All solutions here are **suggested**. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

This is answers for H2 Mathematics (9740). H2 Mathematics (9740), click here.

Numerical Answers (click the questions for workings/explanation)

Question 1:

Question 2:

Question 3:

Question 4:

Question 5:

Question 6:

Question 7: ; Do not reject , Not necessary.

Question 8: Model (D);

Question 9:

Question 10:

(i)

When

When

Length units.

(ii)

Tangent @ P:

@D,

@E,

(ii)

If

Using GC,

(iii)

Using GC,

(i)

*For students: We half our values here as we scale by factor .

x- intercept

y- intercept

(ii)

*For students: We plus one to our values here as we translate by 1 unit in the positive x direction.

x- intercept

y- intercept inconclusive

(iii)

*For students: We plus one to our values here as we translate by 1 unit in the positive x direction. Then, we half our values here as we scale by factor .

x- intercept

y- intercept inconclusive

(iv)

*For students: since and is a reflection about

x- intercept

y- intercept

(b)

(i)

(ii)

Let

(iii)

From GC, the coordinates of intersection between the curves are 1 and 5.5.

Area

Using GC, Area

(b)

(i)

Volume

(ii)

Since , and volume has to be formed in a same way, ,

(iii)

Let denote the number of games Lee takes out at least 4 counters out of the bag, out of 15 games.

Number of ways

(ii)

Number of ways

(iii)

Required probability

Each biscuit has an equal chance of being sampled, independently of each other.

(ii)

unbiased estimate of population mean

unbiased estimate of population variance

(iii)

Let X denote the mass of biscuit bars, in grams

Let denote the population mean mass of biscuit bars, in grams.

Test

against at 1% level of significance

Under approximately, by Central Limit Theorem.

Test Statistic,

Using GC,

Since , we do not reject at 1% level of significance and conclude with insufficient evidence that the mean mass differs from 32g.

(iv)

The sample size, is sufficiently large for the manager to approximate the sample mean distribution of the masses of the biscuit bars to a normal distribution by Central Limit Theorem.

(i)

(ii)

(iii)

(b)

(i)

Model (D) is appropriate.

(ii)

Using GC, and

(iii)

is within given data range, and we are performing interpolation, which is a good practice.

The r value is close to 1 which suggest a strong positive linear correlation between the average yields of corn and the amount of fertiliser applied.

The probability that the lights are faulty is constant.

The event that the light is faulty is independent of another light being faulty.

The light can only be either faulty or non faulty. (This cannot be used as its implied in the question)

(ii)

Let denote the number of faulty lights in a box of 12.

(iii)

Required probability

(iv)

Let denote the number of faulty lights in a carton of 240.

(v)

Events in (iii) is a subset of events in (iv).

(vi)

(vii)

Required Probability

(viii)

From (vii), the quick test seem to be 94% accurate. However, from (vi), we understand that out of the number of lights identified faulty, 42.1% of them will be a mistake. As such, the quick test is not worthwhile, since light identified as faulty are mistakingly discarded. Moreover it will cost money to administer a test.

Let denote the mass of a sphere, in grams.

(ii)

Let

(iii)

Let denote the mass of a bar, in grams.

— (1)

— (2)

Using GC,

Mean g

Standard deviation g

(iv)

g.

### Relevant materials

### KS Comments

[…] This is answers for H2 Mathematics (9740). H2 Mathematics (9758), click here. […]

I thought we only need to give the coordinates of axis interceptions for q3? So if we cant determine the y-intercept then we shouldnt need to write anything for yintercept?

but we can. for inverse function, y and x coordinates will be swapped since its a reflection about

can i just say only has x intercept for (ii) and (iii) then i state whats the x int

How do you determine the y intercept for question 3 part (ii) and (iii)?

you can’t. like others observed, just leave blank. i just put the resultant transformation

I think the statements for Q7i is not correct

Hi, thanks for pointing out. 🙂 Not sure how it appeared there. Thanks again!

Hi ks, to add on to mich, for Q 3(ii) and (iii) you cannot identify to transformed y intercept. is it ok to leave blank?

definitely since they say if possible

for q5 i did a probability tree for part i) eh.. i only did the prob distribution diagram for part (ii) is that okay?

thats fine too. just more time consuming. (ii) still must find the values.

yeah…. i did probability tree and probability distribution diagram before finding expectaion and variance :/ very tedious

For 1ii, why don’t need convert the x into p since the qn says as p varies?

nope, cartesian equation implies only x, y variables.

aw so 1mark deducted for changing into p? I’ve got y=6/x in my prev step.

How did u get answer for 6iii.? Why isit not 1001/5814?

Its a circle. and we are separating the fathers, so we can slot them in.

if you forgot to add in the 15c5 and everything else is correct, how many marks will u probably get? :/

No two fathers together, but can 1 or 3 or 4 or 5 together right?

Ehh 3 is 2 tgt alr..

But they give 4 marks so easily?

I think 9vi should be 0.0552

i think you might have misunderstood it. they want conditional prob here

How many marks do I get if I only got the 0.0552 ans?

For 4a, i left the answer in fraction because it is exact. Is that okay or will marks be deducted?

Hello, if I wrote the wrong model for the c&r qn, will my subsequent part for equation and value of r be wrong too or will there be ecf?

For q3, so long as writing down the axial intercepts will do, no?

yup, just write, no need explain. i explain to help students.

Never say b is positive tho

Nvrmd I dumb

Wait…they did??? How to tell?

thye said its formed in the same way. should b be negative, we have a shape that different already.. :/ the graph is different. so b should have the same behaviour as a.

For question 4, I thought they did not say that b>1? They only stated it for a>1. So is it wrong to put b= 1/2 +/- sqrt(a^2 – a +1)?

Sorry, Forgot the 1/2 in front of the sqrt

i think its alright. but intuitively, b and a should have same behaviour.

How to delete above comment? (Since its answered in another post already)

dont worry about it.

Hi, for Qn3, how can (1, b) and (1/2, b) be possible? Shouldn’t axial intercepts be (0, something) or (something, 0)

Thanks

yes. thats not the answers. i just put like what happens. cos aside from checking answers.. these are meant for other batches to relate too 🙂

For 3bii, if leave g^-1(x) as 1- (1/1-x) can? Because this is the answer in ur final working.

yea, i typed and solve so clearer. the numerical answers are off hand one.

For qn 4(i) can i split it into 3 parts?

1) integrate 1 to 5 for the curve

2) find area of triangle from 1 to 5.5

3) integrate 5 to 5.5 for the curve

Then finally I add the area of curve and triangle – the extra area from 5 to 5.5

thats fine. answer should be same

For 2(i), first term should be 3

yes but the formulae is

Q10 iii, shouldn’t it be 12.1 and 0.216?

I think you might have careless. and they asked for standard deviation, not variance.

Yes.. For invNorm i forgot to change 0.6 to 0.4. It affected my 10iii and iv. Any idea how many marks ill get if other steps are all correct?

Why is qn 3bii for g inverse 1 + 1/(1-x)? Isn’t it 1 – 1/(1-x)?

typo, sorry bout it

Is it OK if for qns 3 we just write all the coordinates oht but not labelling like specifically y intercept =

you mean the intercepts? you can just write what the intercepts are. i merely included all so its easier for other learners.

As in I left it as (x,y) in coordinates form for ALL including those that are not intercept. Will they minus?

i think its ok, since its positive marking. 🙂

How did you get the unbiased estimate for qn 7ii? If I get the estimate for variance wrong, but everything else right, will be part iii be badly affected?

You should know this formula.

if i chose model C, bc i did (x+1) will i get marks for r and regression line based on this?

For standard deviation and mean I never put g at the back can?

thats small issue

Will I minus?

Will they minus?

for 8b if you use model C would there be ECF?

For 10ii) I thought that the 10% increase is for 1 Sphere. And (20, 0.5^2) is the normal distribution of 2 spheres?

i think you misunderstood the question… its the distribution for one sphere

Okay thanks for replying!:)

For ques 8iii) can say that eqn makes the x as the independent variable thats why model suitable? thx

that will be fine too

Also i believe ur 10 part ii and part iv is wrong. Please check to clairfy. Thx

please share your answers. thank you

sorry my bad sir for part ii ure right. for part iv i realised i think its a matter of sf i used for sigma and miu (4sf), while u used calulator value. My answer is 55.9 instead of 55.7, amirite?

you can’t take 4sf for intermediate workings actually.. :/ need at least 5sf.

Btw. For Hypo, I wrote H1 as less than instead of not equal to; because of my understanding that since 32 is requirement, so long as its 32 and above, the product is fine since the manager and consumers wont be concerned if the mass is over- not sure why this isnt correct. But how many marks can i get if H1 is wrongly stated but every step after follows the structure by the book exactly for standard hypothesis testing questions

hmmm. yea, understand. but as a production manager, he will be concerned about the mass be over, he is wasting the resources.

i guess lol. but doees it mean 5 marks wholesale gone alrdy if H1 defined wrongly?

you method should still be there. for the Under h0, etc.

Hi for question 10bii) I thought that they are asking for each sphere. So must we not divide the normal distribution by 2 first? Thanks

can i ask for q1 if i went back to change my answer and i got it correct eventually but i didnt cancel my initial workings. will there be any penalised marks for 2 answers?

for hypothesis testing 5 marks part If I used the 3 sf values of unbiased estimate of population mean and variance and got a diff p value but is still more than 0.01,how many marks will that be?

what r yr comments for this paper

Hi. I used (14!×16C5×5!)÷19! Instead of 15C5!, can I get any method marks from the total of 4 marks part?

Hi if for q9 iv I calculated the probability for at least 20 faulty light using by approximating to normal distribution with N(240(0.08),240(0.08)(0.92)) which give 0.425 will it still be accepted?

thats a different meaning entirely..

I thought since n=240 is large we would be able to approximate binomial to normal?

How do u get the variance for the final part of the last qn!

Hi for qn 3a part ii can i leave the y intercept as (0,f(-1))? Thanks

If I’m careless for 2bii, will we get ecf for biii?

Hey man just asking for instance if we got landa no real solution from calculator can we just say from gc there is no real solution for landa

thats fine

Hi, for 9740 paper it’s taught that n is only large if n=50. As such if t-test is used will I be penalised?

no, n is large for . This is what was taught even to my students last year for 9740.

If for the last question for both E(X) and Var (X) i accidentally take it as X=2A+B instead of X=A1+A2+B and hence my presenation for E(X) is wrong and numerically Var(X) is also wrong, how many marks will i be deducted?

Hi, for Q7(iv), is there a difference between “population distribution of the masses of the biscuit bars” and “distribution of sample mean”, since it is the sample mean that approximates a normal distribution by Central Limit Theorem right? I’m not sure if there’s any misconception on my part. Thanks!

both are ok essentially. i doubt Cambridge will nit pick.

Will there be effor carry forward if i made a mistake at the start of question 10? I calculated the coating as 1.01 instead of 1.1 but my solution subsequently is correct

It actually depends on your presentation. If you do show how in your workings how you arrived at the variance and expectations of the new distributions.

For 10iii Yes.. InvNorm i forgot to change 0.6 to 0.4. It affected my 10iii and iv. Any idea how many marks ill get if other steps are all correct?

will lose the A1 in (iii) and also might be 2 marks for (iv)

if i drew my scatter diagrams in the wrong quadrant isit straight 0 for all 3?

yes

For 9iv), since n=240 is large, can we assume normal dist by CLT and solve that way instead? With a E(X) of 240×0.08 and Var of (240)(0.08)(0.92)

Hi for qn 3a part ii can i leave my y intercept as (0,f(-1))? Thanks

is it possible to write g^2(x)=gg^-1(x) to find g^2(x) after finding g^-1(x)?Since one knows the function is self inverse after finding the inverse.

of course! but self-inverse isn’t in syllabus technically so students do not need to know how to “handle” it..

For Q8, when r=0 can I plot a vertical line?

Can g^-1 in 3ii be 1+(1/(x-1))

thats same

How many marks would be deducted if I used X instead of Y for mass of sphere in 10iv?

i think you might get 1 for the correct method, if you show sufficient presentations for finding your parameters.

For Q8 can I plot a vertical line when r=0?

yes, thats fine too

Thanks 🙂

Based on your experience, what mark would constitute an A for H2 math? Is an average of 80 between 2 papers safe?

yes, that will be safe. 🙂

Thanks!

Hi, for 10(iii) I missed out on the negative signs for my simultaneous eqn and i got a negative standard deviation :// so i just concluded since sqroot sigma^ 2 = +/- sigma and sigma > 0 the ans is the positive value… how will u rate this? ans is correct for both last 2 parts

probably get 2.

Hi, I would like to enquire if the markers would mark solutions written behind graph paper? Meaning in front is graph behind is solutions for the rest of the parts.

actually, you didn’t need a graph paper.

but i believe they will, so long as you wrote in ink and have them numbered.

Thank you Sir:) But btw sir, it is at the back, will they even see it?🤔😯 And i thought the question said ‘draw’ and not ‘sketch’?0.0

Yup. They will see it. They mark with positivity:)

They aren’t there to penalize marks. They are there to test if you guys learnt your stuffs and reward you marks.

Hi, do the markers practice positive marking? I realised i was careless and unthinkingly presented my answers for all 4 parts in Q3 as “Graph cuts x-axis at: (coordinates) and Graph cuts y-axis at (coordinates)”, even though the graph doesn’t cut the y-axis in (ii) and (iii). However, all my coordinates are actually correct for the 4 parts. So I’m wondering if they practice positive marking and just mark the correct coordinates, ignoring the wrong presentation.

Also, if I get an average of 79.5 across both papers, would it be safe for an A? Thanks!

i think thats okay for an A. 🙂

yes, positive marking. so really, dont worry.

Thank you! 🙂

Hi! May i check is 60-65 safe for a B for both papers?

not really. given the paper was not really that hard, as compared to 2016 – 2014. The new syllabus required students to really discern good information and rewards students.

Oh i see, then based yr experience, to attain a B for this kind of papers, what’s a safety range to hit?

67-68 bout there.

Thanks!

Hi what would be a safe range for A this year?

if p1 is rly bad like 50-60 range but p2 probably more than 85 what grade is likely?

if p1 is rly bad like 50-60 range but p2 more than 85?? what grade is likely?

Isn’t S13 when r=1 equal to 13(3) = 39? How could it be 0?

Does Cambridge practise follow through marking? E.g. if I made a careless mistake in differentiating at the start of q1ii, but subsequent methods are correct, will I get method marks?

Based on your past estimates,whats the lowest possible overall score to get an A(but not guaranteed)?

That’s 70, as suggested by schools..

Hi, would it be fine if I did not erase my regression line used to plot my points on the scatter diagram? Would they penalise this?

I think it’s ok. They will do positive marking 🙂

Hi if I lost 60 marks for p2, any idea approx what grade i’d be getting.i lost about 50 for p1.

Hello, for Q10, if i didnt show the workings on how i got the values for the new mean and variance of the sphere and just wrote there Y~N(22,0.55^2), but i defined Y as the new mass, will i be penalised?

They did want you to state the parameters.

Hello, for question 10 , if i did not show the workings on how i got the new mean and variance of the sphere, will i be marked down? I just wrote the new distribution as Y~N(22,0.55^2) and defined Y

Just curious based on your own estimates,what is the lowest possible score for an A?

79.5 round shouts 🙂

Hi if my answer for part 4bi is wrong will my entire answer for 4bii be completely wrong also or will I get ECF?

Will get method marks

Hi I made a careless for 5i so my Drv table is wrong, but for 5ii my calculations are based on the drv I drew in 5i, so will I get ecf for using the correct method? And is around 75-77 okay for an A? Thanks

hi, do the markers practise follow through marking?

Technically yes, with positivity

even within the same question part?

Ya they will give method marks accordingly still.

ok thanks!!

Hi, for Q2ii, when r = 1, why is S13 = 0? The numerator and denominator both tends to zero. Shouldn’t it be S13 = 3 + 3 + … + 3 = 13 x 3 = 39 or use LHopital which also gives 39? Thanks!

L’hospital cant be applied on “”. The limit will just be 0 and we are done.

Given the standard of this paper, will an average of 77 get me an A? Also, is there ecf (error carry forward) for H2 math?

there isn’t error carry forward in h2 math. we call it method 1.

answer mark when your answer is correct, which pretty much sums up one’s precision in Mathematics.

method mark when your method is correct, which conveys to the marker that you have the correct idea. this can be thought as ecf. but its really just whether or not, you understood the question and did the correct method. this will not consider your previous mistakes and your precision. so you can say its ecf.

I would be highly obliged if you know of any sources for answers to the recent chem and phy a levels this year. Also, is getting a 72% overall for math enough to get an A?

I don’t know about the resources. This blog and the solutions I put, are purely out of personal interests. 😉

And I won’t say 72% is safe..

Hi, may I know if 75% stands a chance of getting an A? Thanks

Not too sure, to be honest. :/