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P1 Revision topic - 1:15pm 9th June - Edexcel watch

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    (Original post by mik1a)
    If you actually read what I wrote, I derived them in the first post... :confused:
    really? thx...hhaaha
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    (Original post by KOH)
    Given that tan 75° = 2+√3, find in the form m+n√3 the following:

    (a) Tan 15°

    (b) Tan 105°
    Tan 75 = 2 + √3

    Look at the graph of tan. We know:

    tan 75 = 2 + √3
    tan 60 = √3
    tan 45 = 1
    tan 30 = 1/√3
    tan 15 = ?

    The pattern is fairly clear, and a simple check on the calculator will assure you that tan 15 = 1/(2+√3). By rationalising the denominator, we find this equals 2 - √3. (the form we are looking for).

    The second one is easier, because of the symmetry of the curve. 90 - 15 = 75, 90 + 15 = 115. So we reverse the sign to get -2 -√3 and that is equal to tan 115. Be careful, the calculator says this equals -75, but this value can equal infinite values of tan x, because the graph is repeating.

    So the answers are:

    (a) 2 - √3
    (b) -2 -√3
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    (Original post by BlueAngel)
    (a) Tan 15° = 2+√3 / 5 = 2/5 + √3/5

    (b) Tan 105° = Tan 75 x 1.4 = 105 = (2+√3)1.4

    Actually I think thats all wrong, what are the answers???
    You assume that the graph is linear. But it's not.
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    wow, will this kinda crap be in the exam?
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    1. Given that a is a constant, and that:
    f(x) = 4ax² - 3x - 3a/x²
    Find, in terms of a:
    (a) f'(x)
    (b) f''(x)


    f(x) = 4ax² - 3x - 3a/x²
    f'(x) = 8ax - 3 + 6a/x^3
    f''(x) = 8a - 18a/x^4

    2. Given the two equations:
    3^x = 27^(y-1)
    4^(x+2) = 2^(y+1)
    Find the values of x and y


    3^x = 27^(y-1)
    3^x = (3^3)^(y-1)
    3^x = 3^(3y - 3)
    x = 3y - 3

    4^(x+2) = 2^(y+1)
    (2^2)^(x+2) = 2^(y+1)
    2^(2x + 4) = 2^(y+1)
    2x + 4 = y + 1

    y = 2x + 3
    x = 3y - 3

    y = 2(3y - 3) + 3
    y = 6y - 6 + 3
    -5y = - 3
    y = 3/5

    x = 3(3/5) - 3
    x = 9/5 - 15/5
    x = -6/5

    3. Evaluate: (pi/0){ 3x - 2 dx, giving your answer to 3 significant figures.

    (pi/0){ 3x - 2 dx = [(3/2)x² - 2x] pi/0
    = (3/2)pi² - 2pi = 8.52 (3s.f.)

    4. A series has first term 1.1. The sum of the first 100 terms is 19044. Find:
    (a) The common difference, when the series is arithmetic
    (b) The common ratio, when the series is geometric.


    a = 1.1
    S(100) = 100/2(2*1.1 + (100-1)d)
    S(100) = 50(2.2 + 99d) = 19044

    19044 / 50 = 2.2 + 99d
    99d = 19044/50 - 2.2
    d = (19044/50 - 2.2) / 99 = 3.83 (3s.f.)

    The geometric one is not P1, sry about that.

    5. Find, to one decimal place, the possible values if theta if:
    0 < theta < 360
    2cos² theta - cos theta - 1 = sin² theta


    2cos² theta - cos theta - 1 = sin² theta
    2cos² theta - cos theta - 1 = 1 - cos² theta
    3cos² theta - cos theta - 2 = 0
    (cos theta - 1)(3cos theta + 2) = 0

    cos theta = 1
    no values of this in the given range.

    cos theta = -2/3
    acute angle = 48.190

    this is in the S and T quadrants (2nd and third)
    so 180 - 48.190, 180 + 48.190

    theta = 131.8, 228.2
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    mik1a is so hardworking...
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    P1 us actually pretty easy.. just like M1.. the hardest is S1
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    (Original post by Bhaal85)
    Nice work, I feel inclined to give you rep, I too have been asked by numerous users to create a similiar thing for P3, would anybody be interested?
    yes definetly!
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    (Original post by daydream)
    P1 us actually pretty easy.. just like M1.. the hardest is S1
    i agree
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    (Original post by Tanaz)
    yes definetly!
    its already there! look at the sticky
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    M1 is meant to be the hardest but its jus that this yr was kinda... easy
    P1 is easiest for sure.
    S1 is ok.
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    everyone r gonna get A's in here
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    I asked earlier but noone replied.Ive been looking at www.mathsnet.net and am finding it very useful, is it wise to spend most of time revising on that?, or would i be better of reading my notes,books and doing my own past papers? does anyone have experience of this website and has it helped you get the grades u wanted?
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    (Original post by chats)
    I asked earlier but noone replied.Ive been looking at www.mathsnet.net and am finding it very useful, is it wise to spend most of time revising on that?, or would i be better of reading my notes,books and doing my own past papers? does anyone have experience of this website and has it helped you get the grades u wanted?
    Do you have the Heinemann textbooks? Becuase I would say they are far better for revision. Firstly, they are offline, secondly, they are by the examiners for the Edexcel syllabus, and thirdly, they have SO MANY questions. Maybe 200 in the P1 book I think.

    That's what I used anyway.
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    (Original post by mik1a)
    Do you have the Heinemann textbooks? Becuase I would say they are far better for revision. Firstly, they are offline, secondly, they are by the examiners for the Edexcel syllabus, and thirdly, they have SO MANY questions. Maybe 200 in the P1 book I think.

    That's what I used anyway.
    yes i do, ok i will use them. thanks for that
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    (Original post by z!D4N)
    everyone r gonna get A's in here
    I'll be gutted If I don't get at least 80 in P1 but P3 is an entirely different story!!!
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    Hmm... not very many P1 stuff going in here! Maybe more people will come asking questions closer to the exams... I need the revision!

    Keep doing Heinemann textbook review questions, make sure you know how to do every questions, and if you get one wrong ask on here becuase the books don't give any explanations. TBH, you either can't do a question, or you do and get it wrong. If the former, most likely because you haven't practiced with that question. If the latter, it's likely that you can do the question, but you need to tkake more time and check back more. It's a shame losing marks for silly errors, becuase then your grade doesn't represent your understanding!
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    (Original post by mik1a)
    Hmm... not very many P1 stuff going in here! Maybe more people will come asking questions closer to the exams... I need the revision!

    Keep doing Heinemann textbook review questions, make sure you know how to do every questions, and if you get one wrong ask on here becuase the books don't give any explanations. TBH, you either can't do a question, or you do and get it wrong. If the former, most likely because you haven't practiced with that question. If the latter, it's likely that you can do the question, but you need to tkake more time and check back more. It's a shame losing marks for silly errors, becuase then your grade doesn't represent your understanding!
    This happened to me with P2 in January, I knew the answer to every question on the paper but I made one or two stupid arithmetic error (I rarely use a calculator with fractions etc...) and so I ended up dropping silly marks that I really should have got.
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    here's a simple question... but i don't get it...

    Q5b from 5 june 2001
    it says:

    f ' ( x ) = x² - 2 + 1/x²

    a) find f '' ( x ) at x = 4
    easy, it's 7 and 31/32

    b) given that f ( 3 ) = 0, find f ( x )
    here i don't get it, what does it mean by f (x )?
    first thing you integrate f ' ( x ) right?

    you get f ( x ) = 1/3 x³ - 2x - 1/x + C

    but what then? you put 3 insted of the x and you get 0 = 9 - 6 - 1/3 +C
    and the answer then says C = - 8/3

    but why do we have to find C? is C the same as f ( x )??? :eek:

    :confused: :confused: :confused:
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    (Original post by SkylineGTR)
    here's a simple question... but i don't get it...

    Q5b from 5 june 2001
    it says:

    f ' ( x ) = x² - 2 + 1/x²

    a) find f '' ( x ) at x = 4
    easy, it's 7 and 31/32

    b) given that f ( 3 ) = 0, find f ( x )
    here i don't get it, what does it mean by f (x )?
    first thing you integrate f ' ( x ) right?

    you get f ( x ) = 1/3 x³ - 2x - 1/x + C

    but what then? you put 3 insted of the x and you get 0 = 9 - 6 - 1/3 +C
    and the answer then says C = - 8/3

    but why do we have to find C? is C the same as f ( x )??? :eek:

    :confused: :confused: :confused:
    Whenever you Integrate a function, you add the constant (+ C usually), because differentiang a function the constant get removed:
    eg. y = 5x^2 + 5
    dy/dx = 10x
    therefore whenever we integrate a function we dont know the constant (it could be 0 but we dont know that) so we write + C.
    eg. integrating: 10x => 10/2x^2 + C = 5x^2 + C
    back to the question..
    f(x) = 1/3 x³ - 2x - 1/x + C
    f(3) = 0 therefore 0 = 9 - 6 - 1/3 + C
    C = - 8/3
    now we know C we can write out the function again (this time we know the constant):
    f(x) = 1/3 x³ - 2x - 1/x - 8/3
 
 
 
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