2007 CJC Prelims Paper 2

# 2007 CJC Prelims Paper 2 - CATHOLIC JUNIOR COLLEGE...

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2 Section A: Pure Mathematics [40 marks] 1 . The variables x and u are related by x e dx du xe u u 4 (I) (i) By means of the substitution u xe y , obtain a differential equation relating y and x . [2] (ii) Hence show that the general solution of (I) is x k x u 2 ln , k is an arbitrary constant. [2] (iii) Sketch the solution curve for k = -1, stating clearly any asymptotes and axial intercepts. [2] 2. (a) (i) Find the fourth roots of the complex number -1 + i 3 , giving your answers exactly in the form r e i where r > 0 and < . [3] (ii) Deduce the solutions of the equation 0 4 2 4 8 z z , giving your answers exactly in the form
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2007 CJC Prelims Paper 2 - CATHOLIC JUNIOR COLLEGE...

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