark out of three already?
    And for specific qn such as paper 2 qn 4(a)(ii) if i only found the coordinate of (-5,1) and managed to only list down equation of circle but wrongly indicate the equation of the line how much will I exactly get out of 4? Or is it a 0 already?

    I am probably at 70 marks combined. Is it very unlikely that I can get a A?

    1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

      method marks in general, is simply displaying correct approach/ methods to the questions. Its awarding you for understanding what you’re doing.
      qn4. no marks should be given for the bisector, unless you used it and apply geometry to find the answers. If you use cartesian equations, the coordinate (-5,1) shouldn’t have much credit, as it isn’t of much relevance to the answers. You need to at least achieve both cartesian to have 1m i feel.

      As for your marks, its hard. but maybe you got more marks here and there. don’t worry and you should focus on other papers. all the best.

  163. Should the answer for 3ii) be 2^(N+2)? If it is 2^(n+3)-8, if we sub n=2, distance after 2 stages is 24 but distance after 2 stages should be 16.

  164. I cried so hard after maths paper got around 60 for both paper. Feel like the world is ending. So sad:(

    1. First of all, its just Alevels. There are much more in life. To put it simply, once you finish a degree and start working, Alevels is obsolete. No one really asks you how much your PSLE was. You have more papers that are within your control, so move on and focus on doing them well. 🙂

  165. For the complex last part, when n = 5, the angle is – pi isn’t that out of range? So shouldn’t the ans be 11,23,35?

    1. Hi, sorry I’m really sick today from the h1 and h2 papers yesterday plus the comments.

      hmm i don’t really have the question paper. But that range for theta was meant to be considered for the previous part. and w^6/w* once we simplify, is an expression independent of theta.

      1. So last year 81 82 although its harder than 2012, do this year harder than last year is 90? According to logical trend…

      2. So high :(? Do you think Cambridge will have ecf or at least BOD marks? I know maths doesnt have ecf… But yeahh just asking 🙁

  167. Hi! I’m asking about a question in h2 maths paper 1 which I really need to know. :/ For question 9 i) if I got the equation of plane q wrong, would I get any method marks for 9ii) cuz i used the GC? And its worth 4 marks(its alot). And for question 8iii) instead of integrating, i differentiated sin-1(x) then i would get f(x) then differentiated f(x). Then I plugged in f(0) to all my differentiated funtions to get the maclaurin series. Is that another possible way? I really need to know. :/ Thank you.

    1. hi
      9. since you used the GC, there is no form of credit that can be given. unless you attempted to cross the normals to return the direction vector of line.
      8. its fine. you used “otherwise”. But you should get the same answer. 🙂

  169. Hi i want to ask for partial fraction, if i put A/[2x-5] + B/[x^2+9] instead of Bx +c, i get last ans A C and D value correct, only B wrong, how many marks will i be penalised though my integration method all is correct. Thanks

    1. Hi,
      I think you might lose a fair amount of marks. I believed they were testing on System of Linear Equations there with the equations… And the question wasn’t in parts, so you might lose credit for the integration though marks should be given for correct methods.

      1. But given that they say show the values of A B C D, i got 3 correct and the integration
        I should get 4 at least right? Sorry i am a bit worried cos so many ppl ace in paper2

        1. And given that A C D values are not affected by the Bx+C as well as the partial fraction, i got them exact answer, they should give me answer mark?

          1. but you will get marks for the 3. I’ll honestly say, 2-3m, cos the integration has three terms and you need to have leave them in rational numbers too.

  173. if our critical t value in wrong in part ii(cos of using invnorm and not invt), do we still get any marks? Also since part iii requires the same critical value as well, will there be method mark for part iii?
    For the complex qn, finding the possible values of z: i did it by finding the two equations of the loci, followed by finding the intersection by solving them simultaneously. However, j made a careless mistake halfway when transferring values across workings, hence had the wrong x values and corresponding y values. Isit a gonecase/ costly mistake for the 4 marks qn?
    Sorry, i know you are busy entertaining the many many questions, so do take ur time answering and ty !

    1. 4. i think so long as your cartesians are right and you perform good substitution and manipulation to solve. but only got wrong answers to do a careless, you should probably lose 1-2marks for the answer marks. So its not a gone case.

      9. tbh, i understand some teachers say that z-test might be acceptable (since distribution is normal) though t-test is appropriate (since pop var is unknown), primarily because invT shouldn’t be in syllabus. but one can argue, you can find the invT values through the T-table given in MF15. So its really up to the cambridge’s mark scheme (there is a reason why there isn’t any official answers and return of scripts) to decide the Test Statistic. In any cases, stating the correct conditions for rejection or non-rejection should give you some method marks alr.

      Don’t worry and all the best for the other papers!

  174. For paper 1, if i didnt use cross product to derive the normal for plane q, but used dot product (dot direction vector of line and normal of plane p = 0) , hence getting an expression with an unknown k which i factored out, getting the same normal as you did. Everything else is the same. Would i get full credit? Thanks and get well soon yeah?

    1. I meant dotting normal of q with normal of p, and also dotting normal of q with direction vector of line

      1. Hi
        It sounds fine actually: so long as you wrote the same Cartesian equation or something similar and have the a+λb form

  175. National A rate is about 50% yearly. A low 70 has a high chance of getting an A – just to answer many of you.

    1. Definitely not. Given the simplicity of the papers, a low 70 will not garner enough marks for an A

    3. I highly doubt that it’s 50%. There are 3000 As out of 16000 which is closer to 20% than to 50%. If I were to guess it would be similar to last year about 80 marks for an A.

    4. I don’t think so but I really do hope you are right…….. Sigh…. Seems like I will be getting a B which is the same as my prelims. 🙁

      1. Yea, shouldn’t go to 50% for nation A rate haha that will defeat the very purpose of a bell curve; we end up with a skewed one if so

        1. Hi Sir,

          But the teachers at my school says that the national distinction rate is 50%.
          Also, I think someone quoted from kiasuparents a few years ago that the distinction rate 3 years ago was 50.4%.

          I don’t think the teachers in my school would say that just to give us false hope or lie to us to make us feel better /:

          Only 3000s A? I mean, I heard that people in RJ and HCI have 40%~50% 4As and there are approximately 1.2k~1.5k people in each of the schools. That contributed to already 1k As. And this does not include the 1~3As studenet who have A for their maths /:

          But do correct me if I’m wrong!
          Thanks…

  176. For qn4, I believe there is no need to draw the perpendicular bisector since the locus for that is defined only in part (ii) after part (i) which requests you to draw the locus of |z+5-i|=4 only

    1. hi
      yes, there is no need to draw it. I merely draw it and label (ii) so it doesn’t confuse with the original answer of (i). using both loci, solves the question much efficiently too.

    1. hi,
      as mentioned previously,
      s^2 = 10(k^2)/9
      s^2/n = k^2/9
      So its correct, i skipped the steps as i applied bessel’s correction formula instead

    1. hi, no its perfectly fine. Some schools don’t have it. But one can easily find the numerals through the T-table found in mf15.

  179. Hi for the hypo test question if you got the hypothesis wrong in part I means the whole question zero marks ?
    I used the t test and inverse t though just that my assumed hypothesis was wrong !

    2. hi
      i think you should still have marks for stating the appropriate statements in subsequent marks. just method marks

  180. Hi sorry but I can’t seem to post on the page regarding H2 Paper 1 math solutions. can I check is it necessary for us to prove that volume is the maximum for q11(i)? and for q2, how many marks will we be deducted if we did not manage to show that there is only one point? thank you!

    1. hi, yes, that’s why I used the GC to check the second order derivative value as r1 is the value that gives the maximum value of V.

  181. OMG my alternative hypothesis and null hypothesis was wrong !
    i put Ho : μ 4.3
    will I lose all the marks for that question?!

  182. Hi Mr Teng, so now both papers are out, what do you think are the standards of this year’s maths papers? What’s the minimum mark to get an A for maths (in your opinion @@) will there be moderation?
    And yeah, get well soon, take care!!! 🙂 thanks for posting all the answers!

    1. hi, i think 80-82 in general. the papers were easier than last year. given full 3hs, most students shouldn’t have a problem.

      1. and thanks.
        they are mere suggested solutions, not accurate as i was just rushing to have up within an hour..

  185. For Complex q4, can use cartesian eqns of both the line and circle to find the coords of intersection and hence the complex numbers? I think I got a different answer from your solution.

    1. regardless of the method used, your answer should be the same. but yes, Cartesian equation can be used.

  186. Hi admin… For question 4(i) I left out the negative sign for 5… So will I lose the entire 2 marks or maybe I can get one mark? Haha.

    1. Forgot to add on I plot the graph that way too…. So yeah my circle is on the right side ;(

  187. Hi
    If for the pnc qn(iii), if i listed down the possible cases but left out one, will i get credit? 1or 2 out of the 3 marks?

    And,for the hypo testing, if i leave out the n/n-1, for both parts but logical and coherent working, do i lose 2 or 3 marks out of the 7 marks?

    And for the apgp, if i never fully simplify the expression like changing the 8 to 2^3, still got marks?

    Thxthx

    1. hi
      if you had presented your answers nicely with explanation (means unlike mine), you will get marks. 🙂

      for hypothesis testing, you will probably lose the answers mark if you did what you mentioned 🙂 Since you weren’t tasked to find s^2

      I think the apgp doesn’t matter since they didnt mandate for simplification

  188. i got the alternative hypothesis and null hypothesis wrong too!!
    Does anyone know if the markers would be lenient enough tho offer me some method marks in the following two parts because my answers there were correct based on my wrong alternative hypothesis:(((

      1. Hi,
        I guess that’s fine. But you lose the part (I) marks. You should still get credit for stating the rejection conditions. But answer marks will be lost at the back

  189. Hi sir, For paper 1 if i get my plane equation wrong but the methods to derive are exactly the same, how many method marks would i get?

    2. If it’s a careless with the calculation of the normal vector, you should probably just get 1 mark

  190. For qn 2, will I be penalised if I don’t specific the values for a,b,c,d? I got the same final ans.

  193. Hi I just wanna check Q2 if my ans is -3/2ln(45/13) + (8/3)tan inverse (2/3) isit ok? If u key into the calculator it will be the same ans it’s just that I took out the negative sign. And for Q 6iii they say one of the remaining can be the midifielders or defender. I assumed that it can be anyone? Not just that particular student? So I only have 2 cases which also adds up to 8820 isit ok?

    1. Yup no worries since they didn’t say if they just be positive or negative, simply rational.
      You should still get credit like 1 mark I guess 🙂

  194. Hi Mr Teng,
    May you please tell us your predicted score for an A? We need your professional judgement on this but will also consider it at our own discretions and not hold you responsible for anything. For some of us, it can give us a peace of mind or encourage us to work harder for the other subjects.
    Thank u. 🙂

  195. Hi for 11(iii), shouldn’t CLT be unsuitable since one of the conditions for CLT is for us to find sample mean or sample sum, which in this case is not applicable?

    1. Hi, that’s true. But CLT can be applied to approximate sum of independent random variables too. I finally found some time to add on the remarks. you can read more. Since each week is an independent random poisson variable, 52 weeks is the sum of the independent random poisson variables (consider it the sample mean here). So its suitable to apply CLT as n is large enough and its non-normal. Hope it helps. Poisson approximation will work here too.

  196. After all that’s said and done, math has one of the most generous bell curves, 45-50% get A. So don’t stress if you don’t get 75 or something! I hardly thing we are so good half of the cohort can get >80% for a paper like this hahaha. In any case, a B is a good grade too, and A levels are not the end of the world. Like come on, how many of the most successful people you know, or those who are the happiest in life, got straight As? Pretty sure that if you did a survey of all the millionaires in Singapore majority won’t be straight A students. Grades =/=self worth or even intelligence, with tuition and all these other factors warping things. So try your best but don’t be too stressed! If you’re awesome you’re gonna be awesome regardless. Period. 🙂

  197. Hi here to ask a qn for paper1
    For the last 2 qns graph sketching, if i get the general shape right but no values attached, will i get credit?
    And for the last qn (iii), if i chose the wrong value of r1 but calculated the correct h for the wrong r1 that i chose, will i still get marks?

    Last qn though, is 84-85 a safe bet for A?
    Thx sir.

  198. Hi! For qn 8 of paper 1, i expanded wrongly for 8ii but my method for 8iii is correct. So will I get any method marks? As for qn 10, I made careless mistake in 10ii but my method and the shape of graph is correct for 10iii. Will i get any method marks? Thanks!

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