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Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 1

www.maths.cam.ac.uk/undergrad/pastpapers/files/2020/paperii_1_2020.pdf

Table of contents 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
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
- 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
      - Solution i
    - ii a 1
      - Solution ii
    - iii a 1
      - Solution iii
  - b 11I 6
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
    - iv b 1
      - Solution iv
- 12F Paper 1 7
  - a 12F 1
    - Solution a
  - b 12F 1
    - Solution b
  - c 12F 2
    - ii c 1
      - Solution ii
- 13J Paper 1 8
  - i 13J 1
    - Solution i
  - ii 13J 1
    - Solution ii
  - iii 13J 1
    - Solution iii
  - iv 13J 1
    - Solution iv
- 14E Paper 1 6
  - i 14E 1
    - Solution i
  - ii 14E 1
    - Solution ii
  - iii 14E 1
    - Solution iii
- 15D Paper 1 1
  - Solution 15D
- 16H Paper 1 6
  - i 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
  - a 18G 1
    - Solution a
  - b 18G 8
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
    - iv b 1
      - Solution iv
- 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
      - Solution i
    - ii b 1
      - Solution ii
  - n 22I 1
    - Solution n
- 23I Paper 1 7
  - a 23I 1
    - Solution a
  - b 23I 4
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
- 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
      - Solution i
    - ii c 1
      - Solution ii
    - iii c 1
      - Solution iii
- 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
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
    - iv b 1
      - Solution iv
- 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
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
- 41E Paper 1 4
  - a 41E 1
    - Solution a
  - b 41E 1
    - Solution b

1H (Number Theory)

Articles: 1

Solution

2H (Topics in Analysis)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

3I (Coding and Cryptography)

Articles: 9

a

Articles: 1

Solution

b

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

4F (Automata and Formal Languages)

Articles: 1

Solution

5J (Statistical Modelling)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

n

Articles: 1

Solution

c

Articles: 1

Solution

6B (Mathematical Biology)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

7E (Further Complex Methods)

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

8B (Classical Dynamics)

Articles: 1

Solution

9D (Cosmology)

Articles: 1

Solution

10C (Quantum Information and Computation)

Articles: 10

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

v

Articles: 1

Solution

11I (Coding and Cryptography)

Articles: 14

a

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

b

Articles: 6

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

12F (Automata and Formal Languages)

Articles: 7

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 2

ii

Articles: 1

Solution

13J (Statistical Modelling)

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

14E (Further Complex Methods)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

15D (Cosmology)

Articles: 1

Solution

16H (Logic and Set Theory)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

17G (Graph Theory)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

18G (Galois Theory)

Articles: 11

a

Articles: 1

Solution

b

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

19F (Representation Theory)

Articles: 1

Solution

20G (Number Fields)

Articles: 1

Solution

21F (Algebraic Topology)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

22I (Linear Analysis)

Articles: 9

a

Articles: 1

Solution

b

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

n

Articles: 1

Solution

23I (Analysis of Functions)

Articles: 7

a

Articles: 1

Solution

b

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

24F (Riemann Surfaces)

Articles: 1

Solution

25F (Algebraic Geometry)

Articles: 1

Solution

26I (Differential Geometry)

Articles: 11

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

27K (Probability and Measure)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

28K (Applied Probability)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

29J (Principles of Statistics)

Articles: 1

Solution

30K (Stochastic Financial Models)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

31J (Mathematics of Machine Learning)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

32E (Dynamical Systems)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

33C (Integrable Systems)

Articles: 11

a

Articles: 1

Solution

b

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

34A (Principles of Quantum √ Mechanics)

Articles: 1

Solution

35C (Applications of Quantum Mechanics)

Articles: 1

Solution

36A (Statistical Physics)

Articles: 1

Solution

37D (Electrodynamics)

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

38D (General Relativity)

Articles: 10

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

v

Articles: 1

Solution

39B (Fluid Dynamics II)

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

40B (Waves)

Articles: 9

a

Articles: 1

Solution

b

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

41E (Numerical Analysis)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

 Ancestors (8)