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    If I wanted to go a few maths modules durin the summer for my A-Levels nex year is it that important to read each module consecutively???
    could i not read M2 first and then go back to M1 at a later date or is it advised to read P1 then P2 and so on???
    Do the more advanced modules require you to read through the previous
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    The later modules do require some of the knowledge gained in earlier ones.
    If you're going to begin doing work for September i'd advise you to actually start working through P1 and possibly M1 if you finish it. The only way to learn and understand maths really is to do the questions - every question.
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    You have very little time left, and believe me this type of thing takes longer than you would originally estimate. All modules MUST be read consecutively apart from P5 and P6 which depend on P4 but not each other.
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    (Original post by Amrad)
    You have very little time left, and believe me this type of thing takes longer than you would originally estimate. All modules MUST be read consecutively apart from P5 and P6 which depend on P4 but not each other.
    true
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    I would advise going out, getting and working through the Heinemann P1 book, starting with the essential skills, then going throw the actual chapters.

    It's nice to be a little ahead of everyone when you go back, thus being able to help everyone out and look really smart ^^. Just don't rub it in too much.

    Hrm, P3 integration sucks so much. Give me differentiation any day....
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    would it be easy to teach myself m1 and m2? i'm good at maths
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    (Original post by winged_hippo)
    would it be easy to teach myself m1 and m2? i'm good at maths
    yes ofcourse..i did it so anyone can do it...btw i did the whole maths+f maths course on my own (no teacher wot so ever :eek: )
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    Thats some acheivement!!!
    well done with that.
    But how long did it take????
    What did you did when you were stuck??
    Which are the hardest concepts to understand??
    By the way thanx for the help with this....
    nex year cnt wait for the A-levels to begin for the first time :eek:
    (yeh rite)
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    (Original post by Fade Into Black)
    Thats some acheivement!!!
    well done with that.
    But how long did it take????
    What did you did when you were stuck??
    Which are the hardest concepts to understand??
    By the way thanx for the help with this....
    nex year cnt wait for the A-levels to begin for the first time :eek:
    (yeh rite)
    first year 3 modules P1,S1,M1
    second year 9 modules P2-P6, M2,D1-D2, S2

    when i got stuck i asked my physics teacher if he had time he helped me but only sometimes he had a degree in maths, and P3 was the hardest and P5 was nasty too...hate stats but its too easy..decision is simple but useful...pure was my speciality and a real challenge..mechanics just did it as i did physics alevel...
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    How did you manage to get through 9 modules of maths in a matter of months???
    I assume you got an overall A grade as you seem determined and interesting in maths.
    are you some maths prodigy then???
    should i start learning now if im doin futher maths next yer like yourself???
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    (Original post by Fade Into Black)
    How did you manage to get through 9 modules of maths in a matter of months???
    I assume you got an overall A grade as you seem determined and interesting in maths.
    are you some maths prodigy then???
    should i start learning now if im doin futher maths next yer like yourself???
    im waiting for my results (day after tomorrow) i wasnt planning to do f maths, until i started year 12 (i started my AS in year 11 whilei was doin GCSEs and i did some GCSEs in year 10 long story) anyway yea i did AS maths in year 11, and when i started year 12 i wanted to f maths, so i managed to go through 5 modules for january and 4 for june...im hoping to get As in maths, f maths, physics, ICT, business st...im not a maths prodigy as i was turned down by cambridge trinity college...but hopefully will be starting maths and computing at Imperial...

    if u need any help/advice PM me..
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    I'm thinking of dropping general studies and doing the following in september:
    Biology A2.
    Chemistry A2.
    ICT A2.
    Maths A2.
    Further Maths AS.

    Do you think that's realistic and possible to do? Considering that i have one chemistry module that i may need to resit. Bear in mind that i'm just polishing off P3 right now and aim to have M2/P2/P3 all done and to have gone through some past papers by September.
    If i am going to pick up further maths i'd aim to have done all 6 modules of my maths A2/FurtherAS by January, and take them in January.
    What do you think? Worth going for? I'm addicted to maths at the moment.
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    (Original post by Gaz031)
    I'm thinking of dropping general studies and doing the following in september:
    Biology A2.
    Chemistry A2.
    ICT A2.
    Maths A2.
    Further Maths AS.

    Do you think that's realistic and possible to do? Considering that i have one chemistry module that i may need to resit. Bear in mind that i'm just polishing off P3 right now and aim to have M2/P2/P3 all done and to have gone through some past papers by September.
    If i am going to pick up further maths i'd aim to have done all 6 modules of my maths A2/FurtherAS by January, and take them in January.
    What do you think? Worth going for? I'm addicted to maths at the moment.
    do u really have to carry on with ICT? as i said before quite frankly its useless...however, if u dont have to put any effort in for it then do it but dont bother working hard for it (i did that for business st)...that wat u may well be able to do full f maths!! its certainly possible to do the subjects ur planing to do but it will be a lot of self studying..if that doesnt bother u then go for it...considering u will have done P3,M2,P2 by september u will be in a better position then me...so just go for it and do alot of past papers thats they key....

    hope this helps...
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    (Original post by IntegralNeo)
    do u really have to carry on with ICT? as i said before quite frankly its useless...however, if u dont have to put any effort in for it then do it but dont bother working hard for it (i did that for business st)...that wat u may well be able to do full f maths!! its certainly possible to do the subjects ur planing to do but it will be a lot of self studying..if that doesnt bother u then go for it...considering u will have done P3,M2,P2 by september u will be in a better position then me...so just go for it and do alot of past papers thats they key....

    hope this helps...
    Thanks for the advice.
    I don't really enjoy ICT and last year i didn't really learn much. However, last year i picked up fairly good A/B grades and i'm pretty sure i'll be able to get such a grade at the end of next year. It's mainly coursework based so i'll only have to take one exam in it in January. I will also be able to do the coursework quickly and get it over with, now that i've started working harder. The fact that it's a two year course, and supposedly isn't split into AS' make it harder to drop and quite frankly a pain.

    General studies is 'ok' but i was very disappointed at how badly the AQA papers were written. Universities don't consider it so i'll proabably drop it if i'm allowed to do further maths.

    I don't think i'd be allowed to do full further maths in one year unfortunately, i'll proabably have to talk to my teacher. It kinda depends how chemistry goes i guess. If i do worse than i expected and really messed up in more than one module i'll drop it and start further maths AS+A2. If not i should proabably devote some time to it, retake the module and carry on.

    I wish i could go back a year in time =/, i'd do biology/physics/maths/further maths -_-;;.

    Heh, would you believe i failed M1 in January and was on the verge of dropping maths? However, then, i hadn't opened the maths book outside of a lesson.
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    (Original post by Gaz031)
    Thanks for the advice.
    I don't really enjoy ICT and last year i didn't really learn much. However, last year i picked up fairly good A/B grades and i'm pretty sure i'll be able to get such a grade at the end of next year. It's mainly coursework based so i'll only have to take one exam in it in January. I will also be able to do the coursework quickly and get it over with, now that i've started working harder. The fact that it's a two year course, and supposedly isn't split into AS' make it harder to drop and quite frankly a pain.

    General studies is 'ok' but i was very disappointed at how badly the AQA papers were written. Universities don't consider it so i'll proabably drop it if i'm allowed to do further maths.

    I don't think i'd be allowed to do full further maths in one year unfortunately, i'll proabably have to talk to my teacher. It kinda depends how chemistry goes i guess. If i do worse than i expected and really messed up in more than one module i'll drop it and start further maths AS+A2. If not i should proabably devote some time to it, retake the module and carry on.

    I wish i could go back a year in time =/, i'd do biology/physics/maths/further maths -_-;;.

    Heh, would you believe i failed M1 in January and was on the verge of dropping maths? However, then, i hadn't opened the maths book outside of a lesson.
    yes drop general studies and AS further maths should be fine...
    I failed M2,S2 (U grades) in June last year but that was coz i opened the book a day before the exam!! i was preparing for GCSEs so didnt bother...but i did well after...so carry on with ur self studying..and gud luck
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    Thanks. I'm just finishing the nastyl P3 integration chapter.
    Vectors looks easy, similar to some of the early M1 work. Is it deceptively difficult or do i have it right?
    If i've already done my three A2 modules i don't see how they can stop me doing AS further maths, as i'll still be doing three modules throughout the year.
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    (Original post by Gaz031)
    Thanks. I'm just finishing the nasty P3 integration chapter.
    Vectors looks easy, similar to some of the early M1 work. Is it deceptively difficult or do i have it right?
    If i've already done my three A2 modules i don't see how they can stop me doing AS further maths, as i'll still be doing three modules throughout the year.
    Vectors isn't that difficult but examiners can give a really tricky questions, as it happened to me...i left it out.... thats y i got less than 90 its hard to imagine 3D vector problems....my tip is that u work on unusual situations like working out the area of one face of a 3D triangle given the equations of two lines its based on...

    the question im talking about (which i left in the exam) is attached
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    Yeah, i'd agree it's much harder to work in 3d on 2d paper.
    Just finished the integration chapter and starting vectors ^^. Differential equations of the first kind wasn't as bad as some of the earlier functions that had to be integrated.
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    (Original post by IntegralNeo)
    Vectors isn't that difficult but examiners can give a really tricky questions, as it happened to me...i left it out.... thats y i got less than 90 its hard to imagine 3D vector problems....my tip is that u work on unusual situations like working out the area of one face of a 3D triangle given the equations of two lines its based on...

    the question im talking about (which i left in the exam) is attached
    8)
    l1: r = 9i + 2j + 4k + t(-8i - 3j + 5k)
    l2: r = -16i + aj + 10k + s(i - 4j + 9k)

    l1 and l2 intersect at A.

    a)
    (9 - 8t)i + (2 - 3t)j + (4 + 5t)k = (-16 + s)i + (a - 4s)j + (10 + 9s)k

    equating vector coefficients,

    9 - 8t = -16 + s --------------- (1)
    2 - 3t = a - 4s -----------------(2)
    4 + 5t = 10 + 9s ---------------(3)

    using (1) and (3),

    9 - 8t = -16 + s -> 25 - 8t = s
    4 + 5t = 10 + 9s -> -6 + 5t = 9s
    -6 + 5t = 225 - 72t (using s = 25 - 8t)
    77t = 231
    t = 3
    ====
    s = 1
    ====

    2 - 3t = a - 4s (using eqn (2))
    2 - 9 = a - 4
    a = -3
    =====

    b)
    using t = 3,
    l1(A) = (9 - 8t)i + (2 - 3t)j + (4 + 5t)k
    A = (9-24)i + (2 - 9)j + (4 + 15)k
    A = -15i - 7j + 19k
    ==============

    c)
    l1: r = P1 + tv1, where P1 = (9i + 2j + 4k), v1 = (-8i - 3j + 5k)
    l2: r = P2 + sv2, where P2 = (-16i -3j + 10k) [using a = -3], v2 = (i - 4j + 9k)

    v1.v2 = |v1||v2|.cosø
    (-8 -3 5).(1 -4 9) = √(64 + 9 + 25).√(1 + 16 + 81).cosø
    -8 + 12 + 45 = √(98).√(98).cosø
    49 = 98.cosø
    cosø = 0.5
    ø = 60°
    =====

    d)
    B = (b1 b2 b3)

    B is a point on l1 and so its coordinates are defined by the eqn for l1.

    (9 - 8t)i + (2 - 3t)j + (4 + 5t)k = b1i + b2j + b3k
    9 - 8t = b1
    2 - 3t = b2
    4 + 5t = b3

    length of AB given by,

    |AB| = 14√2
    or
    |AB|² = 392
    A(-15 -7 19), B(b1 b2 b3)

    (-15 - b1)² + (-7 - b2)² + (19 - b3)² = 392

    substituting for b1, b2, b3 in terms of t,

    (-15 - 9 + 8t)² + (-7 - 2 + 3t)² + (19 - 4 - 5t)² = 392
    (-24 + 8t)² + (-9 + 3t)² + (15 - 5t)² = 392
    576 - 384t + 64t² + 81 - 54t + 9t² + 225 - 150t + 25t² = 392
    98t² - 588t + 490 = 0
    t² - 6t + 5 = 0
    (t - 1)(t - 5) = 0
    t = 1 or t = 5
    ===========

    Depending upon which value of t is taken, B will lie on one side of A (which is when t = 3) or the other.

    Taking t = 1
    =========

    b1 = 9 - 8t = 9 - 8 = 1
    b2 = 2 - 3t = 2 - 3 = -1
    b3 = 4 + 5t = 4 + 5 = 9

    B = (1 -1 9)
    =========

    Taking C as a point defined by l2 and doing the same as for B, I get the point C as,

    C = (-17 1 1)
    ==========

    This method is pretty long and roundabout. It seems much too long for an exam question with only 4 marks. Can you spot how do do it faster ?
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    (Original post by Fermat)
    8)
    l1: r = 9i + 2j + 4k + t(-8i - 3j + 5k)
    l2: r = -16i + aj + 10k + s(i - 4j + 9k)

    l1 and l2 intersect at A.

    a)
    (9 - 8t)i + (2 - 3t)j + (4 + 5t)k = (-16 + s)i + (a - 4s)j + (10 + 9s)k

    equating vector coefficients,

    9 - 8t = -16 + s --------------- (1)
    2 - 3t = a - 4s -----------------(2)
    4 + 5t = 10 + 9s ---------------(3)

    using (1) and (3),

    9 - 8t = -16 + s -> 25 - 8t = s
    4 + 5t = 10 + 9s -> -6 + 5t = 9s
    -6 + 5t = 225 - 72t (using s = 25 - 8t)
    77t = 231
    t = 3
    ====
    s = 1
    ====

    2 - 3t = a - 4s (using eqn (2))
    2 - 9 = a - 4
    a = -3
    =====

    b)
    using t = 3,
    l1(A) = (9 - 8t)i + (2 - 3t)j + (4 + 5t)k
    A = (9-24)i + (2 - 9)j + (4 + 15)k
    A = -15i - 7j + 19k
    ==============

    c)
    l1: r = P1 + tv1, where P1 = (9i + 2j + 4k), v1 = (-8i - 3j + 5k)
    l2: r = P2 + sv2, where P2 = (-16i -3j + 10k) [using a = -3], v2 = (i - 4j + 9k)

    v1.v2 = |v1||v2|.cosø
    (-8 -3 5).(1 -4 9) = √(64 + 9 + 25).√(1 + 16 + 81).cosø
    -8 + 12 + 45 = √(98).√(98).cosø
    49 = 98.cosø
    cosø = 0.5
    ø = 60°
    =====

    d)
    B = (b1 b2 b3)

    B is a point on l1 and so its coordinates are defined by the eqn for l1.

    (9 - 8t)i + (2 - 3t)j + (4 + 5t)k = b1i + b2j + b3k
    9 - 8t = b1
    2 - 3t = b2
    4 + 5t = b3

    length of AB given by,

    |AB| = 14√2
    or
    |AB|² = 392
    A(-15 -7 19), B(b1 b2 b3)

    (-15 - b1)² + (-7 - b2)² + (19 - b3)² = 392

    substituting for b1, b2, b3 in terms of t,

    (-15 - 9 + 8t)² + (-7 - 2 + 3t)² + (19 - 4 - 5t)² = 392
    (-24 + 8t)² + (-9 + 3t)² + (15 - 5t)² = 392
    576 - 384t + 64t² + 81 - 54t + 9t² + 225 - 150t + 25t² = 392
    98t² - 588t + 490 = 0
    t² - 6t + 5 = 0
    (t - 1)(t - 5) = 0
    t = 1 or t = 5
    ===========

    Depending upon which value of t is taken, B will lie on one side of A (which is when t = 3) or the other.

    Taking t = 1
    =========

    b1 = 9 - 8t = 9 - 8 = 1
    b2 = 2 - 3t = 2 - 3 = -1
    b3 = 4 + 5t = 4 + 5 = 9

    B = (1 -1 9)
    =========

    Taking C as a point defined by l2 and doing the same as for B, I get the point C as,

    C = (-17 1 1)
    ==========

    This method is pretty long and roundabout. It seems much too long for an exam question with only 4 marks. Can you spot how do do it faster ?
    thanx so much Fermat for doing that...but i already had the solution (mark scheme) i only posted it so Gaz can have a go...anyway ur a star!!
 
 
 
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