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Past exam of the mathematics course of the University of Cambridge
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2016
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Course of the University of Cambridge
Mathematics course of the University of Cambridge
Past exam of the mathematics course of the University of Cambridge
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Articles: 734
Table of contents
734
ia
2016
224
Paper 1
ia
40
1A
Paper 1
6
i
1A
1
Solution
i
ii
1A
1
Solution
ii
iii
1A
1
Solution
iii
2C
Paper 1
1
Solution
2C
3D
Paper 1
1
Solution
3D
4F
Paper 1
1
Solution
4F
5A
Paper 1
6
a
5A
1
Solution
a
b
5A
1
Solution
b
c
5A
1
Solution
c
6B
Paper 1
1
Solution
6B
7B
Paper 1
1
Solution
7B
8C
Paper 1
4
a
8C
1
Solution
a
b
8C
1
Solution
b
9E
Paper 1
1
Solution
9E
10E
Paper 1
1
Solution
10E
11D
Paper 1
4
a
11D
1
Solution
a
b
11D
1
Solution
b
12F
Paper 1
1
Solution
12F
Paper 2
ia
73
1A
Paper 2
6
a
1A
1
Solution
a
b
1A
1
Solution
b
c
1A
1
Solution
c
2A
Paper 2
4
a
2A
1
Solution
a
b
2A
1
Solution
b
3F
Paper 2
1
Solution
3F
4F
Paper 2
1
Solution
4F
5A
Paper 2
11
a
5A
1
Solution
a
b
5A
8
i
b
1
Solution
i
ii
b
1
Solution
ii
iii
b
1
Solution
iii
iv
b
1
Solution
iv
6A
Paper 2
7
a
6A
4
i
a
1
Solution
i
ii
a
1
Solution
ii
b
6A
1
Solution
b
7A
Paper 2
6
a
7A
1
Solution
a
b
7A
1
Solution
b
c
7A
1
Solution
c
8A
Paper 2
4
a
8A
1
Solution
a
b
8A
1
Solution
b
9F
Paper 2
1
Solution
9F
10F
Paper 2
8
a
10F
1
Solution
a
b
10F
1
Solution
b
c
10F
1
Solution
c
d
10F
1
Solution
d
11F
Paper 2
6
a
11F
1
Solution
a
b
11F
1
Solution
b
c
11F
1
Solution
c
12F
Paper 2
6
a
12F
1
Solution
a
b
12F
1
Solution
b
c
12F
1
Solution
c
Paper 3
ia
51
1D
Paper 3
4
i
1D
1
Solution
i
ii
1D
1
Solution
ii
2D
Paper 3
1
Solution
2D
3C
Paper 3
1
Solution
3C
4C
Paper 3
1
Solution
4C
5D
Paper 3
10
i
5D
1
Solution
i
ii
5D
1
Solution
ii
iii
5D
1
Solution
iii
iv
5D
1
Solution
iv
v
5D
1
Solution
v
6D
Paper 3
1
Solution
6D
7D
Paper 3
1
Solution
7D
8D
Paper 3
1
Solution
8D
9C
Paper 3
4
a
9C
1
Solution
a
b
9C
1
Solution
b
10C
Paper 3
1
Solution
10C
11C
Paper 3
6
a
11C
1
Solution
a
b
11C
1
Solution
b
c
11C
1
Solution
c
12C
Paper 3
8
a
12C
1
Solution
a
b
12C
1
Solution
b
c
12C
1
Solution
c
d
12C
1
Solution
d
Paper 4
ia
56
1E
Paper 4
1
Solution
1E
2E
Paper 4
1
Solution
2E
3B
Paper 4
14
i
3B
1
Solution
i
ii
3B
1
Solution
ii
iii
3B
1
Solution
iii
iv
3B
1
Solution
iv
v
3B
1
Solution
v
vi
3B
1
Solution
vi
vii
3B
1
Solution
vii
4B
Paper 4
1
Solution
4B
5E
Paper 4
9
a
5E
1
Solution
a
b
5E
6
i
b
1
Solution
i
ii
b
1
Solution
ii
iii
b
1
Solution
iii
6E
Paper 4
1
Solution
6E
7E
Paper 4
1
Solution
7E
8E
Paper 4
4
a
8E
1
Solution
a
b
8E
1
Solution
b
9B
Paper 4
6
a
9B
1
Solution
a
b
9B
1
Solution
b
c
9B
1
Solution
c
10B
Paper 4
1
Solution
10B
11B
Paper 4
4
a
11B
1
Solution
a
b
11B
1
Solution
b
12B
Paper 4
1
Solution
12B
ib
2016
508
Paper 1
ib
142
1F
Paper 1
4
a
1F
1
Solution
a
b
1F
1
Solution
b
2A
Paper 1
1
Solution
2A
3F
Paper 1
8
a
3F
1
Solution
a
b
3F
1
Solution
b
c
3F
1
Solution
c
d
3F
1
Solution
d
4C
Paper 1
4
a
4C
1
Solution
a
b
4C
1
Solution
b
5C
Paper 1
4
a
5C
1
Solution
a
b
5C
1
Solution
b
6D
Paper 1
4
a
6D
1
Solution
a
b
6D
1
Solution
b
7H
Paper 1
1
Solution
7H
8H
Paper 1
1
Solution
8H
9F
Paper 1
8
a
9F
1
Solution
a
b
9F
1
Solution
b
c
9F
1
Solution
c
d
9F
1
Solution
d
10E
Paper 1
6
a
10E
1
Solution
a
b
10E
1
Solution
b
c
10E
1
Solution
c
11G
Paper 1
15
a
11G
1
Solution
a
b
11G
10
i
b
1
Solution
i
ii
b
1
Solution
ii
iii
b
1
Solution
iii
iv
b
1
Solution
iv
v
b
1
Solution
v
c
11G
1
Solution
c
12E
Paper 1
1
Solution
12E
13A
Paper 1
6
a
13A
1
Solution
a
b
13A
1
Solution
b
c
13A
1
Solution
c
14A
Paper 1
9
a
14A
1
Solution
a
b
14A
6
i
b
1
Solution
i
ii
b
1
Solution
ii
iii
b
1
Solution
iii
15B
Paper 1
7
a
15B
4
i
a
1
Solution
i
ii
a
1
Solution
ii
b
15B
1
Solution
b
16D
Paper 1
12
a
16D
1
Solution
a
b
16D
1
Solution
b
c
16D
1
Solution
c
d
16D
1
Solution
d
e
16D
1
Solution
e
f
16D
1
Solution
f
17C
Paper 1
11
a
17C
1
Solution
a
b
17C
1
Solution
b
c
17C
6
i
c
1
Solution
i
ii
c
1
Solution
ii
iii
c
1
Solution
iii
18D
Paper 1
8
a
18D
1
Solution
a
b
18D
1
Solution
b
c
18D
1
Solution
c
d
18D
1
Solution
d
19H
Paper 1
6
a
19H
1
Solution
a
b
19H
1
Solution
b
c
19H
1
Solution
c
20H
Paper 1
6
a
20H
1
Solution
a
b
20H
1
Solution
b
c
20H
1
Solution
c
Paper 2
ib
120
1F
Paper 2
1
Solution
1F
2E
Paper 2
1
Solution
2E
3G
Paper 2
6
a
3G
1
Solution
a
b
3G
1
Solution
b
c
3G
1
Solution
c
4E
Paper 2
4
a
4E
1
Solution
a
b
4E
1
Solution
b
5A
Paper 2
1
Solution
5A
6D
Paper 2
6
a
6D
1
Solution
a
b
6D
1
Solution
b
c
6D
1
Solution
c
7C
Paper 2
6
a
7C
1
Solution
a
b
7C
1
Solution
b
c
7C
1
Solution
c
8H
Paper 2
1
Solution
8H
9H
Paper 2
1
Solution
9H
10F
Paper 2
6
a
10F
1
Solution
a
b
10F
1
Solution
b
c
10F
1
Solution
c
11E
Paper 2
6
a
11E
1
Solution
a
b
11E
1
Solution
b
c
11E
1
Solution
c
12G
Paper 2
6
a
12G
1
Solution
a
b
12G
1
Solution
b
c
12G
1
Solution
c
13A
Paper 2
1
Solution
13A
14F
Paper 2
6
a
14F
1
Solution
a
b
14F
1
Solution
b
c
14F
1
Solution
c
15C
Paper 2
6
a
15C
1
Solution
a
b
15C
1
Solution
b
c
15C
1
Solution
c
16A
Paper 2
4
a
16A
1
Solution
a
b
16A
1
Solution
b
17B
Paper 2
12
a
17B
1
Solution
a
b
17B
1
Solution
b
c
17B
1
Solution
c
d
17B
1
Solution
d
e
17B
1
Solution
e
f
17B
1
Solution
f
18D
Paper 2
8
a
18D
1
Solution
a
b
18D
1
Solution
b
c
18D
1
Solution
c
d
18D
1
Solution
d
19D
Paper 2
9
a
19D
1
Solution
a
b
19D
1
Solution
b
c
19D
4
i
c
1
Solution
i
ii
c
1
Solution
ii
20H
Paper 2
9
a
20H
1
Solution
a
b
20H
6
i
b
1
Solution
i
ii
b
1
Solution
ii
iii
b
1
Solution
iii
Paper 3
ib
121
1E
Paper 3
1
Solution
1E
2G
Paper 3
11
a
2G
1
Solution
a
b
2G
8
i
b
1
Solution
i
ii
b
1
Solution
ii
iii
b
1
Solution
iii
iv
b
1
Solution
iv
3E
Paper 3
1
Solution
3E
4A
Paper 3
1
Solution
4A
5F
Paper 3
4
a
5F
1
Solution
a
b
5F
1
Solution
b
6C
Paper 3
1
Solution
6C
7A
Paper 3
1
Solution
7A
8B
Paper 3
4
a
8B
1
Solution
a
b
8B
1
Solution
b
9H
Paper 3
1
Solution
9H
10F
Paper 3
6
i
10F
1
Solution
i
ii
10F
1
Solution
ii
iii
10F
1
Solution
iii
11E
Paper 3
6
a
11E
1
Solution
a
b
11E
1
Solution
b
c
11E
1
Solution
c
12G
Paper 3
6
a
12G
1
Solution
a
b
12G
1
Solution
b
c
12G
1
Solution
c
13G
Paper 3
6
a
13G
1
Solution
a
b
13G
1
Solution
b
c
13G
1
Solution
c
14F
Paper 3
6
a
14F
1
Solution
a
b
14F
1
Solution
b
c
14F
1
Solution
c
15B
Paper 3
6
a
15B
1
Solution
a
b
15B
1
Solution
b
c
15B
1
Solution
c
16B
Paper 3
4
a
16B
1
Solution
a
b
16B
1
Solution
b
17D
Paper 3
13
a
17D
1
Solution
a
b
17D
10
i
b
1
Solution
i
ii
b
1
Solution
ii
iii
b
1
Solution
iii
iv
b
1
Solution
iv
v
b
1
Solution
v
18C
Paper 3
6
a
18C
1
Solution
a
b
18C
1
Solution
b
c
18C
1
Solution
c
19D
Paper 3
6
a
19D
1
Solution
a
b
19D
1
Solution
b
c
19D
1
Solution
c
20H
Paper 3
6
a
20H
1
Solution
a
b
20H
1
Solution
b
c
20H
1
Solution
c
21H
Paper 3
4
a
21H
1
Solution
a
b
21H
1
Solution
b
Paper 4
ib
121
1F
Paper 4
1
Solution
1F
2E
Paper 4
1
Solution
2E
3G
Paper 4
6
a
3G
1
Solution
a
b
3G
1
Solution
b
c
3G
1
Solution
c
4G
Paper 4
1
Solution
4G
5A
Paper 4
1
Solution
5A
6B
Paper 4
8
a
6B
1
Solution
a
b
6B
1
Solution
b
c
6B
1
Solution
c
d
6B
1
Solution
d
7D
Paper 4
9
a
7D
1
Solution
a
b
7D
6
i
b
1
Solution
i
ii
b
1
Solution
ii
iii
b
1
Solution
iii
8D
Paper 4
4
a
8D
1
Solution
a
b
8D
1
Solution
b
9H
Paper 4
4
a
9H
1
Solution
a
b
9H
1
Solution
b
10F
Paper 4
4
a
10F
1
Solution
a
b
10F
1
Solution
b
11E
Paper 4
6
a
11E
1
Solution
a
b
11E
1
Solution
b
c
11E
1
Solution
c
12G
Paper 4
6
a
12G
1
Solution
a
b
12G
1
Solution
b
c
12G
1
Solution
c
13E
Paper 4
7
a
13E
1
Solution
a
b
13E
4
i
b
1
Solution
i
ii
b
1
Solution
ii
14A
Paper 4
11
a
14A
1
Solution
a
b
14A
1
Solution
b
c
14A
6
i
c
1
Solution
i
ii
c
1
Solution
ii
iii
c
1
Solution
iii
15F
Paper 4
6
a
15F
1
Solution
a
b
15F
1
Solution
b
c
15F
1
Solution
c
16C
Paper 4
6
a
16C
1
Solution
a
b
16C
1
Solution
b
c
16C
1
Solution
c
17B
Paper 4
4
a
17B
1
Solution
a
b
17B
1
Solution
b
18C
Paper 4
8
a
18C
1
Solution
a
b
18C
1
Solution
b
c
18C
1
Solution
c
d
18C
1
Solution
d
19H
Paper 4
4
a
19H
1
Solution
a
b
19H
1
Solution
b
20H
Paper 4
4
a
20H
1
Solution
a
b
20H
1
Solution
b
Ancestors
(6)
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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