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Past exam of the mathematics course of the University of Cambridge
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Course of the University of Cambridge
Mathematics course of the University of Cambridge
Past exam of the mathematics course of the University of Cambridge
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Words: 55k
Articles: 2k
Table of contents
55k
2k
ia
2021
8k
284
Paper 1
ia
2k
69
1C
Paper 1
125
4
a
1C
1
b
1C
1
2B
Paper 1
1
Solution
2B
3F
Paper 1
1
Solution
3F
4F
Paper 1
1
Solution
4F
5C
Paper 1
1
Solution
5C
6A
Paper 1
284
11
a
6A
1
b
6A
1
c
6A
137
4
d
6A
1
7A
Paper 1
1
Solution
7A
8B
Paper 1
236
9
a
8B
1
b
8B
150
6
9F
Paper 1
321
11
a
9F
1
b
9F
174
8
10F
Paper 1
131
4
a
10F
1
b
10F
1
11F
Paper 1
135
4
a
11F
1
b
11F
1
12F
Paper 1
285
9
a
12F
185
6
b
12F
1
Paper 2
ia
2k
46
1A
Paper 2
1
Solution
1A
2A
Paper 2
1
Solution
2A
3D
Paper 2
1
Solution
3D
4F
Paper 2
1
Solution
4F
5A
Paper 2
1
Solution
5A
6A
Paper 2
1
Solution
6A
7A
Paper 2
1
Solution
7A
8A
Paper 2
1
Solution
8A
9E
Paper 2
372
10
a
9E
135
4
b
9E
237
4
10E
Paper 2
226
9
a
10E
1
b
10E
167
6
11D
Paper 2
1
Solution
11D
12F
Paper 2
185
6
i
12F
1
ii
12F
1
iii
12F
1
Paper 3
ia
2k
80
1D
Paper 3
99
4
i
1D
1
ii
1D
1
2D
Paper 3
1
Solution
2D
3B
Paper 3
118
7
a
3B
1
b
3B
67
4
4B
Paper 3
86
4
a
4B
1
b
4B
1
5D
Paper 3
368
14
a
5D
1
b
5D
1
c
5D
110
4
d
5D
108
4
6D
Paper 3
216
6
a
6D
1
b
6D
1
c
6D
1
7D
Paper 3
1
Solution
7D
8D
Paper 3
285
9
a
8D
142
4
b
8D
1
c
8D
1
9B
Paper 3
163
6
a
9B
1
b
9B
1
c
9B
1
10B
Paper 3
120
6
a
10B
1
b
10B
1
c
10B
1
11B
Paper 3
137
6
a
11B
1
b
11B
1
c
11B
1
12B
Paper 3
134
4
a
12B
1
b
12B
1
Paper 4
ia
2k
85
1E
Paper 4
145
6
i
1E
1
ii
1E
1
iii
1E
1
2E
Paper 4
168
6
i
2E
1
ii
2E
1
iii
2E
1
3C
Paper 4
1
Solution
3C
4C
Paper 4
1
Solution
4C
5E
Paper 4
196
7
a
5E
142
4
b
5E
1
6E
Paper 4
228
7
a
6E
132
4
b
6E
1
7E
Paper 4
382
14
a
7E
1
b
7E
80
4
c
7E
1
d
7E
80
4
8E
Paper 4
288
12
a
8E
1
b
8E
128
4
c
8E
109
4
9C
Paper 4
1
Solution
9C
10C
Paper 4
236
11
a
10C
1
b
10C
1
c
10C
147
6
11C
Paper 4
246
6
i
11C
1
ii
11C
1
iii
11C
1
12C
Paper 4
1
Solution
12C
ib
2021
15k
382
Paper 1
ib
4k
106
1E
Paper 1
1
Solution
1E
2F
Paper 1
1
Solution
2F
3B
Paper 1
1
Solution
3B
4D
Paper 1
1
Solution
4D
5B
Paper 1
1
Solution
5B
6H
Paper 1
247
6
a
6H
1
b
6H
1
c
6H
1
7H
Paper 1
141
6
a
7H
1
b
7H
1
c
7H
1
8E
Paper 1
235
12
a
8E
90
4
b
8E
145
6
9G
Paper 1
1
Solution
9G
10F
Paper 1
370
12
i
10F
1
ii
10F
1
a
10F
1
b
10F
1
c
10F
1
d
10F
1
11F
Paper 1
1
Solution
11F
12G
Paper 1
343
6
a
12G
1
b
12G
1
c
12G
1
13C
Paper 1
123
4
a
13C
1
b
13C
1
14C
Paper 1
158
4
i
14C
1
ii
14C
1
15D
Paper 1
158
6
a
15D
1
b
15D
1
c
15D
1
16A
Paper 1
159
6
a
16A
1
b
16A
1
c
16A
1
17B
Paper 1
167
6
i
17B
1
ii
17B
1
iii
17B
1
18H
Paper 1
233
8
a
18H
1
b
18H
1
c
18H
1
d
18H
1
19H
Paper 1
233
4
a
19H
1
b
19H
1
Paper 2
ib
3k
88
1G
Paper 2
1
Solution
1G
2F
Paper 2
93
4
a
2F
1
b
2F
1
3C
Paper 2
77
4
i
3C
1
ii
3C
1
4D
Paper 2
1
Solution
4D
5A
Paper 2
93
4
a
5A
1
b
5A
1
6H
Paper 2
1
Solution
6H
7H
Paper 2
1
Solution
7H
8E
Paper 2
241
9
a
8E
1
b
8E
177
6
9G
Paper 2
1
Solution
9G
10F
Paper 2
1
Solution
10F
11E
Paper 2
1
Solution
11E
12B
Paper 2
225
7
a
12B
1
b
12B
122
4
13D
Paper 2
1
Solution
13D
14A
Paper 2
223
8
a
14A
1
b
14A
1
c
14A
1
d
14A
1
15C
Paper 2
172
4
a
15C
1
b
15C
1
16D
Paper 2
320
6
a
16D
1
b
16D
1
c
16D
1
17B
Paper 2
199
4
a
17B
1
b
17B
1
18H
Paper 2
259
12
a
18H
111
4
b
18H
148
6
Paper 3
ib
4k
93
1G
Paper 3
1
Solution
1G
2E
Paper 3
1
Solution
2E
3B
Paper 3
1
Solution
3B
4D
Paper 3
1
Solution
4D
5A
Paper 3
1
Solution
5A
6C
Paper 3
77
4
i
6C
1
ii
6C
1
7A
Paper 3
95
6
a
7A
1
b
7A
1
c
7A
1
8H
Paper 3
134
6
a
8H
1
b
8H
1
c
8H
1
9E
Paper 3
215
7
a
9E
103
4
b
9E
1
10G
Paper 3
408
10
i
10G
1
ii
10G
1
iii
10G
1
iv
10G
1
v
10G
1
11F
Paper 3
1
Solution
11F
12E
Paper 3
1
Solution
12E
13G
Paper 3
1
Solution
13G
14A
Paper 3
200
6
a
14A
1
b
14A
1
c
14A
1
15D
Paper 3
173
4
a
15D
1
b
15D
1
16A
Paper 3
179
6
a
16A
1
b
16A
1
c
16A
1
17B
Paper 3
196
6
a
17B
1
b
17B
1
c
17B
1
18H
Paper 3
214
10
i
18H
1
ii
18H
1
iii
18H
1
iv
18H
1
v
18H
1
19H
Paper 3
1
Solution
19H
Paper 4
ib
4k
91
1E
Paper 4
123
4
i
1E
1
ii
1E
1
2F
Paper 4
201
6
a
2F
1
b
2F
1
c
2F
1
3G
Paper 4
1
Solution
3G
4C
Paper 4
1
Solution
4C
5D
Paper 4
1
Solution
5D
6B
Paper 4
87
4
a
6B
1
b
6B
1
7H
Paper 4
1
Solution
7H
8E
Paper 4
312
6
a
8E
1
b
8E
1
c
8E
1
9G
Paper 4
1
Solution
9G
10F
Paper 4
162
4
a
10F
1
b
10F
1
11F
Paper 4
1
Solution
11F
12B
Paper 4
1
Solution
12B
13D
Paper 4
210
6
a
13D
1
b
13D
1
c
13D
1
14C
Paper 4
1
Solution
14C
15C
Paper 4
225
4
a
15C
1
b
15C
1
16A
Paper 4
238
8
a
16A
1
b
16A
1
c
16A
1
d
16A
1
17H
Paper 4
275
12
a
17H
1
b
17H
1
c
17H
1
d
17H
1
e
17H
1
f
17H
1
18H
Paper 4
604
11
a
18H
1
b
18H
1
c
18H
406
6
ii
2021
32k
1k
Paper 1
ii
13k
304
1I
Paper 1
1
Solution
1I
2H
Paper 1
1
Solution
2H
3K
Paper 1
324
6
i
3K
1
ii
3K
1
iii
3K
1
4F
Paper 1
1
Solution
4F
5J
Paper 1
1
Solution
5J
6E
Paper 1
327
12
a
6E
88
4
b
6E
239
6
7E
Paper 1
1
Solution
7E
8D
Paper 1
137
4
a
8D
1
b
8D
1
9B
Paper 1
258
6
a
9B
1
b
9B
1
c
9B
1
10D
Paper 1
219
4
a
10D
1
b
10D
1
11K
Paper 1
1
Solution
11K
12F
Paper 1
352
6
i
12F
1
ii
12F
1
iii
12F
1
13J
Paper 1
596
12
a
13J
328
6
b
13J
268
4
14E
Paper 1
366
8
a
14E
1
b
14E
1
c
14E
1
d
14E
1
15B
Paper 1
345
8
a
15B
1
b
15B
1
c
15B
1
d
15B
1
16G
Paper 1
321
6
a
16G
1
b
16G
1
c
16G
1
17G
Paper 1
313
6
a
17G
1
b
17G
1
c
17G
1
18I
Paper 1
479
4
a
18I
1
b
18I
1
19I
Paper 1
466
11
a
19I
1
b
19I
1
c
19I
144
6
20G
Paper 1
318
6
a
20G
1
b
20G
1
c
20G
1
21F
Paper 1
295
6
a
21F
1
b
21F
1
c
21F
1
22H
Paper 1
489
14
a
22H
162
4
b
22H
1
c
22H
238
6
23H
Paper 1
300
4
a
23H
1
b
23H
1
24F
Paper 1
449
8
a
24F
1
b
24F
1
c
24F
1
d
24F
1
25I
Paper 1
296
9
Solution
25I
i
25I
1
ii
25I
1
Decomposition of the given vanishing locus
25I
1
Non-isomorphism of the two unions of lines
25I
1
26F
Paper 1
339
10
a
26F
1
b
26F
1
c
26F
147
5
27H
Paper 1
152
6
a
27H
1
b
27H
1
c
27H
1
28K
Paper 1
256
6
a
28K
1
b
28K
1
c
28K
1
29J
Paper 1
254
6
a
29J
1
b
29J
1
c
29J
1
30K
Paper 1
413
10
a
30K
1
b
30K
1
c
30K
1
d
30K
1
e
30K
1
31J
Paper 1
1
Solution
31J
32A
Paper 1
611
11
a
32A
1
b
32A
1
c
32A
268
4
d
32A
1
33D
Paper 1
242
6
a
33D
1
b
33D
1
c
33D
1
34B
Paper 1
309
4
a
34B
1
b
34B
1
35B
Paper 1
383
11
a
35B
1
b
35B
269
8
36C
Paper 1
305
8
a
36C
1
b
36C
1
c
36C
1
d
36C
1
37C
Paper 1
357
8
a
37C
1
b
37C
1
c
37C
1
d
37C
1
38C
Paper 1
348
9
a
38C
1
b
38C
1
c
38C
182
4
39A
Paper 1
458
11
a
39A
1
b
39A
382
8
40A
Paper 1
344
6
a
40A
1
b
40A
1
c
40A
1
41E
Paper 1
348
4
a
41E
1
b
41E
1
Paper 2
ii
7k
254
1I
Paper 2
1
Solution
1I
2H
Paper 2
171
8
i
2H
1
ii
2H
1
iii
2H
1
iv
2H
1
3K
Paper 2
1
Solution
3K
4F
Paper 2
1
Solution
4F
5J
Paper 2
1
Solution
5J
6E
Paper 2
185
8
a
6E
1
b
6E
1
c
6E
1
d
6E
1
7E
Paper 2
248
16
a
7E
75
6
b
7E
99
6
c
7E
1
8D
Paper 2
1
Solution
8D
9B
Paper 2
133
7
a
9B
48
4
b
9B
1
10D
Paper 2
1
Solution
10D
11H
Paper 2
374
14
a
11H
1
b
11H
1
c
11H
1
d
11H
1
e
11H
1
f
11H
1
g
11H
1
12K
Paper 2
172
6
a
12K
1
b
12K
1
c
12K
1
13E
Paper 2
108
4
a
13E
1
b
13E
1
14D
Paper 2
143
6
a
14D
1
b
14D
1
c
14D
1
15D
Paper 2
159
4
a
15D
1
b
15D
1
16G
Paper 2
1
Solution
16G
17G
Paper 2
340
8
a
17G
1
b
17G
1
c
17G
1
d
17G
1
18I
Paper 2
200
9
a
18I
137
6
b
18I
1
19I
Paper 2
234
6
a
19I
1
b
19I
1
c
19I
1
20G
Paper 2
1
Solution
20G
21F
Paper 2
177
6
a
21F
1
b
21F
1
c
21F
1
22H
Paper 2
209
6
a
22H
1
b
22H
1
c
22H
1
23H
Paper 2
112
4
a
23H
1
b
23H
1
24F
Paper 2
1
Solution
24F
25I
Paper 2
1
Solution
25I
26F
Paper 2
1
Solution
26F
27H
Paper 2
1
Solution
27H
28K
Paper 2
224
6
a
28K
1
b
28K
1
c
28K
1
29J
Paper 2
229
6
a
29J
1
b
29J
1
c
29J
1
30K
Paper 2
213
8
a
30K
1
b
30K
1
c
30K
1
d
30K
1
31J
Paper 2
145
4
a
31J
1
b
31J
1
32A
Paper 2
143
9
a
32A
43
4
b
32A
1
c
32A
1
33A
Paper 2
234
6
a
33A
1
b
33A
1
c
33A
1
34D
Paper 2
215
8
a
34D
1
b
34D
1
c
34D
1
d
34D
1
35B
Paper 2
99
4
a
35B
1
b
35B
1
36B
Paper 2
131
8
a
36B
1
b
36B
1
c
36B
1
d
36B
1
37C
Paper 2
156
7
a
37C
1
b
37C
98
4
38C
Paper 2
164
11
a
38C
1
b
38C
1
c
38C
64
4
d
38C
1
39A
Paper 2
143
4
a
39A
1
b
39A
1
40A
Paper 2
158
4
a
40A
1
b
40A
1
41E
Paper 2
133
4
a
41E
1
b
41E
1
Paper 3
ii
7k
245
1I
Paper 3
1
Solution
1I
2H
Paper 3
154
4
i
2H
1
ii
2H
1
3K
Paper 3
1
Solution
3K
4F
Paper 3
1
Solution
4F
5J
Paper 3
1
Solution
5J
6E
Paper 3
115
8
a
6E
1
b
6E
1
c
6E
1
d
6E
1
7E
Paper 3
132
8
a
7E
1
b
7E
1
c
7E
1
d
7E
1
8D
Paper 3
1
Solution
8D
9B
Paper 3
109
6
a
9B
1
b
9B
1
c
9B
1
10D
Paper 3
1
Solution
10D
11I
Paper 3
1
Solution
11I
12F
Paper 3
262
6
i
12F
1
ii
12F
1
iii
12F
1
13E
Paper 3
176
6
a
13E
1
b
13E
1
c
13E
1
14B
Paper 3
155
6
a
14B
1
b
14B
1
c
14B
1
15D
Paper 3
262
12
a
15D
136
4
b
15D
126
6
16G
Paper 3
234
4
a
16G
1
b
16G
1
17G
Paper 3
190
4
a
17G
1
b
17G
1
18I
Paper 3
1
Solution
18I
19I
Paper 3
251
12
a
19I
76
4
b
19I
175
6
20F
Paper 3
146
6
a
20F
1
b
20F
1
c
20F
1
21H
Paper 3
278
8
a
21H
1
b
21H
1
c
21H
1
d
21H
1
22H
Paper 3
165
4
a
22H
1
b
22H
1
23F
Paper 3
237
6
a
23F
1
b
23F
1
c
23F
1
24I
Paper 3
284
4
i
24I
1
ii
24I
1
25F
Paper 3
1
Solution
25F
26H
Paper 3
1
Solution
26H
27K
Paper 3
196
6
a
27K
1
b
27K
1
c
27K
1
28J
Paper 3
163
6
a
28J
1
b
28J
1
c
28J
1
29K
Paper 3
175
6
a
29K
1
b
29K
1
c
29K
1
30A
Paper 3
110
4
a
30A
1
b
30A
1
31A
Paper 3
313
8
a
31A
1
b
31A
1
c
31A
1
d
31A
1
32D
Paper 3
176
8
a
32D
1
b
32D
1
c
32D
1
d
32D
1
33B
Paper 3
145
6
a
33B
1
b
33B
1
c
33B
1
34B
Paper 3
149
4
a
34B
1
b
34B
1
35C
Paper 3
160
8
a
35C
1
b
35C
1
c
35C
1
d
35C
1
36C
Paper 3
165
6
a
36C
1
b
36C
1
c
36C
1
37C
Paper 3
203
11
a
37C
1
b
37C
1
c
37C
129
6
38A
Paper 3
160
6
a
38A
1
b
38A
1
c
38A
1
39A
Paper 3
187
8
a
39A
1
b
39A
1
c
39A
1
d
39A
1
40E
Paper 3
141
4
a
40E
1
b
40E
1
Paper 4
ii
5k
256
1I
Paper 4
1
Solution
1I
2H
Paper 4
116
6
a
2H
1
b
2H
1
c
2H
1
3K
Paper 4
1
Solution
3K
4F
Paper 4
96
6
i
4F
1
ii
4F
1
iii
4F
1
5J
Paper 4
1
Solution
5J
6E
Paper 4
98
4
a
6E
1
b
6E
1
7E
Paper 4
116
7
a
7E
1
b
7E
84
4
8D
Paper 4
1
Solution
8D
9B
Paper 4
84
4
a
9B
1
b
9B
1
10D
Paper 4
86
6
a
10D
1
b
10D
1
c
10D
1
11I
Paper 4
187
8
a
11I
1
b
11I
1
c
11I
1
d
11I
1
12H
Paper 4
1
Solution
12H
13J
Paper 4
103
8
a
13J
1
b
13J
1
c
13J
1
d
13J
1
14E
Paper 4
149
10
a
14E
1
b
14E
1
c
14E
1
d
14E
1
e
14E
1
15D
Paper 4
117
8
a
15D
1
b
15D
1
c
15D
1
d
15D
1
16G
Paper 4
1
Solution
16G
17G
Paper 4
1
Solution
17G
18I
Paper 4
151
6
a
18I
1
b
18I
1
c
18I
1
19I
Paper 4
150
9
a
19I
1
b
19I
108
6
20G
Paper 4
180
4
a
20G
1
b
20G
1
21F
Paper 4
69
4
a
21F
1
b
21F
1
22H
Paper 4
174
8
a
22H
1
b
22H
1
c
22H
1
d
22H
1
23H
Paper 4
119
4
a
23H
1
b
23H
1
24I
Paper 4
1
Solution
24I
25F
Paper 4
151
6
i
25F
1
ii
25F
1
iii
25F
1
26H
Paper 4
1
Solution
26H
27K
Paper 4
141
6
a
27K
1
b
27K
1
c
27K
1
28J
Paper 4
174
8
a
28J
1
b
28J
1
c
28J
1
d
28J
1
29K
Paper 4
165
8
a
29K
1
b
29K
1
c
29K
1
d
29K
1
30J
Paper 4
1
Solution
30J
31A
Paper 4
88
8
a
31A
1
b
31A
1
c
31A
1
d
31A
1
32A
Paper 4
149
9
a
32A
1
b
32A
1
c
32A
42
4
33B
Paper 4
77
4
a
33B
1
b
33B
1
34B
Paper 4
185
11
a
34B
1
b
34B
1
c
34B
87
4
d
34B
1
35C
Paper 4
184
8
a
35C
1
b
35C
1
c
35C
1
d
35C
1
36C
Paper 4
93
6
a
36C
1
b
36C
1
c
36C
1
37C
Paper 4
155
12
a
37C
128
4
b
37C
27
6
38A
Paper 4
151
8
a
38A
1
b
38A
1
c
38A
1
d
38A
1
39A
Paper 4
97
6
a
39A
1
b
39A
1
c
39A
1
40E
Paper 4
106
4
a
40E
1
b
40E
1
Ancestors
(6)
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
List of universities
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