# 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.

http://www.math.uiuc.edu/~hildebr/370/408clt.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 Responses to Suggested Answers to 2014 A Level H2 Math 9740 PAPER 2

1. Guest says:

6ii

shouldnt it be 3c1 x 8c4 x 4c1 x 5c4 + 3c1 x 8c4 x 4c2 x 5c3 = 16 800?

Hi,

Yes, Thanks so much! I counted wrongly. :/ Thanks!

• anon says:

Why is it 5c3 but not 5c4? (For the second part)

I corrected it thanks. My bad for the confusion

• guest says:

Yes same

2. Julie says:

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’

• sian says:

Yeah me too 🙁

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

3. sigh says:

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. Anon says:

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

I corrected it thanks. My bad for the confusion

5. A says:

For the hypothesis question why is it less than 4.3 and not more than 4.3?

6. lee says:

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

I corrected it thanks. My bad for the confusion

7. Anon says:

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

can do clt too since n=52 is sufficeinelty large.

8. MR mr says:

FOR qn 9, if i use sample variance throughout the qn, hw many marks will i be deducted?

you should still get credit for you calculations at subsequent parts.

9. Wow says:

@gg_jialat

10. anon says:

6 (ii) I got 16800 too, 6 (iii) I got 8820 :/ as for hypo I did I t-test 🙁

• question says:

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

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. s says:

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

You should still get credit for the calculations and test statistic.

12. Omg says:

Shouldn’t it be a t test?

I corrected it thanks. My bad for the confusion

13. X says:

Isnt it supposed to be t-test? For qn 9?

I corrected it thanks. My bad for the confusion

14. I hope i pass math says:

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??

I corrected it thanks. My bad for the confusion

15. Crystal says:

Hello! If you get an estimated 60 for both papers, is A still possible?

• Another student says:

Hi mate, think you’ll get C or B if you’re lucky.

16. Huh says:

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

I corrected it thanks. My bad for the confusion
cc isn’t required as I did CLT here.

17. Anon says:

For the test shouldnt it be t test , and invT should be used?

I corrected it thanks. My bad for the confusion

18. Thanks says:

Thanks a lot teacher!!

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

19. anon says:

And 11 (iii) shdnt there be continuity correction? I got 0.816

• X says:

I think theres no cc because it is clt.

yes, CLT do not require cc.

• Qw says:

Can we approximately to normal since mean=572 is large >10. Hence c.c?

yes

• K says:

So is 0.816 acceptable?

• math says:

omg I got 0.816 too!

• K.S. Teng says:

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. L. says:

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!

I corrected it thanks. My bad for the confusion

21. anon says:

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?

yes I did that. maybe I didn’t state the formula clearly.

22. Panicking says:

3ii) You didnt take into consideration distance OA1. Answer should be 1736m?

it was when you calculate total distance since first term is 8.

23. hi says:

it should be a t test as n is small and population variance is unknown 🙂

I corrected it thanks. My bad for the confusion

24. j2math says:

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

Hi, yes thanks. counted wrongly

25. Lala says:

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

Yes

• math says:

then if we approx don’t we have to cc?

• Lala says:

Yes, if you approx need to cc. But if it’s CLT then don’t need.

• math says:

thank u so much!

• ming says:

If use clt no need cc , if use approx np>10 then use cc

yes. thanks!

• Han says:

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

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.

• hi says:

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?

yes. I believe both methods are fine.

• -- says:

Then in this case can use cc?

26. anon says:

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?)

hi, it was used

27. anonMathTeacher says:

The hypo is a t-test, they gave sample variance.

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.

28. lee zy says:

hi is t test completely wrong? so that q will be zero marks for me? thanks!

no, i made a mistake. changed to t test. sorry bout it.

• anon says:

• pieceofshit says:

lol lee zheyi

29. question says:

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

30. -- says:

11iii) no need continuity correction?

Hi, CLT was done, so didn’t do cc.

• question says:

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

yea. I didn’t choose cc simply because i did cc in the previous question.

• anon says:

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

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.

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

n is 52 here. you can also do Po -> N and include cc

• hsjsj says:

hi so does that mean if I use CLT I’m correct too?

ya

31. help says:

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. Lala says:

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

yes. that will be better. I was rushing so overlooked it. Thanks.

33. Hellothere says:

Scatter sketching diagram wrong and so is the explanation

Z and T test

CC
… Thanks anyways

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.

34. xxx says:

qn 6 part 3 is double counted

I corrected it thanks. My bad for the confusion

35. siao liao says:

For 11 iii why is there no continuity correction?

Cos I used CLT, it doesn’t require cc.

36. Hihi says:

Is it possible for you to roughly estimate the marks for an A? What about 75? 🙁

37. Anon says:

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

I corrected it thanks. My bad for the confusion.

38. math says:

hi, for question 11iii, don’t we need to CC?

CLT was used, no need for cc. Unless you approximate

39. C.C says:

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

I did via CLT

40. Ashton says:

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 ?

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 says:

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.

I corrected it thanks. My bad for the confusion

42. anon says:

Shouldn’t qn 9 be t test because n=10 is small? I got 3.475 for ii and 0.423 for iii…

Yes, I changed it. Thanks.

43. anon says:

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)?

I corrected it thanks. My bad for the confusion

44. Ashton says:

Since the paper was over, how much will it be to score an A?

45. wong says:

Hi. After doing the 2 papers can you suggest the bell curve gor A grade.
Thanks

I think its best we leave it as it is, as it might affect other students’ mood

46. anon says:

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?

I corrected it thanks. My bad for the confusion

47. anon says:

Pretty sure the t test value is wrong.. Z critical should be -1.383 not -1.281

yes that’s T critical. changed it.

48. hello says:

The last question arent u suppose to approximation? So there should be cc

I do via CLT. If you approximated, I guess its fine.

49. anonymous says:

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

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

50. DD says:

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

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

51. P says:

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?

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.

52. hey says:

Hi, if you used t test instead of z test, but used inv norm instead of inv t, is it wrong?

hi, yes I changed the test alr. you need to invT

• hey says:

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 !

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…

• hey says:

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. really says:

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

yes guess that’s fine.

54. anon says:

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?

I corrected it thanks. My bad for the confusion

55. anon says:

why is t test wrong?

hi,
I’m wrong. I changed it. Thanks

56. noobkenneth says:

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.

I corrected it thanks. My bad for the confusion

57. hsjsj says:

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

58. DD says:

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

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

59. Oh shit says:

OMG I ADDED ALL THE P AND C

60. z says:

will 70+ marks get A?

61. anon says:

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.

I corrected it thanks. My bad for the confusion

62. Distressed says:

Just wanted to ask why it isn’t z-test but t-test?

Because population variance is unknown.

63. Akai says:

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!!

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. Worried says:

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!

I don’t think so. I think you still get credit for the rejections statements etc.

65. abc says:

Q11(iii) forgot to c.c. isit

No, I did via CLT. if you do approximation, must cc

66. Sean says:

Hey so how many did you all get?:/what did u think is the A grade or B grade:/

I leave this as open discussion. 🙂

• Lenzy says:

Im guessing it takes around 78-80 for an A.

• Tanzy says:

No obviously its 90

67. anon says:

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

you should get marks for your statistics, etc.

68. Anon says:

For 10ic, question says in any order. So order does not matter?

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. pumpk says:

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)

Hi, thanks! I agree. My bad. Thanks for pointing it out. 🙂

70. Worried says:

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?

• A says:

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.:)

• bob says:

Do you mean should focus on?

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

• Tan Jiawei says:

Around 90 this time should be

• h3 student says:

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.

• pink says:

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!! 🙂

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.

• Anon_1 says:

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.

• upset says:

Very worried as well.Scored roughly a 65% combined..

• Tan Jiawei says:

Don’t worry la cannot get A still got B ma. Don’t give up!

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!

Yes I believe there should be. The method should be right

72. Tan Jiawei says:

Wah damn lose 40 marks alr

Don’t be discouraged. More papers to come 🙂

73. ABC says:

for 9i)
shouldn’t the
H0 = 4.3 which the company claim H0 4.3 ?

yes. I think I wrote that

• ABC says:

Sorry i meant
shouldn’t H1 > 4.3, since the company claim mean waiting should be reduced?

74. Davidoff says:

Sir, can you please suggest how you felt the paper was, and what mark would get me an A

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. Anon says:

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?

• Hmm... says:

The bisector is the locus of z as well i think, since z satisfy both equations

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

• hope says:

Can i draw bisector in solid line and label it as part ii?

yes. my line segment should be dashed. overlooked it.

76. anon says:

6iii) 9C5? So you choose 5 defenders when they only asked for 4?

77. Anon says:

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

• Anon says:

It’s ok nvm!

s^2 = 10/9(3.2)

78. concern says:

is T-critical in syllabus? if not how they expect us to use.

79. concern says:

is T-critical in syllabus? if not how they expect us to know.

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

80. Sletar says:

Hi, I estimate that I can get 80 percent in total… Is it secure to get A?

81. Anon says:

For 9 part 3 shouldnt it be root k^2 divided by 10 instead of 9?

yes, I skipped a step. the 10 cancels out and you’re left with 9. since the s^2 = 10k^2/9

82. anon says:

for q11iii, I think continuity correction is needed?

I did via CLT. so it isn’t required

83. Hi says:

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

hi, I changed it. thanks. so sorry for the confusion

84. Anoymous says:

For 7(ii) isnt it between 5 and 8. I did not include 5 and 8 then i did cc

• Anoymous says:

Same for part (iii)

They stated inclusive. :/

85. boy says:

I said the artist died. Is that an acceptable assumption?

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.

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. anonym says:

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?

• anonym says:

sorry! also, if we 0.286 x the distance in stage 11 for q3, will we lose all 5 marks?

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

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. Anonnnn says:

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.

yes. I changed it. let me know if I’m still wrong. thanks.

88. gg says:

for the scatter plot for p and t both positive shouldnt the graph be increasing? thanks

yea, I just drew the other part of the U shaped curve.

• GG says:

But won’t the other part only appear at Negative x axis? The qn asked for positive haha

yup. I should draw the other side. thanks for pointing out.

89. mr handsome says:

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

yes Thanks! I changed it!

• mr handsome says:

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. whoputstheirrealnamehere says:

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?

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.

91. AJ says:

Dear Teacher,
Thanks for the ans!!;)

pleasure. just suggested. as you can see. its crazy lot of mistakes haha

92. C.k yap says:

Yup this time round both test accepted heard from my teachers

oh great!

93. Anonnnn says:

Also, fo question 4(b) the argument must be between 0 and 2pi ehh!

• Anonnnn says:

opps saw wrongly sorry

94. ... says:

i think ur ques 3 part 3 is wrong, cos u didnt include the first 4 metres of OA1

I think it is included in the formula

95. Anon says:

Predicted A mark?? Is 76 safe???

96. hey there says:

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

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

97. Sian says:

For q9, what if i forget to divide the k by n ? Will i lose all the marks in the question ?

you mean you didn’t use s^2? you can still get credit for the subsequent parts.

98. Violet says:

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. 🙂

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

99. Hello says:

For 4aii, will lose mark cos i solve the eqn instead of drawing ?

no. drawing isn’t required at all for 4ii

100. anon... says:

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]

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

101. Mathismylife says:

Q8(ai) shouldn’t the scatter diagram be a normal positive quadratic curve?

I corrected it thanks. My bad for the confusion

102. Hisnka says:

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)

• Hisnka says:

?

its just your s^2 that will be wrong. you will still get credit for the rejection steps.

103. Student says:

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

nope. haha cos im terribly wrong. :/

104. hope says:

If we used z test, is the ans the same?

no it wouldn’t

• hope says:

Do u mind to tell us what would be the ans if z test is used? Thxs a lot 🙂

{t > 3.53}
{-0 < k^2 < 0.493}

105. Anonnnn says:

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

Yes thanks. I addressed it. 🙂

106. Worried says:

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…

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

107. Jorndan says:

If i made as many careless mistakes as you did will i still get an A??

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

108. Students says:

For 4a(ii), is it okay if we solve algebraically and not draw the perpendicular bisector?

of course. its not part of questions. 🙂

109. boy says:

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?

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. anon123 says:

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?

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. h3 student says:

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

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

And Thanks a lot!!!

• Anononymous says:

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” ?

yes. I got tricked too. haha cos they want price of a car.

• Anononymous says:

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 🙁

IKR. That 1 mark damn sneaky zz I feel cheated too lol

112. :) says:

Hi did you accidentally miss out the negative sign at the final answer for Qn 4(b)(i)?

no. it should be just +pi since there is a range given for theta.

113. Zhihao says:

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. 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. :) says:

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)?

you just lose 1 for answermark

115. handsome says:

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?

• Hi says:

I think it’s because you didn’t exclude the probability of none of them being chosen!

• handsome says:

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

• Hi says:

Yupyup I tried it out and it works! Hehe all the best (:

• K.S. Teng says:

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 🙂

116. Clara says:

Sorry if I’m wrong but for 9(iii) isn’t it k/ (square root 10) and not 9?

hi, we use the s^2 formula here. I skipped a few lines actually. but it should be right

117. anon says:

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.

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.

• C.k yap says:

I too put 4c1 since it is one of the midfielder

• K.S. Teng says:

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.

118. :c says:

hi do u think this year paper overall is one of the hardest throughout the years?

actually, paper 1 was easier than last year. paper 2 also. but paper 2 was quite tricky.

119. anastasia says:

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

I corrected it thanks. My bad for the confusion

120. Clara says:

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?

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. Anononymous says:

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?

yes, different answers. but both okay so long as you cc correctly

122. Jack says:

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

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!

• Jack says:

Thank how about question 1 and 3. What is the usual A score?

• K.S. Teng says:

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.

123. Jack says:

Admin can you comment on my mistake if there is any method mark.

tot I sent it out. my bad

124. Screwedup says:

Thanks for the help
MJ Boleh

• Guest says:

why MJboleh?

125. screwed says:

Hi sir for q9, if i used z test, will the whole question be wrong?

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.

• screwed says:

Thanks alot! 🙂

126. Hopeful says:

Hi used z test for both will i get marked down very badly?

you still have subsequent parts for method marks

127. Sup says:

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”. =)

oh dear. you make sense too. haha my English is terrible. -.-

• h3 student says:

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.

• Hi says:

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

• sigh says:

I agree. 10 cars as in the 10 included in the table. But aiya 1 mark only

• K.S. Teng says:

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

128. Guest says:

q11)iii) Pls remember to do CC…Think you forgot…

I did CLT.

129. Hopeful says:

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

• Hopeful says:

• Jack says:

Likely to C i think. I got 69 minimum and 80 maximum Which i think no chance of A

• K.S. Teng says:

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. mr handsome says:

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

131. handsome says:

hi looking forward to ur ans to my comment thank you!!

132. Hello says:

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 ?

Im quite confused haha. cos you ended with diff ans. and got the correct again.

• Hello says:

Uhm, but is it right to square both sides and solve for z?

• K.S. Teng says:

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. Anon says:

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?

ya. got mod so it clears

• Anon says:

Ohhh okok thankyou !

134. :) says:

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?

• Anon says:

Do you think u will recieve any marks for this qn?

• K.S. Teng says:

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.

135. Guest says:

Also for 9)iii) the denominator should be root(10k^2/9)… Think you missed out the 10…

• K.S. Teng says:

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

• Hey says:

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)

• K.S. Teng says:

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

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?

• K.S. Teng says:

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

137. Kel says:

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

• Nomoremath says:

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.

• K.S. Teng says:

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

• K.S. Teng says:

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. mr handsome says:

Hi sir,

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

• :) says:

i noticed that too!! been staring at the solution

• asd says:

There is no need for 11, as u already assume that 1 of the 2 brothers is in the team.

• mr handsome says:

Did you get 23100 as the answer? 🙂

16800 is the ans i think! he corrected it

• mr handsome says:

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

• tom says:

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

• mr handsome says:

Haha great! Coincidently I’m Tom too haha 😉

• Hi says:

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!

• K.S. Teng says:

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

Thanks for helping me clarify. 🙂

139. asd says:

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:@#\$%%^&^%

• asd says:

Must question 8ai scatter diagram be positive in the y-axis?

• Hi says:

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)

• asd says:

I did draw positive x, but i let p=-1 and t=1

• K.S. Teng says:

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.

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!

• asd says:

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.

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

• asd says:

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

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

• K.S. Teng says:

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.

142. Sup says:

Hey, what if i forgot to round off to 3sf 🙁

• K.S. Teng says:

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.

143. K says:

Any idea how much to get A? I got around 83%…..quite scared it’s on the edge

• uhm says:

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

• Sletar says:

The same with you… Quiet anxious

• Wow says:

i think 83 cannot get A need at least 85

• Wow says:

i got 89% but most of my friends got above 90% . and they said the paper was relatively easier .

• Jack says:

Wtf i got 69-77.5 only i think 80 and above is a sure A

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

• Puppies says:

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

• Haha says:

Just curious which school are you all from? Mind sharing?

• LOL says:

83 cfm A alr la why come here and scare the rest :/

• K.S. Teng says:

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.

144. tom says:

hi sir, for 6(ii), is it possible to use the complement method instead?

• Hi says:

Yes (: I tried out both methods and got the same answer!

• Guest says:

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

• asd says:

nice method.

• K.S. Teng says:

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

Thanks for helping!

145. Hello says:

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?

• K.S. Teng says:

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. sigh says:

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

• K.S. Teng says:

yea. i realised. haha sorry, english language has always been my kryptonite

147. teoheng says:

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

148. jon says:

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..?

• K.S. Teng says:

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

149. Well maths over says:

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?

• Hey says:

S^2 = (n/n-1) x sample variance

• K.S. Teng says:

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 says:

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?

• K.S. Teng says:

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.

151. Anon says:

I read the w^n/w* wrongly as w^6n/w* and ended up with n =1.2,3. Will I lose all 4 marks??

• Guest says:

Yes

152. idk says:

For qn 6, shldnt we divide 8C4 by 2 since there may be an overlap in grouping?

153. C.k yap says:

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

• K.S. Teng says:

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. Guest says:

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!

• K.S. Teng says:

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.

155. Jack says:

so high for paper 2 likely A i think

156. A says:

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?

• K.S. Teng says:

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.

157. Guests says:

For invT What if i used 0.01 instead of 0.1 careless. How many marks will i get

• K.S. Teng says:

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. mathsnoob says:

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?

• K.S. Teng says:

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!

• c.k yap says:

get well soon Teng!

159. Anon says:

what do you guys think about the bell curve for grade C,B andA?

• weiJai says:

hmm c~60 b~70-85 a>85

160. Anon says:

Hi. If u get 79.5% will your grades be rounded up to 80%?

161. D says:

In Q9(iii), why is the n=9 and not 10 to find k^2?

• K.S. Teng says:

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. Alice says:

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?

• K.S. Teng says:

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.

• Student1 says:

I got 70+ combined too,kind of prepared to score B hehe

163. Anon says:

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.

• Anon says:

Oh wait sorry I got it my bad

164. Reena says:

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

• K.S. Teng says:

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. Kk says:

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?

• K.S. Teng says:

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.

166. :c says:

what’s last year cut off point for A ah, anyone any idea?

• Student1 says:

80++ My friend scored around that range

• K.S. Teng says:

last year was about 81-82 range.

• die says:

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

• Worried says:

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

• :c says:

90? r u srs, haha this is not psle

167. Anon says:

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.

• K.S. Teng says:

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. 🙂

• Anon says:

Wow, I lost 8 marks just cuz I wasnt careful enough. Hmm but thanks!

• ahwei says:

dont worry! still gt 92 marks

168. Hey admin, I carelessly used dx/dy for my first Qns. Will I still get working marks ?

• K.S. Teng says:

did you get the correct t value? if not, i doubt so.

169. cmi says:

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

• K.S. Teng says:

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.

• cmi says:

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

• cmi says:

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?

• K.S. Teng says:

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.

170. cmi says:

Why everyone do well in paper 2 rather than paper1, paper 1 so much easier…

• Guest says:

Some people find stats easier than pure.

171. anon says:

11 iii needs to use cc so ans is 0.816

• K.S. Teng says:

hi
I applied CLT, so cc is not required.

172. hi! says:

im not really sure but i think Q11 part iii we need to C.C right? thanks a lot for the answers!

• K.S. Teng says:

Hi,
i applied CLT, so cc is not required.

173. hey says:

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 !

• K.S. Teng says:

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. hello says:

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?

• hello says:

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

• K.S. Teng says:

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

175. Hellothere says:

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

• Mr Po says:

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

• Puppies says:

honestly, i doubt so.

• cheer says:

it Will probably be 77 or 78 judging the difficulty compared to last year, wont be low 70.

• Y says:

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.

• Worried says:

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. 🙁

• K.S. Teng says:

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

• A says:

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. Student says:

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

• K.S. Teng says:

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.

177. B says:

Q9iii, shouldn’t it be (4-4.3)/(k/sqroot10)? Instead of sqroot9? The answer would be 0.471

• K.S. Teng says:

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

178. Anon says:

If I used invT which is not in syllabus is it wrong?My sch lecture notes had it

• K.S. Teng says:

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. hello says:

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 !

• salt says:

same as me! guess we will have to get zero for that ques

• K.S. Teng says:

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

180. hello says:

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!

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 says:

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. Jckid says:

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!

• K.S. Teng says:

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

• K.S. Teng says:

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

• Jckid says:

Erm so if its the case, means all the grades will be pushed up too? B?

• K.S. Teng says:

Yes all grades should be pushed out. You can’t have too many getting Bs, etc..

183. Anon says:

Guys what do you all think is the bell curve for C?

• LOL says:

Estimate should be around 54%?

• Hopeful says:

184. Anon says:

So will Z test give u full marks?

185. John says:

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.

• asd says:

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

• K.S. Teng says:

yup, you should get the same thing. cos i did it with the jc1s today. 🙂

186. Worried says:

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.

• Worried says:

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

• jWEI says:

highly doubt they will give any ecf

• K.S. Teng says:

yea. the circle is wrong, the marks will be gone. :/

187. Hello says:

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

• K.S. Teng says:

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. how how how says:

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:(((

• jWEI says:

doubt so. maths do not have any ecf. im afraid you will have to face a zero

• Crystal says:

Omg me too! I am looking forward to a reply ;_;

• K.S. Teng says:

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. Hopeful says:

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?

• mr ong c.l says:

• K.S. Teng says:

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

190. SG says:

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.

• Guest says:

won’t.
as long as u split the partial fractions correctly.

191. PTHL says:

Hi shouldn’t the last part undergo continuity correction

• K.S. Teng says:

Hi, I did via CLT so cc is not required

192. idk says:

Hello can i ask for qn 6, shldnt we divide 8C4 by 2 since there may be an overlap in grouping?

193. Anon says:

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?

• K.S. Teng says:

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. Very Worried says:

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. anon0000 says:

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?

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. Aleoca says:

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. 🙂

• alevelisnteverything says:

very well said. best comment ever.

197. Hello says:

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. kelvin says:

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!

199. All the best says:

Hi! Whats the B grade range for this year? I got like 65 %lowest combined

200. anon says:

I didnt write down my GC model will i die?!?!?