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    You can sub in values which satisfy your inequality to check your answers !
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    (Original post by Rather_Cynical)
    I have terrible handwriting but made a worked solution.
    this is very thorough thanks
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    i'm having a look through C1 spec and im a bit stuck on this bit. i understand what they mean by ''knowledge of the effect of simple...'' but what does the first paragraph mean? can you give me an example?
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    (Original post by ihatePE)
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    i'm having a look through C1 spec and im a bit stuck on this bit. i understand what they mean by ''knowledge of the effect of simple...'' but what does the first paragraph mean? can you give me an example?
    they just mean that if they give you a quadratic then you'll be able to sketch it, and that you recognise that the number roots of an equation can be determined by the number of intersections of a graph.
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    (Original post by fefssdf)
    they just mean that if they give you a quadratic then you'll be able to sketch it, and that you recognise that the number roots of an equation can be determined by the number of intersections of a graph.
    ok thanks i think i know how to do that. is it something to do with the discriminant, completing the square, then find minimum/max points?
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    (Original post by ihatePE)
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    i'm having a look through C1 spec and im a bit stuck on this bit. i understand what they mean by ''knowledge of the effect of simple...'' but what does the first paragraph mean? can you give me an example?
    It's already been said, you just need to know how to find key points of F(x) like the points of intersection ect...

    You learn the manipulation of functions at GCSE so it shouldn't be too difficult.
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    (Original post by ihatePE)
    ok thanks i think i know how to do that. is it something to do with the discriminant, completing the square, then find minimum/max points?
    discriminant lets to know how many roots their are.

    >0 means two roots
    = 0 means one root.
    <0 means no roots

    Completing the square will give you the max or minimum point of a curve. eg. (x-2)^2-9, the minimum point of that curve will be( 2, -9)
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    (Original post by 34908seikj)
    discriminant lets to know how many roots their are.

    >0 means two roots
    = 0 means one root.
    <0 means no roots

    Completing the square will give you the max or minimum point of a curve. eg. (x-2)^2-9, the minimum point of that curve will be( 2, -9)
    is this what the paragraph means?
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    It means you'll be able to sketch curves with simple equations like  x^2, x^3-x^2, as its restricted to the form  y=f(x) it seems you won't have to sketch circles (any conic section for that matter), exponentials/log graphs, implicit functions. Basically things that you did at GCSE.
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    If we had a graph of a quadratic that intersects the x-axis at the points x = 1 and x = -6, you need to be able to figure out that it means

    f(x) = (x + 6)(x - 1) = x2 + 5x - 6

    If one of the brackets is solved as zero, then f(x) = zero.

    The curve is defined as y = f(x) and when it equals zero, you have the x-intercept.
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    (Original post by 34908seikj)
    discriminant lets to know how many roots their are.

    >0 means two roots
    = 0 means one root.
    <0 means no roots

    Completing the square will give you the max or minimum point of a curve. eg. (x-2)^2-9, the minimum point of that curve will be( 2, -9)
    :eyeball: :naughty:
    Any polynomial with degree n has n roots (multiple roots). But every polynomial (complex coefficients) has at least one root.
    The discriminant of a cubic can be less than 0 but does that mean there are no real roots?
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    (Original post by ihatePE)
    is this what the paragraph means?
    The top paragraph literally just means that you should know how to use the intersection of points to solve equations. It's as simple as that. Eg. when two curves, or a straight line means a curve and you have worked how say the equations of both, you can find the values for x.

    The bottom part of the paragraph is GCSE.


    y=aF(x) - means multiply the y values of the function by a
    yY=F(x) + a - means move the y values of F(x) up by a units

    y=F(x+a) - means add the x vales of F(x) by a, e.g., the minimum point of f(x) was (1,1) then F(x+a), where a = 4, the minimum point will now be 5,1

    y=f(ax) - means divide the x values of F(x) by a, similarly if y=F(x/a) then you multiply the values of x by a.

    Just remember inside the bracket manipulates the X axis and it's always opposite and that anything outside the bracket manipulates the Y axis and is NOT opposite.
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    It'll be easiest to show you with an exam paper question, it's harder to talk in abstract if you're not familiar with the concepts as a whole.
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    (Original post by B_9710)
    :eyeball: :naughty:
    Any polynomial with degree n has n roots.
    The discriminant of a cubic can be less than 0 but does that mean there are no real roots?
    idk, In the context of C1, I don't think you have to find the discriminant of a cubic. I may have passed over it, but I don't remember covering cubics and discriminants. Or at least you could factorise it into a quadratic first.
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    (Original post by 34908seikj)
    idk, In the context of C1, I don't think you have to find the discriminant of a cubic. I may have passed over it, but I don't remember covering cubics and discriminants. Or at least you could factorise it into a quadratic first.
    For the following equation  ax^3+bx^2+cx+d the discriminant is  18abcd-4b^3d+b^2c^2-4ac^3-27a^2d^2 .
    This isn't C1 but I'm just responding to what you said about if the discriminant is < or = or > 0.
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    (Original post by B_9710)
    For the following equation  ax^3+bx^2+cx+d the discriminant is  18abcd-4b^3d+b^2c^2-4ac^3-27a^2d^2 .
    This isn't C1 but I'm just responding to what you said about if the discriminant is < or = or > 0.
    Interesting! Though, my knowledge of the discriminant doesn't go past C1 right now, I've taken a small detour onto FP1 instead of C2.

     b^2-4ac

    Is as far as it goes for me, right now at least.
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    (Original post by 34908seikj)
    Interesting! Though, my knowledge of the discriminant doesn't go past C1 right now, I've taken a small detour onto FP1 instead of C2.

     b^2-4ac

    Is as far as it goes for me, right now at least.
    It doesn't come up anywhere at A level.
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    What does this notation mean?

    i'm on binomial expansion and came across this, i understand the substitution part, the factorial equation substitution but what does that notation mean? 'n' on top of 'r' . does it mean n take away r? cos thats the pattern i see in the equation
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    (Original post by ihatePE)


    i'm on binomial expansion and came across this, i understand the substitution part, the factorial equation substitution but what does that notation mean? 'n' on top of 'r' . does it mean n take away r? cos thats the pattern i see in the equation
    It means n "choose" r if that makes sense.
    I'm on my phone so I can't do much but look at the C2 equation sheet. If I remember correctly it's on there. It's like n!/r!(n-r)!

    Whatever is within that matrix substitute accordingly into it.
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    (Original post by 34908seikj)
    It means n "choose" r if that makes sense.
    i still dont get it :rofl:
 
 
 
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