# 2015 A-level H2 Mathematics (9740) Suggested Solutions

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

### Paper 1

Numerical Answers (click the questions for workings/explanation)

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

### Paper 2

Numerical Answers (click the questions for workings/explanation)

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

MF15

### KSΒ Comments

Showing 241 comments
• Student a

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

• KS Teng

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

• Student a

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

• KS Teng

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

• student b

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

• Student 97

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

• KS Teng

like on the dot for an A? hmm 25~30. I can tell you that 170/200 is a safe A. π Hope it helps.

• Student B

Question 8. shouldnt 63.84 approximate to 63.8

• KS Teng

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

• :(

Can I get C with 50+

• Anonymous

This was definitely one of the hardest Alevel papers.

• kahwee

I hope you fare well!

• Bob

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

• KS Teng

hard to say. a lot depends on Paper 2 too, same weightage after all π

• Bob

Will bell curve help the weaker students

• KS Teng

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

• student

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

• KS Teng

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

• jen

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

• KS Teng

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

• Random

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

• KS Teng

definitely! dont give up. π yes this paper is really tricky in my opinion. :/

• Random

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

• KS Teng

Don’t worry so much. There is still a Paper 2 which is equal weightage. π

• lim

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

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

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

• KS Teng

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

• KS Teng

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

• student

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

• student

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

• KS Teng

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

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

• another student

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

• KS Teng

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

• Stranger

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

• KS Teng

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

• Eileen

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

• KS Teng

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

• Eileen

H1 math is upon 95 marks tho ! π would 73/95 be a safe bet ?

• KS Teng

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

• Student Sadness

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

• KS Teng

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

• Student Sadness

That’s nice to hear!!! Thanks!! π

• Bro

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

• KS Teng

k bro, I’ll say >131

• :(

I got about 73 marks. Is this enough to A? π

• KS Teng

There is still a paper 2! π

• :(

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

• KS Teng

sounds good. π but why limit yourself

• Student

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

• KS Teng

i’ll reckon > 131.

• john

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

• KS Teng

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

• john

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

• KS Teng

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

• Studentr

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

• KS Teng

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

• student

Hi do think this is harder than 2013?

• KS Teng

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

• Student

Yea definitely harder
The first few qns were difficult

• KS Teng

all the graphs. very tedious. haha

• Sigh

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

• KS Teng

oh, but thats a different curve alr. :/

• Rys

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

• KS Teng

probably tomorrow haha cos i have lessons at 5pm

• student

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

• KS Teng

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

• student

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

• KS Teng

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

• KS Teng

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

• Student

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

• Student JR

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

• KS Teng

probably 1 mark. :/

• Jackie Ng

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

• KS Teng

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

• student

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

• KS Teng

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

• student u

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

• f

Hello!! π I got the limits and substitution correct but the rest wrong. How many marks would I get?

• KS Teng

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

• HARDESTMATHPAPERTHUSFAR

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

• KS Teng

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

• student

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

• KS Teng

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

• student m

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

• anon

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

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

• KS Teng

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

• J

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

• KS Teng

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

• X

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

• Student

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

• dannyfentun

I study so hard still fail πππ

• Dianne

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

• Anxious

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

• KS Teng

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

• Students

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

• Amanda

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

• Amanda

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

• A for Math

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

• KS Teng

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

• Student A

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

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

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

• KS Teng

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

• J

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

• KS Teng

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

• Student :)

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

• KS Teng

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

• Student :)

Alright! Thanks for the reassurance π

• Student c

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

• Student c

Sorry maximum*

• Student c

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

• stewdunt

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

• KS Teng

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

• stewdunt

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

• KS Teng

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

• Student A

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

• Vanessa

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

• KS Teng

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

• S

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

• Janel

Is there ecf for math?

• KS Teng

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

• student x

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

• KS Teng

Haha thats good to hear. π

• Student T

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

• Student

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

• Student

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

• Student

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

• Ting

Hello, will there be any suggested solutions for h1 math? π

• KS Teng

I’m doing it after my lessons only.

• KS Teng

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

• student

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

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

• Noelle

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

• KS Teng

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

• Ex A level Student

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

• KS Teng

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

• Noelle

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

• abc

80++?? So high? π I thought this year’s paper was quite difficult π

• KS Teng

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

• Student

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

• Student c

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

• Student

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

• KS Teng

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

• Student c

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

• KS Teng

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

• A Student

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

• KS Teng

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

• A Student

Thank you very much for replying to all your comments!

• Corn-cerned

sigh math

• Screwed

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

• Screwed

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

• KS Teng

yes, there will be method marks too. π

• hi

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

• KS Teng

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

• ROOOOT 3

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

• KS Teng

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

• student m

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

• Anon

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

• KS Teng

yup, there are always method marks π

• D

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

• D

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

• KS Teng

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

• ooh

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

• KS Teng

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

• Pizzalover

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

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

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

• J

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

• Pizzalover

last year math distinction rate is how much??

• Shawn

Is 96 a good score?

• KS Teng

Yes Shawn. Good job!

• ?????

U fokin wot m8??!?!?

• student

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

• help me pls!

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

• KS Teng

Just do your best for paper 2 π

• AimingHighINeedSelfEsteem

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

• KS Teng

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

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

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

• ooh

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

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

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

Thank you!!!:)

• ooh

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

• KS Teng

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

• ooh

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

• Pi bond

From what i heard from others, 75~90

• aaa

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

• KS Teng

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

• diego

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

• diego

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

• KS Teng

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

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

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

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

• diego

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

• KS Teng

I can’t suggest a sufficient mark here. But a necessary mark is above 70. I feel that 170/200 will be super safe. π

• squirrel

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

• KS Teng

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

• Ecfpls

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

• KS Teng

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

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

• student

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

• KS Teng

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

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

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

• student

Hahaha…. thank you π

• aaa

wow ur teacher said 75 only??

• student

Yeah he did… maybe it’s not completely accurate, don’t take my word for it. All the best. π

• aaa

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

• student

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

• Student U

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

• KS Teng

thats good! hopefully paper 2 will be better!

• Student U

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

• KS Teng

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

• Almighty

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

• Lazystudent

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

• DJmax

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

• PleasegivemeAforMath

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

• PleasegivemeAforMath

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

• student

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

• Student

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

• Mango Ice blend

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

• Student A

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

• KS Teng

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

And thats great! keep up the good work with Paper 2. π

• J

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

• KS Teng

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

• Student g

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

• KS Teng

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

• Student

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

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

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

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

• aaa

don’t mind me asking: which year did u graduate? π

• DJmax

Dude read, he said last year…

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

Last year? I said in the post lol

• aaa

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

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

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

• Student

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

• Student x

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

• KS Teng

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

• late

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

• KS Teng

you might get 2-4 marks. π Dont worry and good luck for the remaining papers

• Student

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

• approximation

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

• KS Teng

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

• aabcde

Hi KS just curious, what do you base your estimates for the min. number of marks to get A on? π

• lol

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

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