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Wednesday, 21 September 2016

U6FM Hwk

Total: 27 marks. Show all working out. Those not showing mathematical rigour will be penalised.

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  1. Express \cos 6\theta in terms of \cos^n \theta

    [3 marks]

  2. Express \cos^6 \theta in terms of \cos (n\theta)

    [4 marks]

  3. Solve, giving your answers in the form re^{i\theta} with -\pi < \theta \leq \pi , z^6=1-\sqrt3 i Represent your solutions on an Argand diagram

    [4 marks]

  4. Represent on an Argand diagram the locus of z s.t.
    1. \arg{(z-3-2i)} = -\frac{5\pi}{6}

      [3 marks]

    2. |z+1|=|z-2i| also give the cartesian equation

      [3 marks]

    3. |z+1|=|4z-8i| also give the cartesian equation

      [4 marks]

    4. Give the cartesian equation and sketch the locus \arg (\frac{z+3}{z-3}) = 3\pi /4

      [6 marks]

L6FM Hwk 3 Due Mon 26.9.16

Total: 26 marks. Show all working out. Those not showing mathematical rigour will be penalised.

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  1. Write in the from a(x+b)^2 + c
    i.e. complete the square: 2x^2-5x-3

    [3 marks]

  2. Simplify \frac{2}{x^2-3x-10} - \frac{3}{x^2-25}

    [4 marks]

  3. Simplify as far as possible: \frac{15}{\sqrt {3}} - \frac{11}{2\sqrt{7} + 3\sqrt{3}}

    [4 marks]

  4. Solve -3-4x-5x^2>0 showing how you arrived at your answer.

    [3 marks]

  5. f(x)=\frac{2\sqrt x-x^2}{3x\sqrt x}
    1. Find the equation of the tangent at x=4, giving your answer in the form ax+by+c=0 where a,b,c are integers

      [5 marks]

    2. Find the equation of the normal at x=4, giving your answer in the form ax+by+c=0 where a,b,c are integers

      [4 marks]

    3. Find f''(4)

      [3 marks]

Wednesday, 14 September 2016

L6FM Homework 2 Due Mon 19.9.16

Total: 20 marks. Show all working out. Those not showing mathematical rigour will be penalised.

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  1. Write in the from a(x+b)^2 + c
    i.e. complete the square: 3x^2-7x-20

    [3 marks]

  2. Simplify \frac{3}{x^2-5x +4} - \frac{5}{x^2-16}

    [4 marks]

  3. Simplify as far as possible: \frac{15}{\sqrt {5}} - \frac{46}{2\sqrt{7} - \sqrt{5}}

    [4 marks]

  4. Solve 6x^2+x-12>0

    [3 marks]

  5. Solve 5+x+x^2>0

    [3 marks]

  6. Solve x^2 = 4+5xy \\ x=5y +1

    [3 marks]

Monday, 5 September 2016

L6 FM Homework

Total: 10 marks. Show all working out. Those not showing mathematical rigour will be penalised.
  1. Factorise fully 6x^2-7x-20

    [2 marks]

  2. Simplify as far as possible: \frac{8}{4^{5x-1}}=\sqrt{32^{3+x}}

    [4 marks]

  3. Simplify as far as possible: \frac{26}{\sqrt {13}} - \frac{8}{\sqrt{13} - \sqrt{11}}

    [4 marks]

Friday, 5 February 2016

Further Maths Progress Check due Wed 10.2.16

Total: 51 marks. Show all working out. Those not showing mathematical rigour will be penalised.
  1. Solve \sin (2x-\frac{\pi}{2}) = -\frac{1}{2} for -\pi \leq x \leq \pi

    [5 marks]

  2. By expressing \cos x + \sin x in the form R\cos(x- \alpha) with 0 \leq \alpha \leq \frac{\pi}{2}, find the maximum value of 2 - \cos x - \sin x State the smallest positive value of x for which this occurs.

    [5 marks]

  3. Prove that \sin 4A + \sin 2A \equiv 2\sin 3A \cos A

    [4 marks]

  4. Solve \cos \theta + 1 = 2 \sec \theta for -\pi \leq x \leq \pi

    [4 marks]

  5. A is acute and B is obtuse. \text{cosec} A = \frac{5}{3} \\ \sec B = -\frac{13}{5} Find \tan (A+B) without a calculator

    [4 marks]

  6. f(x) = x^3 - ax^2 + x + b (x-2) is a factor of f(x) and the remainder is 5 when f(x) is divided by (2x+1). Find f(3).

    [5 marks]

  7. \frac{x^4-x-1}{x^2+2} \equiv ax^2 +bx+c + \frac{dx+e}{x^2+2}

    [4 marks]

  8. Simply as far as possible 1+ \frac{2x}{x^2-2x-8} - \frac{6}{x^2-16}

    [4 marks]

  9. Express in partial fractions:
    1. \frac{2x}{(x^2-4)(x+1)}
    2. \frac{2-x}{(x^2-4)(x+2)}
    3. \frac{3x+2}{(x^2+4)(x+1)}
    4. \frac{x^3}{(x^2-1)(x+1)}

    [16 marks]