Advanced level 2023 northwest regional mock further mathematics 3
Advanced level 2023 northwest regional mock further mathematics 3
1. .(a)The probability density fiinction of a continuous random variable X is given by
Find
(i).the valueofthe constant a
(ii)the mean ofX’:1,1 !<v 1
(b) 10 percentof the students in a certain college study on scholarship.
(i)Given that 8 students .e selected atrandom fronrthis college, findtheprobability that at least3 ofthem study
on scholarship.
(ii)Given that400 stuu^nts are selected atrandom from this college, use the normal approximation to findthe
probability that more than 34 ofthem study on scholarship
A light elastic stringofnatural length 2a is fastened at one end to a fixedpoint.Ithangs vertically and carries at its other
end,aparticle ofmass —
(i)Findthemodulus ofelasticity ofthe string
The particle is pulled down through a distance below its equilibrium position andthen released from rest.
(ii)Show thatit begins to move with simple harmonic motion ofperiod (6mks)
(iii)Findthetime thatelapses before the string firstbecomes slack.
