C2 Past Paper Booklet - The Grange School Blogs
C2 Past Paper Booklet - The Grange School Blogs C2 Past Paper Booklet - The Grange School Blogs
4Jan 20127 (a) Find ∫ (x2 + 4)(x − 6) dx. [3](b)yOx32The diagram shows the curve y = 6x and part of the curve y = 8 2 − 2, which intersect at the point (1, 6). Usexintegration to find the area of the shaded region enclosed by the two curves and the x-axis. [8]8 (a) Use logarithms to solve the equation 7 w – 3 − 4 = 180, giving your answer correct to 3 significantfigures. [4](b) Solve the simultaneous equationslog 10x + log 10y = log 103, log 10(3x + y) = 1. [6]9 (i) Sketch the graph of y = tan ( 1 x) for2 −2π x 2π on the axes provided.On the same axes, sketch the graph of y = 3cos( 1 x) for2 −2π x 2π, indicating the point of intersectionwith the y-axis. [3](ii) Show that the equation tan ( 1 2 x) = 3 cos ( 1 x) can be expressed in the form23 sin 2 ( 1 2 x) + sin ( 1 x)2 − 3 = 0.Hence solve the equation tan ( 1 2 x) = 3 cos ( 1 x) for2 −2π x 2π. [6]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 possibleopportunity.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 adepartment of the University of Cambridge.© OCR 20124722 Jan12
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4Jan 20127 (a) Find ∫ (x2 + 4)(x − 6) dx. [3](b)yOx32<strong>The</strong> diagram shows the curve y = 6x and part of the curve y = 8 2 − 2, which intersect at the point (1, 6). Usexintegration to find the area of the shaded region enclosed by the two curves and the x-axis. [8]8 (a) Use logarithms to solve the equation 7 w – 3 − 4 = 180, giving your answer correct to 3 significantfigures. [4](b) Solve the simultaneous equationslog 10x + log 10y = log 103, log 10(3x + y) = 1. [6]9 (i) Sketch the graph of y = tan ( 1 x) for2 −2π x 2π on the axes provided.On the same axes, sketch the graph of y = 3cos( 1 x) for2 −2π x 2π, indicating the point of intersectionwith the y-axis. [3](ii) Show that the equation tan ( 1 2 x) = 3 cos ( 1 x) can be expressed in the form23 sin 2 ( 1 2 x) + sin ( 1 x)2 − 3 = 0.Hence solve the equation tan ( 1 2 x) = 3 cos ( 1 x) for2 −2π x 2π. [6]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 possibleopportunity.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 adepartment of the University of Cambridge.© OCR 20124722 Jan12
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