This is an HTML version of an attachment to the Freedom of Information request 'Percentage marks distribution for part C maths courses'.

link to page 1 link to page 1 link to page 8 link to page 8 Examiners’ Report: Final Honour School of Mathematics
Part C Trinity Term 2016
October 20, 2016
Part I
A. STATISTICS
• Numbers and percentages in each class.
See Table 1, page 1.
• Numbers of vivas and effects of vivas on classes of result.
As in previous years there were no vivas conducted for the FHS of Mathematics Part C.
• Marking of scripts.
The dissertations and mini-projects were double marked. The remaining scripts were
all single marked according to a pre-agreed marking scheme which was very closely
adhered to. For details of the extensive checking process, see Part II, Section A.
• Numbers taking each paper.
See Table on page 8.
Table 1: Numbers in each class
Number
Percentages %
2016
(2015)
(2014)
(2013)
(2012)
2016
(2015)
(2014)
(2013)
(2012)
I
44
(45)
(45)
(56)
(45)
50.57
(46.39)
(45.92)
(47.46)
(45.45)
II.1
31
(39)
(42)
(41)
(36)
35.63
(40.21)
(42.86)
(34.75)
(36.36)
II.2
9
(13)
(11)
(15)
(15)
10.34
(13.4)
(11.22)
(12.71)
(15.15)
III
3
(0)
(0)
(4)
(3)
3.45
(0)
(0)
(3.39)
(3.03)
F
0
(0)
(0)
(2)
(0)
0
(0)
(0)
(1.69)
(0)
Total
87
(97)
(98)
(118)
(99)
100
(100)
(100)
(100)
(100)
1

2

Determination of University Standardised Marks
The Mathematics Teaching Committee issued each examination board with broad guidelines
on the proportion of candidates that might be expected in each class. This was based on
the average in each class over the last four years, together with recent historic data for Part
C, the MPLS Divisional averages, and the distribution of classifications achieved by the
same group of students at Part B.
The examiners followed established practice in determining the University standardised
marks (USMs) reported to candidates. This leads to classifications awarded at Part C
broadly reflecting the overall distribution of classifications which had been achieved the
previous year by the same students.
We outline the principles of the calibration method.
The Department’s algorithm to assign USMs in Part C was used in the same way as last
year for each unit assessed by means of a traditional written examination. Papers for which
USMs are directly assigned by the markers or provided by another board of examiners are
excluded from consideration. Calibration uses data on the Part B classification of candi-
dates in Mathematics and Mathematics & Statistics (Mathematics & Computer Science and
Mathematics & Philosophy students are excluded at this stage). Working with the data for
this population, numbers N1, N2 and N3 are first computed for each paper: N1, N2 and N3
are, respectively, the number of candidates taking the paper who achieved in Part B overall
3

link to page 5 link to page 5 average USMs in the ranges [70, 100], [60, 69] and [0, 59], respectively.
The algorithm converts raw marks to USMs for each paper separately (in each case, the
raw marks are initially out of 50, but are scaled to marks out of 100). For each paper,
the algorithm sets up a map R → U (R = raw, U = USM) which is piecewise linear. The
graph of the map consists of four line segments: by default these join the points (100, 100),
P1 = (C1, 72), P2 = (C2, 57), P3 = (C3, 37), and (0, 0). The values of C1 and C2 are set by
the requirement that the proportion of I and II.1 candidates in Part B, as given by N1 and
N2, is the same as the I and II.1 proportion of USMs achieved on the paper. The value of
C3 is set by the requirement that P2P3 continued would intersect the U axis at U0 = 10.
Here the default choice of corners is given by U -values of 72, 57 and 37 to avoid distorting
nonlinearity at the class borderlines.
The results of the algorithm with the default settings of the parameters provide the starting
point for the determination of USMs. The examiners have scope to make changes, usually
by adjusting the position of the corner points P1, P2, P3 by hand, so as to alter the map
raw → USM, to remedy any perceived unfairness introduced by the algorithm, in particular
in cases where the number of candidates is small. They also have the option to introduce
additional corners.
Table on page gives the final positions of the corners of the piecewise linear maps used
to determine USMs from raw marks. For each paper, P1, P2, P3 are the (possibly adjusted)
positions of the corners above, which together with the end points (100, 100) and (0, 0)
determine the piecewise linear map raw → USM. The entries N1, N2, N3 give the number
of incoming firsts, II.1s, and II.2s and below respectively from Part B for that paper, which
are used by the algorithm to determine the positions of P1, P2, P3.
Following customary practice, a preliminary, non-plenary, meeting of examiners was held
two days ahead of the plenary examiners’ meeting to assess the results produced by the
algorithm alongside the reports from assessors. Adjustments were made to the default
settings as appropriate, paying particular attention to borderlines and to raw marks which
were either very high or very low. These revised USM maps provided the starting point for
a review of the scalings, paper by paper, by the full board of examiners.
4

Table 2: Position of corners of piecewise linear function
Paper
P1
P2
P3
Additional corners
N1
N2
N3
C1.1
(14.59,37)
(25.4,57)
(43.4,72)
4
4
3
C1.2
(12.24,37)
(21.3,57)
(33,72)
3
4
2
C1.3
(8.96,37)
(15.6,57)
(27.6,72)
9
8
2
C1.4
(9.77,37)
(17,57)
(32,72)
5
9
3
C2.1
(13.04,37)
(22.74,57)
(33.5,72)
8
0
1
C2.2
(9.77,37)
(17,57)
(32,72)
9
5
1
C2.3
(18.79,37)
(33,70)
3
0
0
C2.4
(8,37)
(17,57)
(25,72)
2
3
0
C2.5
(16.49,37)
(28,57)
(39,72)
5
0
0
C2.6
(21.37,37)
(33,57)
(45,70)
4
2
0
C2.7
(7.7,37)
(19,57)
(35.5,72)
8
6
1
C3.1
(11.55,37)
(20.1,57)
(28,72)
5
4
0
C3.2
(9.59,37)
(17,57)
(29,72)
5
0
0
C3.3
(14.42,37)
(20,57)
(33,72)
5
2
0
C3.4
(11.89,37)
(27,57)
(37.2,72)
7
7
0
C3.5
(10,37)
(23,57)
(35.4,72)
3
1
1
C3.6
(14.99,37)
(26.5,57)
(41,72)
4
7
0
C3.7
(12,37)
(24,57)
(37,72)
8
9
1
C3.8
(10.34,37)
(24,57)
(34,72)
7
11
1
C4.1
(6.32,37)
(22,57)
(36,72)
7
9
1
C4.2
(8.5,37)
(19,57)
(30,72)
5
7
0
C4.3
(6.15,37)
(20,57)
(30,72)
4
3
0
C4.4
(11.32,37)
(22,57)
(30,72)
3
0
0
C4.5
(10.57,37)
(23,57)
(36.4.72)
4
6
0
C4.6
3
0
0
C4.7
1
2
0
C5.1
(15,37)
(29,57)
(40,70)
2
14
0
C5.2
(8,37)
(25,57)
(36,72)
5
12
0
C5.3
(10.51,37)
(18.3,57)
(32,72)
1
4
0
C5.4
(23,37)
(56,57)
(70,72)
7
9
1
C5.5
(8,37)
(21,57)
(35,72)
7
16
1
C5.6
(11.6,37)
(22,57)
(31,72)
7
6
0
C5.7
(10.4,37)
(19,57)
(37.6,72)
6
10
0
C5.9
(10,37)
(22,57)
(36,72)
1
7
0
C5.11
(12,37)
(19,57)
(35,72)
2
7
0
C5.12
(12.29,37)
(23,57)
(36,72)
4
16
2
C6.1
(8.67,37)
(25,57)
(39,72)
2
9
3
C6.2
(10.46,37)
(21,57)
(36,72)
2
10
3
C6.3
(17,37)
(27,57)
(40,70)
1
11
4
5

link to page 6 link to page 6 Paper
P1
P2
P3
Additional corners
N1
N2
N3
C6.4
(17.41,37)
(31,57)
(40,70)
6
13
4
C7.3
(13,37)
(23.8,57)
(36,72)
1
4
0
C7.4
(18.44,37)
(32.1,57)
(40,70)
0
6
1
C7.5
(16.09,37)
(30,57)
(39,72)
1
3
0
C7.6
(13.44,37)
(25,57)
(37,72)
1
3
0
C8.1
(16.2,37)
(28.2,57)
(37.2,72)
7
3
0
C8.2
(13,37)
(22,57)
(35,72)
6
2
0
C8.3
(12.52,37)
(25,57)
(40,70)
13
17
4
C8.4
(10.23,37)
(22,57)
(38,72)
14
13
5
SC1
(14.25,37)
(26,57)
(40,70)
9
13
1
SC2
(10.91,37)
(23,57)
(42,72)
4
15
2
SC3
(11.2,37)
(23,57)
(32,72)
1
5
0
SC4
(10.91,37)
(21,57)
(30,72)
3
13
3
SC5
(7.58,37)
(20,57)
(35,72)
3
13
1
Table on page gives the rank of candidates and the number and percentage of candidates
attaining this or a greater (weighted) average USM.
Table 4: Percentile table for overall USMs
Av USM
Rank
Candidates with this USM or above
%
92
1
1
1.15
91
2
2
2.3
88
3
3
3.45
84
4
6
6.9
83
7
10
11.49
82
11
12
13.79
79
13
13
14.94
77
14
16
18.39
76
17
20
22.99
75
21
22
25.29
74
23
28
32.18
73
29
35
40.23
72
36
39
44.83
71
40
40
45.98
70
41
44
50.57
69
45
46
52.87
68
47
48
55.17
67
49
52
59.77
66
53
56
64.37
65
57
61
70.11
64
62
66
75.86
63
67
68
78.16
62
69
73
83.91
61
74
74
85.06
6

link to page 7 link to page 7 Av USM
Rank
Candidates with this USM or above
%
60
75
75
86.21
59
76
76
87.36
58
77
79
90.8
57
80
80
91.95
56
81
82
94.25
54
83
83
95.4
53
84
84
96.55
49
85
86
98.85
44
87
87
100
B. Breakdown of the results by gender
Table 6, on page shows the performances of candidates broken down by gender.
Table 6: Breakdown of results by gender
Class
Total
Female
Male
Number
%
Number
%
Number
%
I
44
50.57
10
41.67
34
53.97
II.1
31
35.63
10
41.67
21
33.33
II.2
9
10.34
4
16.67
5
7.94
III
3
3.45
0
0
3
4.76
F
0
0
0
0
0
0
Total
87
100
24
100
63
100
7

C. Detailed numbers on candidates’ performance in each part of the exam
Data for papers with fewer than six candidates are not included.
Table 7: Numbers taking each paper
Paper
Number of
Avg
StDev
Avg
StDev
Candidates
RAW
RAW
USM
USM
C1.1
11
33.91
11.4
65.45
17.53
C1.2
9
27.44
10.25
63
18.49
C1.3
19
25.68
6.97
69.21
9.91
C1.4
17
26.47
7.05
66.88
8.51
C2.1
9
34.22
9.83
73.67
16.29
C2.2
15
31.2
9.52
72.07
14.15
C2.3
3
-
-
-
-
C2.4
6
14.67
8.98
47.83
23.79
C2.5
5
-
-
-
-
C2.6
6
45.17
3.71
77.67
12.09
C2.7
15
30.2
10.75
67.4
14.76
C3.1
10
24.8
4.83
65.3
7.39
C3.2
6
23.17
5.27
64.83
6.62
C3.3
7
35.57
9.14
77.57
13.75
C3.4
14
36.29
8.04
72.71
14.66
C3.5
5
-
-
-
-
C3.6
12
38.83
6.93
72.42
11.65
C3.7
19
33.84
6.99
69.11
10.2
C3.8
20
31.25
8.1
68.55
13
C3.9
2
-
-
-
-
C4.1
16
31.75
9.31
68.81
12.01
C4.2
12
23.92
10.67
62.67
16.23
C4.3
6
24.33
11.36
63.33
16.49
C4.4
3
-
-
-
-
C4.5
10
32.8
8.13
69.5
12.27
C4.6
3
-
-
-
-
C4.7
3
-
-
-
-
C5.1
16
36.56
10.15
69.19
17.29
C5.2
17
33.47
7.68
69.82
11.91
C5.3
5
-
-
-
-
C5.4
18
62.06
14.15
64.28
12.89
C5.5
22
30.91
7.44
68.86
10.37
C5.6
13
30.62
6.17
70.92
9.56
C5.7
16
32.5
7
69.25
8.13
C5.9
8
32
7.71
68.62
9.93
C5.11
9
29.22
8.71
65.56
12.24
C5.12
22
31.18
5.46
66.86
7.67
C6.1
13
31.92
12
66.23
16.16
C6.2
16
27.69
7.36
64
8.77
C6.3
16
36.38
8.02
70.19
14.16
8

Paper
Number of
Avg
StDev
Avg
StDev
Candidates
RAW
RAW
USM
USM
C6.4
24
38.38
5.59
69.83
11.05
C7.1
2
-
-
-
-
C7.3
4
-
-
-
-
C7.4
5
-
-
-
-
C7.5
4
-
-
-
-
C7.6
4
-
-
-
-
C8.1
8
36.75
4.8
72.25
8.92
C8.2
6
31.67
9.44
69.5
14.11
C8.3
31
35.1
8.58
68.71
13.09
C8.4
27
31.56
9.19
66.63
12.18
SC1
13
40.23
6.52
76
12.01
SC2
10
31.4
9.67
66.4
14.01
SC3
1
-
-
-
-
SC4
9
27.56
4.5
67.67
7.47
SC5
4
-
-
-
-
CCD
32
-
-
74.69
6.354
COD
7
-
-
74
9.06
CCS1
2
-
-
-
-
CCS2
1
-
-
-
-
CCS3
3
-
-
-
-
The tables that follow give the question statistics for each paper for Mathematics candi-
dates. Data for papers with fewer than six candidates are not included.
Paper C1.1: Model Theory
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
15.9
15.9
6.9
10
0
Q2
7
7
1
0
Q3
18.82
18.82
4.92
11
0
Paper C1.2: G¨
odel’s Incompleteness Theorems
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
11
11
4.24
4
0
Q2
15.67
15.67
6.63
9
0
Q3
12.4
12.4
5.37
5
0
Paper C1.3: Analytic Topology
9

Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
13.05
13.05
3.99
19
0
Q2
11.78
12.41
4.21
17
1
Q3
14.5
14.5
12.02
2
0
Paper C1.4: Axiomatic Set Theory
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
13.57
13.57
4.93
14
0
Q2
10.83
10.83
5.04
6
0
Q3
13.93
13.93
3.85
14
0
Paper C2.1: Lie Algebras
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
17.71
17.71
6.05
7
0
Q2
16.29
16.29
4.61
7
0
Q3
14
17.5
8.92
4
1
Paper C2.2: Homological Algebra
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
13
15.6
7.85
5
1
Q2
13.08
14.45
5.28
11
2
Q3
16.5
16.5
5.81
14
0
Paper C2.4: Infinite Groups
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
8.67
8.67
6.06
6
0
Q2
6.8
6.8
3.11
5
0
Q3
2
2
1
0
Paper C2.6: Introduction to Schemes
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
23
23
3.08
5
0
Q2
22
22
1
0
Q3
22.33
22.33
2.5
6
0
Paper C2.7: Category Theory
10

Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
13.9
14.78
6.72
9
1
Q2
16
16
4.76
10
0
Q3
13.31
14.55
6.74
11
2
Paper C3.1: Algebraic Topology
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
10.11
11.57
6.17
7
2
Q2
9.17
10.25
3.25
4
2
Q3
14
14
2.35
9
0
Paper C3.2: Geometric Group Theory
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
16
16
3.61
3
0
Q2
11.8
11.8
3.35
5
0
Q3
8
8
2.71
4
0
Paper C3.3: Differentiable Manifolds
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
16
16
6.48
4
0
Q2
19.4
22.75
8.02
4
1
Q3
15.67
15.67
5.35
6
0
Paper C3.4: Algebraic Geometry
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
18
18
5.26
14
0
Q2
18.63
18.63
4.24
8
0
Q3
17.83
17.83
2.64
6
0
Paper C3.6: Modular Forms
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
18.6
18.6
4.97
10
0
Q2
19.7
19.7
4.47
10
0
Q3
18.4
20.75
5.81
4
1
11

Paper C3.7: Elliptic Curves
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
19.47
19.47
3.59
17
0
Q2
12.69
13.58
6.2
12
1
Q3
16.56
16.56
3.81
9
0
Paper C3.8: Analytic Number Theory
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
17.44
17.44
3.93
18
0
Q2
14.77
16
6.17
12
1
Q3
11.9
11.9
6.03
10
0
Paper C4.1: Functional Analysis
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
19.06
20.33
7.24
15
1
Q2
12.5
12.5
6.76
12
0
Q3
10.6
10.6
4.22
5
0
Paper C4.2: Linear Operators
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
13.33
13.33
5.69
12
0
Q2
12.22
12.22
4.87
9
0
Q3
8.5
8.5
4.95
2
0
Paper C4.3: Functional Analytical Methods for PDEs
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
15.67
15.67
4.41
6
0
Q2
9
9
8.29
4
0
Q3
8
16
11.31
1
1
Paper C4.5: Ergodic Theory
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
19.6
19.6
5.27
10
0
Q2
14.71
14.71
3.95
7
0
Q3
9.5
9.67
4.51
3
1
12

Paper C5.1: Solid Mechanics
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
17.53
19.23
7.81
13
2
Q2
14.17
19.13
7.93
8
4
Q3
15.85
16.55
5.93
11
2
Paper C5.2: Elasticity and Plasticity
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
12.5
15.33
7.72
3
1
Q2
16.53
17.56
5.22
16
1
Q3
16.13
16.13
4.45
15
0
Paper C5.5: Perturbation Methods
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
14.39
15.06
5.7
17
1
Q2
15.71
16.25
4.63
16
1
Q3
13.75
14.91
4.61
11
1
Paper C5.6: Applied Complex Variables
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
17.33
17.33
1.8
9
0
Q2
12.38
12.38
3.54
8
0
Q3
14.7
15.89
6.38
9
1
Paper C5.7: Topics in Fluid Mechanics
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
15.14
15.14
2.04
7
0
Q2
15.21
15.21
4.15
14
0
Q3
18.27
18.27
4.36
11
0
Paper C5.9: Mathematical Mechanical Biology
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
16
20
9.62
4
1
Q2
12.2
12.2
5.45
5
0
Q3
16.43
16.43
2.99
7
0
13

Paper C5.11: Mathematical Geoscience
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
11.5
11.5
4.8
4
0
Q2
17.22
17.22
4.76
9
0
Q3
12.4
12.4
6.43
5
0
Paper C5.12: Mathematical Physiology
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
16.78
16.78
2.41
18
0
Q2
14.85
14.85
3.48
13
0
Q3
14.69
14.69
4.09
13
0
Paper C6.1: Numerical Linear Algebra
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
13.82
14.8
5.76
10
1
Q2
17.91
17.91
7.45
11
0
Q3
12.29
14
6.24
5
2
Paper C6.2: Continuous Optimization
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
14.38
14.38
4.06
16
0
Q2
12.67
12.67
6.74
6
0
Q3
13.09
13.7
4.64
10
1
Paper C6.3: Approximation of Functions
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
19.2
19.2
4.48
15
0
Q2
17.27
18.77
5.57
13
2
Q3
12.2
12.5
3.7
4
1
Paper C6.4: Finite Element Methods for Partial Differential Equations
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
18.81
19.74
4.26
19
2
Q2
18.62
18.6
3.06
20
1
Q3
17.4
19.33
7.43
9
1
14

Paper C8.1: Stochastic Differential Equations
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
15.5
15.5
3
4
0
Q2
17.25
17.25
2.22
4
0
Q3
20.38
20.38
4.14
8
0
Paper C8.2: Stochastic Analysis and PDEs
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
15.25
15.25
7.37
4
0
Q2
14.8
17
6.42
4
1
Q3
15.25
15.25
5.74
4
0
Paper C8.3: Combinatorics
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
18.6
18.6
4.58
30
0
Q2
16.74
16.74
4.91
23
0
Q3
16.11
16.11
4.91
9
0
Paper C8.4: Probabilistic Combinatorics
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
15.48
15.48
4.76
27
0
Q2
16.27
16.27
4.83
26
0
Q3
11
11
1
0
Paper SC1: Stochastic Models in Mathematical Genetics
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
20
20
2.96
9
0
Q2
21.36
21.36
2.69
11
0
Q3
18
18
5.1
6
0
Paper SC2: Probability and Statistics for Network Analysis
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
15.56
15.56
5.68
9
0
Q2
14.6
18
8.25
8
2
Q3
8.75
10
3.3
3
1
15

Paper SC4: Statistical Data Mining and Machine Learning
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
18
18
2
5
0
Q2
11.71
12.67
3.55
6
1
Q3
11.5
11.71
2.51
7
1
Paper SC5: Advanced Simulation Methods
Question
Mean Mark
Std Dev
Number of attempts
All
Used
Used
Unused
Q1
16.25
16.25
3.1
4
0
Q2
12
12
4.24
2
0
Q3
10.5
10.5
2.12
2
0
16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

6
31

32

33

34

35

36