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Past exam of the mathematics course of the University of Cambridge
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2009
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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
2009
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Articles: 587
Table of contents
587
Paper 1
ii
156
1G
Paper 1
1
Solution
1G
2F
Paper 1
4
i
2F
1
Solution
i
ii
2F
1
Solution
ii
3F
Paper 1
1
Solution
3F
4H
Paper 1
6
i
4H
1
Solution
i
ii
4H
1
Solution
ii
iii
4H
1
Solution
iii
5I
Paper 1
1
Solution
5I
6A
Paper 1
1
Solution
6A
7E
Paper 1
1
Solution
7E
8B
Paper 1
1
Solution
8B
9E
Paper 1
1
Solution
9E
10D
Paper 1
1
Solution
10D
11F
Paper 1
1
Solution
11F
12H
Paper 1
6
i
12H
1
Solution
i
ii
12H
1
Solution
ii
iii
12H
1
Solution
iii
13I
Paper 1
1
Solution
13I
14B
Paper 1
1
Solution
14B
15D
Paper 1
4
i
15D
1
Solution
i
ii
15D
1
Solution
ii
16G
Paper 1
1
Solution
16G
17F
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6
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17F
1
Solution
i
ii
17F
1
Solution
ii
iii
17F
1
Solution
iii
18H
Paper 1
1
Solution
18H
19F
Paper 1
1
Solution
19F
20H
Paper 1
6
i
20H
1
Solution
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ii
20H
1
Solution
ii
iii
20H
1
Solution
iii
21G
Paper 1
1
Solution
21G
22H
Paper 1
6
a
22H
1
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a
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22H
1
Solution
b
c
22H
1
Solution
c
23G
Paper 1
4
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23G
1
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a
b
23G
1
Solution
b
24G
Paper 1
1
Solution
24G
25H
Paper 1
8
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25H
1
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i
ii
25H
1
Solution
ii
iii
25H
1
Solution
iii
iv
25H
1
Solution
iv
26J
Paper 1
1
Solution
26J
27J
Paper 1
6
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27J
1
Solution
a
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27J
1
Solution
b
c
27J
1
Solution
c
28I
Paper 1
6
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1
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ii
28I
1
Solution
ii
iii
28I
1
Solution
iii
29J
Paper 1
6
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29J
1
Solution
a
b
29J
1
Solution
b
c
29J
1
Solution
c
30B
Paper 1
8
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30B
1
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ii
30B
1
Solution
ii
iii
30B
1
Solution
iii
iv
30B
1
Solution
iv
31A
Paper 1
1
Solution
31A
32B
Paper 1
1
Solution
32B
33C
Paper 1
1
Solution
33C
34D
Paper 1
1
Solution
34D
35C
Paper 1
6
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35C
1
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35C
1
Solution
ii
iii
35C
1
Solution
iii
36D
Paper 1
1
Solution
36D
37E
Paper 1
4
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37E
1
Solution
i
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37E
1
Solution
ii
38A
Paper 1
1
Solution
38A
39B
Paper 1
8
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39B
1
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39B
1
Solution
ii
iii
39B
1
Solution
iii
iv
39B
1
Solution
iv
Paper 2
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149
1G
Paper 2
1
Solution
1G
2F
Paper 2
4
a
2F
1
Solution
a
b
2F
1
Solution
b
3F
Paper 2
1
Solution
3F
4H
Paper 2
1
Solution
4H
5I
Paper 2
1
Solution
5I
6A
Paper 2
1
Solution
6A
7E
Paper 2
4
i
7E
1
Solution
i
ii
7E
1
Solution
ii
8B
Paper 2
4
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8B
1
Solution
i
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8B
1
Solution
ii
9E
Paper 2
1
Solution
9E
10D
Paper 2
4
a
10D
1
Solution
a
b
10D
1
Solution
b
11F
Paper 2
6
a
11F
1
Solution
a
b
11F
1
Solution
b
c
11F
1
Solution
c
12H
Paper 2
1
Solution
12H
13A
Paper 2
1
Solution
13A
14C
Paper 2
4
i
14C
1
Solution
i
ii
14C
1
Solution
ii
15E
Paper 2
4
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15E
1
Solution
i
ii
15E
1
Solution
ii
16G
Paper 2
4
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16G
1
Solution
i
ii
16G
1
Solution
ii
17F
Paper 2
4
i
17F
1
Solution
i
ii
17F
1
Solution
ii
18H
Paper 2
1
Solution
18H
19F
Paper 2
6
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19F
1
Solution
i
ii
19F
1
Solution
ii
iii
19F
1
Solution
iii
20H
Paper 2
6
i
20H
1
Solution
i
ii
20H
1
Solution
ii
iii
20H
1
Solution
iii
21G
Paper 2
1
Solution
21G
22H
Paper 2
6
a
22H
1
Solution
a
b
22H
1
Solution
b
c
22H
1
Solution
c
23G
Paper 2
4
a
23G
1
Solution
a
b
23G
1
Solution
b
24G
Paper 2
1
Solution
24G
25H
Paper 2
6
a
25H
1
Solution
a
b
25H
1
Solution
b
c
25H
1
Solution
c
26J
Paper 2
1
Solution
26J
27J
Paper 2
4
a
27J
1
Solution
a
b
27J
1
Solution
b
28I
Paper 2
1
Solution
28I
29I
Paper 2
1
Solution
29I
30J
Paper 2
1
Solution
30J
31B
Paper 2
7
a
31B
1
Solution
a
b
31B
1
Solution
b
c
31B
2
x
c
1
Solution
x
32B
Paper 2
1
Solution
32B
33C
Paper 2
1
Solution
33C
34D
Paper 2
1
Solution
34D
35D
Paper 2
6
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35D
1
Solution
i
ii
35D
1
Solution
ii
iii
35D
1
Solution
iii
36D
Paper 2
1
Solution
36D
37E
Paper 2
1
Solution
37E
38A
Paper 2
1
Solution
38A
39B
Paper 2
6
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39B
1
Solution
i
ii
39B
1
Solution
ii
iii
39B
1
Solution
iii
Paper 3
ii
148
1G
Paper 3
1
Solution
1G
2F
Paper 3
4
a
2F
1
Solution
a
b
2F
1
Solution
b
3F
Paper 3
1
Solution
3F
4H
Paper 3
1
Solution
4H
5I
Paper 3
1
Solution
5I
6A
Paper 3
1
Solution
6A
7E
Paper 3
1
Solution
7E
8B
Paper 3
1
Solution
8B
9E
Paper 3
4
a
9E
1
Solution
a
b
9E
1
Solution
b
10D
Paper 3
4
a
10D
1
Solution
a
b
10D
1
Solution
b
11G
Paper 3
1
Solution
11G
12F
Paper 3
6
a
12F
1
Solution
a
b
12F
1
Solution
b
c
12F
1
Solution
c
13A
Paper 3
1
Solution
13A
14E
Paper 3
6
i
14E
1
Solution
i
ii
14E
1
Solution
ii
iii
14E
1
Solution
iii
15D
Paper 3
4
i
15D
1
Solution
i
ii
15D
1
Solution
ii
16G
Paper 3
1
Solution
16G
17F
Paper 3
6
a
17F
1
Solution
a
b
17F
1
Solution
b
c
17F
1
Solution
c
18H
Paper 3
1
Solution
18H
19F
Paper 3
6
i
19F
1
Solution
i
ii
19F
1
Solution
ii
iii
19F
1
Solution
iii
20G
Paper 3
4
i
20G
1
Solution
i
ii
20G
1
Solution
ii
21H
Paper 3
6
a
21H
1
Solution
a
b
21H
1
Solution
b
c
21H
1
Solution
c
22G
Paper 3
4
i
22G
1
Solution
i
ii
22G
1
Solution
ii
23G
Paper 3
1
Solution
23G
24H
Paper 3
4
a
24H
1
Solution
a
b
24H
1
Solution
b
25J
Paper 3
1
Solution
25J
26J
Paper 3
6
a
26J
1
Solution
a
b
26J
1
Solution
b
c
26J
1
Solution
c
27I
Paper 3
1
Solution
27I
28I
Paper 3
1
Solution
28I
29J
Paper 3
1
Solution
29J
30B
Paper 3
8
a
30B
1
Solution
a
b
30B
1
Solution
b
c
30B
1
Solution
c
d
30B
1
Solution
d
31A
Paper 3
1
Solution
31A
32B
Paper 3
4
i
32B
1
Solution
i
ii
32B
1
Solution
ii
33C
Paper 3
4
i
33C
1
Solution
i
ii
33C
1
Solution
ii
34D
Paper 3
1
Solution
34D
35D
Paper 3
6
i
35D
1
Solution
i
ii
35D
1
Solution
ii
iii
35D
1
Solution
iii
36C
Paper 3
1
Solution
36C
37E
Paper 3
1
Solution
37E
38A
Paper 3
1
Solution
38A
39B
Paper 3
2
k
39B
1
Solution
k
Paper 4
ii
130
1G
Paper 4
1
Solution
1G
2F
Paper 4
1
Solution
2F
3F
Paper 4
1
Solution
3F
4H
Paper 4
8
i
4H
1
Solution
i
ii
4H
1
Solution
ii
iii
4H
1
Solution
iii
iv
4H
1
Solution
iv
5I
Paper 4
1
Solution
5I
6A
Paper 4
1
Solution
6A
7E
Paper 4
1
Solution
7E
8D
Paper 4
1
Solution
8D
9E
Paper 4
4
a
9E
1
Solution
a
b
9E
1
Solution
b
10D
Paper 4
4
a
10D
1
Solution
a
b
10D
1
Solution
b
11G
Paper 4
1
Solution
11G
12F
Paper 4
2
ii
12F
1
Solution
ii
13I
Paper 4
1
Solution
13I
14E
Paper 4
1
Solution
14E
15E
Paper 4
1
Solution
15E
16G
Paper 4
1
Solution
16G
17F
Paper 4
1
Solution
17F
18H
Paper 4
6
a
18H
1
Solution
a
b
18H
1
Solution
b
c
18H
1
Solution
c
19F
Paper 4
6
a
19F
1
Solution
a
b
19F
1
Solution
b
c
19F
1
Solution
c
20H
Paper 4
1
Solution
20H
21G
Paper 4
1
Solution
21G
22H
Paper 4
8
a
22H
1
Solution
a
b
22H
1
Solution
b
c
22H
1
Solution
c
d
22H
1
Solution
d
23G
Paper 4
1
Solution
23G
24H
Paper 4
6
a
24H
1
Solution
a
b
24H
1
Solution
b
c
24H
1
Solution
c
25J
Paper 4
1
Solution
25J
26J
Paper 4
4
a
26J
1
Solution
a
b
26J
1
Solution
b
27I
Paper 4
1
Solution
27I
28I
Paper 4
4
a
28I
1
Solution
a
b
28I
1
Solution
b
29J
Paper 4
1
Solution
29J
30B
Paper 4
1
Solution
30B
31A
Paper 4
1
Solution
31A
32C
Paper 4
1
Solution
32C
33D
Paper 4
1
Solution
33D
34D
Paper 4
8
i
34D
1
Solution
i
ii
34D
1
Solution
ii
iii
34D
1
Solution
iii
iv
34D
1
Solution
iv
35C
Paper 4
1
Solution
35C
36D
Paper 4
1
Solution
36D
37E
Paper 4
1
Solution
37E
38A
Paper 4
1
Solution
38A
39B
Paper 4
4
a
39B
1
Solution
a
b
39B
1
Solution
b
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Ancestors
(7)
2009
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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