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Unformatted text preview: UCLES 2010 91**4023334091* Sixth Term Examination Papers 9465 MATHEMATICS 1 Afternoon MONDAY 21 JUNE 2010 Time: 3 hours Additional Materials: Answer Paper Formulae Booklet Candidates may not use a calculator INSTRUCTIONS TO CANDIDATES Please read this page carefully, but do not open this question paper until you are told that you may do so. Write your name, centre number and candidate number in the spaces on the answer booklet. Begin each answer on a new page. INFORMATION FOR CANDIDATES Each question is marked out of 20. There is no restriction of choice. You will be assessed on the six questions for which you gain the highest marks. You are advised to concentrate on no more than six questions. Little credit will be given for fragmentary answers. You are provided with a Mathematical Formulae Booklet. Calculators are not permitted. Please wait to be told you may begin before turning this page. _____________________________________________________________________________ This question paper consists of 7 printed pages and 1 blank page. [Turn over Section A: Pure Mathematics 1 Given that 5 x 2 + 2 y 2- 6 xy + 4 x- 4 y a ( x- y + 2) 2 + b ( cx + y ) 2 + d , find the values of the constants a , b , c and d . Solve the simultaneous equations 5 x 2 + 2 y 2- 6 xy + 4 x- 4 y = 9 , 6 x 2 + 3 y 2- 8 xy + 8 x- 8 y = 14 . 2 The curve y = x- a x- b e x , where a and b are constants, has two stationary points. Show that a- b < or a- b > 4 . (i) Show that, in the case a = 0 and b = 1 2 , there is one stationary point on either side of the curves vertical asymptote, and sketch the curve. (ii) Sketch the curve in the case a = 9 2 and b = 0 . 3 Show that sin( x + y )- sin( x- y ) = 2 cos x sin y and deduce that sin A- sin B = 2 cos 1 2 ( A + B ) sin 1 2 ( A- B ) ....
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