| Date | May 2012 | Marks available | 2 | Reference code | 12M.3.SL.TZ2.14 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 2 |
| Command term | Define | Question number | 14 | Adapted from | N/A |
Question
This question is about the development of the universe.
Define, with reference to the flat model of the universe, critical density.
The diagram represents how the universe might develop if its density were greater than the critical density.
The dotted line represents the development of the universe if the density of the universe were zero.
On the diagram above,
(i) label with the letter N the present time.
(ii) draw a line labelled F to represent the development of the universe corresponding to a flat universe.
(iii) draw a line labelled O to represent the development of the universe corresponding to the universe if its density were less than the critical density.
Markscheme
critical density is the density for which the universe stops expanding;
after an infinite amount of time;
radius of the universe 
(i) the time corresponding to where the two lines touch; {(labelled N on the time axis or the graph)
(ii) a slightly curved line between the dotted line and the closed universe line;
(labelled F)
(iii) a slightly curved line between the dotted line and the flat universe line;
(labelled O)
Allow an accelerating universe graph labelled either F or O.
Examiners report
