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

As these workings and answers are rushed out asap, please pardon me for my mistakes and let me know if there is any typo. Many thanks.

I’ll try my best to attend to the questions as there is H2 Math Paper 2 coming up.

Question 1

(i)

(ii)

Question 2

(rejected since ) or

Question 3

(i)

(ii)

Using GC, required answer (3SF)

(iii)

When

(3SF)

(iv)

Question 4

(i)

Let

When

When

Coordinates

(ii)

When . So is a minimum point.

When . So is a maximum point.

(iii)

x-intercept

(iv)

Using GC,

Question 5

(i)

Area of ABEDFCA

(ii)

Perimeter

When (rejected since )

When

Question 6

(i)

The store manager has to survey male students and female students in the college. He will do random sampling to obtain the required sample.

(ii)

Stratified sampling will give a more representative results of the students expenditure on music annually, compared to simple random sampling.

(iii)

Unbiased estimate of population mean,

Unbiased estimate of population variance,

Question 7

(i)

[Venn diagram to be inserted]

(ii)

(a)

(b)

(iii)

Question 8

(i)

Required Probability

(ii)

Find the probability that we get same color. then consider the complement.

Required Probability

(iii)

Question 9

(i)

Let X denote the number of batteries in a pack of 8 that has a life time of less than two years.

(a)

Required Probability

(b)

Required Probability

(ii)

Let Y denote the number of packs of batteries, out of 4 packs, that has at least half of the batteries having a lifetime of less than two years.

Required Probability

(iii)

Let W denote the number of batteries out of 80 that has a life time of less than two years.

Since n is large,

approximately

Required Probability

by continuity correction

Question 10

(i)

Let X be the top of speed of cheetahs.

Let be the population mean top speed of cheetahs.

Under

Test Statistic,

Using GC, is rejected.

…

(ii)

For to be not rejected,

(round down to satisfy the inequality)

Question 11

(i)

[Sketch to be inserted]

(ii)

Using GC, (3SF)

(iii)

Using GC,

(3SF)

(iv)

When (3SF)

Time taken minutes

Estimate is reliable since is within the given data range and is close to 1.

(v)

Using GC, (3SF)

(vi)

The answers in (ii) is more likely to represent since is close to 1. This shows a strong positive linear correlation between x and y.

Question 12

Let X, Y denotes the mass of the individual biscuits and its empty boxes respectively.

(i)

(ii)

(iii)

Let and

Hello! I’m not sure whether it’s something wrong with my phone or some other problem like that but I can’t see any of the answers!

hi, sorry. but h1 has to wait. H2 was more fun. So I did H2 first..

Understood! Thanks for your effort!!

Hello roughly how much do you need to get in order to get an A in h1 math?

what time will the answers be out? ESTIMATE PLS

Hi what time will you be uploading the answers?

thanks a lot for trying to upload the ans ASAP!

hello! for 6iii), the question mentioned in hundreds of dollars, is there a need to take all the answers x100?

no need. since its already defined to be X

This is an odd question but if you leave the answer as mean=$3.9, and variance=$1.41, will I not get the answer mark because of the units? Or is it alright?

the mean is fine. but variance will need to be which is rather awkward.

I see. Thanks! So I guess that’s one answer mark gone, sighs. Thanks agn!

Hello! Will the rest of the answers be uploaded as well? Thanks very much for getting all these answers out for us π

yea. haha cos I’m having lessons now. But will be out.

hi! based on the difficulty of this paper, what mark range do you think A and B will be? π

hey how can 8ii be a negative probability

its a typo. you can just key the answer in yourself.

The probability question is wrg? How can u have a negative probability

just key it into the GC yourself. I’m having lessons now for H2 math.

what’s the rough marks to get an A for h1 maths in A levels?

Hi, I think there is an error in 8(iii), how can it be that your answer in 8(ii) is 11/18 (different balls) and yet you use 11/18 for same balls? I think it should be 1/30 divided by 7/18, giving you an answer of 3/35. Thanks for uploading the answers, greatly appreciate it π

hi, thanks for that. cos i’m just blindly typing them on the phone as I’m having H2 Math class now. Too careless.

Hello! For Q4iii, isn’t there 3 x intersections?

yea, my bad. didnt read the question. sorry, iβll typing the h1 on the phone while having h2 math classes now. cos i only planned on doing h1 at 10pm lol

Thanks for pointing it out!

Q4 asking for coordinates that cut x-axis and it should be 3 points (1,0), (-0.157,0), (-1.593,0). Cutting at y-axis is not required

oh right. didnt read the question. sorry, i’ll typing the h1 on the phone while having h2 math classes now. cos i only planned on doing h1 at 10pm lol.

Thanks for pointing it out!

getting 95/100 will definitely be A even if the bell curve is high right?

haha idk. it seems like everybody is getting >90 for this paper… tough moderation.:/

Just a minor mistake for 11(v) when you rounded it off to 3 s.f the decimal point went missing. Omg I just realised my careless mistakes and how I didn’t x 1/2 for the probability qn I am feeling q depressed now LOL ohwell thanks for uploading the answers for all of us! π gladly appreciate it π

Oops! Thanks so much for pointing that out! Its over! Focus on the papers to come π

why 8(i) need to multiply by 1/2

You have to pick the box first that’s why x 1/2 I guess! I didn’t do that too bc I was afraid it’ll lead to “double counting” π

Yup, passerby is right. you need to consider which box you’re picking cos they said a box is picked at random. π

For 10ii why do we test the claim at less than 95 instead of more than 95?

Does anybody know how h1 bellcurves are usually like? Is 70 an A, or really harsh like >90?

its harsh. especially given this paper, tough moderation

It is a question that confused us with words. The last part stated ” he finds that the mean top speed….is NOT greater than 95″, which have to reject the Ho that is greater than 95.

oh I see thank you! π

Hello, I think for Q10ii, you should test for u>95 since Probability of X being more than 95 is not achieved (insufficient evidence to prove H1 is true) and hence H0 is not rejected, and is more than 0.05 (critical region)

P(X > x) > 0.05, hence find X values to satisfy this using sample mean distribution.

No? π

I took “he finds that mean top speed is not greater than 95…” to refer to the rejection of H1 and to work from this rejection

*sry last comment*

You rejected H0: u = 95 to derive the range of sample mean values.

But question only stated not more than 95, so there is a possibility of u=95 and u95 and thus not reject H0: u=95 to derive our sample values from there π

*Possibility of u=95 and u<95 (less than 95) oh god sorry for the spam just very worried

Hi, yup you’re right. I didnt read carefully enough. thanks! and sorry for the confusion

For 10 ii, can my alternate hypothesis more than 95? After which I show that Ho is valid, hence mean is not greater than 95.

And questiom 11vi, isnt the p value in part v more accurate? Because the increase in sample size will provide a more accurate representation of the entire population?

you’re correct. sorry I forgot to switch the inequality in 10ii

Daphe, thanks for your sharing. Then my mark gone-lah ;-(

yea, this question is really tricky. Must really read precisely. :/

For 10ii shouldn’t Zcal>Zcritical since we do not reject Ho? Then shouldn’t the answer be 93.sth if I’m not wrong?

Hi, this is a right tailed test. So to not reject