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Oxford Cambridge and RSA Examinations STEP Mathematics STEP 9465, 9470, 9475 STEP Solutions June 2007 STEP2007

STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local

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Page 1: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local

Oxford Cambridge and RSA Examinations

STEP

Mathematics STEP 9465, 9470, 9475

STEP Solutions June 2007

STEP2007

Page 2: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local

OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local Examinations Syndicate and the RSA Examinations Board in January 1998. OCR provides a full range of GCSE, A level, GNVQ, Key Skills and other qualifications for schools and colleges in the United Kingdom, including those previously provided by MEG and OCEAC. It is also responsible for developing new syllabuses to meet national requirements and the needs of students and teachers. This mark scheme is published as an aid to teachers and students, to indicate the requirements of the examination. It shows the basis on which marks were awarded by Examiners. It does not indicate the details of the discussions which took place at an Examiners� meeting before marking commenced. All Examiners are instructed that alternative correct answers and unexpected approaches in candidates� scripts must be given marks that fairly reflect the relevant knowledge and skills demonstrated. Mark schemes should be read in conjunction with the published question papers and the Report on the Examination. OCR will not enter into any discussion or correspondence in connection with this mark scheme. © OCR 2007 Any enquiries about publications should be addressed to: OCR Publications PO Box 5050 Annesley NOTTINGHAM NG15 0DL Telephone: 0870 870 6622 Facsimile: 0870 870 6621 E-mail: [email protected]

Page 3: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local

CONTENTS

STEP Mathematics (9465, 9470, 9475)

Unit Content Page 9465 STEP Mathematics I

9470 STEP Mathematics II

9475 STEP Mathematics III

Page 4: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 5: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local

Step I, Solutions June 2007

Page 6: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 7: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 8: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 9: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 10: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
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Page 12: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
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Page 15: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
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Step II, SolutionsJune 2007

Page 22: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
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Page 24: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
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Step III, SolutionsJune 2007

Page 30: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 31: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
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Page 33: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 34: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
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Page 36: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 37: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 38: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 39: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 40: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 41: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 42: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 43: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 44: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 45: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 46: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 47: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 48: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 49: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 50: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
Page 51: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
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Page 54: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local
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Page 56: STEP Solutions - Microsoft · Solutions June 2007 STEP2007. OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local

Oxford Cambridge and RSA Examinations is a Company Limited by Guarantee Registered in England Registered Office; 1 Hills Road, Cambridge, CB1 2EU Registered Company Number: 3484466 OCR is an exempt Charity OCR (Oxford Cambridge and RSA Examinations) Head office Telephone: 01223 552552 Facsimile: 01223 552553 © OCR 2007

OCR (Oxford Cambridge and RSA Examinations) 1 Hills Road Cambridge CB1 2EU OCR Customer Contact Centre (General Qualifications) Telephone: 01223 553998 Facsimile: 01223 552627 Email: [email protected] www.ocr.org.uk For staff training purposes and as part of our quality assurance programme your call may be recorded or monitored