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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. We will try our best to answer.

Errata:

Qn3 I misread it. Answer should be 2/3 and need not be evaluated.

Qn5i I copied wrongly off GC. answer should -3+4i. It shouldn’t affect the back parts.

Qn7 I copied wrongly off GC. So rounding off, the answers should α=1.885(3dp)

Advice and tips from Mr Teng for H2 Math exam 2014 paper 2

Please focus on tomorrow’s paper 2 and not let paper 1 affect you too much.

Errata:

Qn3 I misread it. Answer should be 2/3 and need not be evaluated.

Qn5i I copied wrongly off GC. answer should -3+4i. It shouldn’t affect the back parts.

Qn7 I copied wrongly off GC. So rounding off, the answers should α=1.885(3dp)

Much thanks for those that point it out.

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3iii should be the cosine of the angle i think! and 7ii should be abs(integrand) for a positive area!

yes. it has been corrected. Thanks.

and no for 7, they asked to evaluate the integral, not an area.

Qn 8 isn’t it 1/3 sin-1(x)?

And for q3iii they asked for cosine of the angle.

http://www.wolframalpha.com/input/?i=integrate+%289-xx%29%5E-0.5

you can check qn8 as follows.

Yes qn3 has been corrected. Thanks

q5i should b -3+4i for z2.

q3iii is asking for cosine, not the angle

q7i should be 1.885 from GC

some errors I found just in case you’d like to know 🙂

Yes. I copied wrongly haha. but it shouldn’t affect the back parts for qn5. qn3 was a mis-read on my part. and yes yes, I copied wrong off the gc again for qn7.

Thanks so much! Let me know if there are more. 🙂

Hi for 7ii, shouldn’t it be a positive number as it is to find an area?

No. They asked to evaluate the integral, but not the area. The integral is still negative.

yup it didn’t affect anything at all 🙂 thanks so much for posting the answers for us!

Yup! Thanks a lot! You must have done it with ease.

For 3ii, I think they’re asking for the cosine of the angle but not specifically for the angle itself

Yes. Its been corrected. I misread on my part. Thanks

For 4i, shouldn’t the graph be more of a squarish oval shape as mentioned in the answer for 4ii that the gradients at the x intercepts are parallel to the y axis

cos the value of d is unknown, we can’t determine actually.

So if we draw it as a squarish oval it’ll be correct as well?

Yea its fine. I think they are giving students a benefit of doubt here. All the best for P2!

Wow… I really scored badly… Got like 60 marks only…

Don’t worry. 🙂 Focus on P2.

For question 3(iii) they asked “Cosine of the acute angle”, not ask to find the angle.

Should be 2/3.

yup. it has been rectified in the errata. thanks.

nice. i just passed this paper.

For 7 (iii) , shouldn’t it be (abs Integral – 7root 3) instead of (negative integral – 7root3)? o.o

i actually used -f(x) to reflect the graph about x axis, then translate it by 7 units. After that i integrate the full thing. I guess there are several other methods that will work so long as you ensure you have a positive area there. 🙂

I think for 10iv, supposed to draw only within 0 <X <0.5

Oh wait I saw wrong

Does anyone know if there’s ecf for math?

there isn’t ecf, unlike sciences. but there will be method marks given. No one knows the exact mark scheme, so don’t worry. Focus on P2. 🙂

Hi what would be an okay grade for this paper. Based on it’s level of difficulty , how much do you think someone would roughly need to score to be above average ? Just your opinion :p

to gauge the difficulty, you should consider the cohort. I think your social media should be able to tell you if your peers enjoyed their morning today. 🙂 Furthermore, you still have p2 tomorrow so all is too early to tell. 🙂

What do you think the bell curve will be like? Still high 70s/80s? 🙁

too early to tell 🙂 Focus on p2. Its not just about p1.

Qn 4:Shouldn’t the right part of the transformation curve be pointing outwards. Instead of like an asymptote?

you need to increase increasingly there. there should be a change in concavity. and there isn’t a vertical asymptote there as it is not indicated in workings

Tomorrow is Math Paper 2. Some students are very affected after checking their solutions against yours. They felt that they have done badly and have no mood to study for paper 2. I think that as an educator, you must be more thoughtful and considerate for students’ emotions. It is very irresponsible for you to post up the paper 1 solutions so quickly. Afterall is there a need for them to know the exact answers after the paper? Isn’t studying for paper 2 more important for them now?

Well, it might actually motivate some students to work harder or be more careful in reading the questions for tomorrow. It also may save some students time, instead of them asking around and getting unnecessarily worried.

I’m honestly thankful for this teacher for bothering to rush out the answers and uploading it for everyone to see. What he’s doing is really helping us, whether we’re just curious why we couldn’t get the answers or want to know how we’ve done. After all, there’s always something to be learnt from our mistakes. It’s not as if he put it up and forced everyone to check; students had the choice of reading this or not. But if just because those who didn’t do well were affected after reading this the teacher shouldn’t be uploading this and just deprive all the other students who genuinely want to know and learn (after all that’s what we go to school for. Not for a levels but to learn) right till the last exam even though it won’t matter to the grades, then I think it would be really selfish of them.

As a student taking the exams, I can say that the aftermath of the posting of the answer key shouldn’t be the concern of the site owner, and I might add that just as many are curious about their answers. I have friends who were worried about the checking of their answers and simply deleted the link to this page so they weren’t tempted to open it despite being given the link.

Do you think there’ll be ECF for part 8ii,9ii and iii if part i careless?

you will still get credit for the methods. but you will lose your answer part. All the best for tomorrow!

May i know around how many marks to get a for this paper

its rather too early to tell. Its your combined p1 and p2 score after all. Focus on p2 which is still in your control. All the best for p2!

Hi mr teng, what would you say would be the range for A and B for this paper?

its rather too early to tell. Its your combined p1 and p2 score after all. Focus on p2 which is still in your control. All the best for p2!

Do you post answers for H1 math?

sorry. we didn’t have the time to do it. Hope it went well for you.

If r = 3.951 for 11iii) the value of h should be 0.624 instead of 0.625? Unless you used more decimal places

Yes i do agree with that. since its in the same part, and you’re tasked to find the corresponding h. presenting your answers clearly and then rounding them off to 3SF should be fine.. All the best for p2!

Thanks 🙂

What’s a good estimate of the A grade for this paper?

its rather too early to tell. Its your combined p1 and p2 score after all. All the best for p2!

For qn 9 i got the cartesian equation in (i) wrong. So (ii) and (iii) answers are wrong but the method is correct, how much credit would i get? Thanks.

you will just lose the answer marks. All the best for p2!

Q9iii) GC Shows 2,0.5,1 instead of 4,1,2. So isn’t it 2,0.5,1?

yes. i scaled it for my convenience as I don’t like fractions. :/ its a direction vector after al.

Hopefully the bellcurve will not be so steep. Scored 65 instead of my usual > 70. Now I regret checking the answers! 🙁 all the best for paper 2 tmr all of you

all the best four your p2. Focus p2. you still have another 100 marks there.

What is likely the range of marks for A based on this paper? Or is it like what Zhou Enlai mentioned in GP, “It is too early to say.”?

Yes its rather too early to tell. Its your combined score after all. All the best for p2!

die alrd la 50 marks gone

there is still a paper 2; half the battle to go. so focus on it now.

got H1 answers bo?

sorry. we didn’t have the time to do it. Hope it went well for you.

ohhh noo mr teng, i scored 65, do you think an A is possible?

its rather too early to tell. Its your combined p1 and p2 score after all. All the best for p2!

Hi if I scored at most 45 marks for this what would be my likely grade for this paper? Is it still possible to get a C overall for math sigh pie

Hi, I think you shouldn’t worry so much. There is still a 100marks later; don’t forget they are EQUAL weightage. So just focus on it already. Furthermore, I’m really slack on the presentation so perhaps you can have a fair amount of presentation marks too. All the best later!

I think 6bii is wrong

hmmm. I can’t really see how.

1 – 1/(n+1)! – (1-1/n!)

= 1 – 1/(n+1)! – 1 + 1/n!

= 1/n! – 1/(n+1)!

= (n+1)/(n+1)! – 1/(n+1)!

= (n+1-1)/(n+1)!

= n/(n+1)!

10iiia) missing a negative sign

No. It isn’t. I flipped the natural log function

Arent you suppose to further differentiate the ans for 8iii

Because its asking for macluarins series not the equation of sin^-1(x/3)

Yes, you can approach the question via “otherwise”, then we can differentiate arcsin(x/3) a few times to resolve for the expansion. You should end up with the same series for arcsin(x/3).

http://www.wolframalpha.com/input/?i=Series%5BArcSin%5Bx%2F3%5D%2C+%7Bx%2C+0%2C+12%7D%5D

Thanks so much for the help 🙂

Shouldnt the first term for 8 part (iii) be (1/9)x ?

Hi there

Not so. Probably made a careless mistake when factoring the 9 out.

http://www.wolframalpha.com/input/?i=Series%5BArcSin%5Bx%2F3%5D%2C+%7Bx%2C+0%2C+12%7D%5D

You can consider referring to this 🙂

All the best later! 🙂

Hi, just a few questions for you,

For Qn1i, is it necessary to specify the domain?

For Qn 7iv, can we just say that the roots are reflected about the y-axis?

For Qn9iii, can we use the foot of perpendicular method to solve?

For Qn10iv, is there ECF mark from using the equation we obtained in 10ii and drawing the graph? Got the same graph as the answer above though.

Yeah, that’s basically it, thanks for posting the suggested solutions so quickly anyway!

Hi,

Qn1. I would the domain to be more precise as I want to show that ff(x)=f-1(x) for the entire domain. I’m not particularly sure strict they will be since the question is just asking you to show. Writing domain removes the misunderstanding that this could be a mere intersection of the given functions.

Qn7. I think the showing of f(x) is even function is rather straight forward. And you should do more to explain about the roots (which is what they are interested in) instead of the graphs being a reflection.

Qn9. Of course you can, since the question does say “otherwise”

Qn10. I take it that you obtain (ii) and plotted the equation without expressing x=f(t). You should still get marks for the graph although you might lose a mark for not using “this equation” they suggest.

And no worries, pleasure is mine. 🙂 I’m also equally curious haha. All the best tomorrow!

Thanks man!

Hi Mr Teng, for

q1ii) do we need to include the domain (eg. x belongs to all real number, and x cannot be equal to 0 and 1?)

I just wrote that f3(x) = x ( with workings ) but without domains or restrictions

Hi

Qn1. I put the domain to be more precise as I want to show that ff(x)=f-1(x) for the entire domain. I’m not particularly sure strict they will be since the question is just asking you to show. Writing domain removes the misunderstanding that this could be a mere intersection of the given functions.

Its one mark for (ii) so if you show your workings, you shouldn’t be penalised. Its just a habit to include domains of functions 🙂

All the best for tomorrow!

Shouldn’t ques 10ii) be -5/square root of 5 ln(…) since you have to multiply (-5) to get from -1/5t to t?

you’re right. but 5/√5 gives √5 since 5=√5√5

Is it possible for you to provide the H1 answers as well?

Okay, I’ll see what I can do. I need to find the H1 math paper haha.

Hi, are there suggested answers for 2014 H1 Math?

Okay, I’ll see what I can do. I need to find the H1 math paper haha.

Hi please leave H1 ans, thank you

Okay, I’ll see what I can do. I need to find the H1 math paper haha.

Hello, for q10ii, why is there no need for modulus sign after integrating? I.e ln|…..|

hi,

We can observe from the MF15 that to apply that formula used, the condition is |x|<a and the modulus resolves. Since we have that x=0.5 is our initial conditions and x always decreases, the condition is satisfied.

But you don't have to worry if you put modulus, since the subsequent answers shouldn't be affected.

All the best for tomorrow! 🙂

Would be good if you could provide h1 too, and possible range of marks for A?:)

Hi

It’s really too early to say since there is still a paper 2 which has equal weightage. The h1 suggested ans has been placed. 🙂 All the best!

H1 answers please?

Hi

It’s there alr 🙂 do let me know jf there are discrepancies

I can email you the H1 qn paper if you need

Sent

Thanks!

Hi Sir,thanks for the answers. Just wanted you opinion on what the estimated bell curve for A for this paper would be like.

Hi, I’m really not in position to comment. Furthermore, the paper 2 isn’t over and there is still a 100 marks there. Should focus on that! 🙂 All the best tmr!

Hi for 7iv Isit possible to jus write there are 3 pair of conjugate pair?

Hi, I can’t really recall the marks for it. But I would think it will be better to discuss more about the roots since they ask for what can be said of the six roots. But you don’t have to worry. Focus on tmr’s paper! 🙂 all the best!

Hey! Ques 10iiia, I put it as square root 5 ln|(-21-4^0.5)/19| Can? Since it ask for exact .

Hi, of course. I believe you rationalized and simplify it. So long as you did it precisely, it’s fine. 🙂

For Qn 2 if i dont write the x=-y part is it okay? or will minus like 1 or 2 marks?

and for Qn 4, the left side of the graph, i drew a hump, instead of just like a circle as you’ve drawn. For the DE qn: if i drew the graph for y<0 will minus like 1 or 2 marks only right? Not like a major part right? Will it be marked wrong? Thank you so much for uploading the answers! Really appreciate it! Grateful!

Hi, I think the other solution is required to explain why there is only one solution 🙂 As for qn4 graph, it’s fine as value of d isn’t given; the examiner is probably giving you guys a benefit of doubt here. Lastly, the DE did mention for relevant parts so you should remove it. You won’t get the entire wrong. Don’t worry. All the best tmr!

if u dont include the other solution for qn2, how many marks do u think will be deducted?

hi,

i’ll say 1 or 2 marks. I don’t have the question paper with me alr. haha But i recall you’re required to show there is only one turning point, so it probably the last part la. don worry! There is still 100marks more tomorrow!

hi, for part 4ii is ‘They are undefined.’ accepted?

Hi, they asked for the tangents, the gradient is undefined but tangent is parallel to y-axis. All the best tmr:)

I would love to know if anyone could give a link for the qns paper itself!

Hi, I can’t scan it for you since it’s copyrighted. If you lost your papers, maybe borrow from peers? But you should be focusing on paper 2 instead.

I got the second term wrong for 8(ii)!! Meaning my 2nd term for 8(iii) is also wrong… god. Do I get the whole question wrong then?

Hi, won’t be that bad. You will still get method marks here. All the best tmr!

what if i extract out the 9 root it istead and get 3 instead of 1/3? i also get the method marks right?

hi,

I can’t really tell honestly. Cos its actually a careless right from the start, it depends on their leniency. But you should get credit for using the correct expansion formulae.

For 9(ii) it’s actually 4 marks. Could you please show the working to get the eqn? Thank you very much.

And how do you even use the GC to get the eqn?

Hi,

Using GC, x=6+2z, y=3+0.5z, z=z

We would then have the equation required.

I conveniently omitted them, as I was rushing it.

For q4, I think the graph that passes through a and b should have an egg like shape. The gradient at a and b should be plus minus infinity.

Hi,

Agree with that. But the result might vary if the value of d is different actually, for d1. I reckon the examiners give you guys a benefit of doubt too.

For qn 11 in part iii i proved using the derivative test and got r=1.207 as a point of inflexion. Is the working wrong?

Hi,

yea thats fine too. Haha you’re really quite patient to do that differentiation actually. crazy good!

http://www.wolframalpha.com/input/?i=y%3D2%2F3%28pi%29x%5E3%2B1%2F3%28pi%29xxsqrt%2816-xx%29%2C+x%3D1.207%2C+d2y%2Fdx2

And yes, its actually inflexion.

All the best tomorrow! 🙂

What is over is over ? Focus on the next paper.

For the tutor, do be more considerate and thoughtful. For those students who did well, they will be happy. For those who did not do too well, they will be stressed up and may affects all subsequent papers. If you are really trying to help the students, put up after the A level is over and not now !

I really hope you do not put up the answers to paper 2 tomorrow to create unnecessary stress to the students.

Hi I think that Mr Teng was being considerate by putting up the suggested solutions for those who wish to get a closure after doing the paper. Furthermore, he repeatedly advises us to focus on paper 2 and not harp on our mistakes. He did it out of good will by putting up his solutions, please do not discourage him from uploading paper two answers. Those who do not wish to see them are free to ignore the post.

We will be putting up the answers to paper 2 tomorrow as scheduled, including answers to H1 Math as well. Almost every A-Level taker in this country is at least 18 years old, so we believe they have the resilience and the emotional maturity to give the right response to setbacks.

Hello! For qn 10 if i multiply the value of k into the expression that i completed the square with, and i did it accordingly. I would be using the 3rd formula instead of the 4th integration formula in the mf15. My final answer is t = 1/sqr5 ln( – (2x-1-sqr5 / 2x-1+sqr5)) is it still correct? Thank you 🙂

hi,

yea its actually the same thing if you keep your k there. however, you should have sqrt(5) instead of q/sqrt(5). You might have made a careless mistake.

http://www.wolframalpha.com/input/?i=integrate+-5%2F%281%2Bx-x%5E2%29

I hope this link helps you to see. In any case, don’t worry too much. 🙂 All the best for tomorrow.

Hi, for question 7ii, i evaluated the answer correctly but i put 1.73 in my working instead of rt 3, will i be penalised?

and for qn 7iii, i left out units^2 in my answer, would they deduct marks here as well?

thanks a lot in advance

hi,

for qn7, I recall they ask for exact value so you should be giving them exact.. The units is quite minor. haha not doing physics here. 🙂

Don’t worry and all the best tomorrow!

is there a need to add first or second derivative test for 11a)? cos i added it in

hi,

you should be doing it. But I used the calculator to evaluate the derivative at that point using (MATH)(8) for TI84 as the calculation was too much hassle.

All the best tomorrow! 🙂

Hey! For qn 11 part(i), i manipulated my answers so that i get 45r^4-768r^2+1024=0 . I know i was careless somewhere at the end… Do you think i will be able to fool the examiners and get 6/6 for that part? Thanks

hi.

haha I think that’s gonna be dependent on how meticulous the examiner is, I really can’t say for sure. Pray he is tired & lazy. :p

All the best tomorrow!

For question 8iii ain’t it differentiating part ii answers 6 times and using those values, following the macclaurin series formula to find it?

Hi,

Yes, there should give you the same answer. However, you will be doing “otherwise”. 🙂

All the best tomorrow!

hi could you do h1 paper and upload too? additionally, would you be able to give the range for A grade? whats the % usually to get A?:)

hi,

yes, one of the kind soul emailed me. But the utility to do Math at night is rather low. Will do it tomorrow morning 8am, should be done by 9am. I think j2s taking stats can consider reading it if you have peers with the qn papers. 🙂

I can’t comment on the range of grades. After all, there is still 100marks more to go.

All the best tomorrow!

Hi, will you be uploading answers for the H1 paper too? Thanks!

Hi,

I’ll do tomorrow. Should be done by 9am.

For 3a) can I just say that a=b ? Since we know that a x a = 0

Hi,

It won’t be sufficient since its 2m, but you should get partial credit. 🙂

All best later!

Hi, for the vectors question, when you differentiate, do you need to show that it is a minimum distance? I forgot to do it:(

Hi,

I think will be complete to show the second order derivative.

All the best later!

Just hope the bellcurve for A is not 90 like in O level…

well, there still a 100 marks to go later. 🙂 All the best!

For the sum to infinity, i was told that we are supposed to “equate to 1” rather than to show that it “tends to 1”. I was marked wrong before in my prelims. Anyway glad to be able to check my answers this quickly. Thanks!

Hi,

It was just to explain the convergence part. The Soo was written with equals to at the last step. 🙂

All the best tmr!

For question 3a) can I just say a=b since we noe a x a = 0??

Oh sorry I didn’t realised it has been answered already. Thank you

H1 ans out yet?:/

Hi

Yes it is alr. Too early for math :p

wow it seems like getting A will be quite hard :/

Hi, well its all over. 🙂 Now you should focus on the rest of you Alevels.