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 10

If P =  =    and PQ = QP,

find the values of c and d.

1. Using the trapezium rule with five ordinates, calculate, correct to

two decimal places, the approximate value of .

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Observation

Majority of the candidates who attempted this question were reported to have performed better in part (a) then in part (b).  Their performance in part (b) was described as poor.  Majority of them could not apply the trapezium rule correctly.
In part (a) candidates were expected to show that if P =  and Q =  then
PQ =   =   and QP  =   = .

Since PQ = QP, then, 32 = 24 + 2c which gave c = 4.  Similarly, 8 + 2d = 18, hence d = 5. i.e. c and d are 4 and 5 respectively.
In part (b), candidates were expected to obtain the following table:

 x 2 3 4 5 6 y = 0.5 0.333 0.25 0.2 0.167

Using the trapezium rule,   = [(0.5 + 0.167) + 2(0.333 + 0.25 + 0.2)] = 1.12, correct to 2 decimal places.