Past Examination papers
The previous six years of papers (including corrections) are available electronically
The Library keeps printed copies of examination papers in the reserve 4 hour loan collection.
Note that previous examination papers may test material which is not current and may have a different format - consult your lecturer at an early stage if you require any sort of clarification.
It is department policy not to provide solutions to past exam papers; the lectures and tutorials / problems classes in the Easter term are normally used to go over exam questions from previous years.
Within the Department of Mathematical Sciences, `collections' is the name given to formative tests (i.e. not taken into account in the calculation of end-of-year marks) covering the material taught in Level 1 mathematics modules during the first term (Michaelmas) of the first year of study at Durham.
Collections for level 1 Calculus, Linear Algebra, Analysis, Statistics, Discrete Mathematics, Maths for Engineers and Scientists, Single Mathematics A and Single Mathematics B are taken in week 11, i.e. during the first week of the Epiphany term, according to the Collections timetable. The time allocated to answer each collection paper is 45 minutes. Collections are therefore not in the same format as end-of-year exams. They test whether students have revised efficiently, and give them an opportunity to consolidate their learning if necessary. Feedback on collections is usually given during early second term tutorials.
Although formative, collections are compulsory. Medical evidence is required if a collection is missed. Absences for non-medical reasons must be discussed in advance of the collection period with the relevant Course Director.
Dictionaries in Examinations
Dictionaries are not permitted in examinations in Mathematical Sciences.
Calculators in Examinations
The use of electronic calculators is allowed in some exams as detailed in the list of papers below.
Science Faculty Policy on Calculators
The use of electronic calculators is allowed in some module examinations and other module assessments. Each student registered on a Maths degree, which specify that calculators be allowed in assessments, are offered a calculator, free of charge, at the beginning of their course. The models are those from Casio fx-83 and fx-85 series.
Calculators will become the property of students who will be responsible for their upkeep. No replacement calculators will be provided free of charge, but may be available to purchase from departments/schools, depending on availability. The specified calculator will also be generally available, in shops and online, should a replacement purchase be necessary.
Where the use of calculators is allowed in assessments, including examinations, the only models that will be allowed are those from the Casio fx-83 or fx-85 series. In particular, examination invigilators will refuse to allow a candidate to use any calculator other than the model(s) specified, which will be explicitly stated on the front of the examination paper. During examinations no sharing of calculators between candidates will be permitted, nor will calculators or replacement batteries be supplied by the Department or the Student Registry Office.
List of examination papers
The tables below list all examination papers for undergraduate modules, whether or not the module is being taught this year. The only modules not listed below are the ones which do not have final examination papers: Mathematical Modelling II (MATH2637), Mathematics Teaching III (MATH 3121) and the project modules, Project III (MATH 3382) and Project IV (MATH 4072).
In a module code such as MATH 1061 the first digit gives the level and the last digit is 1 or 2 for a single or double module. The MATH obviously indicates a Mathematics department module.Previously the department was denoted by the 2-digit code 06 to form a 6-digit module code such as 061061, so you may see this type of paper code on older past papers. The paper code is formed from the module code appended with the letters "WE" (for "Written Exam") and a 2 digit number indicating the assessment component. In the tables below this is either 01 or 02 for papers 1 or 2.
The third column in the tables below indicates whether calculators are allowed in the examination. By default calculators are not allowed. A `C' indicates that calculators can be used.
|Paper Title||Paper code||Calculators|
|Calculus I||MATH 1061-WE01|
|Probability I||MATH 1597-WE02|
|Linear Algebra I||MATH 1071-WE01|
|Analysis I||MATH 1051-WE01|
|Dynamics I||MATH 1607-WE01|
|Discrete Mathematics||MATH 1031-WE01||C|
|Statistics I||MATH 1617-WE01||C|
|Mathematics for Engineers & Scientists||MATH 1551-WE01|
|Single Mathematics A||MATH 1561-WE01|
|Single Mathematics B||MATH 1571-WE01||C|
|Paper Title||Paper Code||Calculators|
|Complex Analysis II||MATH 2011-WE01|
|Analysis in Many Variables II||MATH 2031-WE01|
|Statistical Concepts II||MATH 2041-WE01||C|
|Numerical Analysis II||MATH 2051-WE01||C|
|Mathematical Physics II||MATH 2071-WE01|
|Algebra II||MATH 2581-WE01|
|Elementary Number Theory II||MATH 2617-WE01|
|Geometric Topology II||MATH 2627-WE01|
|Probability II||MATH 2647-WE01|
|Special Relativity and Electromagnetism II||MATH 2657-WE01|
|Monte Carlo II||MATH-2667-WE01||C|
|Paper Title||Paper Code||Calculators||Alternate-Year Module?|
|Analysis III||MATH 3011-WE01||Y|
|Differential Geometry III||MATH 3021-WE01|
|Number Theory III||MATH 3031-WE01||C||Y- not running in 2017-18|
|Galois Theory III||MATH 3041-WE01|
|Statistical Methods III||MATH 3051-WE01||C|
|Decision Theory III||MATH 3071-WE01||C|
|Numerical Differential Equations III||MATH 3081-WE01||C||Y- not running in 2017-18|
|Dynamical Systems III||MATH 3091-WE01|
|Continuum Mechanics III||MATH 3101-WE01||Y|
|Quantum Mechanics III||MATH 3111-WE01|
|Operations Research III||MATH 3141-WE01||C|
|Mathematical Biology III||MATH 3171-WE01|
|Geometry III||MATH 3201-WE01||Y- not running in 2017-18|
|Probability III||MATH 3211-WE01||Y- not running in 2017-18|
|Solitons III||MATH 3231-WE01||Y|
|Stochastic Processes III||MATH 3251-WE01||Y|
|Topology III||MATH 3281-WE01|
|Partial Differential Equations III||MATH 3291-WE01||C|
|Mathematical Finance III||MATH 3301-WE01||C|
|Bayesian Statistics III||MATH 3341-WE01||C||Y|
|Statistical Mechanics III||MATH 3351-WE01||Y- not running in 2017-18|
|Topics in Statistics III||MATH 3361-WE01||C||Y- not running in 2017-18|
|Representation Theory III||MATH 3371-WE01||Y|
|Quantum Information III||MATH 3391-WE01|
|Cryptography and Codes III||MATH 3401-WE01||C|
|Paper Title||Paper Code||Calculators||Alternate-Year Module?|
|Bayesian Statistics IV||MATH 4031-WE01||C||Y|
|Partial Differential Equations IV||MATH 4041-WE01||C|
|General Relativity IV||MATH 4051-WE01|
|Advanced Quantum Theory IV||MATH 4061-WE01|
|Topics in Statistics IV||MATH 4071-WE01||C||Y- not running in 2017-18|
|Continuum Mechanics IV||MATH 4081-WE01||Y|
|Stochastic Processes IV||MATH 4091-WE01||Y|
|Solitons IV||MATH 4121-WE01||Y|
|Probability IV||MATH 4131-WE01||Y- not running in 2017-18|
|Geometry IV||MATH 4141-WE01||Y- not running in 2017-18|
|Elliptic Functions IV||MATH 4151-WE01|
|Topics in Algebra and Geometry IV||MATH 4161-WE01|
|Riemannian Geometry IV||MATH 4171-WE01|
|Mathematical Finance IV||MATH 4181-WE01||C|
|Analysis IV||MATH 4201-WE01||Y|
|Number Theory IV||MATH 4211-WE01||C||Y- not running in 2017-18|
|Numerical Differential Equations IV||MATH 4221-WE01||C||Y- not running in 2017-18|
|Statistical Mechanics IV||MATH 4231-WE01||Y- not running in 2017-18|
|Representation Theory IV||MATH 4241-WE01||Y|
Further information for level I papers
All level I papers have resits in the Autumn exam period. Students at Level 1 may resit all failed modules, but resit marks are capped at 40%.
Linear Algebra I, Calculus I and Analysis I each have one 3-hour paper containing 10 questions which are all compulsory.
Dynamics I, Probability I and Statistics I has two 1.5-hour papers each containing 5 questions which are all compulsory.
Programming I is assessed by in-year assessment covering the Michaelmas term. The in-year assessment contributes 40% of the module mark, 75% of which comes from the submitted coursework and 25% of which comes from the weekly homework submissions.
Discrete Maths is assessed by in-year assessment covering the Epiphany term group work, and a final exam covering the material from the lectures in Michaelmas term and the start of Epiphany term. The in-year assessment contributes 40% of the module mark, 50% of which comes from the presentation and 50% from the summative report. The 2-hour exam contributes 60% of the module mark and has 6 questions. Any number of these questions may be attempted and credit will be given for the best 4.
Rubric for Calculus I, Probability I, Linear Algebra I, Analysis I and Dynamics I: Attempt all questions. All questions carry the same marks. Use of electronic calculators is forbidden.
Rubric for Discrete: Credit will be given for the best FOUR answers. All questions carry the same marks. Approved electronic calculators may be used
Other Level I Modules
Each module has one 3-hour exam which contains 8 questions, except for Single Maths A and B exams, they contain 7 questions. For Maths for Engineers and Scientists, all 8 questions are compulsory and for Single Maths A and B, all 7 questions are complusory. For Statistics, any number may be attempted and credit is given for the best 6 answers. For some papers tables, and/or graph paper, and/or a formula sheet may be provided. If so, the lecturer makes this clear in advance and the rubric includes the appropriate statement. For Single Maths A and Single Maths B the final exam contributes 100% of the module mark. For Statistics and Maths for Engineers and Scientists the final exam contributes 90% of the module mark and the in-year homework sumissions contribute 10% of the module mark.
Rubric for Single Maths A and B: Attempt all questions. All questions carry the same marks. Use of electronic calculators is forbidden.
Rubric for MES: Attempt all questions. All questions carry the same marks. Use of electronic calculators is forbidden.
Rubric for Statistics: Credit will be given for the best SIX answers. All questions carry the same marks. This is an open-book examination: you may keep one folder of notes at your desk. Approved electronic calculators may be used.
Further information for level II, III and IV papers.
All Level II papers have resits in the Autumn exam period. Students at Level II may resit at most 3 modules, and resit marks are capped at 40%. Resits are not available at levels III and IV.
The only modules with continuous assessment components are Numerical Analysis II (20% from electronic assessments), Mathematical Modelling II (no exam - assessed entirely on Michaelmas term work), Monte Carlo II (25% from computer exams), Statistical Methods III (30% in total from two computer exams, one at the end of each term), Mathematics Teaching III (no exam - assessed entirely on in-year work), Project III (no exam - assessed entirely on project work) and Project IV (no exam - assessed entirely on project work). In all other modules the module mark comes entirely from the exam(s).
All examinations last 3 hours except for Statistical Methods III (MATH 3051) which lasts 2 hours and 30 minutes, and the level 2 10-credit modules which each last 2 hours except for Monte Carlo II (MATH 2667) which lasts 1 hour and 30 minutes.
All 3 hour examination papers have 6 questions in Section A and 4 in Section B. Statistical Methods III has 4 questions in Section A and 3 questions in Section B. All level 2 10-credit examination papers have 3 questions in Section A and 3 in Section B except for Monte Carlo II which has 3 questions in section A and 2 in section B.
For level IV papers in modules which have both level III and level IV versions taught together, there is an additional Section C which is a single compulsory question on the additional reading material for level IV students.
For some papers tables, and/or graph paper, and/or a formula sheet may be provided. If so, the lecturer makes this clear in advance and the rubric includes the appropriate statement.
Level II 2 hour papers
This applies to the examination papers for the 10-credit Level II modules.
Rubric: Credit will be given for the best TWO answers from Section A and the best TWO answers from Section B. Questions in Section B carry ONE and a HALF times as many marks as those in Section A.
Monte Carlo II
Rubric: Credit will be given for: the best TWO answers from Section A and the best ONE answer from Section B. Questions in Section B carry THREE TIMES as many marks as those in Section A.
Level IV papers for III/IV modules
This applies to the Level IV modules where there is also a level III version taught in the same lectures.
Rubric: Credit will be given for: the best TWO answers from Section A, the best THREE answers from Section B, and the answer to the section C question. Questions in Sections B and C carry TWICE as many marks as those in Section A.
Statistical Methods III
Rubric: Credit will be given for: the best THREE answers from Section A and the best TWO answers from Section B. Questions in Section B carry TWICE as many marks as those in Section A.
All other papers
Rubric: Credit will be given for the best FOUR answers from Section A and the best THREE answers from Section B. Questions in Section B carry TWICE as many marks as those in Section A.