Mathematics AI: MATRICES Topical Past Paper Questions

[Maximum mark: 18] The Fibonacci sequence has the initial values 0, 1, 2, 3, 5, 8, ... To find the next number in the sequence, the previous two numbers are added. This can be written as $ f_{n+1} = f_n + f_{n-1} $, together with $ f_1 = 0 $ and $ f_2 = 1 $. Consecutive pairs in…

[Maximum mark: 16] The drivers of a delivery company can park their vans overnight either at its headquarters or at home. Urvashi is a driver for the company. If Urvashi has parked her van overnight at headquarters on a given day, the probability that she parks her van at the fol…

[Maximum mark: 14] François is a video game designer. He designs his games to take place in two dimensions, relative to an origin O. In one of his games, an object travels on a straight line $ L_{1} $ with vector equation $$ \boldsymbol{r}=\binom{-1}{1}+\lambda\binom{2}{-1}. $$ (…