Edexcel 2020 Further Maths Mechanics Paper 2 (Question Paper)
Edexcel 2020 Further Maths Mechanics Paper 2 (Mark Scheme)
- 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
- 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
- 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
- (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.
- (a) y = tan−1 x
Assuming the derivative of tanx , prove that
- (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
- 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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