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Past exam of the mathematics course of the University of Cambridge / 2019 / ib / Paper 4

www.maths.cam.ac.uk/undergrad/pastpapers/files/2019/paperib_4_2019.pdf

Table of contents 111
- 1F Paper 4 1
  - Solution 1F
- 2G Paper 4 4
  - a 2G 1
    - Solution a
  - b 2G 1
    - Solution b
- 3E Paper 4 6
  - i 3E 1
    - Solution i
  - ii 3E 1
    - Solution ii
  - iii 3E 1
    - Solution iii
- 4F Paper 4 1
  - Solution 4F
- 5D Paper 4 1
  - Solution 5D
- 6B Paper 4 4
  - a 6B 1
    - Solution a
  - b 6B 1
    - Solution b
- 7A Paper 4 1
  - Solution 7A
- 8C Paper 4 1
  - Solution 8C
- 9H Paper 4 2
  - b 9H 1
    - Solution b
- 10F Paper 4 1
  - Solution 10F
- 11G Paper 4 6
  - a 11G 1
    - Solution a
  - b 11G 1
    - Solution b
  - c 11G 1
    - Solution c
- 12E Paper 4 10
  - a 12E 2
    - ii a 1
      - Solution ii
  - b 12E 6
    - i b 1
      - Solution i
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
- 13G Paper 4 6
  - a 13G 1
    - Solution a
  - b 13G 1
    - Solution b
  - c 13G 1
    - Solution c
- 14D Paper 4 6
  - a 14D 1
    - Solution a
  - b 14D 1
    - Solution b
  - c 14D 1
    - Solution c
- 15E Paper 4 8
  - a 15E 1
    - Solution a
  - b 15E 1
    - Solution b
  - c 15E 1
    - Solution c
  - d 15E 1
    - Solution d
- 16A Paper 4 6
  - a 16A 1
    - Solution a
  - b 16A 1
    - Solution b
  - c 16A 1
    - Solution c
- 17B Paper 4 6
  - a 17B 1
    - Solution a
  - b 17B 1
    - Solution b
  - c 17B 1
    - Solution c
- 18C Paper 4 6
  - a 18C 1
    - Solution a
  - b 18C 1
    - Solution b
  - c 18C 1
    - Solution c
- 19H Paper 4 6
  - a 19H 1
    - Solution a
  - b 19H 1
    - Solution b
  - c 19H 1
    - Solution c
- 20H Paper 4 9
  - a 20H 1
    - Solution a
  - b 20H 4
    - ii b 1
      - Solution ii
    - iii b 1
      - Solution iii
  - c 20H 1
    - Solution c

1F (Linear Algebra)

Articles: 1

Solution

2G (Groups, Rings and Modules)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

3E (Analysis II)

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

4F (Complex Analysis)

Articles: 1

Solution

5D (Methods)

Articles: 1

Solution

6B (Quantum Mechanics)

Articles: 4

a

Articles: 1

Solution

b

Articles: 1

Solution

7A (Electromagnetism)

Articles: 1

Solution

8C (Numerical Analysis)

Articles: 1

Solution

9H (Markov Chains)

Articles: 2

b

Articles: 1

Solution

10F (Linear Algebra)

Articles: 1

Solution

11G (Groups, Rings and Modules)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

12E (Analysis II)

Articles: 10

a

Articles: 2

ii

Articles: 1

Solution

b

Articles: 6

i

Articles: 1

Solution

ii

Articles: 1

Solution

iii

Articles: 1

Solution

13G (Metric and Topological Spaces)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

14D (Complex Methods)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

15E (Geometry)

Articles: 8

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

d

Articles: 1

Solution

16A (Variational Principles)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

17B (Methods)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

18C (Fluid Dynamics)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

19H (Statistics)

Articles: 6

a

Articles: 1

Solution

b

Articles: 1

Solution

c

Articles: 1

Solution

20H (Optimisation)

Articles: 9

a

Articles: 1

Solution

b

Articles: 4

ii

Articles: 1

Solution

iii

Articles: 1

Solution

c

Articles: 1

Solution

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