C2 Past Paper Booklet - The Grange School Blogs
C2 Past Paper Booklet - The Grange School Blogs C2 Past Paper Booklet - The Grange School Blogs
9Jan 2011y4xThe diagram shows the curve y = f(x), where f(x) = −4x 3 + 9x 2 + 10x − 3.(i) Verify that the curve crosses the x-axis at (3, 0) and hence state a factor of f(x). [2](ii) Express f(x) as the product of a linear factor and a quadratic factor. [3](iii) Hence find the other two points of intersection of the curve with the x-axis. [2](iv) The region enclosed by the curve and the x-axis is shaded in the diagram. Use integration to findthe total area of this region. [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 and is freely available to download from our public website (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 2011 4722 Jan11
1June 2011B29 cmA40°17 cmCThe diagram shows triangle ABC, with AB = 9 cm, AC = 17 cm and angle BAC = 40 ◦ .(i) Find the length of BC. [2](ii) Find the area of triangle ABC. [2](iii) D is the point on AC such that angle BDA = 63 ◦ . Find the length of BD. [3]2 (i) Find (6x 1 2− 1) dx. [3](ii) Hence find the equation of the curve for which dydx = 6x1 2− 1 and which passes through thepoint (4, 17). [3]3AB8 cmThe diagram shows a sector AOB of a circle, centre O and radius 8 cm. The perimeter of the sectoris 23.2 cm.O(i) Find angle AOB in radians. [3](ii) Find the area of the sector. [2]© OCR 2011 4722 Jun11
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9Jan 2011y4x<strong>The</strong> diagram shows the curve y = f(x), where f(x) = −4x 3 + 9x 2 + 10x − 3.(i) Verify that the curve crosses the x-axis at (3, 0) and hence state a factor of f(x). [2](ii) Express f(x) as the product of a linear factor and a quadratic factor. [3](iii) Hence find the other two points of intersection of the curve with the x-axis. [2](iv) <strong>The</strong> region enclosed by the curve and the x-axis is shaded in the diagram. Use integration to findthe total area of this region. [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 <strong>Booklet</strong>. This is produced for each series of examinations and is freely available to download from our public website (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 2011 4722 Jan11
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