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Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1

www.maths.cam.ac.uk/undergrad/pastpapers/files/2019/paperii_1_2019.pdf

Table of contents 287
- 1I Paper 1 4
  - a 1I 1
    - Solution a
  - b 1I 1
    - Solution b
- 2H Paper 1 1
  - Solution 2H
- 3G Paper 1 1
  - Solution 3G
- 4H Paper 1 11
  - a 4H 1
    - Solution a
  - b 4H 6
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
  - c 4H 1
    - Solution c
- 5J Paper 1 1
  - Solution 5J
- 6C Paper 1 1
  - Solution 6C
- 7A Paper 1 4
  - a 7A 1
    - Solution a
  - b 7A 1
    - Solution b
- 8E Paper 1 4
  - a 8E 1
    - Solution a
  - b 8E 1
    - Solution b
- 9B Paper 1 1
  - Solution 9B
- 10D Paper 1 6
  - a 10D 1
    - Solution a
  - b 10D 1
    - Solution b
  - c 10D 1
    - Solution c
- 11G Paper 1 6
  - a 11G 1
    - Solution a
  - b 11G 1
    - Solution b
  - c 11G 1
    - Solution c
- 12H Paper 1 1
  - Solution 12H
- 13J Paper 1 8
  - a 13J 1
    - Solution a
  - b 13J 1
    - Solution b
  - c 13J 1
    - Solution c
  - d 13J 1
    - Solution d
- 14A Paper 1 8
  - a 14A 1
    - Solution a
  - b 14A 1
    - Solution b
  - c 14A 1
    - Solution c
  - d 14A 1
    - Solution d
- 15B Paper 1 10
  - a 15B 1
    - Solution a
  - b 15B 1
    - Solution b
  - c 15B 1
    - Solution c
  - d 15B 1
    - Solution d
  - e 15B 1
    - Solution e
- 16I Paper 1 1
  - Solution 16I
- 17G Paper 1 8
  - a 17G 1
    - Solution a
  - b 17G 1
    - Solution b
  - c 17G 1
    - Solution c
  - d 17G 1
    - Solution d
- 18F Paper 1 6
  - a 18F 1
    - Solution a
  - b 18F 1
    - Solution b
  - c 18F 1
    - Solution c
- 19I Paper 1 12
  - a 19I 1
    - Solution a
  - b 19I 4
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
  - c 19I 4
    - i c 1
      - Solution i
    - ii c 1
      - Solution ii
- 20G Paper 1 6
  - a 20G 1
    - Solution a
  - b 20G 1
    - Solution b
  - c 20G 1
    - Solution c
- 21F Paper 1 6
  - a 21F 1
    - Solution a
  - b 21F 1
    - Solution b
  - c 21F 1
    - Solution c
- 22H Paper 1 8
  - a 22H 1
    - Solution a
  - b 22H 1
    - Solution b
  - c 22H 1
    - Solution c
  - d 22H 1
    - Solution d
- 23H Paper 1 10
  - a 23H 1
    - Solution a
  - b 23H 1
    - Solution b
  - c 23H 1
    - Solution c
  - d 23H 1
    - Solution d
  - e 23H 1
    - Solution e
- 24F Paper 1 6
  - a 24F 1
    - Solution a
  - b 24F 1
    - Solution b
  - c 24F 1
    - Solution c
- 25F Paper 1 11
  - a 25F 8
    - i a 1
      - Solution i
    - ii a 1
      - Solution ii
    - iii a 1
      - Solution iii
    - iv a 1
      - Solution iv
  - b 25F 1
    - Solution b
- 26H Paper 1 6
  - a 26H 1
    - Solution a
  - b 26H 1
    - Solution b
  - c 26H 1
    - Solution c
- 27K Paper 1 11
  - a 27K 1
    - Solution a
  - b 27K 8
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
    - iv b 1
      - Solution iv
- 28K Paper 1 11
  - a 28K 1
    - Solution a
  - b 28K 1
    - Solution b
  - c 28K 4
    - i c 1
      - Solution i
    - ii c 1
      - Solution ii
  - d 28K 1
    - Solution d
- 29J Paper 1 10
  - a 29J 1
    - Solution a
  - b 29J 1
    - Solution b
  - c 29J 1
    - Solution c
  - d 29J 1
    - Solution d
  - e 29J 1
    - Solution e
- 30K Paper 1 11
  - a 30K 1
    - Solution a
  - b 30K 1
    - Solution b
  - c 30K 6
    - i c 1
      - Solution i
    - ii c 1
      - Solution ii
    - iii c 1
      - Solution iii
- 31E Paper 1 10
  - i 31E 1
    - Solution i
  - ii 31E 1
    - Solution ii
  - iii 31E 1
    - Solution iii
  - iv 31E 1
    - Solution iv
  - v 31E 1
    - Solution v
- 32C Paper 1 10
  - a 32C 1
    - Solution a
  - b 32C 1
    - Solution b
  - c 32C 1
    - Solution c
  - d 32C 1
    - Solution d
  - e 32C 1
    - Solution e
- 33B Paper 1 1
  - Solution 33B
- 34B Paper 1 4
  - a 34B 1
    - Solution a
  - b 34B 1
    - Solution b
- 35D Paper 1 4
  - a 35D 1
    - Solution a
  - b 35D 1
    - Solution b
- 36E Paper 1 1
  - Solution 36E
- 37D Paper 1 8
  - a 37D 1
    - Solution a
  - b 37D 1
    - Solution b
  - c 37D 1
    - Solution c
  - d 37D 1
    - Solution d
- 38A Paper 1 4
  - a 38A 1
    - Solution a
  - b 38A 1
    - Solution b
- 39A Paper 1 9
  - a 39A 1
    - Solution a
  - b 39A 6
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
- 40C Paper 1 6
  - a 40C 1
    - Solution a
  - b 40C 1
    - Solution b
  - c 40C 1
    - Solution c

1I (Number Theory)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

2H (Topics in Analysis)

Articles: 1

Solution

3G (Coding and Cryptography)

Articles: 1

Solution

4H (Automata and Formal Languages)

Articles: 11

a

Articles: 1

Solution

b

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

c

Articles: 1

Solution

5J (Statistical Modelling)

Articles: 1

Solution

6C (Mathematical Biology)

Articles: 1

Solution

7A (Further Complex Methods)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

8E (Classical Dynamics)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

9B (Cosmology)

Articles: 1

Solution

10D (Quantum Information and Computation)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

11G (Coding and Cryptography)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

12H (Automata and Formal Languages)

Articles: 1

Solution

13J (Statistical Modelling)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

14A (Further Complex Methods)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

15B (Cosmology)

Articles: 10

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

e

Articles: 1

Solution

16I (Logic and Set Theory)

Articles: 1

Solution

17G (Graph Theory)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

18F (Galois Theory)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

19I (Representation Theory)

Articles: 12

a

Articles: 1

Solution

b

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

c

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

20G (Number Fields)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

21F (Algebraic Topology)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

22H (Linear Analysis)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

23H (Analysis of Functions)

Articles: 10

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

e

Articles: 1

Solution

24F (Riemann Surfaces)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

25F (Algebraic Geometry)

Articles: 11

a

Articles: 8

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

b

Articles: 1

Solution

26H (Differential Geometry)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

27K (Probability and Measure)

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

28K (Applied Probability)

Articles: 11

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 4

i

Articles: 1

Solution

ii

Articles: 1

Solution

d

Articles: 1

Solution

29J (Principles of Statistics)

Articles: 10

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

e

Articles: 1

Solution

30K (Stochastic Financial Models)

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

31E (Dynamical Systems)

Articles: 10

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

iv

Articles: 1

Solution

v

Articles: 1

Solution

32C (Integrable Systems)

Articles: 10

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

e

Articles: 1

Solution

33B (Principles of Quantum Mechanics)

Articles: 1

Solution

34B (Applications of Quantum Mechanics)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

35D (Statistical Physics)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

36E (Electrodynamics)

Articles: 1

Solution

37D (General Relativity)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

38A (Fluid Dynamics)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

39A (Waves)

Articles: 9

a

Articles: 1

Solution

b

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

40C (Numerical Analysis)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

 Ancestors (8)