File Format:PDF/Adobe Acrobat -Quick View 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...
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday 13th January 1993. Time allowed Three and a half hours. Instructions • Full written solutions are...
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD 1974. Time allowed: 3 hours. Each question should be answered on a fresh sheet of paper. Use one side of the paper...
File Format:PDF/Adobe Acrobat -Quick View 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...
File Format:PDF/Adobe Acrobat -Quick View NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. BRITISH MATHEMATICAL OLYMPIAD. Wednesday 17th January 1990. Time allowed - Three and a halt hours...
File Format:PDF/Adobe Acrobat -Quick View Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 25 February 2003. Time allowed Three and a half hours. Each question is worth 10 marks....
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 13 January 1999. Time allowed Three and a half hours. Instructions • Full written solutions - not...
File Format:PDF/Adobe Acrobat -Quick View Supported by. British Mathematical Olympiad. Round 1 : Wednesday, 30 November 2005. Time allowed 31. 2 hours. Instructions • Full written solutions - not just...
File Format:PDF/Adobe Acrobat -Quick View Supported by. British Mathematical Olympiad. Round 1 : Wednesday, 1 December 2004. Time allowed Three and a half hours....
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday 15th January 1992. Time allowed. Instructions 0. Three and a half hours....
File Format:PDF/Adobe Acrobat -Quick View 10 Aug 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...
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 17 January 2001. Time allowed Three and a half hours. Instructions • Full written solutions - not...
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Thursday, 15 February 1996. Time allowed Three and a half hours. Each question is worth 10 marks....
File Format:PDF/Adobe Acrobat -Quick View Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 1 February 2005. Time allowed Three and a half hours. Each question is worth 10 marks....
File Format:PDF/Adobe Acrobat -Quick View United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 2 : Thursday, 28 January 2010. Time allowed Three and a half hours. Each question...
File Format:PDF/Adobe Acrobat -Quick View United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 2 : Thursday, 29 January 2009. Time allowed Three and a half hours. Each question...
File Format:PDF/Adobe Acrobat -Quick View Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 30 January 2007. Time allowed Three and a half hours. Each question is worth 10 marks....
File Format:PDF/Adobe Acrobat -Quick View 2. BRITISH MATHEMATICAL OLYMPIAD. Wednesday 16th January 1991. Time allowed - Three and a half hours. Instructions: '...
File Format:PDF/Adobe Acrobat -Quick View NATIONAL OQ'1MI'I'I'EE FOR MATHEMATICAL CONTESTS. Further International Selection Test. Friday 5th February 1988. Time allowed - 355 hours. PLEASE...
File Format:PDF/Adobe Acrobat -Quick View United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 2 : Thursday, 31 January 2008. Time allowed Three and a half hours. Each question...
File Format:PDF/Adobe Acrobat -Quick View 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...
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Wednesday, 23 February 2000. Time allowed Three and a half hours. Each question is worth 10 marks....
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Thursday, 27 February 1997. Time allowed Three and a half hours. Each question is worth 10 marks....
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday 13th January 1993. Time allowed Three and a half hours. Instructions • Full written solutions are...
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 17th January 1996. Time allowed Three and a half hours. Instructions • Full written solutions - not...
File Format:PDF/Adobe Acrobat -Quick View British Mathematical Olympiad. Round 1 : Wednesday, 5 December 2001. Time allowed Three and a half hours. Instructions • Full written solutions - not just...
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Thursday, 25 February 1999. Time allowed Three and a half hours. Each question is worth 10 marks....
File Format:PDF/Adobe Acrobat -Quick View British Mathematical Olympiad. Round 2 : Tuesday, 26 February 2002. Time allowed Three and a half hours. Each question is worth 10 marks. Instructions • Full...
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Tuesday, 27 February 2001. Time allowed Three and a half hours. Each question is worth 10 marks....
File Format:PDF/Adobe Acrobat -Quick View United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 2 : Thursday, 27 January 2011. Time allowed Three and a half hours. Each question...
File Format:PDF/Adobe Acrobat -Quick View NATIONAL COMMITTEE FOR MATHEMATICAL CONTES'I'S. British Mathematical Olympiad. Friday 20th November 1987. Time allowed - 3% hours...
File Format:PDF/Adobe Acrobat -Quick View Supported by. British Mathematical Olympiad. Round 1 : Friday, 1 December 2006. Time allowed 31. 2 hours. Instructions • Full written solutions - not just...
File Format:PDF/Adobe Acrobat -Quick View 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...
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 15 January 1997. Time allowed Three and a half hours. Instructions • Full written solutions - not...
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 14 January 1998. Time allowed Three and a half hours. Instructions • Full written solutions - not...
File Format:PDF/Adobe Acrobat -Quick View 16 Jul 2009 –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...
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday 18th January 1995. Time allowed Three and a half hours. Instructions • Full written solutions are...
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 12 January 2000. Time allowed Three and a half hours. Instructions • Full written solutions - not...
File Format:PDF/Adobe Acrobat -Quick View NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. Further International Selection Test. Friday, 23rd March 1984. Time allowed - 3} hours. Write on...
File Format:PDF/Adobe Acrobat -Quick View Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 24 February 2004. Time allowed Three and a half hours. Each question is worth 10 marks....
File Format:PDF/Adobe Acrobat -Quick View Supported by. British Mathematical Olympiad. Round 1 : Wednesday, 11 December 2002. Time allowed Three and a half hours. Instructions • Full written...
File Format:PDF/Adobe Acrobat -Quick View NATIONAL CUMMITTEE FOR MATHEMATICAL CUNTESTS. British Mathematical Olympiad. Tuesday 4th March 1986. Time allowed ~ 3ž hours . Write on one...
File Format:PDF/Adobe Acrobat -Quick View National Committee for Mathematical Contests. Second International Selection Test. Reading, 23rd April 1988. Time allowed : 355 hours...
File Format:PDF/Adobe Acrobat -Quick View Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 31 January 2006. Time allowed Three and a half hours. Each question is worth 10 marks....
File Format:PDF/Adobe Acrobat -Quick View NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. British Mathematical Olympiad. 13:11 March, 1980. Time allowed - 3% hours. Write on one side of the paper only...
File Format:PDF/Adobe Acrobat -Quick View NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. BRITISH MATHEMATICAL OLYMPIAD. Tuesday 13th December 1988. Time allowed - 3% hours...
File Format:PDF/Adobe Acrobat -Quick View NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. British Mathematical Olympiad. Tuesday 5 March, 1985. Time allowed - 3% hours. Write on one...
File Format:PDF/Adobe Acrobat -Quick View FIST 2, Bristol , May, 1985. Q1 Let x1,x2,. . .xn be real numbers such that 0' xig 2 £01- each 1. . Prove that. n n. E 3% [xi-xii Q n?...
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Thursday, 24 February 1994. Time allowed Three and a half hours. Each question is worth 10 marks....
File Format:PDF/Adobe Acrobat -Quick View NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. British Mathematical Olympiad. Tuesday, 13th March l984. Time allowed ~ 3% hours. Write on one...
File Format:PDF/Adobe Acrobat -Quick View THE MATHEMATICAL ASSOCIATION. National Committee for Mathematical Contests. British Mathematical Olympiad. 10th March 1983. Time allowed — 3%...
File Format:PDF/Adobe Acrobat -Quick View BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Thursday, 16 February 1995. Time allowed Three and a half hours. Each question is worth 10 marks....
File Format:PDF/Adobe Acrobat -Quick View NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. Second International Selection Test. Reading, Saturday 10th May 1.986. 3% hours...
File Format:PDF/Adobe Acrobat -Quick View NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. British Mathematical Olympiad. Friday 20th March 1987. Time allowed — 3'/2 hours. PLEASE...
File Format:PDF/Adobe Acrobat -Quick View 2 Jun 2010 –NST 4. 2 June 2010. 1. Consider the sequence (ai) such that a0 = 4, a1 = 22 and an − 6an−1 + an−2 = 0 for n ≥ 2. Prove that there are integral...
File Format:PDF/Adobe Acrobat -Quick View AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE. 2011 IMO Team Training. Exam T14. • Each question is worth 7 points. • Time allowed is 41. 2 hours....
File Format:PDF/Adobe Acrobat -Quick View SECOND INTERNATIONAL SELECTION TEST. 'h'in.ity College, Cambridge, 14th April 1991. Time allowed: Three-and-a-half hours....
File Format:PDF/Adobe Acrobat -Quick View NATIONAL (XX“MI'I'I'EE KR MATHE4ATICAL CDNTESTS. Training Weekend 1989. GEIMETRY TEST. Tine allowed = IX hours. A, B are two points on a sphere whose centre...
File Format:PDF/Adobe Acrobat -Quick View 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...
File Format:PDF/Adobe Acrobat -Quick View r1.-iy 12th 1918 — 3% hours. A plane convex pentagon ABCDE is said to have the "unit triangle preperty" if the area of each of the triangles ABC , BCD, CUE,...
File Format:PDF/Adobe Acrobat -Quick View 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...
File Format:PDF/Adobe Acrobat -Quick View AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE. 2008 IMO Team Training. Exam T15. • Each question is worth 7 points. • Time allowed is 41. 2 hours....
File Format:PDF/Adobe Acrobat -Quick View 1. 2. 3. FINAL SELECTION TEST. SUNDAY 31 MARCH 1996. Time Allowed: 451- hours. Two circles F1 and I'; intersect at D and E....
File Format:PDF/Adobe Acrobat -Quick View Next Selection Test: Paper 3. Oundle School. 31st May 2011. 1. If X is a set of integers, define D(X) to be the set of differences between elements of X: D(X) = {n...
File Format:PDF/Adobe Acrobat -Quick View AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE. 2010 IMO Team Training. Exam T16. • Each question is worth 7 points. • Time allowed is 41. 2 hours....
File Format:PDF/Adobe Acrobat -Quick View 1. 2. 5. 4. Further International Selection Test. May l'7, 1972. Time 5 Fours. Only your best 5 answers will score,. Show ho-sf to assign to the vertices of a regular...
File Format:PDF/Adobe Acrobat -Quick View Next Selection Test: Exam 1. IMO camp, Oundle School. 25-v-2008. Problem 1 Let M and N be vertices of a cube. Assign the number 1 to...
File Format:PDF/Adobe Acrobat -Quick View 1. 2. 3. FINAL SELECTION TEST. SUNDAY 5 APRIL 1998. Time allowed: 4% hours. Let P(:c) be a polynomial with real coefficients such that...
File Format:PDF/Adobe Acrobat -Quick View 1. 2. 3. NST 2, Eton and Oundle, 2009. There are 2008 red cards and 2008 white cards. They are shuffled and dealt to 2008 people seated facing inwards in a...
File Format:PDF/Adobe Acrobat -Quick View 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)...
File Format:PDF/Adobe Acrobat -Quick View 1. 2. 3. Oundle Test 3. 29 May 2007. Let ABC be a triangle with LB 7-4 LC. The incircle I of ABC touches the sides BC, CA AB at the points D, E, F , respectively....
File Format:PDF/Adobe Acrobat -Quick View TEAM SELECTION TEST 2. TUESDAY 29 MAY 2001. 08.30-13.00. 1. Let a, b, c, x, y, z be positive reals, with a ≥ b ≥ c and x ≥ y ≥ z. Prove that a2x2...
File Format:PDF/Adobe Acrobat -Quick View Next Selection Test: Paper 4. Oundle School. 1st June 2011. 1. Let A be the set of all integers of the form a2 + 13b2, where a and b are integers and b is nonzero...
File Format:PDF/Adobe Acrobat -Quick View Romanian Master in Mathematics. Unofficial Edition, 2008, Bucharest. Problem 1. Let ABC be an equilateral triangle. P is a variable point internal to the triangle...
File Format:PDF/Adobe Acrobat -Quick View Next Selection Test: Paper 1. Oundle School. 29th May 2011. 1. Circles Γ1 and Γ2 meet at M and N. Let A be on Γ1 and D on Γ2. The lines AM and AN meet Γ2...
File Format:PDF/Adobe Acrobat -Quick View 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...
File Format:PDF/Adobe Acrobat -Quick View 1. 2. 3. NST3 2009. Eton May 21, Oundle May 26. Let ABC be an acute-angled triangle, and M be a point in its plane distinct from the vertices. Show that the...
File Format:PDF/Adobe Acrobat -Quick View 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...
File Format:PDF/Adobe Acrobat -Quick View 1. 2. 3. Oundle Test 4. 30 May 2007. Consider triangle ABC'. B1 is on the line AC and the line BB1 passes through the incentre I. The point C1 is similarly defined...
File Format:PDF/Adobe Acrobat -Quick View FINAL SELECTION. TEST. SUNDAY. )) APRIL )999. 08. )5-)2 .4 5. 1. A sequence of positive integers ai, a2, . . . is defined as follows: ai = 1 and, for n > 1,...
File Format:PDF/Adobe Acrobat -Quick View 1. 2. 3. FST1 2006. Trinity College Cambridge. Let E be the intersection of the diagonals of the cyclic quadrilateral...
File Format:PDF/Adobe Acrobat -Quick View Next Selection Test: 4 hours 30 minutes. Oundle, May 27, 2003. Let p1,p2, . . . , pn be distinct prime numbers greater than 3. Show that...
File Format:PDF/Adobe Acrobat -Quick View First Selection Test: Paper 2. Trinity College, Cambridge. 18th April 2011. 1. For any positive integer n, let an be the exponent of the largest power of 2 which...
File Format:PDF/Adobe Acrobat -Quick View 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...
File Format:PDF/Adobe Acrobat -Quick View UK IMO FST1. Trinity College, Cambridge. 9 April 2005. 1. An infinite sequence a0,a1,a2,... of real numbers satisfies the condition...
File Format:PDF/Adobe Acrobat -Quick View FST 1 2010. Trinity College, Cambridge. 10th April 2010. 1. Find all polynomials P(x) with real coefficients which have the property that if a is a real number and...
File Format:PDF/Adobe Acrobat -Quick View FST 2 2010. Trinity College, Cambridge. 12th April 2010. 4. Find all solutions to p(p + 1) + q(q + 1) = n(n + 1) where p and q are prime numbers and n is a...
No comments:
Post a Comment