Further Mathematics Paper 2, Nov/Dec. 2011
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
Weakness/Remedies
Strength
Question 9
1. Use the trapezium rule with ordinates at x = 1, 2, 3, 4 and 5 to calculate, correct to two decimal places, an approximate value for .
1. Given that f: x  x2 + 1 and g: x , x ≠ 1, find:
2. gof;
3. gof(2).

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Observation

The report stated that part (a), was not attempted by majority of the candidate but majority of those who attempted it performed well. They were expected to complete a table of values for the relation       y = 2x + 8x-2 for 1 ≤ x ≤ 5

 X 1 2 3 4 5 Y 10.00 6.00 6.89 8.50 10.32

Using the formula [(yo + yn) + 2(y1 + y2 + … + yn-1)],
the integral = [(10 + 10.32) + 2(6 + 6.89 + 8.50)] = 31.55 units
The performance of candidates in part (b) was reported not to be different from that of         part (a).    Candidates were expected to recall that gof = g(f(x)) and the carry out successive         substitutions and  simplification to obtain gof = g(f(x)) =  = 3 + .
gof(2) = 3 +  = 4.