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Past exam of the natural sciences course of the University of Cambridge
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2019
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ia
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Paper 2
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University of Cambridge
Course of the University of Cambridge
Natural sciences course of the University of Cambridge
Past exam of the natural sciences course of the University of Cambridge
2019
ia
Created
2026-09-24
Updated
2026-09-24
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www.maths.cam.ac.uk/undergradnst/files/2019/papernst_ia_2_2019.pdf
Table of contents
1
Paper 2
Solution
1
2
Paper 2
a
2
Solution
a
b
2
Solution
b
3
Paper 2
Solution
3
4
Paper 2
a
4
Solution
a
b
4
Solution
b
5
Paper 2
a
5
Solution
a
b
5
Solution
b
6
Paper 2
a
6
Solution
a
b
6
Solution
b
7
Paper 2
Solution
7
8
Paper 2
Solution
8
9
Paper 2
Solution
9
10
Paper 2
a
10
Solution
a
b
10
Solution
b
11
Paper 2
a
11
ii
a
Solution
ii
iii
a
Solution
iii
b
11
Solution
b
c
11
Solution
c
12
Paper 2
a
12
Solution
a
b
12
Solution
b
c
12
Solution
c
d
12
Solution
d
13
Paper 2
a
13
Solution
a
b
13
Solution
b
c
13
Solution
c
d
13
Solution
d
14
Paper 2
a
14
Solution
a
b
14
i
b
Solution
i
ii
b
Solution
ii
c
14
i
c
Solution
i
ii
c
Solution
ii
d
14
i
d
Solution
i
ii
d
Solution
ii
iii
d
Solution
iii
15
Paper 2
a
15
i
a
Solution
i
ii
a
Solution
ii
b
15
i
b
Solution
i
ii
b
Solution
ii
iii
b
Solution
iii
16
Paper 2
a
16
Solution
a
b
16
Solution
b
17
Paper 2
a
17
Solution
a
b
17
i
b
Solution
i
ii
b
Solution
ii
iii
b
Solution
iii
c
17
i
c
Solution
i
ii
c
Solution
ii
18
Paper 2
a
18
Solution
a
b
18
Solution
b
c
18
Solution
c
19
Paper 2
a
19
Solution
a
b
19
Solution
b
c
19
Solution
c
20
Paper 2
a
20
i
a
Solution
i
ii
a
Solution
ii
b
20
Solution
b
1
0
0
0
Paper 2
Solution
0
0
0
1
2
0
0
0
Paper 2
a
0
0
0
2
Solution
0
0
0
a
b
0
0
0
2
Solution
0
0
0
b
3
0
0
0
Paper 2
Solution
0
0
0
3
4
0
0
0
Paper 2
a
0
0
0
4
Solution
0
0
0
a
b
0
0
0
4
Solution
0
0
0
b
5
0
0
0
Paper 2
a
0
0
0
5
Solution
0
0
0
a
b
0
0
0
5
Solution
0
0
0
b
6
0
0
0
Paper 2
a
0
0
0
6
Solution
0
0
0
a
b
0
0
0
6
Solution
0
0
0
b
7
0
0
0
Paper 2
Solution
0
0
0
7
8
0
0
0
Paper 2
Solution
0
0
0
8
9
0
0
0
Paper 2
Solution
0
0
0
9
10
0
0
0
Paper 2
a
0
0
0
10
Solution
0
0
0
a
b
0
0
0
10
Solution
0
0
0
b
11
0
0
0
Paper 2
a
0
0
0
11
ii
0
0
0
a
Solution
0
0
0
ii
iii
0
0
0
a
Solution
0
0
0
iii
b
0
0
0
11
Solution
0
0
0
b
c
0
0
0
11
Solution
0
0
0
c
12
0
0
0
Paper 2
a
0
0
0
12
Solution
0
0
0
a
b
0
0
0
12
Solution
0
0
0
b
c
0
0
0
12
Solution
0
0
0
c
d
0
0
0
12
Solution
0
0
0
d
13
0
0
0
Paper 2
a
0
0
0
13
Solution
0
0
0
a
b
0
0
0
13
Solution
0
0
0
b
c
0
0
0
13
Solution
0
0
0
c
d
0
0
0
13
Solution
0
0
0
d
14
0
0
0
Paper 2
a
0
0
0
14
Solution
0
0
0
a
b
0
0
0
14
i
0
0
0
b
Solution
0
0
0
i
ii
0
0
0
b
Solution
0
0
0
ii
c
0
0
0
14
i
0
0
0
c
Solution
0
0
0
i
ii
0
0
0
c
Solution
0
0
0
ii
d
0
0
0
14
i
0
0
0
d
Solution
0
0
0
i
ii
0
0
0
d
Solution
0
0
0
ii
iii
0
0
0
d
Solution
0
0
0
iii
15
0
0
0
Paper 2
a
0
0
0
15
i
0
0
0
a
Solution
0
0
0
i
ii
0
0
0
a
Solution
0
0
0
ii
b
0
0
0
15
i
0
0
0
b
Solution
0
0
0
i
ii
0
0
0
b
Solution
0
0
0
ii
iii
0
0
0
b
Solution
0
0
0
iii
16
0
0
0
Paper 2
a
0
0
0
16
Solution
0
0
0
a
b
0
0
0
16
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ia
2019
Past exam of the natural sciences course of the University of Cambridge
Natural sciences course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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