BoS trials Maths and Chemistry 2022 (1 Viewer)

[dan964]

Hi all,
I've posted more detailed markers notes for Q12 and Q14, and a set of solutions (not the official ones but ones I used heavily to mark with, so they may at times differ as they are based on the original set of questions (although I have since adjusted Q12(c), but I have cross checked against the official ones to make sure that they are correct but I may have made a latex error knowing me)

I will still have the question papers until the end of the week so if you want specific feedback send me a DM.

Q12: https://community.boredofstudies.or...mx2-trials-q12-solutions-markers-notes.20036/
Q14: https://community.boredofstudies.or...mx2-trials-q14-solutions-markers-notes.20037/

Some additional general comments/pointers:
Q12 (a) - Some students used a method more complicated then what was needed. Remember that for something to be even, you only need to show that it is or is not a multiple of 2M (where M is any choice of integer). If you did use cases and proof by contradiction for each, you needed to cover all cases even if it was just a cursory statement using W.L.O.G or similarly.

Q12 (b) - Students struggled with this question, expanding and then simplifying was the easiest approach and it was a test of patience and algebra skills. Main tip for this one, is to rework the formula to use the information given (in this case it could be used twice). Also check your solutions are valid (in fact only one student managed to get 2 marks, so close but forgot to eliminate spurious solutions that caused the cosec function to be undefined), its helpful to specify the range for variables in the question e.g. etc.

Q12 (c) - Many people used the projection formula, to derive the result in part (i), but neglected to explain why they are using the formula (you did not need to use it for part (iii)). Diagrams were also helpful. In part (ii), students often had statements about the shortest distance that were insufficient to show that it was parallel (easiest way was to argue that they shared the same normal implied by an appropriate choice of the (x,y,z) vector, and comment on that the normal was orthogonal (perpendicular) for any choice of normal)

Q12 (d) - Generally this question was done well by all students. But when you setup IBP, don't use the DI table notation (with +/- as rows) that some students had employed as it is non standard notation and not very coherent. With the recursion in part (ii), make sure to evaluate the last term correctly (some students did not or did not show where the recursion ended).

Q14 (a) - Most students did part (i) well. For part (ii), harmonic motion formula need to be careful when choosing to use sin or cos, and substituting initial conditions correctly - if in doubt derive via integration (either method was accepted, provided you set up the harmonic motion correctly). For part (iii), most students recognised that the particles didn't collide if the two equations didn't have a solution. This part was dependent on part (ii) and so was marked accordingly. If you used definite integrals, you need to ensure that the variable you are integrating against isn't one of the limits of the integral.

Q14 (b) - A correct diagram would help with this one. There are multiple ways to derive the result but the cosine angle formula (2 different ways) and using the equal angles of the equilateral triangle were the simplest.

Q14 (c) - Main piece of feedback is check you are actually reading all the parts of the question, including many students forgot their example had to satisfy, having an inverse and . For the proof in part (ii), proof by contradiction as per solutions was the simplest method. (I've included some extra background on the definition of the inverse but this can be assumed). Part (iii) relied on using the previous parts so could be done even if you struggled to do part (i) and part (ii) by assuming the result was proven.

 

[Daedalus13]

[/QUOTE

If you used definite integrals, you need to ensure that the variable you are integrating against isn't one of the limits of the integral.

Is this something you would be penalised for in the HSC? If so, what is the best way to avoid this?

 

[dan964]

[/QUOTE


Is this something you would be penalised for in the HSC? If so, what is the best way to avoid this?

To answer the first question, not sure. (I didn't penalize it when marking Bos trials)

You can use indefinite integrals and then evaluate the initial condition to find the value of the constant.

The issue is that t is a variable not a constant. Hence why its not a great idea to do, thankfully if t represents time then it is well defined since t > 0 for time:

You can also do this:

or even better:

 

[1039213]

Hi all, I marked Q13 of the MX2 and below is my feedback. Keep in mind that I will still have the question papers until the end of the week so if you want specific feedback send me a DM. Overall, a tough question at face value, but once the tricks are recognised, and if strong justification is provided, students tended to score many more marks can be obtained.

13(a)(i) expected candidates to recognise an obscure decomposition, but (ii) was given as a show question for candidates to reverse-engineer the partial fraction decomposition. Some responses used a complex number approach as well, although those responses tended to be more tedious, and were less likely to obtain the full 3/3. The integration in (ii) was routine as per the syllabus.

13(b)(i) used the previous results to derive the time taken, of which the majority of candidates failed to divide by the 8 in the numerator. Those who integrated with bounds saved a lot more time, but ensure to be careful which terms to place on the upper or lower bound. (ii) required the final answer, for one mark, and the justification for the other. Candidates who only provided one of the two received a maximum of 1 mark. Remember to use (a)(ii) to help differentiate the response by the Fundamental Theorem of Calculus, as it greatly assists in showing that it is a maximum.

13(c) requires use of the Complex Conjugate Theorem as well as transformation of roots between polynomials. Without mention of the Complex Conjugate Theorem, difficult progress could be made from P(iz) as (x+iy) is not a root of P(iz). Some candidates brute-forced the answer via algebra which is considered very prone to error and costly of time; not good examination technique.

13(d) deemed the hardest of the 4 parts, and was marked the most leniently. Progress could only be made if the centre was assumed to be a point (a,b,c); different to candidates who assumed the centre was at 0. Only one candidate received full marks on (d)(i).

 

[Paradoxica]

Hi all,
I've posted more detailed markers notes for Q12 and Q14, and a set of solutions (not the official ones but ones I used heavily to mark with, so they may at times differ as they are based on the original set of questions (although I have since adjusted Q12(c), but I have cross checked against the official ones to make sure that they are correct but I may have made a latex error knowing me)

I will still have the question papers until the end of the week so if you want specific feedback send me a DM.

Q12: https://community.boredofstudies.or...mx2-trials-q12-solutions-markers-notes.20036/
Q14: https://community.boredofstudies.or...mx2-trials-q14-solutions-markers-notes.20037/

At the top of page 3, for Question 14, you need to specify non-trivial involution.

Also I see you are unfamiliar with some of the underneath stuff of LaTeX. To get proper 66 and 99 quotation marks, the first pair should be replaced with two backticks `` .

 

[wendyredvelvet]

DOES ANYONE HAVE THE CHEMISTRY BOS TRIAL SOLUTIONS?? IF SO PLEASE SEND THEM THRU

 

[dan964]

At the top of page 3, for Question 14, you need to specify non-trivial involution.

Also I see you are unfamiliar with some of the underneath stuff of LaTeX. To get proper 66 and 99 quotation marks, the first pair should be replaced with two backticks `` .

Only quotation marks, first time using them, rest of latex I'm fairly/mostly familiar with. Might add the csquotes package to my standard template though so thanks for the suggestion! TBH not concerned enough about the quotation marks to be bothered to change them this time around, but I'll note that for next time.

I have reuploaded Q14, with the change to Q14(c) to exclude f(x)=x.

 

[wendyredvelvet]

Now that the BoS trial events are done, I want to extend my sincere thanks to the rest of the team who helped put the questions and paper together for Maths and Chemistry (in particular to Paradoxica, sharky564, jazz519, Dazzling_Light, IAmWinston and edwxnsamuel).

Also massive thanks to Carrotsticks for allowing us to hold the events at the Sydney Centre of Mathematics venue.

...and now here's what you've all been waiting for.........................................






































































































































Please find the papers attached with some minor edits. If you find any minor typos/errors, feel free to call them out for us to consider.

We have commenced the process of solution writing and marking the papers. Please be patient as this will take time to get through and write up (especially given we had more attendees than last year).

In the meantime, we are more than happy to offer answers to any specific questions that you want to know about sooner than later. Just let us know in this thread!

Also, please let us know your thoughts on the papers. Were there any questions you particularly liked/disliked?

Hey do you have solutions for the chem paper????

 

[Trebla]

Hey do you have solutions for the chem paper????

They’re still being written up. Do you have any specific questions you want answers to?

 

[Paradoxica]

Remarks for MX1, Q13

a) Most were able to get at least 2 marks, quite a few made miscellaneous errata in their working and got the wrong result at the end, so lost a mark.

For some reason, a fairly large percentage of students think you need a triangle diagram to justify the conversion from θ back to x. This is superfluous, and simply going from tan(θ) back to x is fine.

b) Only about half of the students attempted this, and about half of those attempts did not explicitly use the chain rule anywhere in the question, just a few handwavy lines of equalities.

c)

i) No comment for this one.

ii) Many students plucked some kind of equality out of thin air that would lead to the correct result when the square root of both sides was taken.

No student received any marks for their attempts, as the only valid solution uses a diagram to show that the line segment representing -cotθ is always tangent to the curve, and hence, it's rate of change is identical to the rate of change of the length of the curve.

An algebraic solution is impossible, as it is equivalent to deriving a special case of the Euler-Lagrange Equations, which requires some form of the Calculus of Variations.

Though not my sub-question, in hindsight, a hint definitely should have been provided.

iii) Some students realised they could proceed without the previous part from here, and most of those attempts got full marks. A couple made some unfortunate sign error and got an incorrect solution.

iv) Dependent on the previous part, no further comment.

d)

i) Of the attempts, some were stumped by the base case, and a few tried to explicitly find the root(s). I did not penalise students who only found the positive root for this part, for that is not a significant error until the second part.

Some students tried to "expand" the LHS resulting in an unworkable mess of a massive fraction and product under a square root, and promptly gave up; only a handful of students saw that they could reduce the RHS into a simple fraction of two terms.

ii) Students were penalised if they did not justify why the limit had to be the positive root.

Students were penalised for making incorrect technical claims about why the denominator tends to ∞, as well as not justifying it entirely.

The two types of claims I observed were:

1. The product terms are all greater than 1. This is a necessary, but not sufficient condition.

For example, the product (1+1)(1+1/2)(1+1/4)(1+1/8)(1+1/16)... has all of its terms greater than one, but converges to approximately 4.768462...

2. The product terms are all greater than 0. This is quite obviously false, just take all the product terms to be 0.5, and the product converges to 0.

 

[Trebla]

Hi all,

Unfortunately there has been a delay in the marking for Mathematics Extension 1. Apologies for this. We will try to get this done as soon as possible.

However, the solutions have now been written up and can be released to help with your studies.

Please also note that the question paper has been updated (which the solutions are aligned to) with some minor adjustments to a few questions. The updated file is attached in my original post of the papers to replace the older version.

 

[Trebla]

Some general feedback comments from me on Q12:

In Q12a), a number students stated 196x0.04 as the mean. This is incorrect for a number of reasons - the number itself is not in the right units as a percentage unemployment rate and 4% is the proportion from the one sample of 196, not the proportion from the “population” (which is the average unemployment rate in history). Better responses recognised the application of the Z score to solve a quadratic equation to find the mean.

Q12b), a number of students confused the initial radii of the spheres with the variable radii at time t. The question has updated wording to make this more obvious. A common assertion was that if the rate of change of both radii is the same constant then their ratios remain equal (leading to many asserting the new radii are R and R/2). However, this is like saying that since y = 2x + 1 and y = 2x + 2 have the same dy/dx and y-intercept ratio of 1:2 then the ratio of the y-vales is also 1:2 (which is clearly not always true). Better responses were able to derive the linear relationships explicitly to find the radii needed for the volume calculation.

 

[1039213]

Marking Feedback for Q11 MX1:
All around a good performance on a question with parts of varying difficulty. Students should learn to try and manage their time well, so attempting the start of questions can easily help pick up marks.

For 11(a), multiple methods worked, especially simplifying the identity down, or splitting the

by adding and subtracting a multiple of it. Students who chose to use substitutions (

) struggled, as in Extension 1, the question must give a substitution if it is to be designed to be completed that way. Also remember to re-express in the correct variables that the question gave.

11(b)(i) was over-complicated by the majority of students; it was a simple factorise and solve question and no polynomial techniques taught in the HSC syllabus needed to be used. (ii) was done much better with little errors throughout. The combination of (i) and (ii) was needed for (iii), which few students recognised to begin with using

which allowed for simplification down to the result in (iii). From there, only very few students recognised that from (ii), becuase of the range of the function, one solution must be excluded. It is very important to note the information given in previous parts as (iii) couldn't be done without (i). Note that n o marks were received for simplifying the cubic expression given in (iii).

11(c)(i) was on the more straightforward side, and a lot of candidates could pick up marks in the first two parts. Note that supplementary means that the angles add to

and make sure that the vectors are either travelling both outwards, or both inwards when taking the dot product. Good conclusions used inverse cosine identities, and no marks were given for calculator approximated conclusions.

No student received full marks for 11(d) as the obvious approach was to use sum-to-product, however by creating two terms in the denominator, the expression became much harder to simplify. Rather, the approach to re-express the numerator as

helps split and simplify each fraction easier upon using the trigonometric expansion. This part was marked generously for those who made some progress.

 

[dan964]

Marking Feedback for Q14:
(a) Some students had difficulty working out a suitable substitution to manipulate the expression to be . However some students were able to do the last couple of steps and so were awarded 2 marks for that.

(b)(i) While it was not expected to be an exact graph, students lost 1 mark if they didn't show how they derived the graph from and . (Marks were not deducted, if you did not have to graph all graphs on the one axis, but on separate axes)

Students lost one mark if their graph had obvious errors such as unintentional intersection points (other than at (0,1)), individual graphs were not labelled at all or incorrectly or were incomplete. (Marks were not deducted if the axis was not labelled or if the point of inflection was not identified)

(ii) This question was a strict inequality, if you put a or , then you did lose the mark.

(c)(i) Students need to work on setting out working and reviewing conditions for a T.P as students forgot to conclude why k must be positive.
Students tried using concavity to prove that graph has a minimum T.P. but often made mistakes in deriving the second derivative or their conclusions were inconclusive or incorrect.

(ii) Most students managed to recognise the connection between this part and (b)(ii). Students were awarded the mark even if the answer was correct if it was based on their response in (b)(ii).

(iii) Only one student managed to produce a solution with the correct range (although they forgot to check all cases such as k=1). Most students did not attempt this part.

(d) A small handful students managed to produce a result with a variety of methods. Students that derived the following expression:
were awarded 1 mark for using the results in the question.

 

[Trebla]

... and here are the student results for the 2022 Mathematics Extension 1 BoS trials! Apologies for having released this so late

Once again, thank you to everyone who participated and for your patience! Thanks to the other members of the marking team Paradoxica, dan964 and 1039213 for their efforts in helping to get the marking done.

As for the results, congrats to the student who scored the top mark of 47, again with two others following closely behind!

Once again you are reminded that:

Note: These are not your average trial papers. These papers are skewed towards the more challenging questions (i.e. without most of the boring/repetitive easy stuff in a typical trial paper). Students who may be worried about losing motivation after attempting the paper are reminded that this is NOT intended to be an accurate reflection of the difficulty of the HSC.

 

[Run hard@thehsc]

Can I also have the answer to question 27 for the BOS Chemistry trial? Thanks!

 

[firefly15]

Hi, also waiting for the BOS Chemistry trial solutions as well thank you in advance

 

[Trebla]

Hi all,

Thank you for your patience.

There is one minor loose end to be tied up with the marking, which we hope to resolve soon before releasing the results.

However, the marking guidelines have now been written up and can be released to help with your studies. Please find this attached.

Massive thanks to Dazzling_Light, IAmWinston, jazz519 and edwxnsamuel for contributing to the marking guidelines!

 

[Trebla]

… and here are the results for the 2022 Chemistry BoS Trials!

Thank you for your patience and thanks to IAmWinston and edwxnsamuel for helping to mark the papers.

As for the results, congrats to the top student who scored 71!

Once again you are reminded that:

Note: These are not your average trial papers. These papers are skewed towards the more challenging questions (i.e. without most of the boring/repetitive easy stuff in a typical trial paper). Students who may be worried about losing motivation after attempting the paper are reminded that this is NOT intended to be an accurate reflection of the difficulty of the HSC.

 

[Trebla]

Also, fantastic effort from the students who came consistently in the top 5 across all three subjects in the BoS trials this year!