Edexcel 2020 Further Maths, 9FM0/01

Edexcel 2020 Further Maths Paper 1 (Question Paper)
Edexcel 2020 Further Maths Paper 1 (Mark Scheme)

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

Check out our most popular games!

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.