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Further Mathematics Paper 2, Nov/Dec. 2007  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
General Comments
Weakness/Remedies
Strength











Question 4

Given that tan P =  1     and tan Q   =   2
                          m–1                       m + 1
(a)
Find tan (P – Q).
(b) For what values of m is tan (P – Q) = 1?

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Observation

This question was popular with most candidates.  However, some of them got it wrong by claiming that tan (P – Q) = tan P – tan Q.  They should understand that tan (P-Q) = tan P – tan Q   which by substituting for tan P and tan Q gives                                                                                               1+ tan P tan Q  
 
tan (p – Q)  =  3–m . When tan (P – Q) = 1, then 3-m    =   1 » m2+m – 2 = 0
                       m2+1                                                m2+1

which gives m =  −2  or  1.
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