2017 A-level H2 Mathematics (9758) Paper 2 Suggested Solutions

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: 2 \sqrt{15}; xy=6
Question 2: d = 1.5;~ r \approx 1.21 \text{~or~} r \approx -1.45;~n=42
Question 3: (\frac{1}{2}a, 0), (0,b);~ (a+1, 0,);~ (\frac{a+1}{2}, 0);~ (0, a), (b, 0);~ a = 1;~ gg(x) = x, x \in \mathbb{R}, x \neq 1 , ~ g^{-1}(x) = 1 - \frac{1}{1-x}, x \in \mathbb{R}, x \neq 1;~b= 2 \text{~or~}0
Question 4: 15.1875;~ \frac{\pi}{2a(a-1)};~ b = \frac{1}{2} + \frac{1}{2}\sqrt{1-a+a^2}
Question 5: \frac{5}{12}, \frac{5}{14}, \frac{5}{28}, \frac{1}{21};~ \mathbb{E}(T) = \frac{20}{7}, \text{Var}(T) = \frac{75}{98};~ 0.238
Question 6: 955514880;~ 1567641600;~ \frac{1001}{3876}
Question 7: 31.8075, 0.245;~ p = 0.0139; Do not reject h_0, Not necessary.
Question 8: Model (D); a \approx 4.18, b \approx 74.0;~ r \approx 0.981
Question 9: 0.632;~ 1.04 \times 10^{-4};~ 0.458;~ 0.421;~ 0.9408
Question 10: 0.345;~ 0.612;~ \mu = 12.3, \sigma = 0.475;~ k \approx 55.7

Relevant materials

MF26

KS Comments

Showing 161 comments
  • mich
    Reply

    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?

    • KS Teng
      Reply

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

      • rach
        Reply

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

      • gTojo
        Reply

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

        • KS Teng
          Reply

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

    • ttyz
      Reply

      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?

      • KS Teng
        Reply

        definitely since they say if possible

  • rach
    Reply

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

    • KS Teng
      Reply

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

      • rach
        Reply

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

  • ping
    Reply

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

    • KS Teng
      Reply

      nope, cartesian equation implies only x, y variables.

      • Ping
        Reply

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

  • joong ku
    Reply

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

    • KS Teng
      Reply

      = \frac{(15-1)! \times ^{15}C_5 \times 5!}{(20-1)!} = \frac{1001}{3876}

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

      • lazerbag
        Reply

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

      • Jehxbbd
        Reply

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

        • KS Teng
          Reply

          Ehh 3 is 2 tgt alr..

          • Jdjfbfn

            But they give 4 marks so easily?

  • alex
    Reply

    I think 9vi should be 0.0552

    • KS Teng
      Reply

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

      • Andy
        Reply

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

  • alex
    Reply

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

  • Stef
    Reply

    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?

  • Confusecious
    Reply

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

    • KS Teng
      Reply

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

  • Scrub
    Reply

    Never say b is positive tho

    • Scrub
      Reply

      Nvrmd I dumb

      • gTojo
        Reply

        Wait…they did??? How to tell?

        • KS Teng
          Reply

          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.

  • gTojo
    Reply

    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)?

    • gTojo
      Reply

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

      • KS Teng
        Reply

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

      • gTojo
        Reply

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

  • hipsterfish
    Reply

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

    • KS Teng
      Reply

      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 🙂

  • alex
    Reply

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

    • KS Teng
      Reply

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

  • Lalala
    Reply

    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

    • KS Teng
      Reply

      thats fine. answer should be same

  • Alvin
    Reply

    For 2(i), first term should be 3

  • alex
    Reply

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

    • KS Teng
      Reply

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

      • alex
        Reply

        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?

  • ...
    Reply

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

  • Jake
    Reply

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

    • KS Teng
      Reply

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

      • Jake
        Reply

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

        • KS Teng
          Reply

          i think its ok, since its positive marking. 🙂

  • ...
    Reply

    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?

    • KS Teng
      Reply

      s^2 = \frac{1}{n-1} [\sum (x-c)^2 - \frac{(\sum (x-c))^2}{n}]

      You should know this formula.

  • maryann
    Reply

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

  • Jake
    Reply

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

    • KS Teng
      Reply

      thats small issue

      • Jake
        Reply

        Will I minus?

      • Jake
        Reply

        Will they minus?

  • wowowow
    Reply

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

  • Bbdd
    Reply

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

    • KS Teng
      Reply

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

      • Bbdd
        Reply

        Okay thanks for replying!:)

  • bellcurve follower
    Reply

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

  • bellcurve follower
    Reply

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

    • KS Teng
      Reply

      please share your answers. thank you

      • bellcurve follower
        Reply

        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?

        • KS Teng
          Reply

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

      • bellcurve follower
        Reply

        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

        • KS Teng
          Reply

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

          • bellcurve follower

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

          • KS Teng

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

  • Bbdd
    Reply

    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

  • rainbow
    Reply

    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?

  • Tay Lam
    Reply

    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?

  • clxriss
    Reply

    what r yr comments for this paper

  • Jia
    Reply

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

  • Lin
    Reply

    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?

    • KS Teng
      Reply

      thats a different meaning entirely..

      • Lin
        Reply

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

  • Hi
    Reply

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

  • Red
    Reply

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

  • Worriedperson
    Reply

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

  • Jake
    Reply

    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

  • :-)))))
    Reply

    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?

    • KS Teng
      Reply

      no, n is large for n \ge 20. This is what was taught even to my students last year for 9740.

  • Jyh
    Reply

    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?

  • sk
    Reply

    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!

    • KS Teng
      Reply

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

  • Help
    Reply

    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

    • KS Teng
      Reply

      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.

  • Jon
    Reply

    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?

    • KS Teng
      Reply

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

  • hi
    Reply

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

  • hello
    Reply

    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)

  • Belll
    Reply

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

  • Tay Lam
    Reply

    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.

    • KS Teng
      Reply

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

      • Query
        Reply

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

  • Jay
    Reply

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

  • Justin Ang
    Reply

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

    • KS Teng
      Reply

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

  • Query
    Reply

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

    • KS Teng
      Reply

      yes, thats fine too

      • Query
        Reply

        Thanks 🙂

  • A
    Reply

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

    • KS Teng
      Reply

      yes, that will be safe. 🙂

      • A
        Reply

        Thanks!

  • Zoom
    Reply

    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

  • Chandice
    Reply

    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.

    • KS Teng
      Reply

      actually, you didn’t need a graph paper.
      but i believe they will, so long as you wrote in ink and have them numbered.

      • Chandice
        Reply

        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

        • KS Teng
          Reply

          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.

  • Coco
    Reply

    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!

    • KS Teng
      Reply

      i think thats okay for an A. 🙂
      yes, positive marking. so really, dont worry.

      • Coco
        Reply

        Thank you! 🙂

  • Static
    Reply

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

    • KS Teng
      Reply

      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.

      • Static
        Reply

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

        • KS Teng
          Reply

          67-68 bout there.

          • Static

            Thanks!

  • gabb
    Reply

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

  • hi
    Reply

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

  • hi
    Reply

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

  • Johnster
    Reply

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

  • Ash
    Reply

    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?

  • Tay Lam
    Reply

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

    • KS Teng
      Reply

      That’s 70, as suggested by schools..

  • Barry
    Reply

    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?

    • KS Teng
      Reply

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

  • Jack
    Reply

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

  • BeepBoop
    Reply

    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?

    • KS Teng
      Reply

      They did want you to state the parameters.

  • Whitish Black
    Reply

    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

  • Tay Lam
    Reply

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

  • Worriedguy
    Reply

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

  • Worriedguy
    Reply

    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

  • Ash
    Reply

    hi, do the markers practise follow through marking?

    • KS Teng
      Reply

      Technically yes, with positivity

      • Ash
        Reply

        even within the same question part?

        • KS Teng
          Reply

          Ya they will give method marks accordingly still.

          • Ash

            ok thanks!!

  • Test
    Reply

    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!

    • KS Teng
      Reply

      L’hospital cant be applied on “\frac{0}{\infty}”. The limit will just be 0 and we are done.

  • scared
    Reply

    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?

    • KS Teng
      Reply

      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.

  • TJ
    Reply

    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?

    • KS Teng
      Reply

      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..

  • rainbowmonster124
    Reply

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

    • KS Teng
      Reply

      Not too sure, to be honest. :/

pingbacks / trackbacks

Leave a Reply to bellcurve follower Cancel reply

18 + fourteen =

Contact Us

CONTACT US We would love to hear from you. Contact us, or simply hit our personal page for more contact information

Not readable? Change text. captcha txt

Start typing and press Enter to search