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Maths GCSE 2011 AQA

Discussion in 'Mathematics' started by cousingeorge, Jun 7, 2011.

  1. I think Q25 on AQA Higher GCSE Maths Paper 1 (June 6th) is trivial and can be answered using the property of rotational symmetry. I've run it by a colleague, who agrees. Is this too simplistic? Are we missing something?
     
  2. I think Q25 on AQA Higher GCSE Maths Paper 1 (June 6th) is trivial and can be answered using the property of rotational symmetry. I've run it by a colleague, who agrees. Is this too simplistic? Are we missing something?
     
  3. It does if you know how

    see



    put less than p more than between lines
     
  4. I agree.


    Was it six marks in total for proving the triangles are congruent and then that the lines are parallel? How they can have missed the fact that rotational symmetry can be used as solution for both parts of the question, and a very simple one at that, I don't know.


    Let's hope that the markers are all sufficiently on their game to recognise a symmetry-based proof and not just follow the mark scheme.


    There's still the problem of equivalence for students who get the question nearly-right by one method or the other.


    The symmetry proof only has 2 statements (at most) - so if they made an error (for example by saying it was rotationally symmetrical through 90º instead of 180º) then do they get 3 marks or 1 mark for that part of the question?

    Does that mistake get penalised again in part 2 of the question, or is it carried through?

    Surely these papers are trialled before being approved?

    How can we expect students who are on the grade boundaries not to feel aggrieved that they lost out on an A* because of a single small mistake when the exam board also makes errors?

    It also seemed a shame to mix stats with surds. The stats marks are bankers for those non A* students who are freaked out by surds. Wasn't the idea to give them the opportunity to demonstrate their skills, not just catch them out with clever questions that bare no resemblance to anything on a past paper?
     
  5. No - GCSE and A level papers are not trialled and must be kept completely confidential before the exam date. Haven't seen this question - is the paper available anywehre?
     
  6. I think it's not available yet - but basically it was a parallelogram (they were told this). Let's call the parallelogram ABCD where AB and CD are the longest sides. (ABCD marked clockwise).

    They were told there was a point - E - fixed proportion along AB, and another - F - the same proportion along CD. E was then joined to C and F was joined to A. This created a triangle at each end of the parallelogram.

    They had to first deduce that the triangles were congruent (4 marks). Then that the lines ED and AF were parallel (2 marks).

    I understand that they can't trial the paper 'as is' but can they not produce a large number of potential questions and check them? Or at least get other people within the exam board to verify the questions? I can see that there would be a concern that the questions might be leaked, but there must be a better solution than the current system, surely?
     
  7. Maths_Mike

    Maths_Mike New commenter

    Clealry the questions cant be trialled as otherwise the potential for students to see them in advance is too great.

    I am sure that more than one person at the exam board would be responsible for the setting and checking of the paper however and it does beg the question how such an error could be missed - but then we are all human.
     
  8. Maths_Mike

    Maths_Mike New commenter

    Also having now seen the question - or at least the description of it above - I am not convinced that rotational symmetry is going to prove congruence - you would need to prove that it is a rotation of 180 degrees not just state it.
     
  9. Maths_Mike

    Maths_Mike New commenter

    Is proving that BE = DF and AD = BC and the angles are equal using rot sym that much easier than referring to properties of the parallelogram?


     
  10. Don't you think the following works:

    For a)
    1) A parallelogram has rotational symmetry of 180 degrees about its center.
    2) Given EA and FC are congruent and parallel then these points also respect this symmetry.
    3) Symmetry implies congruence, so if ADF and EBC are rotationally symmetrical then they are congruent.

    For b)
    4) 180º degree rotational symmetry between 2 lines implies that they are parallel. So AF and EC are parallel.

    It's not *that* much easier, but my point is that because it's fewer statements than the 6 mark conventional solution, what happens if instead of 180 you put 160? Slip of the pen for example.

    Do you get deducted 1 mark for the mistake, and get 5? Or do you get positive marks for correct statements, and score 2 out of 4 for the first part and 2 marks for the second part?

    Why is a partly-correct short proof worth more marks or less marks than a partly-correct long proof?

    A single mark on a grade boundary is a big difference.

    I can't imagine the mark scheme outlines 2 different ways of answering the question - at least I've never seen that before (except in one stats question where there were different answers depending on whether the student had assumed replacement or not).

    Have you ever seen alternative answer mark schemes on a proof? So that makes me think it's an oversight. I could be wrong, but it seems unlikely that they'd deliberately introduce that complexity in the allocation of marks, when they could have just added the words "without using rotational symmetry" to the question.
     
  11. sorry - formatting again!


    Here is is less squished...


    Don't you think the following works:


    For a)

    1) A parallelogram has rotational symmetry of 180 degrees about its center.

    2) Given EA and FC are congruent and parallel then these points also respect this symmetry.

    3) Symmetry implies congruence, so if ADF and EBC are rotationally symmetrical then they are congruent.

    For b)

    4) 180º degree rotational symmetry between 2 lines implies that they are parallel. So AF and EC are parallel.


    It's not *that* much easier, but my point is that because it's fewer statements than the 6 mark conventional solution, what happens if instead of 180 you put 160? Slip of the pen for example.


    Do you get deducted 1 mark for the mistake, and get 5? Or do you get positive marks for correct statements, and score 2 out of 4 for the first part and 2 marks for the second part?


    Why is a partly-correct short proof worth more marks or less marks than a partly-correct long proof?


    A single mark on a grade boundary is a big difference. I can't imagine the mark scheme outlines 2 different ways of answering the question - at least I've never seen that before (except in one stats question where there were different answers depending on whether the student had assumed replacement or not).


    Have you ever seen alternative answer mark schemes on a proof?


    So that makes me think it's an oversight. I could be wrong, but it seems unlikely that they'd deliberately introduce that complexity in the allocation of marks, when they could have just added the words "without using rotational symmetry" to the question.
     
  12. No need to prove rotational symmetry as the question states it is a parallelogram and that the line sections are equal.
     
  13. Putting 160 instead of 180 would - to me - seem like a slip of the pen and not a major misconception.

    Do you never write down something different to what you intended?
     
  14. We're talking Maths Mike here - he NEVER makes mistakes!!
     
  15. Maths_Mike

    Maths_Mike New commenter

  16. Lol!


    To quote Maths Mike earlier in the thread:


    "Clealry the questions cant be trialled as otherwise the potential for students to see them in advance is too great."


    That was just a typo, right? You don't really think Clealry is the correct spelling ;)


    We know that human perception is flawed - we see what we think we're about to see. And Tahts the rseaon you can raed tihs snetcene.


    So interpreting that sort of slip as a complete misunderstanding of the whole way angles work - is surely unfounded neurologically? We could, in those situations, be looking at other geometry questions on the paper to verify that they do have the understanding, and just knocking off one mark for accuracy in most cases.


    Hopefully they did consider the two alternative methods, and have some sort of consistent mark scheme for this situation - I have looked back through old mark schemes and can find evidence of markschemes for proofs that vary slightly in which angles / sides you choose, but not a symmetry vs congruence alternative.


    There are multiple-strategy geometry questions where you have to find a value - but it's much easier to mark those than a proof.


    But maybe it's intentional - part of the new style...
     

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