1. simplify (0.05)^2 expressing your answer to 3 significant figure 2.Evaluate 0.5+(2.5) give your answer in 2 significant figure
3. Express 2log10=x in index form
4. Evaluate log 1
5. Given that= 1, find the value of 1
6. find the common ratio of given sequence 16,-8,4
7. How many terms are there in the series 3+6+12++384?
8. find the value of a in the equation 4a-3=2a+5
9. Evaluate (3.2)^2-(1.8)
10. if the ratios x:1=7:10 and y:z=6:11 find x:z
11. if log 2=0.69 and log 3=1.10 evaluate log 4
12. simplify without the use of logarithm table log 49+log (1/7)
13. in a geometric progression the fourth term exceed the third term by 72 and the third term exceed the second term by 24 determine the first term
14. make u the subject of the formula 1/u+1/v=1/f
15. Evaluate log a√44+log a√257-log(11a)
16. A stick 2.4cm long measured as 2.5cm find the percentage error

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Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.