Further Mathematics Paper 2, May/June. 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 2

If the quadratic equation (2x -1) - p(X2 + 2) = 0 where p is a constant, has real roots
(a) show that 2 p2 + P - 1 .::: 0;
(b) find the values ofp.

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Observation

It was reported that this question was well attempted by majority of the candidates but their performance in part (a) was better than that of part (b). In part (a), candidates were expected to remove the brackets and compare the resulting equation 2x - px2 - (l +2p) = 0 with the general quadratic equation

ax2 + bx + C = 0 to obtain a = -p, b = 2 and c = -(1 + 2p). They should then substitute these values for a, b and C into the rule b2 - 4ac ~ 0 and simplify to obtain 2p2+ p - 1 ~ O.

In part (b), candidates were expected to factorize this expression to obtain (2p-1) s 0 and (p+ 1) ;::: 0 which upon investigation gave -1:::; p s ~. Many candidates were reported not to have investigated correctly.