
	Trending ▼ ICSE CBSE 10th ISC CBSE 12th CTET GATE UGC NET Vestibulares ResFinder

GCE JUN 2006 : AS, F2: Further Pure Mathematics 2

4 pages, 14 questions, 0 questions with responses, 0 total responses,

	gce	+Fave Message
	Profile Timeline Uploads Q & A

Home > gce >

Instantly get Model Answers to questions on this ResPaper. Try now!
NEW ResPaper Exclusive!

Formatting page ...

ADVANCED General Certificate of Education 2006 Mathematics assessing Module FP2: Further Pure Mathematics 2 AMF21 Assessment Unit F2 [AMF21] WEDNESDAY 21 JUNE, AFTERNOON TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number on the Answer Booklet provided. Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. You are permitted to use a graphic or a scientific calculator in this paper. INFORMATION FOR CANDIDATES The total mark for this paper is 75 Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. A copy of the Mathematical Formulae and Tables booklet is provided. Throughout the paper the logarithmic notation used is ln z where it is noted that ln z log e z AMFP2S6 740 Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 (i) Show that 1 11 1 = r r + 2 r (r + 2) 2 [4] n r(r1+ 2) = 4(n(3+n1+)(5n)+ 2) [5] (ii) Hence show that n r =1 2 Find in radians the general solution of 2 sin + 5 cot + cosec = 0 3 2 0 If A = use the method of induction to show that for n 1 2 2n A = n 1 n2 n AMFP2S6 740 2 0 2n [10] 1 [7] [Turn over 4 (i) By considering the complex number z = cos + i sin , show that 1 1 z = sin 2i z [3] (ii) Hence, using De Moivre s theorem, show that sin 5 = 1 {sin 5 5 sin 3 + 10 sin } 16 [8] (iii) Hence find 5 sin 5 d [2] A parabola is given by the equation y2 = 12x (i) Write down the focus and directrix of the parabola. [2] The points P(3k2, 6k) and Q 3 , 6 lie on the parabola. k2 k (ii) Find, in terms of the parameter k, the equation of the tangent to the parabola at Q. [5] The equation of the tangent to the parabola at P is given by ky = x + 3k2 (iii) Show that the tangents at P and Q meet on the directrix. 6 (i) Use Maclaurin s theorem to show that the series expansion for [3] 1 up to the term 1+ x in x3 is given by 1 = 1 x + x2 x3 1+ x for x < 1 [5] (ii) Hence use partial fractions to find the series expansion of 3 3x + 4 x 2 (1 + 2 x 2 )(1 3 x ) up to and including the term in x3 AMFP2S6 740 [8] 3 [Turn over 7 (i) Find the general solution of the differential equation dy + y tan x = cos 3 x dx (ii) Find the particular solution for which y = 0 when x = 0 S 6/06 4000 302507(46) [11] [2]

Formatting page ...

Additional Info : Gce Mathematics June 2006 Assessment Unit F2 Module FP2 : Further Pure Mathematics 2
Tags : General Certificate of Education, A Level and AS Level, uk, council for the curriculum examinations and assessment, gce exam papers, gce a level and as level exam papers , gce past questions and answer, gce past question papers, ccea gce past papers, gce ccea past papers

gce chat

Horizontal lines at:
Guest Horizontal lines at:
AutoRM Data:
Box geometries: