# Edexcel 2020 Further Maths, 9FM0/01

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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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1. f(z) = 3z3 + pz2 + 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
2. (a) Explain why
(b) Prove that
3. 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.
4. 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
5. 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
6. (i) Prove by induction that
7. 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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