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Past exam of the mathematics course of the University of Cambridge
/
2020
/
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
2020
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Articles: 1k
Table of contents
1k
Paper 1
ii
266
1H
Paper 1
1
Solution
1H
2H
Paper 1
6
i
2H
1
Solution
i
ii
2H
1
Solution
ii
iii
2H
1
Solution
iii
3I
Paper 1
9
a
3I
1
Solution
a
b
3I
6
i
b
1
ii
b
1
iii
b
1
4F
Paper 1
1
Solution
4F
5J
Paper 1
8
a
5J
1
Solution
a
b
5J
1
Solution
b
n
5J
1
Solution
n
c
5J
1
Solution
c
6B
Paper 1
6
i
6B
1
Solution
i
ii
6B
1
Solution
ii
iii
6B
1
Solution
iii
7E
Paper 1
4
i
7E
1
Solution
i
ii
7E
1
Solution
ii
8B
Paper 1
1
Solution
8B
9D
Paper 1
1
Solution
9D
10C
Paper 1
10
i
10C
1
Solution
i
ii
10C
1
Solution
ii
iii
10C
1
Solution
iii
iv
10C
1
Solution
iv
v
10C
1
Solution
v
11I
Paper 1
14
a
11I
6
i
a
1
ii
a
1
iii
a
1
b
11I
6
ii
b
1
iii
b
1
iv
b
1
12F
Paper 1
7
a
12F
1
Solution
a
b
12F
1
Solution
b
c
12F
2
ii
c
1
13J
Paper 1
8
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13J
1
Solution
i
ii
13J
1
Solution
ii
iii
13J
1
Solution
iii
iv
13J
1
Solution
iv
14E
Paper 1
6
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14E
1
Solution
i
ii
14E
1
Solution
ii
iii
14E
1
Solution
iii
15D
Paper 1
1
Solution
15D
16H
Paper 1
6
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16H
1
Solution
i
ii
16H
1
Solution
ii
iii
16H
1
Solution
iii
17G
Paper 1
4
a
17G
1
Solution
a
b
17G
1
Solution
b
18G
Paper 1
11
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18G
1
Solution
a
b
18G
8
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b
1
ii
b
1
iii
b
1
iv
b
1
19F
Paper 1
1
Solution
19F
20G
Paper 1
1
Solution
20G
21F
Paper 1
6
a
21F
1
Solution
a
b
21F
1
Solution
b
c
21F
1
Solution
c
22I
Paper 1
9
a
22I
1
Solution
a
b
22I
4
i
b
1
ii
b
1
n
22I
1
Solution
n
23I
Paper 1
7
a
23I
1
Solution
a
b
23I
4
i
b
1
ii
b
1
24F
Paper 1
1
Solution
24F
25F
Paper 1
1
Solution
25F
26I
Paper 1
11
a
26I
1
Solution
a
b
26I
1
Solution
b
c
26I
6
i
c
1
ii
c
1
iii
c
1
27K
Paper 1
8
a
27K
1
Solution
a
b
27K
1
Solution
b
c
27K
1
Solution
c
d
27K
1
Solution
d
28K
Paper 1
6
a
28K
1
Solution
a
b
28K
1
Solution
b
c
28K
1
Solution
c
29J
Paper 1
1
Solution
29J
30K
Paper 1
4
a
30K
1
Solution
a
b
30K
1
Solution
b
31J
Paper 1
6
a
31J
1
Solution
a
b
31J
1
Solution
b
c
31J
1
Solution
c
32E
Paper 1
6
i
32E
1
Solution
i
ii
32E
1
Solution
ii
iii
32E
1
Solution
iii
33C
Paper 1
11
a
33C
1
Solution
a
b
33C
8
i
b
1
ii
b
1
iii
b
1
iv
b
1
34A
Paper 1
1
Solution
34A
35C
Paper 1
1
Solution
35C
36A
Paper 1
1
Solution
36A
37D
Paper 1
8
i
37D
1
Solution
i
ii
37D
1
Solution
ii
iii
37D
1
Solution
iii
iv
37D
1
Solution
iv
38D
Paper 1
10
i
38D
1
Solution
i
ii
38D
1
Solution
ii
iii
38D
1
Solution
iii
iv
38D
1
Solution
iv
v
38D
1
Solution
v
39B
Paper 1
8
i
39B
1
Solution
i
ii
39B
1
Solution
ii
iii
39B
1
Solution
iii
iv
39B
1
Solution
iv
40B
Paper 1
9
a
40B
1
Solution
a
b
40B
6
i
b
1
ii
b
1
iii
b
1
41E
Paper 1
4
a
41E
1
Solution
a
b
41E
1
Solution
b
Paper 2
ii
258
1H
Paper 2
1
Solution
1H
2H
Paper 2
1
Solution
2H
3I
Paper 2
7
a
3I
1
Solution
a
b
3I
4
i
b
1
ii
b
1
4F
Paper 2
4
i
4F
1
Solution
i
ii
4F
1
Solution
ii
5J
Paper 2
6
a
5J
1
Solution
a
b
5J
1
Solution
b
c
5J
1
Solution
c
6B
Paper 2
6
i
6B
1
Solution
i
ii
6B
1
Solution
ii
iii
6B
1
Solution
iii
7E
Paper 2
1
Solution
7E
8B
Paper 2
1
Solution
8B
9D
Paper 2
4
i
9D
1
Solution
i
ii
9D
1
Solution
ii
10C
Paper 2
6
i
10C
1
Solution
i
ii
10C
1
Solution
ii
iii
10C
1
Solution
iii
11H
Paper 2
1
Solution
11H
12I
Paper 2
6
i
12I
1
Solution
i
ii
12I
1
Solution
ii
iii
12I
1
Solution
iii
13E
Paper 2
4
i
13E
1
Solution
i
ii
13E
1
Solution
ii
14B
Paper 2
8
i
14B
1
Solution
i
ii
14B
1
Solution
ii
iii
14B
1
Solution
iii
iv
14B
1
Solution
iv
15C
Paper 2
13
a
15C
1
Solution
a
b
15C
1
Solution
b
c
15C
1
Solution
c
d
15C
6
i
d
1
ii
d
1
iii
d
1
16H
Paper 2
7
a
16H
1
Solution
a
b
16H
4
i
b
1
ii
b
1
17G
Paper 2
4
i
17G
1
Solution
i
ii
17G
1
Solution
ii
18G
Paper 2
9
a
18G
1
Solution
a
b
18G
1
Solution
b
c
18G
2
i
c
1
d
18G
1
Solution
d
19F
Paper 2
1
Solution
19F
20G
Paper 2
9
a
20G
1
Solution
a
b
20G
6
i
b
1
ii
b
1
iii
b
1
21F
Paper 2
6
a
21F
1
Solution
a
b
21F
1
Solution
b
c
21F
1
Solution
c
22I
Paper 2
6
a
22I
1
Solution
a
b
22I
1
Solution
b
c
22I
1
Solution
c
23F
Paper 2
1
Solution
23F
24F
Paper 2
6
a
24F
1
Solution
a
b
24F
1
Solution
b
c
24F
1
Solution
c
25I
Paper 2
8
a
25I
1
Solution
a
b
25I
1
Solution
b
c
25I
1
Solution
c
d
25I
1
Solution
d
26K
Paper 2
9
a
26K
1
Solution
a
b
26K
1
Solution
b
c
26K
4
i
c
1
ii
c
1
27K
Paper 2
4
i
27K
1
Solution
i
ii
27K
1
Solution
ii
28J
Paper 2
1
Solution
28J
29K
Paper 2
10
i
29K
1
Solution
i
ii
29K
1
Solution
ii
iii
29K
1
Solution
iii
iv
29K
1
Solution
iv
v
29K
1
Solution
v
30J
Paper 2
8
a
30J
1
Solution
a
b
30J
1
Solution
b
c
30J
1
Solution
c
d
30J
1
Solution
d
31D
Paper 2
10
a
31D
4
i
a
1
ii
a
1
b
31D
4
i
b
1
ii
b
1
32E
Paper 2
9
a
32E
1
Solution
a
b
32E
6
i
b
1
ii
b
1
iii
b
1
33C
Paper 2
6
i
33C
1
Solution
i
ii
33C
1
Solution
ii
iii
33C
1
Solution
iii
34A
Paper 2
7
a
34A
1
Solution
a
b
34A
4
i
b
1
ii
b
1
35C
Paper 2
1
Solution
35C
36A
Paper 2
1
Solution
36A
37D
Paper 2
6
i
37D
1
Solution
i
ii
37D
1
Solution
ii
iii
37D
1
Solution
iii
38B
Paper 2
6
i
38B
1
Solution
i
ii
38B
1
Solution
ii
iii
38B
1
Solution
iii
39B
Paper 2
6
a
39B
1
Solution
a
b
39B
1
Solution
b
c
39B
1
Solution
c
40E
Paper 2
8
a
40E
1
Solution
a
b
40E
1
Solution
b
c
40E
1
Solution
c
d
40E
1
Solution
d
Paper 3
ii
252
1H
Paper 3
1
Solution
1H
2H
Paper 3
1
Solution
2H
3I
Paper 3
1
Solution
3I
4F
Paper 3
4
i
4F
1
Solution
i
ii
4F
1
Solution
ii
5J
Paper 3
6
a
5J
1
Solution
a
b
5J
1
Solution
b
c
5J
1
Solution
c
6B
Paper 3
6
i
6B
1
Solution
i
ii
6B
1
Solution
ii
iii
6B
1
Solution
iii
7E
Paper 3
4
i
7E
1
Solution
i
ii
7E
1
Solution
ii
8B
Paper 3
1
Solution
8B
9D
Paper 3
1
Solution
9D
10C
Paper 3
8
i
10C
1
Solution
i
ii
10C
1
Solution
ii
iii
10C
1
Solution
iii
iv
10C
1
Solution
iv
11H
Paper 3
6
i
11H
1
Solution
i
ii
11H
1
Solution
ii
iii
11H
1
Solution
iii
12F
Paper 3
1
Solution
12F
13B
Paper 3
6
i
13B
1
Solution
i
ii
13B
1
Solution
ii
iii
13B
1
Solution
iii
14D
Paper 3
6
i
14D
1
Solution
i
ii
14D
1
Solution
ii
iii
14D
1
Solution
iii
15C
Paper 3
11
a
15C
1
Solution
a
b
15C
8
i
b
1
ii
b
1
iii
b
1
iv
b
1
16H
Paper 3
1
Solution
16H
17G
Paper 3
8
i
17G
1
Solution
i
ii
17G
1
Solution
ii
iii
17G
1
Solution
iii
iv
17G
1
Solution
iv
18G
Paper 3
4
a
18G
1
Solution
a
b
18G
1
Solution
b
19F
Paper 3
1
Solution
19F
20F
Paper 3
6
a
20F
1
Solution
a
b
20F
1
Solution
b
c
20F
1
Solution
c
21I
Paper 3
8
a
21I
1
Solution
a
b
21I
1
Solution
b
c
21I
1
Solution
c
d
21I
1
Solution
d
22I
Paper 3
7
a
22I
1
Solution
a
b
22I
2
iii
b
1
c
22I
1
Solution
c
23F
Paper 3
1
Solution
23F
24F
Paper 3
8
i
24F
1
Solution
i
ii
24F
1
Solution
ii
iii
24F
1
Solution
iii
iv
24F
1
Solution
iv
25I
Paper 3
8
a
25I
1
Solution
a
b
25I
1
Solution
b
c
25I
1
Solution
c
d
25I
1
Solution
d
26K
Paper 3
11
a
26K
1
Solution
a
b
26K
1
Solution
b
c
26K
6
i
c
1
ii
c
1
iii
c
1
27K
Paper 3
1
Solution
27K
28J
Paper 3
4
i
28J
1
Solution
i
ii
28J
1
Solution
ii
29K
Paper 3
12
a
29K
4
i
a
1
ii
a
1
b
29K
6
i
b
1
ii
b
1
iii
b
1
30D
Paper 3
4
a
30D
1
Solution
a
b
30D
1
Solution
b
31E
Paper 3
11
a
31E
1
Solution
a
b
31E
8
i
b
1
ii
b
1
iii
b
1
iv
b
1
32C
Paper 3
4
a
32C
1
Solution
a
b
32C
1
Solution
b
33A
Paper 3
1
Solution
33A
34C
Paper 3
7
a
34C
1
Solution
a
b
34C
4
i
b
1
ii
b
1
35A
Paper 3
6
i
35A
1
Solution
i
ii
35A
1
Solution
ii
iii
35A
1
Solution
iii
36D
Paper 3
4
i
36D
1
Solution
i
ii
36D
1
Solution
ii
37D
Paper 3
9
a
37D
1
Solution
a
b
37D
6
i
b
1
ii
b
1
iii
b
1
38B
Paper 3
11
a
38B
1
Solution
a
b
38B
8
i
b
1
ii
b
1
iii
b
1
iv
b
1
39B
Paper 3
6
i
39B
1
Solution
i
ii
39B
1
Solution
ii
iii
39B
1
Solution
iii
40E
Paper 3
6
a
40E
1
Solution
a
b
40E
1
Solution
b
c
40E
1
Solution
c
Paper 4
ii
277
1H
Paper 4
1
Solution
1H
2H
Paper 4
1
Solution
2H
3I
Paper 4
4
a
3I
1
Solution
a
b
3I
1
Solution
b
4F
Paper 4
1
Solution
4F
5J
Paper 4
9
a
5J
6
i
a
1
ii
a
1
iii
a
1
b
5J
1
Solution
b
6B
Paper 4
6
i
6B
1
Solution
i
ii
6B
1
Solution
ii
iii
6B
1
Solution
iii
7E
Paper 4
1
Solution
7E
8B
Paper 4
1
Solution
8B
9D
Paper 4
1
Solution
9D
10C
Paper 4
8
i
10C
1
Solution
i
ii
10C
1
Solution
ii
iii
10C
1
Solution
iii
iv
10C
1
Solution
iv
11H
Paper 4
8
a
11H
1
Solution
a
b
11H
1
Solution
b
c
11H
1
Solution
c
d
11H
1
Solution
d
12H
Paper 4
9
a
12H
1
Solution
a
b
12H
6
i
b
1
ii
b
1
iii
b
1
13J
Paper 4
9
a
13J
1
Solution
a
b
13J
6
i
b
1
ii
b
1
iii
b
1
14B
Paper 4
8
i
14B
1
Solution
i
ii
14B
1
Solution
ii
iii
14B
1
Solution
iii
iv
14B
1
Solution
iv
15B
Paper 4
7
a
15B
1
Solution
a
b
15B
1
Solution
b
c
15B
2
i
c
1
16H
Paper 4
11
a
16H
1
Solution
a
b
16H
1
Solution
b
c
16H
6
i
c
1
ii
c
1
iii
c
1
17G
Paper 4
1
Solution
17G
18G
Paper 4
4
a
18G
1
Solution
a
b
18G
1
Solution
b
19F
Paper 4
4
a
19F
1
Solution
a
b
19F
1
Solution
b
20G
Paper 4
1
Solution
20G
21F
Paper 4
7
a
21F
2
ii
a
1
b
21F
1
Solution
b
c
21F
1
Solution
c
22I
Paper 4
9
a
22I
1
Solution
a
b
22I
1
Solution
b
c
22I
4
i
c
1
ii
c
1
23I
Paper 4
6
a
23I
1
Solution
a
b
23I
1
Solution
b
c
23I
1
Solution
c
24F
Paper 4
1
Solution
24F
25I
Paper 4
11
a
25I
1
Solution
a
b
25I
1
Solution
b
c
25I
1
Solution
c
d
25I
4
i
d
1
ii
d
1
26K
Paper 4
9
a
26K
1
Solution
a
b
26K
6
i
b
1
ii
b
1
iii
b
1
27K
Paper 4
6
i
27K
1
Solution
i
ii
27K
1
Solution
ii
iii
27K
1
Solution
iii
28J
Paper 4
1
Solution
28J
29K
Paper 4
10
i
29K
1
Solution
i
ii
29K
1
Solution
ii
iii
29K
1
Solution
iii
iv
29K
1
Solution
iv
v
29K
1
Solution
v
30J
Paper 4
8
i
30J
1
Solution
i
ii
30J
1
Solution
ii
iii
30J
1
Solution
iii
iv
30J
1
Solution
iv
31A
Paper 4
8
i
31A
1
Solution
i
ii
31A
1
Solution
ii
iii
31A
1
Solution
iii
iv
31A
1
Solution
iv
32E
Paper 4
12
a
32E
2
i
a
1
b
32E
8
i
b
1
ii
b
1
iii
b
1
iv
b
1
33A
Paper 4
1
Solution
33A
34C
Paper 4
9
a
34C
1
Solution
a
b
34C
6
i
b
1
ii
b
1
iii
b
1
35A
Paper 4
6
i
35A
1
Solution
i
ii
35A
1
Solution
ii
iii
35A
1
Solution
iii
36D
Paper 4
11
a
36D
1
Solution
a
b
36D
8
i
b
1
ii
b
1
iii
b
1
iv
b
1
37D
Paper 4
8
i
37D
1
Solution
i
ii
37D
1
Solution
ii
iii
37D
1
Solution
iii
iv
37D
1
Solution
iv
38B
Paper 4
6
i
38B
1
Solution
i
ii
38B
1
Solution
ii
iii
38B
1
Solution
iii
39B
Paper 4
7
a
39B
1
Solution
a
b
39B
4
i
b
1
ii
b
1
40E
Paper 4
6
a
40E
1
Solution
a
b
40E
1
Solution
b
c
40E
1
Solution
c
Ancestors
(7)
2020
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
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