Photo Essay

1330 WordsAug 21, 20126 Pages
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. Slide rule may be used. --------------------------------------------------------------------------------------------------------------------SECTION A Question 1 (i) (ii) (iii) (iv) If A 3 1 , find x and y so that A2 + xI2 = yA. 7 5 [10 3] Evaluate: tan[2Tan-1(1/5) - / 4] Find the value(s) of k so that the line 3x – 4y + k = 0 is tangent to the hyperbola x2 – 4y2 = 5. Evaluate: x 1 Lim x 1 log x x 1 (v) [ Evaluate: xe x dx ( x 1) 2 2 (vi) Evaluate 0 2cos x sin 2x dx 2(1 sin x) 1 ISC Specimen Question Paper 2013 (vii) Deepak rolls two dice and gets a sum more than 9. What is the probability that the number on the first die is even? (viii) You are given the following two lines of regression. Find the regression of Y on X and X on Y and justify your answer: 3x + 4y = 8; 4x + 2y = 10 (ix) (x) If w is the cube root of unity, then find the value of (1-3w+w2) (1+w-3w2) Solve: (y + xy)dx + y (1-y2)dy = 0 Question 2 (a) Using properties of determinants, prove that: [5] b2 c2 ba ca (b) ab c2 a 2 cb ac bc 2 a b2 4a 2 b 2c2 Using matrix method, solve the following system of linear equations: x – 2y – 2z – 5 = 0; –x + 3y + 4 = 0 and –2x + z – 4 = 0 [5] Question 3 (a) Verify Rolle’s theorem for f(x) = ex(sinx –

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