A-LEVEL EDEXCEL FURTHER MATHS 202 5
QUESTION PAPER PLUS MARKING SCHEME
Paper 1: Core Pure Mathematics
Question 1: Complex Numbers (3 marks)
Solve (2+3i)+(4−2i)(2 + 3i) + (4 - 2i)(2+3i)+(4−2i).
Question 2: Differentiation (4 marks)
Differentiate f(x)=3x4−5x3+7x−2f(x) = 3x^4 - 5x^3 + 7x - 2f(x)=3x4−5x3+7x−2.
Question 3: Matrices (5 marks)
Given A=(1234)A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}A=(1324) and B=(5678)B = \begin{pmatrix} 5 & 6 \\ 7 & 8 \end{pmatrix}B=(5768), find ABABAB.
Question 4: Differential Equations (6 marks)
Solve the differential equation dydx=2x+3\frac{dy}{dx} = 2x + 3dxdy=2x+3.
Paper 2: Further Pure Mathematics
Question 1: Induction (4 marks)
Prove by induction that 1+3+5+⋯+(2n−1)=n21 + 3 + 5 + \cdots + (2n - 1) = n^21+3+5+⋯+(2n−1)=n2.
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Question 2: Vectors (5 marks)
Given a=(234)\mathbf{a} = \begin{pmatrix} 2 \\ 3 \\ 4 \end{pmatrix}a=234 and b=(105)\mathbf{b} = \begin{pmatrix} 1 \\ 0 \\ 5 \end{pmatrix}b=105, calculate a⋅b\mathbf{a} \cdot \mathbf{b}a⋅b and a×b\mathbf{a} \times \mathbf{b}a×b.
Question 3: Integration (6 marks)
Evaluate the integral ∫(x3+4x2+2x+5) dx\int (x^3 + 4x^2 + 2x + 5) \, dx∫(x3+4x2+2x+5)dx.
Question 4: Roots of Polynomials (7 marks)
Find all the roots of the polynomial x3−3x2+4=0x^3 - 3x^2 + 4 = 0x3−3x2+4=0 by solving it algebraically.
Paper 3: Further Mechanics & Decision Mathematics
Question 1: Kinematics (5 marks)
A particle moves along a straight line such that its displacement sss at time ttt is given by s(t)=2t3−5t2+4ts(t) = 2t^3 - 5t^2 + 4ts(t)=2t3−5t2+4t. Find the velocity and acceleration of the particle at t=2t = 2t=2.
Question 2: Linear Programming (6 marks)
Maximize z=3x+2yz = 3x + 2yz=3x+2y subject to the constraints:
• x+2y≤6x + 2y \leq 6x+2y≤6 • x≥0x \geq 0x≥0 • y≥0y \geq 0y≥0
Question 3: Poisson Distribution (5 marks)
The number of accidents occurring at a busy intersection follows a Poisson distribution with a mean of 2 per hour. What is the probability that exactly 3 accidents occur in one hour?
Question 4: Graph Theory (7 marks)
Draw the graph corresponding to the following adjacency matrix and find the shortest path from vertex AAA to vertex DDD.
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