Further Mathematics Paper 2, Nov/Dec. 2010
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
Weakness/Remedies
Strength
Question 1

A binary operation * is defined on the set R, of real numbers by
X * Y = x²/x=y¹ where x, y ∈ R.
(a) Evaluate (2 * 3) * 5.
(b) If (x + 1) * (x + 2) = 1/3 find the value of x.

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Observation

The Chief Examiner reported that this question was well attempted by majority of the candidates. However, there were few cases where some candidates did not recognize 0 (zero) as one of the solutions in part (b).
In part (a) candidates were expected to follow the rule of BODMAS while substituting for x and y in the operations. Taking the bracket (2 * 3), we have:2²/2+3 = 4/5
( 2 * 3) * 5 now becomes (4/5)²/4/5+5 = 16/25/29/5  = 16/25 x 5/29 x 16/145
In part (b), candidates were expected to substitute (x + 1) for x and (x+2) for y in the expression x²/x+y, equate it to 1/3 and solve the resulting equation to obtain the values of x as follows:
(x + 1)2     = 1/3
(x+1 )+(x+2)
3(x+1)² =2x+3 l.e 3x²+6x+3=2x+3 3x²+4x = 0
x(3x + 4) = 0 x = 0 or 3/4