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Thread: Help for exam in 6 hours

  1. #1
    Aug 2007

    Help for exam in 6 hours

    Hi all,

    I have an exam in 6 hours, which I know nothing about. You can see I'm doing well already. All I know is that the questions are always the same, but the numbers change. From the past papers, I know the following questions (apart from the numbers being different) are going to be on there. If anyone could give me the solutions to the following, step by step, I would bake them a cake and ship it to them. Or, y'know, something else:

    1. A line passes through the points (2,-7) and (6,1).

    Find the equation of the line.

    *I'm guessing just y-b = m(x-a) here? Obviously finding m through m=(y2-y1)/(x2-x1)

    2.A line makes an angle of 50 degrees with the positive direction of the x-axis., where the scales on the axis are equal.

    Find the gradient of the line.


    3. (a) write down the gradient of any line parallel to y=1/2x +3
    (b) write down the gradient of a line perpendicular to y = -3x-1

    A few of the other questions have diagrams, which I'm not sure how to put in. I'll leave those ones, and try and figure them out....

    8 (a) Two functions f and g are givem by f(x) = x(squared) -1 and g(x) = 3x-1.

    Obtain an expression for f(g(x))

    *I seriously have no idea for this one.

    (b) Functions h and k, defined on suibtable domains, are given by h(x) = 4x and k(x) = cos x. Find k(h(x))

    *once again, no idea.

    9. Given y= 1+x4/x2
    find dy/dx
    any help would be great, thank you so much

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  2. #2
    Aug 2007
    (1) correct (use point-slope form)

    (2) the slope is equaled to $\displaystyle \tan \alpha = \tan 50 $

    8(a) $\displaystyle f(x) = x^{2} - 1, \ g(x) = 3x-1 $

    So $\displaystyle f \circ g = (3x-1)^2 - 1 $, same for (b)

    9. $\displaystyle y = 1 + \frac{x^4}{x^2} $

    $\displaystyle \frac{dy}{dx} = 2x $ (use power rule)
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