Skip to content

Course home

Sign up

3 Unit A2 1: Pure Mathematics (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319
Question 281
a.

Find ∫x2cos⁡3x dx\int x^2 \cos 3x \, dx∫x2cos3xdx

[4]
b.

A spherical weather balloon's volume, VVV m3^33, changes over time ttt seconds during a specific atmospheric test. The rate of change is modeled by the differential equation

dVdt=(tcos⁡1.5t)2V2 \frac{dV}{dt} = \frac{(t \cos 1.5t)^2}{V^2} dtdV​=V2(tcos1.5t)2​

where t≥0t \ge 0t≥0. Solve this differential equation to find VVV in terms of ttt, giving your answer in the form Vn=f(t)V^n = f(t)Vn=f(t) where nnn is an integer.

[5]
Markscheme

3 Unit A2 1: Pure Mathematics (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3 Unit A2 1: Pure Mathematics (A-level only)

Question bank