Apr 5, 2013

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notes on BMO marking - British Mathematical Olympiad

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BMO Marking. Each question on the British Mathematical Olympiad is marked out of a total of. 10 marks. The style of marking is rather different to that which most ...
2. [PDF]

Areal Co-ordinate Methods in Euclidean Geometry

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Areal Co-ordinate Methods in Euclidean Geometry. Tom Lovering. April 11, 2008. Introduction. In this article I aim to briefly develop the theory of areal (or ...
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BMO problems from the past - British Mathematical Olympiad

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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday 13th January 1993. Time allowed Three and a half hours. Instructions • Full written solutions are ...
4. [PDF]

NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS ...

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NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. BRITISH MATHEMATlCAL OLYMPIAD. Wednesday 17th January 1990. Time allowed - Three and ...
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24 March 1975 - British Mathematical Olympiad

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BRITISH MATHEMATICAL OLYMPIAD, 1975. 24th March, 1975. Time allowed - 3 hours. Write on one side of the paper only. Start each question on a fresh ...
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Friday, 30 November 2007 - British Mathematical Olympiad

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Nov 30, 2007 – United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 1 : Friday, 30 November 2007. Time allowed 31. 2 hours.
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Problem

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Language: English. Day: 1. Tuesday, July 10, 2012. Problem 1. Given triangle ABC the point J is the centre of the excircle opposite the vertex A. This excircle is ...
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Thursday, 2 December 2010 - British Mathematical Olympiad

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Dec 2, 2010 – United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 1 : Thursday, 2 December 2010. Time allowed 31. 2 hours.
9. [PDF]

25 February 2003 - British Mathematical Olympiad

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Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 25 February 2003. Time allowed Three and a half hours. Each question is worth 10 marks.
10. [PDF]

UK Mathematical Olympiad for Girls (UK MOG) - British ...

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United Kingdom Mathematics Trust. UK Mathematical Olympiad for Girls. 20 September 2012. Instructions. • Time allowed: 3 hours. • Full written solutions – not ...
11. [PDF]

13 February 1992 - British Mathematical Olympiad

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BRlTlSH MATHEMATICAL OLYMPIAD. Round 2 : Thursday 13th February 1992. Time allowed Three and a half hours. Each question is worth 10 marks.
12. [PDF]

BMO Round 1 paper - British Mathematical Olympiad

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Dec 2, 2011 – United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 1 : Friday, 2 December 2011. Time allowed 31. 2 hours. Instructions ...
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Supported by. British Mathematical Olympiad. Round 1 : Wednesday, 3 December 2003. Time allowed Three and a half hours. Instructions • Full written ...
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British Mathematical Olympiad Round 1 Friday 1 December 2006 ...

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Dec 1, 2006 – UKMT Maths Challenges Office, School of Mathematics, University of Leeds, Leeds LS2 9JT. Tel: 0113 343 2339 Fax: 0113 343 5500 Email: ...
15. [PDF]

BMO Round 1 paper - British Mathematical Olympiad

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Supported by. British Mathematical Olympiad. Round 1 : Wednesday, 30 November 2005. Time allowed 31. 2 hours. Instructions • Full written solutions - not just ...
16. [PDF]

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Supported by. British Mathematical Olympiad. Round 1 : Wednesday, 1 December 2004. Time allowed Three and a half hours. Instructions • Full written ...
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15 January 1992 - British Mathematical Olympiad

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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday 15th January 1992. Time allowed. Instructions 0. Three and a half hours. Full wrttten solutions are ...
18. [PDF]

Thursday, 4 December 2008 - British Mathematical Olympiad

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Dec 4, 2008 – United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 1 : Thursday, 4 December 2008. Time allowed 31. 2 hours.
19. [PDF]

EGMO | 2012 - British Mathematical Olympiad

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European Girls' Mathematical Olympiad. EGMO | 2012. UK Mathematical Olympiad for Girls. 23 June 2011. Instructions. Supported by. • Time allowed: 3 hours.
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9th Chinese Girls - British Mathematical Olympiad

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Aug 10, 2010 – 9th Chinese Girls' Mathematics Olympiad. Shijiazhuang, China. Day I. 8:00 AM - 12:00 PM. August 10, 2010. 1. Let n be an integer greater than ...
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BRITISH MATHEMATICAL OLYMPIAD 2001 British Mathematical

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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 17 January 2001. Time allowed Three and a half hours. Instructions • Full written solutions - not ...
22. [PDF]

1 February 2005 - British Mathematical Olympiad

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Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 1 February 2005. Time allowed Three and a half hours. Each question is worth 10 marks.
23. [PDF]

15 February 1996 - British Mathematical Olympiad

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BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Thursday, 15 February 1996. Time allowed Three and a half hours. Each question is worth 10 marks.
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28 January 2010 - British Mathematical Olympiad

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United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 2 : Thursday, 28 January 2010. Time allowed Three and a half hours. Each question ...
25. [PDF]

BMO Round 2 paper - British Mathematical Olympiad

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United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 2 : Thursday, 29 January 2009. Time allowed Three and a half hours. Each question ...
26. [PDF]

BMO Round 2 paper - British Mathematical Olympiad

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Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 30 January 2007. Time allowed Three and a half hours. Each question is worth 10 marks.
27. [PDF]

Wednesday 16th January 1991 - British Mathematical Olympiad

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BRITISH MATHEMATICAL OLYMPIAD. Wednesday 16th January 1991. Time allowed - Three and a half hours. Instructions: '. Start each question on a fresh ...
28. [PDF]

2011/12 British Mathematical Olympiad Round 2

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United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 2 : Thursday, 26 January 2012. Time allowed Three and a half hours. Each question ...
29. [PDF]

BMO Round 2 paper - British Mathematical Olympiad

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United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 2 : Thursday, 31 January 2008. Time allowed Three and a half hours. Each question ...
30. [PDF]

International Mathematical Olympiad - Georg Mohr-Konkurrencen

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Language: English. Day: 1. Monday, July 18, 2011. Problem 1. Given any set A = {a1,a2,a3,a4} of four distinct positive integers, we denote the sum a1 +a2 +a3 ...
31. [PDF]

BMO Round 1 paper - British Mathematical Olympiad

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Nov 30, 2012 – United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 1 : Friday, 30 November 2012. Time allowed 31. 2 hours.
32. [PDF]

23 February 2000 - British Mathematical Olympiad

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BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Wednesday, 23 February 2000. Time allowed Three and a half hours. Each question is worth 10 marks.
33. [PDF]

13 January 1993 - British Mathematical Olympiad

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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday 13th January 1993. Time allowed Three and a half hours. Instructions • Full written solutions are ...
34. [PDF]

BMO Round 1 paper - British Mathematical Olympiad

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Dec 3, 2009 – United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 1 : Thursday, 3 December 2009. Time allowed 31. 2 hours.
35. [PDF]

17 January 1996 - British Mathematical Olympiad

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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 17th January 1996. Time allowed Three and a half hours. Instructions • Full written solutions - not ...
36. [PDF]

BMO Round 2 paper - British Mathematical Olympiad

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United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 2 : Thursday, 31 January 2013. Time allowed Three and a half hours. Each question ...
37. [PDF]

" # \$%£& ©"\$'¥ ( )0)1 ¥¨2 34¡¤§ 576869) 6A@ABC)

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( )0)1 ¥¨2 34¡¤§ 576869). 6A@ABC)EDGFH)E5IBQP"D. RTS UWVEX`Y% aQb' YcVedf bhgiXqprpQdsbtY4 uwvEg x8d¤y €ƒ‚ bh„GvEXTyhdHb a…
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27 February 2001 - British Mathematical Olympiad

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BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Tuesday, 27 February 2001. Time allowed Three and a half hours. Each question is worth 10 marks.
39. [PDF]

British Mathematical Olympiad 2010/11 British Mathematical ...

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United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 2 : Thursday, 27 January 2011. Time allowed Three and a half hours. Each question ...
40. [PDF]

BMO Round 1 paper - British Mathematical Olympiad

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Supported by. British Mathematical Olympiad. Round 1 : Friday, 1 December 2006. Time allowed 31. 2 hours. Instructions • Full written solutions - not just ...
41. [PDF]

14 March 1979

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NATIONAL C0l'iHI.T'i'EE FOR 1'ง,ปง'}_" L'lEhAT ICAL CONTESTS. British Mathe.'.uatica,l 0lympia.d lbth March, 1979. Time allosed - 3% hours. Write on one ...
42. [PDF]

15 January 1997 - British Mathematical Olympiad

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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 15 January 1997. Time allowed Three and a half hours. Instructions • Full written solutions - not ...
43. [PDF]

International Mathematical Olympiad - Georg Mohr-Konkurrencen

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Wednesday, July 15, 2009. Problem 1. Let n be a positive integer and let a1,...,ak (k ≥ 2) be distinct integers in the set. {1,...,n} such that n divides ai(ai+1 −1) for i ...
44. [PDF]

FURTHER INTERNATIONAL SELECTION TEST

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FURTHER INTERNATIONAL SELECTION TEST. May 5th, 1975 3% hours. 1. In this question a "real function" means a function f such that f(x) exists and is real ...
45. [PDF]

4 March 1986 - British Mathematical Olympiad

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NATIONAL CUMMITTEE FOR MATHEMATICAL CGNTESTS. British Mathematical Olympiad. Tuesday 4th March 1986. Time allowed ~ 3% hours . Write on one ...
46. [PDF]

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NATIONAL COMMITTEE FOR MA'I'HEMATICAL CONTESTS. British Mathematical Olympiad. Friday 20th November 1987. Time allowed - 3% hours. PLEASE ...
47. [PDF]

AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE 2012 IMO ...

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AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE. 2012 IMO Team Training. Exam T16. • Each question is worth 7 points. • Time allowed is 41. 2 hours.
48. [PDF]

12 January 2000 - British Mathematical Olympiad

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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 12 January 2000. Time allowed Three and a half hours. Instructions • Full written solutions - not ...
49. [PDF]

13 March 1980 - British Mathematical Olympiad

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Mar 13, 1980 – Write on one side of the paper only. fresh sheet of paper. NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. British Mathematical ...
50. [PDF]

24 February 2004 - British Mathematical Olympiad

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Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 24 February 2004. Time allowed Three and a half hours. Each question is worth 10 marks.
51. [PDF]

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Supported by. British Mathematical Olympiad. Round 1 : Wednesday, 11 December 2002. Time allowed Three and a half hours. Instructions • Full written ...
52. [PDF]

Friday, 23rd March 1984

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Mar 23, 1984 – NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. Further International Selection Test. Friday, 23rd March 1984. Time allowed - 3} ...
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BMO2 2006 - British Mathematical Olympiad

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Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 31 January 2006. Time allowed Three and a half hours. Each question is worth 10 marks.
54. [PDF]

National Committee for Mathematical Contests Second International ...

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National Committee for Mathematical Contests. Second International Selection Test. Reading, 23rd April 1988. Time allowed : 355 hours. Please write on one ...
55. [PDF]

FIST 2, May 1985

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FIST 2, Bristol , May, 1985. Q1 Let x1,x2,...xn be real numbers such that oéxiéz for each 1. . Prove that. n n. 2: Z [X1-xi' \< 11*.' When does equality hold'? Q2 The ...
56. [PDF]

NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS

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NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. Second International Selection Test. Reading, Saturday 10th May 1.986. 3% hours. A, B, C, A ', B ' ...
57. [PDF]

May 12th 1918 - 3% hours

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NATIONAL COMMITTEE FOR MATHEMATICAL CON"I'E.':1TS. Further International Selection Test , 19T8. May 12th 1918 - 3% hours. A plane convex pentagon ...
58. [PDF]

AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE 2011 IMO ...

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AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE. 2011 IMO Team Training. Exam T14. • Each question is worth 7 points. • Time allowed is 41. 2 hours.
59. [PDF]

FST, 7 April 2002

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First Selection Test. Trinity IMO Training Camp. 7 April 2002. 1. We are given a circle Γ and a straight line l which is tangent to the circle at the point B. Through ...
60. [PDF]

'IYin.ity College, Cambridge, 14th April 1991

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SECOND INTERNATIONAL SELECTION TEST. 'IYin.ity College, Cambridge, 14th April 1991. Time allowed: Three-and-a-half hours. Let f be the function ...
61. [PDF]

First Selection Test

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First Selection Test. April 2003. 1. Consider triangle ABC. Let U,V,W be points such that U is on the line through B and C, V is on the line through C and A, W is ...
62. [PDF]

First Selection Test: Paper 1

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First Selection Test: Paper 1. Trinity College, Cambridge. 16th April 2011. 1. Let ABC be an acute triangle with D, E, F the feet of the altitudes lying on BC, CA, AB ...
63. [PDF]

AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE 2008 IMO ...

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AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE. 2008 IMO Team Training. Exam T15. • Each question is worth 7 points. • Time allowed is 41. 2 hours.
64. [PDF]

10 May 1979

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30. NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. Further International Selection Test, 1912. May lOth 1979 - 3% hours. a, b, c , d are different ...
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FST, 31 March 1996

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FINAL SELECTION TEST. SUNDAY 31 MARCH 1996. Time Allowed: 4% hours. 1. Two circles F1 and F2 intersect at D and E. The point B on F1 and the point C ...
66. [PDF]

May 8, 1980 5% hours

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National Committee for Mathematical Contests. Further International Selection Test. May 8, 1980 5% hours. 1. VLMW and VABC are tetrahedra with A,B,C on VL ...
67. [PDF]

GEIMETRY TEST

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NATIONAL CXXMITFEE HR MA'!'HE4ATICAL CDNTESTS. Training Weekend 1989. GEIMETRY TEST. Tine allowed 1% hours. A, B are two points on a sphere ...
68. [PDF]

NST 3, 1 June 2010

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Jun 1, 2010 – NST 3. 1 June 2010. 1. Let n ≥ 2 be an integer. At every point of the co-ordinate plane with integral co-ordinates (i, j) we write i + j modulo n (an ...
69. [PDF]

Oundle Selection Test 1

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Oundle Selection Test 1. 4 hours 30 minutes . Find all nondecreasing functions f : R -> R such that. (Ii) 1%) = 0) f(1) = 1;. (b) f(a) + f(b) : f(a)f(b) + f(a + b — ab) for ...
70. [PDF]

NST 2, 4 June 2012

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Next Selection Test: Paper 2. Oundle School, Northamptonshire. 4th June 2012. 1. Let ABC be an acute triangle. Let ω be a circle whose centre L lies ...
71. [PDF]

FST 2, 2 April 2012

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First Selection Test: Paper 2. Trinity College, Cambridge. 2nd April 2012. 1. Determine all functions f : R → R satisfying the condition. 2f(x) = f(x + y) + f(x + 2y) ...
72. [PDF]

Next Selection Test: Exam 1

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Next Selection Test: Exam 1. IMO carnp7 Oundle School. 25-v-2008. Problem 1 Let M and N be vertices of a cube. Assign the number 1 to these vertices and O ...
73. [PDF]

NST 1, 30 May 2010

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May 30, 2010 – NST 1. 30 May 2010. 1. Consider a regular 2007-gon. Find the smallest positive integer k having the property that in every set of k vertices, ...
74. [PDF]

NST 2, 1 June 2005

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UK IMO Next Selection Test 2. Oundle 2005. 1. Let n ≥ 2 be a natural number. A pyramid P has base A1A2 ···A2n and apex O. The polygon A1A2 ···A2n is ...
75. [PDF]

FINAL SELECTION TEST SUNDAY 5 APRIL 1998

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FINAL SELECTION TEST. SUNDAY 5 APRIL 1998. Time allowed: 4% hours. 1. Let P(:c) be a polynomial with real coefficients such that. P(a:) > O for all 1r 2 O.
76. [PDF]

Oundle Test 3

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Oundle Test 3. 29 May 2007. 1. Let ABC be a triangle with LB 75 LC. The incircle I of ABC touches the sides BC, CA AB at the points D, E, F , respectively. Let AD ...
77. [PDF]

Next Selection Test: Paper 2

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Next Selection Test: Paper 2. Oundle School. 30th May 2011. 1. Find all functions f : Z → Z such that: (a) f(x + f(x + 2y)) = f(2x) + f(2y) for all integers x, y;. (b) f(0) ...
78. [PDF]

NST 2, Eton and Oundle7 2009

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NST 2, Eton and Oundle7 2009. 1. There are 2008 red cards and 2008 white cards. They are shuﬁled and dealt to 2008 people seated facing inwards in a circle ...
79. [PDF]

NST 2, 2004

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Oundle Selection Test 2. 4 hours 30 minutes. 1. Let m be a ﬁxed integer greater than 1. The sequence 51:0, 931,172, . . . is. deﬁned as follows: Find the greatest ...
80. [PDF]

FST1 2009

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FST1 2009. OCR. TCC April 4. 1. Find all prime numbers p such that. 2p_1 — 1. P is a perfect square. 2. Each point of the plane is painted one of three colours.
81. [PDF]

NST 4, 28 May 2008

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Next Selection Test: Exam 4. IMO camp, Oundle School g " 28- -2008 W. M i" i <; (»1*””/1:5 eke'. \jPr0blem 1O Consider an inﬁnite sequence of distinct positive ...
82. [PDF]

Oundle Test 4

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Oundle Test 4. 30 May 2007. 1. Consider triangle ABC'. B1 is on the line AC and the line BB1 passes through the incentre I. The point C1 is similarly deﬁned.
83. [PDF]

UK IMO Next Selection Test 1

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UK IMO Next Selection Test 1. Oundle 2006. 1. Does there exist a bounded function f : R → R with f(1) > 0 satisfying f(x + y)2 ≥ f(x)2 + f(2xy) + f(y)2 for all x, y ...
84. [PDF]

NST 2, 31 May 2010

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May 31, 2010 – NST 2. 31 May 2010. 1. The sequence (ai) is defined by a0 = 2, a1 = 1, and for n ≥ 2 we let an = an−1 + an−2. Show that if p is a prime divisor ...
85. [PDF]

First Selection Test: Exam 2

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First Selection Test: Exam 2. IMO camp, Trinity College Cambridge. 2-iv-2007. Problem 1 Let (1, b be positive integers such that for every positive integer ...
86. [PDF]

Next Selection Test: 4 hours 30 minutes

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Next Selection Test: 4 hours 30 minutes. Oundle, May 27, 2003 . Let p1,p2, . . . , pn be distinct prime numbers greater than 3. Show that. 2P””"4”' + 1 has at least ...
87. [PDF]

FST 1, 31 March 2012

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First Selection Test: Paper 1. Trinity College, Cambridge. 31st March 2012. 1. Let ABCD be a cyclic quadrilateral so that BC and AD meet at a point P. Consider ...
88. [PDF]

FST 1, 8 April 2006

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FSTl 2006. Trinity College Cambridge. 1. Let E be the intersection of the diagonals of the cyclic quadrilateral. ABCD. Let F and G denote the respective ...
89. [PDF]

FST2 2009

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FST2 2009. OCR. TCC April 6. 1. Triangle ABC has a right-angle at C, and the point M' on AB is strictly between A and B. Let S, S1 and S2 denote the ...
90. [PDF]

British Mathematical Olympiad Round 1 Thursday 2nd December ...

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Dec 2, 2010 – UKMT, School of Mathematics Satellite, University of Leeds, Leeds LS2 9JT. Tel: 0113 343 2339 Fax: 0113 343 5500 Email: ...
91. [PDF]

UK IMO FST1

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UK IMO FST1. Trinity College, Cambridge. 9 April 2005. 1. An infinite sequence a0,a1,a2,... of real numbers satisfies the condition an = |an+1 − an+2| for every n ...
92. [PDF]

NST 1, Eton and Oundle, 2009

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NST 1, Eton and Oundle, 2009. 1. The convex quadrilateral ABCD has the property that lAB{ : |AC] =1. |BD{. Let P be the intersection point of its diagonals. Let 0 ...
93. [PDF]

Solutions - British Mathematical Olympiad - Maths

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European Girls' Mathematical Olympiad. EGMO | 2012. UK Mathematical Olympiad for Girls. 23 June 2011. Instructions. Supported by. • Time allowed: 3 hours.
94. [PDF]

solutions - British Mathematical Olympiad - Maths

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United Kingdom Mathematics Trust. UK Mathematical Olympiad for Girls. 20 September 2012. Instructions. • Time allowed: 3 hours. • Full written solutions – not ...
95. [PDF]

press release - British Mathematical Olympiad - Maths

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Jul 16, 2012 – UNITED KINGDOM MATHEMATICS TRUST. The UKMT is a company limited by guarantee and registered in England and Wales. Registered ...
96. [PDF]

day 2

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THE 4th ROMANIAN MASTER OF MATHEMATICS COMPETITION. DAY 2: SATURDAY, FEBRUARY 26, 2011, BUCHAREST. Language: English. Problem 4.
97. [PDF]

Statistics of results - British Mathematical Olympiad

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UK Mathematical Olympiad for Girls. 23 June 2011. Statistics of results. 154 candidates entered UK MOG 2011, of whom 118 returned scripts. Statistics of the ...
98. [PDF]

Statistics of results - British Mathematical Olympiad

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UK Mathematical Olympiad for Girls. 20 September 2012. Statistics of results. 247 candidates entered UK MOG 2012, of whom 160 returned scripts. Statistics of ...
99. [PDF]

day 1

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Language: English. Problem 1. Given a finite number of boys and girls, a sociable set of boys is a set of boys such that every girl knows at least one boy in that ...
100. [PDF]

day 2

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THE 3RD ROMANIAN MASTER OF MATHEMATICS COMPETITION. DAY 2: SATURDAY, FEBRUARY 27, 2010, BUCHAREST. Language: English. Problem 4.