Further Mathematics Paper 2, Nov/Dec. 2014
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Main
Weakness/Remedies
Strength

Question 1

If f(y) = log2 (y + 1) – log2 (y + 3),

1. find the domain of f(y);

• solve f(y) = 1

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Observation

The Chief Examiner reported that candidates performed well in this question.  Majority of the candidates were reportedly able to express the right hand side of the equality sign as a single log i.e. f(y) = log2 (y+ 1) – log2 (y + 3) = log 2(). However, candidates should know that f(y) would not exist when () is less than or equal to zero and this would happen when -3 £ y £ -1.  Therefore, the domain of f(y) was Doman(f) =    y : y  R, y < -3 and y > -1  A good number of the candidates were reported not to get this right.

In part (b), candidates were reportedly able to show that if f(y) = 1, then log2 () =
log22  i.e.  = 2.  By cross multiplying and bringing like terms together, we obtain
y = - 5.