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This page covers Questions and Worked Solutions for Edexcel Further Maths Paper 1 Oct 2020, 9FM0/01.

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Edexcel 2020 Further Maths Paper 1 (Question Paper)

Edexcel 2020 Further Maths Paper 1 (Mark Scheme)

- f(z) = 3z
^{3}+ pz^{2}+ 57z + q

where p and q are real constants.

Given that 3 − 2√2i is a root of the equation f(z) = 0

(a) show all the roots of f (z) = 0 on a single Argand diagram,

(b) find the value of p and the value of q - (a) Explain why

(b) Prove that - Figure 1 shows a sketch of two curves C1 and C2 with polar equations

C1 : r = (1 + sinθ) 0 ≤ θ < 2π

C2: r = 3(1 – sinθ) 0 ≤ θ < 2π

The region R lies inside C1 and outside C2 and is shown shaded in Figure 1.

Show that the area of R is

p √3 − qπ

where p and q are integers to be determined. - The plane Π1 has equation

r = 2i + 4j – k + λ (i + 2j – 3k) + μ(–i + 2j + k)

where λ and μ are scalar parameters.

(a) Find a Cartesian equation for Π1

The line l has equation - Two compounds, X and Y, are involved in a chemical reaction. The amounts in grams of these compounds, t minutes after the reaction starts, are x and y respectively and are modelled by the differential equations
- (i) Prove by induction that
- A sample of bacteria in a sealed container is being studied.

The number of bacteria, P, in thousands, is modelled by the differential equation

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