C2 Past Paper Booklet - The Grange School Blogs

Jan 201048 A sequence u 1, u 2, u 3, . . . is defined byu 1= 8 and u n+1= u n+ 3.(i) Show that u 5= 20. [2](ii) The nth term of the sequence can be written in the form u n= pn + q. State the values of p and q.[2](iii) State what type of sequence it is. [1](iv) Find the value of N such that2N∑n=1u n−N∑n=1u n= 1256. [5]9 (i) Sketch the curve y = 6 × 5 x , stating the coordinates of any points of intersection with the axes.[3](ii) The point P on the curve y = 9 x has y-coordinate equal to 150. Use logarithms to find thex-coordinate of P, correct to 3 significant figures. [3](iii) The curves y = 6 × 5 x and y = 9 x intersect at the point Q. Show that the x-coordinate of Q can bewritten as x = 1 + log 3 22 − log 35 . [5]Copyright InformationOCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holderswhose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR CopyrightAcknowledgements Booklet. This is produced for each series of examinations, is given to all schools that receive assessment material and is freely available to download from our publicwebsite (www.ocr.org.uk) after the live examination series.If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible opportunity.For queries or further information please contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB2 1GE.OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a departmentof the University of Cambridge.© OCR 2010 4722 Jan10