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Past exam of the mathematics course of the University of Cambridge
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2017
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ii
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University of Cambridge
Course of the University of Cambridge
Mathematics course of the University of Cambridge
Past exam of the mathematics course of the University of Cambridge
2017
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Articles: 776
Table of contents
776
Paper 1
ii
176
1G
Paper 1
1
Solution
1G
2F
Paper 1
1
Solution
2F
3G
Paper 1
1
Solution
3G
4H
Paper 1
4
a
4H
1
Solution
a
b
4H
1
Solution
b
5J
Paper 1
6
i
5J
1
Solution
i
ii
5J
1
Solution
ii
iii
5J
1
Solution
iii
6B
Paper 1
1
Solution
6B
7E
Paper 1
1
Solution
7E
8E
Paper 1
1
Solution
8E
9C
Paper 1
1
Solution
9C
10G
Paper 1
4
i
10G
1
Solution
i
ii
10G
1
Solution
ii
11H
Paper 1
4
a
11H
1
Solution
a
b
11H
1
Solution
b
12J
Paper 1
1
Solution
12J
13E
Paper 1
1
Solution
13E
14C
Paper 1
1
Solution
14C
15H
Paper 1
1
Solution
15H
16H
Paper 1
1
Solution
16H
17I
Paper 1
7
a
17I
1
Solution
a
b
17I
4
i
b
1
Solution
i
ii
b
1
Solution
ii
18G
Paper 1
11
a
18G
1
Solution
a
b
18G
6
i
b
1
Solution
i
ii
b
1
Solution
ii
iii
b
1
Solution
iii
c
18G
1
Solution
c
19H
Paper 1
8
a
19H
1
Solution
a
b
19H
1
Solution
b
c
19H
1
Solution
c
d
19H
1
Solution
d
20I
Paper 1
10
a
20I
1
Solution
a
b
20I
1
Solution
b
c
20I
1
Solution
c
d
20I
1
Solution
d
e
20I
1
Solution
e
21F
Paper 1
6
a
21F
1
Solution
a
b
21F
1
Solution
b
c
21F
1
Solution
c
22F
Paper 1
10
a
22F
1
Solution
a
k
22F
1
Solution
k
b
22F
1
Solution
b
c
22F
1
Solution
c
d
22F
1
Solution
d
23F
Paper 1
1
Solution
23F
24I
Paper 1
8
a
24I
1
Solution
a
b
24I
1
Solution
b
c
24I
1
Solution
c
d
24I
1
Solution
d
25I
Paper 1
1
Solution
25I
26J
Paper 1
10
a
26J
1
Solution
a
b
26J
1
Solution
b
c
26J
1
Solution
c
d
26J
1
Solution
d
e
26J
1
Solution
e
27K
Paper 1
6
a
27K
1
Solution
a
b
27K
1
Solution
b
c
27K
1
Solution
c
28K
Paper 1
7
a
28K
1
Solution
a
b
28K
4
ii
b
1
Solution
ii
iii
b
1
Solution
iii
29J
Paper 1
6
a
29J
1
Solution
a
b
29J
1
Solution
b
c
29J
1
Solution
c
30A
Paper 1
4
a
30A
1
Solution
a
b
30A
1
Solution
b
31A
Paper 1
1
Solution
31A
32C
Paper 1
1
Solution
32C
33C
Paper 1
1
Solution
33C
34D
Paper 1
1
Solution
34D
35D
Paper 1
1
Solution
35D
36D
Paper 1
1
Solution
36D
37B
Paper 1
1
Solution
37B
38B
Paper 1
4
i
38B
1
Solution
i
ii
38B
1
Solution
ii
39A
Paper 1
1
Solution
39A
Paper 2
ii
194
1G
Paper 2
1
Solution
1G
2F
Paper 2
6
i
2F
1
Solution
i
ii
2F
1
Solution
ii
iii
2F
1
Solution
iii
3G
Paper 2
1
Solution
3G
4H
Paper 2
10
a
4H
4
i
a
1
Solution
i
ii
a
1
Solution
ii
b
4H
4
i
b
1
Solution
i
ii
b
1
Solution
ii
5J
Paper 2
4
a
5J
1
Solution
a
b
5J
1
Solution
b
6B
Paper 2
1
Solution
6B
7E
Paper 2
1
Solution
7E
8E
Paper 2
1
Solution
8E
9C
Paper 2
1
Solution
9C
10F
Paper 2
1
Solution
10F
11G
Paper 2
1
Solution
11G
12E
Paper 2
1
Solution
12E
13E
Paper 2
1
Solution
13E
14H
Paper 2
10
i
14H
1
Solution
i
ii
14H
1
Solution
ii
iii
14H
1
Solution
iii
iv
14H
1
Solution
iv
v
14H
1
Solution
v
15H
Paper 2
1
Solution
15H
16I
Paper 2
6
a
16I
1
Solution
a
b
16I
1
Solution
b
c
16I
1
Solution
c
17G
Paper 2
4
a
17G
1
Solution
a
b
17G
1
Solution
b
18H
Paper 2
4
a
18H
1
Solution
a
b
18H
1
Solution
b
19I
Paper 2
15
a
19I
2
ii
a
1
Solution
ii
b
19I
4
i
b
1
Solution
i
ii
b
1
Solution
ii
c
19I
6
i
c
1
Solution
i
ii
c
1
Solution
ii
iii
c
1
Solution
iii
20F
Paper 2
6
a
20F
1
Solution
a
b
20F
1
Solution
b
c
20F
1
Solution
c
21F
Paper 2
1
Solution
21F
22I
Paper 2
6
a
22I
1
Solution
a
b
22I
1
Solution
b
c
22I
1
Solution
c
23I
Paper 2
1
Solution
23I
24J
Paper 2
10
a
24J
1
Solution
a
b
24J
1
Solution
b
c
24J
1
Solution
c
d
24J
1
Solution
d
e
24J
1
Solution
e
25K
Paper 2
4
a
25K
1
Solution
a
b
25K
1
Solution
b
26K
Paper 2
8
a
26K
1
Solution
a
b
26K
1
Solution
b
c
26K
1
Solution
c
d
26K
1
Solution
d
27J
Paper 2
8
a
27J
1
Solution
a
b
27J
1
Solution
b
d
27J
1
Solution
d
c
27J
1
Solution
c
28K
Paper 2
6
a
28K
1
Solution
a
b
28K
1
Solution
b
c
28K
1
Solution
c
29E
Paper 2
4
i
29E
1
Solution
i
ii
29E
1
Solution
ii
30A
Paper 2
6
a
30A
1
Solution
a
b
30A
1
Solution
b
c
30A
1
Solution
c
31A
Paper 2
1
Solution
31A
32C
Paper 2
1
Solution
32C
33C
Paper 2
1
Solution
33C
34D
Paper 2
9
a
34D
1
Solution
a
b
34D
6
i
b
1
Solution
i
ii
b
1
Solution
ii
iii
b
1
Solution
iii
35D
Paper 2
4
a
35D
1
Solution
a
b
35D
1
Solution
b
36B
Paper 2
1
Solution
36B
37B
Paper 2
1
Solution
37B
38A
Paper 2
8
i
38A
1
Solution
i
ii
38A
1
Solution
ii
iii
38A
1
Solution
iii
iv
38A
1
Solution
iv
Paper 3
ii
182
1G
Paper 3
1
Solution
1G
2F
Paper 3
6
a
2F
1
Solution
a
b
2F
1
Solution
b
c
2F
1
Solution
c
3G
Paper 3
1
Solution
3G
4H
Paper 3
6
a
4H
1
Solution
a
b
4H
1
Solution
b
c
4H
1
Solution
c
5J
Paper 3
1
Solution
5J
6B
Paper 3
1
Solution
6B
7E
Paper 3
1
Solution
7E
8E
Paper 3
1
Solution
8E
9C
Paper 3
4
a
9C
1
Solution
a
b
9C
1
Solution
b
10G
Paper 3
8
a
10G
1
Solution
a
b
10G
1
Solution
b
c
10G
1
Solution
c
d
10G
1
Solution
d
11H
Paper 3
6
a
11H
1
Solution
a
b
11H
1
Solution
b
c
11H
1
Solution
c
12B
Paper 3
1
Solution
12B
13C
Paper 3
4
a
13C
1
Solution
a
b
13C
1
Solution
b
14H
Paper 3
1
Solution
14H
15H
Paper 3
1
Solution
15H
16I
Paper 3
9
a
16I
1
Solution
a
b
16I
6
i
b
1
Solution
i
ii
b
1
Solution
ii
iii
b
1
Solution
iii
17G
Paper 3
6
a
17G
1
Solution
a
b
17G
1
Solution
b
c
17G
1
Solution
c
18I
Paper 3
1
Solution
18I
19F
Paper 3
8
i
19F
1
Solution
i
ii
19F
1
Solution
ii
iii
19F
1
Solution
iii
iv
19F
1
Solution
iv
20F
Paper 3
8
i
20F
1
Solution
i
ii
20F
1
Solution
ii
iii
20F
1
Solution
iii
iv
20F
1
Solution
iv
21F
Paper 3
1
Solution
21F
22I
Paper 3
6
a
22I
1
Solution
a
b
22I
1
Solution
b
c
22I
1
Solution
c
23I
Paper 3
1
Solution
23I
24J
Paper 3
8
a
24J
1
Solution
a
b
24J
1
Solution
b
c
24J
1
Solution
c
d
24J
1
Solution
d
25K
Paper 3
4
a
25K
1
Solution
a
b
25K
1
Solution
b
26K
Paper 3
8
a
26K
1
Solution
a
b
26K
1
Solution
b
c
26K
1
Solution
c
d
26K
1
Solution
d
27J
Paper 3
6
a
27J
1
Solution
a
b
27J
1
Solution
b
c
27J
1
Solution
c
28K
Paper 3
1
Solution
28K
29E
Paper 3
1
Solution
29E
30A
Paper 3
1
Solution
30A
31A
Paper 3
1
Solution
31A
32C
Paper 3
1
Solution
32C
33C
Paper 3
1
Solution
33C
34D
Paper 3
11
a
34D
1
Solution
a
b
34D
8
i
b
1
Solution
i
ii
b
1
Solution
ii
iii
b
1
Solution
iii
iv
b
1
Solution
iv
35D
Paper 3
1
Solution
35D
36D
Paper 3
8
i
36D
1
Solution
i
ii
36D
1
Solution
ii
iii
36D
1
Solution
iii
iv
36D
1
Solution
iv
37B
Paper 3
1
Solution
37B
38B
Paper 3
1
Solution
38B
39A
Paper 3
6
i
39A
1
Solution
i
ii
39A
1
Solution
ii
iii
39A
1
Solution
iii
Paper 4
ii
220
1G
Paper 4
1
Solution
1G
2F
Paper 4
1
Solution
2F
3G
Paper 4
1
Solution
3G
4H
Paper 4
4
a
4H
1
Solution
a
b
4H
1
Solution
b
5J
Paper 4
8
a
5J
1
Solution
a
b
5J
1
Solution
b
c
5J
1
Solution
c
d
5J
1
Solution
d
6B
Paper 4
1
Solution
6B
7E
Paper 4
1
Solution
7E
8E
Paper 4
1
Solution
8E
9C
Paper 4
4
a
9C
1
Solution
a
b
9C
1
Solution
b
10G
Paper 4
6
a
10G
1
Solution
a
b
10G
1
Solution
b
c
10G
1
Solution
c
11F
Paper 4
10
a
11F
1
Solution
a
b
11F
1
Solution
b
c
11F
1
Solution
c
d
11F
1
Solution
d
e
11F
1
Solution
e
12J
Paper 4
8
a
12J
1
Solution
a
b
12J
1
Solution
b
c
12J
1
Solution
c
d
12J
1
Solution
d
13B
Paper 4
1
Solution
13B
14E
Paper 4
1
Solution
14E
15H
Paper 4
1
Solution
15H
16H
Paper 4
8
i
16H
1
Solution
i
ii
16H
1
Solution
ii
iii
16H
1
Solution
iii
iv
16H
1
Solution
iv
17I
Paper 4
6
a
17I
1
Solution
a
b
17I
1
Solution
b
c
17I
1
Solution
c
18G
Paper 4
6
a
18G
1
Solution
a
b
18G
1
Solution
b
c
18G
1
Solution
c
19H
Paper 4
4
a
19H
1
Solution
a
b
19H
1
Solution
b
20I
Paper 4
8
a
20I
1
Solution
a
b
20I
1
Solution
b
c
20I
1
Solution
c
d
20I
1
Solution
d
21F
Paper 4
6
i
21F
1
Solution
i
ii
21F
1
Solution
ii
iii
21F
1
Solution
iii
22F
Paper 4
8
i
22F
1
Solution
i
ii
22F
1
Solution
ii
iii
22F
1
Solution
iii
iv
22F
1
Solution
iv
23I
Paper 4
6
a
23I
1
Solution
a
b
23I
1
Solution
b
c
23I
1
Solution
c
24I
Paper 4
6
i
24I
1
Solution
i
ii
24I
1
Solution
ii
iii
24I
1
Solution
iii
25J
Paper 4
11
a
25J
1
Solution
a
b
25J
1
Solution
b
c
25J
1
Solution
c
d
25J
4
i
d
1
Solution
i
ii
d
1
Solution
ii
26K
Paper 4
4
a
26K
1
Solution
a
b
26K
1
Solution
b
27K
Paper 4
11
a
27K
1
Solution
a
b
27K
1
Solution
b
c
27K
4
i
c
1
Solution
i
ii
c
1
Solution
ii
d
27K
1
Solution
d
28J
Paper 4
6
a
28J
1
Solution
a
b
28J
1
Solution
b
c
28J
1
Solution
c
29K
Paper 4
1
Solution
29K
30E
Paper 4
1
Solution
30E
31A
Paper 4
5
a
31A
2
i
a
1
Solution
i
b
31A
1
Solution
b
32C
Paper 4
1
Solution
32C
33C
Paper 4
12
a
33C
4
i
a
1
Solution
i
ii
a
1
Solution
ii
b
33C
6
i
b
1
Solution
i
ii
b
1
Solution
ii
iii
b
1
Solution
iii
34D
Paper 4
8
i
34D
1
Solution
i
ii
34D
1
Solution
ii
iii
34D
1
Solution
iii
iv
34D
1
Solution
iv
35D
Paper 4
1
Solution
35D
36D
Paper 4
4
a
36D
1
Solution
a
b
36D
1
Solution
b
37B
Paper 4
1
Solution
37B
38B
Paper 4
4
i
38B
1
Solution
i
ii
38B
1
Solution
ii
39A
Paper 4
4
a
39A
1
Solution
a
b
39A
1
Solution
b
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Ancestors
(7)
2017
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
List of universities
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