Problem 4 Paper A particle can travel at speeds up to 2ms\frac{2m}{s}s2m along the xxx -axis, and up to 1ms\frac{1m}{s}s1m elsewhere in the plane. Provide a labelled sketch of the region which can be reached within one second by the particle starting at the origin. Answer, solutions and source
Problem 5 Paper The function f:N→Rf : \mathbb N \to \mathbb Rf:N→R satisfies f(1)=1,f(2)=2f(1) = 1, f(2) = 2f(1)=1,f(2)=2 and f(n+2)=f(n+2−f(n+1))+f(n+1−f(n)).f (n+2) = f(n+2 - f(n+1) ) + f(n+1 - f(n) ).f(n+2)=f(n+2−f(n+1))+f(n+1−f(n)). Show that 0≤f(n+1)−f(n)≤10 \leq f(n+1) - f(n) \leq 10≤f(n+1)−f(n)≤1 . Find all nnn for which f(n)=1025f(n) = 1025f(n)=1025 . Answer, solutions and source