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PREBOARD EXAMINATION ISC MATHEMATICS (Three hours) (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.) Section A - Answer Question 1 (compulsory) and five other questions. Section B and Section C - Answer two questions from either Section B or Section C. All working, including rough work, should be done on the same sheet as, and adjacent to, the rest of the answer. The intended marks for questions or parts of questions are given in brackets [ ]. Mathematical tables and graph papers are provided. SECTION A Question 1. Each question carries 3 marks. [10X3 = 30] (i) If A is a square matrix of order 3, and adj. A 36, find A . 4 1 3 (ii) Simplify: cos cos x sin x 5 5 (iii) If the line y 2 x k touches the ellipse 3 x 2 5 y 2 15 , find the value of k. 1 1 (iv) Evaluate: Lim x 1 log x x 1 d 2 y b 4 x2 y 2 (v) If 2 2 1, prove that dx 2 a 2 y 3 a b (vi) Evaluate: 1 e x 1 2 dx (vii) A speaks the truth in 55 percent cases and B speaks the truth in 75 percent cases. Find the probability that they will contradict each other in stating the same fact. (viii) Given n 10, x 55, y 55, xy 350, x 2 385. Predict the value of y when x 6. (ix)If 1, , 2 are the cube roots of unity, show that 2 5 2 2 729. 6 (x) Solve the differential equation: dy sin x y sin x y . dx
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