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

GCE JUN 2008 : AS, F2: Further Pure Mathematics 2

4 pages, 15 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 2008 Mathematics assessing Module FP2: Further Pure Mathmatics 2 AMF21 Assessment Unit F2 [AMF21] WEDNESDAY 18 JUNE, MORNING 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 AMFP2S8 3201 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) Express in partial fractions 1 (3k 2)(3k + 1) [5] (ii) Hence show that 1 1 1 n + + ... + = 1 4 4 7 (3n 2)(3n + 1) 3n + 1 2 Find, in radians, the general solution of the trigonometric equation sin 2 x + 2 sin x = 1 + cos x 3 [4] [7] (i) Find the first 4 non-zero terms of the Maclaurin expansion of ln (1 + x) where | x | < 1 (ii) Verify that [6] (1 + x + x2 + x3) (1 x) 1 x4 [1] (iii) Hence find the series expansion of ln (1 + x + x2 + x3) as far as the fourth non-zero term. AMFP2S8 3201 [5] 2 [Turn over 4 (i) Find the general solution of the differential equation d2 y dx (ii) If y = 1 and 5 2 6 dy + 9 y = 13 sin 2 x dx [10] dy = 0 when x = 0, find the particular solution. dx [4] Consider the sequence defined by un+1 = 3un 1 where u1 = 1 Use the method of mathematical induction to prove that un = ( ) 1 n 1 3 +1 2 where n is a positive integer. 6 [7] (i) Solve the equation z 8 1 = 9 8 3 i writing each root in the form reip , where p is a rational number and 0 (ii) Indicate these roots clearly on an Argand diagram. AMFP2S8 3201 3 p<2 [8] [3] [Turn over 7 (a) An ellipse has centre (2, 7) and a focus at (5, 7) with corresponding directrix x = 10 1 3 Find the equation of the ellipse. [7] (b) (i) Verify that a point P with coordinates (2 cos , sin ) lies on the ellipse [1] x2 + y2 = 1 4 (ii) Find the equation of the tangent to the ellipse in (i) at the point P(2 cos , sin ). [4] Fig. 1 below shows the tangent at P intersecting the y-axis at A and the x-axis at B. y A P x2 + y2 = 1 4 B O x Fig. 1 (iii) Find the area of the triangle OAB. S 2/07 531-018-1 [3]

Formatting page ...

Additional Info : Gce Mathematics June 2008 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: