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Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4

www.maths.cam.ac.uk/undergrad/pastpapers/files/2025/paperii_4_2025.pdf

Table of contents 12k 314
- 1G Paper 4 193 9
  - a 1G 48 1
    - Solution a 48
  - b 1G 49 1
    - Solution b 49
  - c 1G 96 4
    - i c 30 1
      - Solution i 30
    - ii c 66 1
      - Solution ii 66
- 2I Paper 4 113 1
  - Solution 2I 113
- 3K Paper 4 181 1
  - Solution 3K 181
- 4F Paper 4 278 11
  - a 4F 39 1
    - Solution a 39
  - b 4F 116 4
    - i b 41 1
      - Solution i 41
    - ii b 75 1
      - Solution ii 75
  - c 4F 53 1
    - Solution c 53
  - d 4F 70 1
    - Solution d 70
- 5K Paper 4 145 1
  - Solution 5K 145
- 6A Paper 4 87 4
  - a 6A 36 1
    - Solution a 36
  - b 6A 51 1
    - Solution b 51
- 7E Paper 4 108 1
  - Solution 7E 108
- 8B Paper 4 174 9
  - a 8B 46 1
    - Solution a 46
  - b 8B 128 6
    - i b 65 1
      - Solution i 65
    - ii b 31 1
      - Solution ii 31
    - iii b 32 1
      - Solution iii 32
- 9E Paper 4 146 6
  - a 9E 59 1
    - Solution a 59
  - b 9E 31 1
    - Solution b 31
  - c 9E 56 1
    - Solution c 56
- 10C Paper 4 166 4
  - a 10C 36 1
    - Solution a 36
  - b 10C 130 1
    - Solution b 130
- 11G Paper 4 237 8
  - a 11G 19 1
    - Solution a 19
  - b 11G 48 1
    - Solution b 48
  - c 11G 106 1
    - Solution c 106
  - d 11G 64 1
    - Solution d 64
- 12I Paper 4 777 5
  - Solution 12I 163
  - i 12I 202 1
    - Solution i 202
  - ii 12I 412 1
    - Solution ii 412
- 13K Paper 4 532 8
  - a 13K 78 1
    - Solution a 78
  - b 13K 201 1
    - Solution b 201
  - c 13K 153 1
    - Solution c 153
  - d 13K 100 1
    - Solution d 100
- 14A Paper 4 270 6
  - a 14A 113 1
    - Solution a 113
  - b 14A 111 1
    - Solution b 111
  - c 14A 46 1
    - Solution c 46
- 15B Paper 4 254 6
  - a 15B 40 1
    - Solution a 40
  - b 15B 75 1
    - Solution b 75
  - c 15B 139 1
    - Solution c 139
- 16H Paper 4 524 12
  - a 16H 51 1
    - Solution a 51
  - b 16H 101 1
    - Solution b 101
  - c 16H 82 1
    - Solution c 82
  - d 16H 137 1
    - Solution d 137
  - e 16H 57 1
    - Solution e 57
  - f 16H 96 1
    - Solution f 96
- 17F Paper 4 617 10
  - a 17F 129 1
    - Solution a 129
  - b 17F 488 7
    - Solution b 51
    - i b 37 1
      - Solution i 37
    - ii b 195 1
      - Solution ii 195
    - iii b 205 1
      - Solution iii 205
- 18J Paper 4 518 6
  - a 18J 205 1
    - Solution a 205
  - b 18J 130 1
    - Solution b 130
  - c 18J 183 1
    - Solution c 183
- 19J Paper 4 453 12
  - a 19J 139 4
    - i a 78 1
      - Solution i 78
    - ii a 61 1
      - Solution ii 61
  - b 19J 314 6
    - i b 31 1
      - Solution i 31
    - ii b 101 1
      - Solution ii 101
    - iii b 182 1
      - Solution iii 182
- 20G Paper 4 476 10
  - a 20G 63 1
    - Solution a 63
  - b 20G 126 1
    - Solution b 126
  - c 20G 49 1
    - Solution c 49
  - d 20G 94 1
    - Solution d 94
  - e 20G 144 1
    - Solution e 144
- 21F Paper 4 445 7
  - Solution 21F 113
  - i 21F 97 1
    - Solution i 97
  - ii 21F 85 1
    - Solution ii 85
  - iii 21F 150 1
    - Solution iii 150
- 22I Paper 4 354 6
  - a 22I 130 1
    - Solution a 130
  - b 22I 104 1
    - Solution b 104
  - c 22I 120 1
    - Solution c 120
- 23H Paper 4 389 14
  - a 23H 135 6
    - i a 43 1
      - Solution i 43
    - ii a 49 1
      - Solution ii 49
    - iii a 43 1
      - Solution iii 43
  - b 23H 254 6
    - i b 85 1
      - Solution i 85
    - ii b 78 1
      - Solution ii 78
    - iii b 91 1
      - Solution iii 91
- 24J Paper 4 304 1
  - Solution 24J 304
- 25I Paper 4 329 8
  - a 25I 112 1
    - Solution a 112
  - b 25I 69 1
    - Solution b 69
  - c 25I 59 1
    - Solution c 59
  - d 25I 89 1
    - Solution d 89
- 26H Paper 4 212 6
  - a 26H 38 1
    - Solution a 38
  - b 26H 78 1
    - Solution b 78
  - c 26H 96 1
    - Solution c 96
- 27L Paper 4 213 7
  - a 27L 104 1
    - Solution a 104
  - b 27L 109 4
    - i b 55 1
      - Solution i 55
    - ii b 54 1
      - Solution ii 54
- 28L Paper 4 319 6
  - a 28L 85 1
    - Solution a 85
  - b 28L 112 1
    - Solution b 112
  - c 28L 122 1
    - Solution c 122
- 29K Paper 4 342 8
  - a 29K 61 1
    - Solution a 61
  - b 29K 49 1
    - Solution b 49
  - c 29K 92 1
    - Solution c 92
  - d 29K 140 1
    - Solution d 140
- 30L Paper 4 347 6
  - a 30L 70 1
    - Solution a 70
  - b 30L 104 1
    - Solution b 104
  - c 30L 173 1
    - Solution c 173
- 31D Paper 4 259 8
  - a 31D 34 1
    - Solution a 34
  - b 31D 25 1
    - Solution b 25
  - c 31D 81 1
    - Solution c 81
  - d 31D 119 1
    - Solution d 119
- 32A Paper 4 532 15
  - Solution 32A 202
  - a 32A 182 6
    - i a 58 1
      - Solution i 58
    - ii a 47 1
      - Solution ii 47
    - iii a 77 1
      - Solution iii 77
  - b 32A 148 6
    - i b 24 1
      - Solution i 24
    - ii b 60 1
      - Solution ii 60
    - iii b 64 1
      - Solution iii 64
- 33C Paper 4 356 10
  - a 33C 35 1
    - Solution a 35
  - b 33C 73 1
    - Solution b 73
  - c 33C 248 5
    - Solution c 38
    - i c 45 1
      - Solution i 45
    - ii c 165 1
      - Solution ii 165
- 34B Paper 4 243 6
  - a 34B 42 1
    - Solution a 42
  - b 34B 110 1
    - Solution b 110
  - c 34B 91 1
    - Solution c 91
- 35C Paper 4 274 6
  - a 35C 74 1
    - Solution a 74
  - b 35C 70 1
    - Solution b 70
  - c 35C 130 1
    - Solution c 130
- 36B Paper 4 420 8
  - a 36B 79 1
    - Solution a 79
  - b 36B 115 1
    - Solution b 115
  - c 36B 107 1
    - Solution c 107
  - d 36B 119 1
    - Solution d 119
- 37E Paper 4 201 6
  - a 37E 48 1
    - Solution a 48
  - b 37E 60 1
    - Solution b 60
  - c 37E 93 1
    - Solution c 93
- 38D Paper 4 222 4
  - a 38D 135 1
    - Solution a 135
  - b 38D 87 1
    - Solution b 87
- 39A Paper 4 142 8
  - a 39A 59 1
    - Solution a 59
  - b 39A 23 1
    - Solution b 23
  - c 39A 35 1
    - Solution c 35
  - d 39A 25 1
    - Solution d 25
- 40D Paper 4 212 4
  - a 40D 113 1
    - Solution a 113
  - b 40D 99 1
    - Solution b 99

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