Edexcel 2020 Further Maths, 9FM0/02

Edexcel 2020 Further Maths Mechanics Paper 2 (Question Paper)
Edexcel 2020 Further Maths Mechanics Paper 2 (Mark Scheme)

1. The curve C has equation
   y = 31 sinh x − 2 sinh 2x
   Determine, in terms of natural logarithms, the exact x coordinates of the stationary points of C
2. In an Argand diagram, the points A and B are represented by the complex numbers −3 + 2i and 5 − 4i respectively. The points A and B are the end points of a diameter of a circle C.
   (a) Find the equation of C, giving your answer in the form
3. A scientist is investigating the concentration of antibodies in the bloodstream of a patient following a vaccination.
   The concentration of antibodies, x, measured in micrograms (μg) per millilitre (ml) of blood, is modelled by the differential equation
4. (a) Use de Moivre’s theorem to prove that
   sin 7θ = 7 sinθ − 56 sin³ θ + 112 sin⁵ θ − 64 sin⁷ θ
   (b) Hence find the distinct roots of the equation
   1 + 7x − 56x³ + 112x⁵ − 64x⁷ = 0
   giving your answer to 3 decimal places where appropriate.
5. (a) y = tan⁻¹ x
   Assuming the derivative of tanx , prove that
6. (a) Given that k ≠ 4, find, in terms of k, the inverse of the matrix M.
   (b) Find, in terms of p, the coordinates of the point where the following planes intersect
7. A student wants to make plastic chess pieces using a 3D printer. Figure 1 shows the central vertical cross-section of the student’s design for one chess piece. The plastic chess piece is formed by rotating the region bounded by the y-axis, the x-axis, the line with equation x = 1, the curve C1 and the curve C2 through 360° about the y-axis.
   The point A has coordinates (1, 0.5) and the point B has coordinates (0.5, 2.5) where the units are centimetres.
   The curve C1 is modelled by the equation

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