9709_s07_ms_3

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS

GCE Advanced Subsidiary Level and GCE Advanced Level

MARK SCHEME for the May/June 2007 question paper

9709 MATHEMATICS

9709/03 Paper 3, maximum raw mark 75

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began.

All Exam iners are instructed that alternative correct answers and unexpected approaches in candidates’ scripts m ust be given m arks that fairly reflect the relevant knowledge and skills demonstrated.

Mark schem es m ust be read in conjunction with the question papers and the report on the examination.

?CIE will not enter into discussions or correspondence in connection with these mark schemes.

CIE is publishing the m ark schem es for the May/June 2007 question papers for m ost IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Mark Scheme Notes

Marks are of the following three types:

M Method mark, awarded for a valid method applied to the problem. Method marks are not lost for numerical errors, algebraic slips or errors in units.

However, it is not usually sufficient for a candidate just to indicate an intention

of using some method or just to quote a formula; the formula or idea must be

applied to the specific problem in hand, e.g. by substituting the relevant

quantities into the formula. Correct application of a formula without the

formula being quoted obviously earns the M mark and in some cases an M

mark can be implied from a correct answer.

A Accuracy mark, awarded for a correct answer or intermediate step correctly

obtained. Accuracy marks cannot be given unless the associated method

mark is earned (or implied).

B Mark for a correct result or statement independent of method marks.

? When a part of a question has two or more "method" steps, the M marks are generally independent unless the scheme specifically says otherwise; and similarly when there are several B marks allocated. The notation DM or DB (or dep*) is used to indicate that a particular M or B mark is dependent on an earlier M or B (asterisked) mark in the scheme. When two or more steps are run together by the candidate, the earlier marks are implied and full credit is given.

? The symbol √ implies that the A or B mark indicated is allowed for work correctly following on from previously incorrect results. Otherwise, A or B marks are given for correct work only. A and B marks are not given for fortuitously "correct" answers or results obtained from incorrect working.

? Note: B2 or A2 means that the candidate can earn 2 or 0.

B2/1/0 means that the candidate can earn anything from 0 to 2.

The marks indicated in the scheme may not be subdivided. If there is genuine doubt whether a candidate has earned a mark, allow the candidate the benefit of the doubt. Unless otherwise indicated, marks once gained cannot subsequently be lost,

e.g. wrong working following a correct form of answer is ignored.

? Wrong or missing units in an answer should not lead to the loss of a mark unless the scheme specifically indicates otherwise.

? For a numerical answer, allow the A or B mark if a value is obtained which is correct to 3 s.f., or which would be correct to 3 s.f. if rounded (1 d.p. in the case of an angle). As stated above, an A or B mark is not given if a correct numerical answer arises fortuitously from incorrect working. For Mechanics questions, allow A or B marks for correct answers which arise from taking g equal to 9.8 or 9.81 instead of

10.

The following abbreviations may be used in a mark scheme or used on the scripts:

AEF Any Equivalent Form (of answer is equally acceptable)

AG Answer Given on the question paper (so extra checking is needed to ensure that the detailed working leading to the result is valid)

BOD Benefit of Doubt (allowed when the validity of a solution may not be absolutely clear)

CAO Correct Answer Only (emphasising that no "follow through" from a previous error is allowed)

CWO Correct Working Only - often written by a ‘fortuitous' answer

ISW Ignore Subsequent Working

MR Misread

PA Premature Approximation (resulting in basically correct work that is insufficiently accurate)

S OS S ee Other S olution (the candidate makes a better attempt at the same question)

S R S pecial Ruling (detailing the mark to be given for a specific wrong solution, or a case where some standard marking practice is to be varied

in the light of a particular circumstance)

Penalties

MR -1 A penalty of MR -1 is deducted from A or B marks when the data of a question or part question are genuinely misread and the object and

difficulty of the question remain unaltered. In this case all A and B marks

then become "follow through √" marks. MR is not applied when the

candidate misreads his own figures - this is regarded as an error in

accuracy. An MR-2 penalty may be applied in particular cases if agreed

at the coordination meeting.

PA -1 This is deducted from A or B marks in the case of premature approximation. The PA -1 penalty is usually discussed at the meeting.