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2009
Thu
12
Nov

GCE A-Level 2009 Oct/Nov H2 Maths 9740 Paper 1 Suggested Answers & Solutions

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Tuition given in the topic of H1/H2 (A Level) Maths Tutor from the desk of The Higher Council at 12:10 am (Singapore time)

OK everyone, the following H2 9740 Maths Paper 1 suggested solutions (see below) that I’ve worked out are merely what it is i.e. suggested answers.

It is most certainly not the actual marking scheme from Cambridge, so don’t be quick to assume the end of the world for your Paper 1 should some of your steps and answers be different from mine. You’ve probably been told countless times that marks will still be awarded even though your answer may not be complete, as long as you have presented your concepts and ideas clearly 🙂

Of course, do kindly point out any mistake that you may spot in the solution. [disclaimer]Afterall, they were compiled rather quickly using whatever spare time I have left after my classes these two days.[/disclaimer]

A-Level 2009 October/November H2 Maths 9740 Paper 1 Solutions

2009 ‘A’ Level October/November H2 Maths (9740) Paper 2 Solutions – click to download

Now that we’re halfway there, it’s time to focus on the following topics in your H2 Maths Paper 2 (while the H1 folks can forget about maths for a long, long time).

Pure Maths Topics

  1. Differential equations, integration by parts
  2. Applications of Differentiation (maxima & minima problems, connected rate of change, equations of tangent & normal)
  3. Vectors (foot of perpendicular distance, area of parallelograms/triangles etc.)
  4. Functions (composite functions, inverse functions, transformations)
  5. Inequalities
  6. Complex numbers (loci – hope you have your compass with you IF it comes out)

Statistics Topics

Though questions on statistics may appear to be quite random and unforeseeable at times, do spend time to look through the statistics portion of the 2007 and 2008 H2 Maths Paper 2 to have a feel of the section. It will be manageable as long as you are confident in your probability concepts. The importance of the 3 Cs in this section i.e. reading the questions/stories Calmly, Carefully and Correctly cannot be overemphasized. Make sure you iron out each question’s logic first instead of charging in like a mad man/woman!

  • Probability (Venn diagram, probability tree, conditional probability, permutations & combinations)
  • Methods & techniques of sampling (do spend bit of time reading it up)
  • Poisson & binomial distributions (know the conditions for Normal approximations & perform continuity correction)
  • Normal distribution (linear combinations of normal variables: sums and multiples)
  • Linear regression (transforming a set of non-linear data to linear form, correlation coefficient r2=bd)
  • Sampling & hypothesis testing (Central Limit Theorem, calculation of unbiased estimates of population mean & variance from a sample)

All the Very Best for Paper 2!!!

頑張って!!!

Revision Exercise

To show that you have understood what Miss Loi just taught you from the centre, you must:

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Comments & Reactions

28 Comments

  1. kohes's Avatar
    kohes commented in tuition class


    2009
    Nov
    12
    Thu
    11:49am
     
    1

    Perhaps we can consider Q4 as a question on transformation? (Refer to link above)

  2. kohes's Avatar
    kohes commented in tuition class


    2009
    Nov
    12
    Thu
    11:50am
     
    2

    mathsguidebook.com/h2maths/h2-maths-2009.php

  3. Nash's Avatar
    Nash commented in tuition class


    2009
    Nov
    12
    Thu
    12:17pm
     
    3

    Yay most of my answers tally =D apart from the ones i mentioned earlier. Although i think i got 15 cm for the 13th bar in qn9... Aiyah lazy to go rework >_<... Thanks alot for the ans can go do paper 2 happily =D

  4. kohes's Avatar
    kohes commented in tuition class


    2009
    Nov
    12
    Thu
    1:28pm
     
    4

    Congratulations! For question 9, a quick way to do this question is to observe that 13 is exactly halfway between 1 and 25. Take geometric mean of 1 and 25, answer is 10.

  5. kohes's Avatar
    kohes commented in tuition class


    2009
    Nov
    12
    Thu
    2:33pm
     
    5

    Just to add, when drawing the perpendicular bisector for question 9, the perpendicular bisector does not just passes through the origin, it passes through z_7 according to the solution diagram.

  6. jas's Avatar
    jas commented in tuition class


    2009
    Nov
    13
    Fri
    11:12am
     
    6

    Hey! Is it possible to add H1's solution as well for this year? Thanks much! (:

  7. Nash's Avatar
    Nash commented in tuition class


    2009
    Nov
    13
    Fri
    12:34pm
     
    7

    Eh Kohes, the question said that it DOES pass through the origin, and if u happen to use a protractor to draw (i had spare time to measure =P) i will pass though both the 7th root and origin.

    Today's paper was average, For question 6 the world record timing should be 3mins 41.4 seconds right? And the family of solution curves were they point of inflextions? I used like C=20 and -20 before i could differentiate between the 3 graphs =X they are like on top of one another =X(for my case anyways)

  8. Labbitan's Avatar
    Labbitan commented in tuition class


    2009
    Nov
    13
    Fri
    12:59pm
     
    8

    10(iii) Another method : Since (0,1,0) from line l and (2,3,4) lie on the plane P3. We will have 2 directional vectors (1,1,-1) and (2,2,4) to define the plane. Crossing these 2 vectors = (6,-6,0). So the vector eqn for the plane is r.(6,-6,0)=-6. Hence the cartesian eqn is z=0 and (x-y) = -1 !!!!

  9. kohes's Avatar
    kohes commented in tuition class


    2009
    Nov
    13
    Fri
    1:02pm
     
    9

    Yeah, Nash that was what I was referring to. The diagram in the suggested solutions did not cut the 7th root though.

  10. passerby's Avatar
    passerby commented in tuition class


    2009
    Nov
    13
    Fri
    6:50pm
     
    10

    Hey, I'm just wondering whether the cartesian equation given to question 10(iii) is correct. Shouldn't it be x - y + 0z = -1, or alternatively, x - y = -1, z can be any real number?

  11. passerby's Avatar
    passerby commented in tuition class


    2009
    Nov
    13
    Fri
    7:07pm
     
    11

    hi when will p2 answers be posted up?? eager to find out answers!!!

  12. kohes's Avatar
    kohes commented in tuition class


    2009
    Nov
    13
    Fri
    8:00pm
     
    12

    @passerby: p2 answers are out at mathsguidebook.com

  13. Nash's Avatar
    Nash commented in tuition class


    2009
    Nov
    13
    Fri
    10:00pm
     
    13

    Thanks for the link kohes, are u a teacher or something O_o? Anyways the last part of Qn 11 is misleading, i thought probability of 0 and 1 is 0.2... tallied the results... ~70 for both papers =D

  14. kohes's Avatar
    kohes commented in tuition class


    2009
    Nov
    14
    Sat
    12:27am
     
    14

    Yeah, its the phrasing, some people interpreted it as P(R=0) or P(R=1). 🙂
    Haha, I'm not a teacher of course. Just happen to be interested in such discussions, maths keeps my brain working!

  15. oka's Avatar
    oka commented in tuition class


    2009
    Nov
    14
    Sat
    12:31pm
     
    15

    hey i was just wondering, how does the grading system work is it >70 for an A or does it fluctuate according to how everyone does?

  16. Ys's Avatar
    Ys commented in tuition class


    2009
    Nov
    14
    Sat
    7:38pm
     
    16

    Hey will the chem 2009 h2 p3 and be out too?

  17. Nash's Avatar
    Nash commented in tuition class


    2009
    Nov
    14
    Sat
    7:46pm
     
    17

    Well for the grading system u can refer to my earlier post on one of miss loi's Sec 4's posts...
    https://www.exampaper.com.sg/miss-loi-the-tutor/gce-o-level-octnov-2009-e-maths-4016-paper-2-suggested-answers-solutions
    Its the same system for JC more or less and 70 is still a B =X... For maths the grade for A hovers around 80

  18. wei zhong's Avatar
    wei zhong commented in tuition class


    2009
    Nov
    14
    Sat
    8:36pm
     
    18

    hello! i'm eagerly waiting for chem 2009 h2 p3 as well, cos i take h1 chem and i want to see if cambridge's style has perhaps changed for this year? (for last year it was organic spammage i heard)

  19. Nash's Avatar
    Nash commented in tuition class


    2009
    Nov
    14
    Sat
    9:39pm
     
    19

    Yes it was an organic spam, every question had it cambridge dosnt like to repeat trends. Just in case u wanna know, P3 had 2 organic question, chem kinetics, protein chem ,grp7. Like i spotted they are gonna put transition for paper 2 and kill alot of ppl like the Cu chem question last year (ugh) Probably Mn or Vanadium this time(might come out as electro though)

    I don't think Little miss Loi covers JC chem so maybe u should try other websites. Its already out according to my tutor but i dun have the links >_< sorry...

    Omg i rank highest in the chatter boxers <_<, just noticed... Well its constructive conv anyways (mostly) =P

  20. wei zhong's Avatar
    wei zhong commented in tuition class


    2009
    Nov
    14
    Sat
    10:31pm
     
    20

    Ikes true, JC chem doesn't seem to be covered here. i tried and tried Google using various search terms, but I guess I'll try again tomorrow, when whichever website hosting it gets indexed by Google. thanks for your info! :DD

  21. Ys's Avatar
    Ys commented in tuition class


    2009
    Nov
    15
    Sun
    7:42am
     
    21

    Oh ok thanks! Do you all mind putting the link here once you all find it? Thanks a million! (: wad ques did you all do for chem?

  22. Mr Loi's Avatar
    Mr Loi Friend Mr Loi on Facebook commented in tuition class


    2009
    Nov
    16
    Mon
    11:25pm
     
    22

    Sorry guys I've been away for the past week as I was busy with my classes and working out the solutions to the rest of the H1/H2 maths papers.

    Anyway for those of you who are not yet aware, my H1 Maths Paper 1 and H2 Maths Paper 2 are now up.

    I appreciate your discussions and comments here, and in response to some of the feedback, I've updated the diagrams in Q9 to more show more accurately that the bisector does indeed pass through the origin and z7.

  23. Mr Loi's Avatar
    Mr Loi Friend Mr Loi on Facebook commented in tuition class


    2009
    Nov
    16
    Mon
    11:28pm
     
    23

    And to elaborate on Labbitan's method to get the cartesian equation of the plane (let's call it p4) in Q10(iii),

    2009 H2 9740 Paper 1 Q10 diagram

    We let d1 be the direction vector of l i.e.
    d1 = (matrix{3}{1}{1 1 {-1}})

    We're given that (2, 3, 4) lies on p4, and since we've proven that l lies on p4
    ⇒ (0, 1, 0) lies on p4 too
    ⇒ we can form another direction vector d2 on the plane as follows:

    d2 = (matrix{3}{1}{2 3 4})-(matrix{3}{1}{0 1 0})=(matrix{3}{1}{2 2 4})=2(matrix{3}{1}{1 1 2})

    We can then cross d1 and d2 to obtain the normal of plane p4:

    d1 × d2
    = (matrix{3}{1}{1 1 {-1}})*(matrix{3}{1}{1 1 2})=(matrix{3}{1}{3 {-3} 0})=3(matrix{3}{1}{1 {-1} 0})

    So to get the cartesian equation of p4:
    r(matrix{3}{1}{1 {-1} 0}) = (matrix{3}{1}{1 0 0})(matrix{3}{1}{1 {-1} 0}) = -1
    xy = −1, z ∈ ℝ
    (yes passerby it's z ∈ ℝ, I've updated the solution 😉 )


    Lastly, I would like to add that we can also show that line l lies in p3 through the following two expressions:

    x+z = 0 ⇒ x = −z
    y+z = 1 ⇒ y = 1−z

    that's obtained using the RREF function in your GC when solving the equations of p1 & p2 in part (ii).

    We can then sub the above expressions into the equation for p3 as follows:
    LHS: 2(−z)+(1−z)+3z−1+k(z+2(1−z)+z−2) = 0 = RHS
    l lies in p3 for any constant k.

  24. stormangel's Avatar
    stormangel commented in tuition class


    2009
    Dec
    31
    Thu
    9:04am
     
    24

    wah.. so late then it's out.... alrd finish a level liao....

  25. 'Cher's Avatar
    'Cher commented in tuition class


    2010
    Jan
    12
    Tue
    5:01pm
     
    25

    hi,
    for qn7ii, you need to expand (a+bx^2)^(-1) one more time as (1+b/a x^2) ^2 will have a term in x^2.

  26. Mr Loi's Avatar
    Mr Loi Friend Mr Loi on Facebook commented in tuition class


    2010
    Jan
    12
    Tue
    10:09pm
     
    26

    Hello there 'Cher.

    Moved your comment here as I believe you're referring to the 2009 H2 Maths P1 and not the 2008 one.

    Errr ... for the relevant part of Q7(ii), the binomial expansion of (a+bx2)−1 is as follows:
    (a+bx^2)^-1
    {}={1/a}(1+{b/a}x^2)^-1

    Since {b/a}x^2 is the b in (1+b)n, the next term would contain a x4 if we were to 'expand one more time' as follows:

    {}={1/a}[1+(matrix{2}{1}{{-1} 1})({b/a}x^2)+(matrix{2}{1}{{-1} 2})({b/a}x^2)^2 + cdots]
    {}={1/a}[1+(-1)(b/a)x^2+(1)(b/a)^2x^4 + cdots]

    From the above we can see that there is no x2 beyond the second term. I suspect that you've taken (1+{b/a}x^2) instead to be your b in (1+b)n?

    stormangel: This blog post was published on 12 Nov 2009 (two days after your H2 Paper 1) - very late meh?

  27. meena's Avatar
    meena commented in tuition class


    2010
    Feb
    7
    Sun
    12:12am
     
    27

    hello
    anyone knows where to find the ans to A level chem our year ?

  28. meena's Avatar
    meena commented in tuition class


    2010
    Feb
    7
    Sun
    12:15am
     
    28

    as in 2009. thanks especially to paper 1.

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