| Date | May 2009 | Marks available | 2 | Reference code | 09M.1.sl.TZ1.14 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 14 | Adapted from | N/A |
Question
The number of cells, C, in a culture is given by the equation \(C = p \times 2^{0.5t} + q\), where t is the time in hours measured from 12:00 on Monday and p and q are constants.
The number of cells in the culture at 12:00 on Monday is 47.
The number of cells in the culture at 16:00 on Monday is 53.
Use the above information to write down two equations in p and q ;
Use the above information to calculate the value of p and of q ;
Use the above information to find the number of cells in the culture at 22:00 on Monday.
Markscheme
p + q = 47 (A1)
4p + q = 53 (A1) (C2)
[2 marks]
Reasonable attempt to solve their equations (M1)
p = 2, q = 45 (A1) (C2)
Note: Accept only the answers p = 2, q = 45.
[2 marks]
C = 2 × 20.5(10) + 45 (M1)
C = 109 (A1)(ft) (C2)
Note: Award (M1) for substitution of 10 into the formula with their values of p and q.
[2 marks]
Examiners report
Concern was expressed about the wording of the question; answers were given great leeway by examiners and suggestions for wording are welcome. The 24 hour clock method of describing time is the norm in IB examinations. It should be recognised that the purpose of this question was to discriminate at the grade 6/7 level.
The concept of the zero index was not understood by many.
Concern was expressed about the wording of the question; answers were given great leeway by examiners and suggestions for wording are welcome. The 24 hour clock method of describing time is the norm in IB examinations. It should be recognised that the purpose of this question was to discriminate at the grade 6/7 level.
The use of the GDC was (as always) expected in solving the simultaneous equations.
Concern was expressed about the wording of the question; answers were given great leeway by examiners and suggestions for wording are welcome. The 24 hour clock method of describing time is the norm in IB examinations. It should be recognised that the purpose of this question was to discriminate at the grade 6/7 level.
Working was required for follow through in this part.
