Click UKMT Challenge and scroll to the relevant section for a detailed description and everything you could possible need to want to know about the Intermediate Challenge and UKMT Challenge in general.
The following intemrediate papers can be found below:
- Intermediate Challenge from 1999 to 2023
- Grey and Pink Kangarooo from 2015 - 2023 (the first paper that exists is 2015)
- Cayley, Hamilton and Maclaurin Olympiad from 2015 - 2023 (the first paper that exists is 2015)
Pathway
The intermediate challenge awards are bronze, silver and gold.
After take the challenge you can either qualify for the Kangaroos (Grey or Pink) or the Olympiad (Cayley, Hamilton and Maclaurin) depending on two factors:
- how highly you score in the Intermediate Challenge.
- what year you are in - The Pink/Grey Kangaroos and the Cayley/Hamilton. Maclaurin Olympiads are year group specific so students would only be able to participate in the Kangaroo/Olympiad that relates to their year group regarless of how highly they score.
Note: Students who qualify for the Maclaurin Olympiad can be selected for the National Mathematics Summer School in July. They get sent to the International Maths Olympiad training camp/squad. They are selected by lottery which selects 48 of the top 1.5% scores in the IMC.
Past papers scores (1999-2023) that obtained bronze, silver, gold in the intermediate challenge and qualified for the Kangaroos (grey or pink) or Olympiad (Cayley, Hamilton or Maclaurin) are as follows:
| Year |
Bronze |
Silver |
Gold |
GK |
PK |
CO |
HO |
MO |
| 1999 |
50 |
64 |
80 |
|
|
|
|
|
| 2000 |
40 |
55 |
73 |
|
|
|
|
|
| 2001 |
32 |
43 |
57 |
|
|
|
|
|
| 2002 |
53 |
62 |
72 |
|
|
|
|
|
| 2003 |
46 |
58 |
74 |
75 |
86 |
88 |
98 |
101 |
| 2004 |
40 |
51 |
68 |
67 |
79 |
84 |
93 |
100 |
| 2005 |
40 |
50 |
65 |
64 |
72 |
76 |
85 |
90 |
| 2006 |
46 |
58 |
72 |
72 |
80 |
84 |
92 |
99 |
| 2007 |
50 |
63 |
78 |
78 |
86 |
90 |
97 |
103 |
| 2008 |
42 |
54 |
70 |
70 |
82 |
85 |
95 |
102 |
| 2009 |
39 |
51 |
66 |
66 |
77 |
83 |
90 |
99 |
| 2010 |
45 |
56 |
70 |
70 |
80 |
83 |
91 |
97 |
| 2011 |
47 |
59 |
78 |
77 |
88 |
92 |
99 |
104 |
| 2012 |
50 |
62 |
77 |
77 |
87 |
90 |
96 |
101 |
| 2013 |
47 |
59 |
74 |
73 |
84 |
88 |
96 |
103 |
| 2014 |
42 |
55 |
72 |
67 |
78 |
90 |
96 |
103 |
| 2015 |
37 |
49 |
64 |
61 |
68 |
81 |
88 |
95 |
| 2016 |
40 |
50 |
62 |
60 |
66 |
81 |
89 |
95 |
| 2017 |
47 |
61 |
78 |
72 |
81 |
97 |
106 |
112 |
| 2018 |
48 |
59 |
73 |
68 |
76 |
93 |
100 |
104 |
| 2019 |
43 |
55 |
71 |
65 |
73 |
91 |
99 |
106 |
| 2020 (online) |
60 |
72 |
89 |
80 |
89 |
110 |
117 |
120 |
| 2021 (online) |
55 |
68 |
86 |
68 |
86 |
100 |
110 |
118 |
| 2022 (online) |
50 |
65 |
81 |
65 |
81 |
101 |
111 |
117 |
| 2023 |
42 |
55 |
71 |
67 |
77 |
95 |
100 |
103 |
Challenge Question Breakdown
The ratio of harder question types (questions 16-25) for 2004-2012 is somewhat interesting:
- 38 Geometry questions
- 16 'Spatial Reasoning' questions(paths through networks, rotating objects, etc)
- 16 General Number questions (e.g. ratio, time, density, etc.)
- 14 Number Theory questions (involving integers, primes, digits, etc.)
- 6 Non-Applied Algebra questions
Conclusion: Clearly the key to a high score in the intermediate challenge is to master the geometry problems, many of which follow a similar approach.
Olympiad Question Breakdown
The topics for the questions in the intermediat challenge are somewhat less evenly distributed than in Junior Challenge (it is more geometry-heavy).
The breakdown of questions across a 8 year period from 2004 to 2012 is as follows:
- 59 Geometry questions
- 28 Number Theory questions
- 25 (non-applied) Algebra questions
- 13 Spatial Reasoning/Logic questions
- 6 Number Grid questions
- 5 Speed/Distance/Time questions
- 4 Sequences
- 1 Probability questions
Obvious conclusion: concentrate on your preparation on Geometry! Because of this, there is an extra worksheet below involving finding difficult areas and lengths which is entitled 'Geometry Challenge Worksheet'.
Questions By Topic
There is a section below when questions are categorised according to topic to help students hone particular skills.
Intermediate Challenge:
All are harder questions from Intermediate Challenge past papers, i.e. the harder questions 16-25, the point at which points are lost for incorrect answers are listed below in the intermediate by topic section.
Intermediate Olympiad (Cayley, Hamilton and Maclaurin):
There is also a section at the bottom which includes Olympiad questions by topic.
Scoring
Intermediate Challenge (includes negative marking):
- 5 marks for correct answers to questions 1-15
- 6 marks for correct answers to questions 16-25
- 0 marks for incorrect answers to questions 1-15
- 0 marks for unanswered questions
- -1 marks for incorrect answers to questions 16-20
- -2 marks for incorrect answers to questions 21-25
Intermediate Pink/Grey Kangaroo :
- 5 marks for correct answers to questions 1-15
- 6 marks for correct answers to questions 16-25
- 0 marks for incorrect/unanswered answers to questions 1-25
Intermediate Olympiad (Cayley, Hamilton and Maclaurin):
All 6 questions are scored out of 10 marks. Partial marks are given for correct working and depend on the clarity of presentation and explanation (i.e. your working out!) as much as the answers themselves. A solution with a correct answer may only score 2 out of 10 if not accompanied by any working. An incomplete solution without the right answer might score 2 or 3 marks, and near complete and complete solutions could score 8,9 or 10 marks each. If a solution is judged to be incomplete, it in marked on a 0+ basis, maximum 3 marks. If it has an evident logical strategy, it is marked on a 10-basis. Rather than to try to rush through the section and answer everything, it is advised that students should fully answer the questions that they can. This is because incomplete answers can only score a maximum of 3 marks. Students are encouraged to write complete answers to 2-4 questions rather than hurry through incomplete answers to all 6.
1999 PaperPDF
