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    Well... I had some requests to do a P1 version of the M1 topic, but P1 isn't as easy as M1 to describe in paragraphs - it's basically learning lots of techniques, such as rationalising denominators, and finding gradients of curves.

    The exam is on at 13:15 this wednesday coming, and it lasts 1 hour and 30 minutes. The questions get more difficult further into the paper, so these ones would be the best to work on. (Of course all of them would be better). The key to getting good marks is having tried every type of question and know what do do, and definately have confidence that you can do it. It makes a large difference - if you go into the exam thinking you can't do any question, you'll give up after a short time and convince yourself that you can't get the right answer. If you know you're going to do well, and you're surprised when you hit the same problem, you'll try a lot harder to solve it.

    I'll do a lot more algebra than other things because it's relevant in all pure maths.

    Algebra:

    You have to be confident solving equations. Here are some you should be able to do:

    1. Find x if 2^x = 4^(x-1)

    Here, you must notice that if you could convert the 4 ion the RHS to a 2, the powers must be equal and that would simplyfy your equations a lot. 4 = 2², so we can write:

    2^x = (2²)^(x-1)
    2^x = 2^(2(x-1))
    2^x = 2^(2x-2)

    Then equate the powers:

    x = 2x - 2
    x = 2

    2. Rationalise the denominator:

    3/(2 - √5)

    This time there is one rule - multiply top and bottom by the denominator, but remember to change the sign. In this case, the denominator is (2 - √5) so we multiply top and bottom by (2 + √5). This, when multiplied out, gets rid of the surds in the denominator and does not change the expression.

    3(2 + √5) / (2 - √5)(2 + √5)
    (6 + 3√5) / (4 - 2√5 + 2√5 - 5)
    (6 + 3√5) / (4 - 5)
    -6 - 3√5

    Inequalities:

    Here, linear inequalities are pretty simple. (linear means does not include any powers of a variable above 1, so x² > 3 is not a linear inequality). Treat them like equals signs, except when you multiply or divide by a negative number. If you do this, change the signs round. eg.

    -5x > 3
    5x < -3

    Quadratic inequalities need more work:

    3. Find the set of values for x that give:
    x² + 6 > 5x
    x² - 5x + 6 > 0
    (x - 2)(x - 3) > 0

    Now draw the graph of f(x) = x² - 5x + 6, mark on the points x=2 and x=3 where f(x) = 0, and decide whether it is when x is between these points, or outside these points that f(x) > 0. From this graph we see is it outside the points so we write:

    x < 2, 3 < x

    Powers are pretty simple: The general rules are:

    a^b = (1/b)√a ................ (eg. ³√27 = 27^(1/3) = 3)
    (a^b)(a^c) = a^(b+c) ..... (eg. 5²x5³ = 5^(2+3))
    (a^b)^c = a^(bc) ...........(eg. (2³)² = 2^(3*2) = 2^6)

    As well as this, revision in other areas should also improve your algebra - most of pure maths is built on algebra, so when you revise that, you also revise algebra as well! (the downside of this is if you're weak at algebra, your whole pure maths will be weak)

    And finally, the factor theorum. This states:

    if f(x) = a polynomial, and f(a) = 0, then -a is a factor of f(x) and will divide. Use this to factorise cubic expressions, such as x³ + 2x² - x - 2. (try this)

    Sequences and Series:

    Just a short revision summary for this one - there are more than enough questions in the Heinemann books!

    Proof of sum of arithmetic series:

    nth term = a + (n-1)d
    S = a + a+d + a+2d + a+3d + ... + L-d + L ---- (where L is the last term of the series)
    S = L + L-d + L-2d + L-3d + ... + a+d + a

    Add these two:

    2S = n(a + L)

    Since L is the last term, we know it equals (a + (n-1)d), where n is the number of terms of the series in the sum.

    2S = n(2a + (n-1)d)
    S = (n/2)(2a + (n-1)d)

    Proof of sum of geometric series:

    nth term = ar^(n-1)

    S = a + ar + ar² + ... + ar^(n-1) ---- (we have no need for L this time )
    Sr = ar + ar² + ar³ + ... + ar^n

    Take the first from the second:

    Sr - S = a - ar^n
    S(r - 1) = a(1 - r^n)
    S = a(1 - r^n)/(r - 1)

    Sum of convergant goemetric series to infinity. This only happens when -1 < r < 1, because if r is any larger than one (or minus one), r^n will tend to infinity rather than zero as n tends to infinity (as it does when you continue the series to infinity!), which will mean there is no sum to infinity.

    So we have:

    S = a(1 - r^n)/(r - 1)

    As n tends to infinity, r^n tends to zero, so (1 - r^n) tends to one, so:

    a(1 - r^n)/(r - 1) tends to a/(r - 1)

    And this is the sum to infinity of a convergant geometric series.

    Trigonometry:

    Some formulas for you to learn:

    (sin x)/(cos x) = tan x
    sin² x + cos² x = 1

    Area of sector: A = ½r²θ
    Length of arc: s = rθ
    Length of chord: x = 2r² - 2r²cos θ
    Area of triangle: A = ½r²sin θ

    Differentiation and integration:

    If y = ax^m, y' = max^(n-1)
    If y' = bx^n, y = (bx^(n+1))/(n+1) + C

    Coordinate Geometry:

    for points (x1, y1), (x2, y2), midpoint M, gradient m1 and perpenducular gradient m2:

    Midpoint: M = ((x1+x2)/2 , (y1+y2)/2 ) --- (simple averages)
    Gradient: m1 = ((y2-y1)/(x2-x1))
    Gradient (perpendicular) : m2 = -1/m1

    Equations of line:

    y - y1 = m(x - x1)

    And that's about it for a revision summary. IU was gonna do a lot more, but thought I'd be close to writing out the textbook so quickly gave up! The exam starts in three and a half days, so if you need any help, ask here and you'll definately get a response.

    There are pure maths past papers at www.mrhughes.net (password=mrhughes, username=alevel), and answers and lots of relevant revision exersices at www.ajimal.com, if your Heinemann book's reviws questions (very good exam type ones) are exhausted. There are no excuses for running out of questions!

    Remember, if you help someone on here by answering a question and explaining it, you are revising as well!

    mike
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    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?
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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?
    yeahh P3 is soo hard so i think it would b helpful for every1!!!
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    thanks alot yur an amazing help, yah.. i asked bhaal for it. we reallllyyy need one for p3, if only i knew the sylabus well
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    (Original post by tammypotato)
    yeahh P3 is soo hard so i think it would b helpful for every1!!!
    *Nods*
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    nice stuff once again - we need to know some proofs too right?


    MOD EDIT - Don't quote HUGE sections of text (corrected a bit of spelling too)
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    (Original post by Leekey)
    *Nods*
    should we make a "hater of p3 society"?
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    I'll be creating a P3 thread later on tonight then. ( Boy oh boy, what did I get myself into.)
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    (Original post by Bhaal85)
    I'll be creating a P3 thread later on tonight then. ( Boy oh boy, what did I get myself into.)
    thank u very much im sure it would b really helpful
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    (Original post by Bhaal85)
    I'll be creating a P3 thread later on tonight then. ( Boy oh boy, what did I get myself into.)
    weeeeee!!! thank00
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    Just for reference, when is the P3 Edexcel exam? As I am on the OCR board, I know that both boards follow roughly the same things.
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    (Original post by Bhaal85)
    Just for reference, when is the P3 Edexcel exam? As I am on the OCR board, I know that both boards follow roughly the same things.
    wednesday morning
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    (Original post by Bhaal85)
    Just for reference, when is the P3 Edexcel exam? As I am on the OCR board, I know that both boards follow roughly the same things.
    3.5 days and counting (same as p1)!!!
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    (Original post by Taslima)
    wednesday morning
    You sure (I thought it was pm?)?!? :confused:
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    (Original post by Leekey)
    You sure (I thought it was pm?)?!? :confused:
    hehehe! your prolly right!
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    (Original post by Leekey)
    You sure (I thought it was pm?)?!? :confused:
    its pm
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    I'm gonna do it later on tonight, I shall cover:

    Binomial expansion,
    Trig & Identities,
    Integration,
    differentiation

    and do the rest tomorrow, as you all know there are quite a few topics inside each module. Any specific requests?
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    (Original post by Bhaal85)
    I'm gonna do it later on tonight, I shall cover:

    Binomial expansion,
    Trig & Identities,
    Integration,
    differentiation

    and do the rest tomorrow, as you all know there are quite a few topics inside each module. Any specific requests?
    Substitution involving trig (or as I like to call it.....satans great nephew)!!!
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    (Original post by Bhaal85)
    I'm gonna do it later on tonight, I shall cover:

    Binomial expansion,
    Trig & Identities,
    Integration,
    differentiation

    and do the rest tomorrow, as you all know there are quite a few topics inside each module. Any specific requests?
    circles and vectors also please, i'd like vectors to be really slow and watered down, as i really dont undertstand them

    thankyou bhaal, yu rock my world
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    oh yeah, implicit & parametric differentiation and rates of change (differentiation topic), they are a real pickle to get round
 
 
 
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