Apr 18, 2011

A level maths revision -  for AS and A2 mathematics students

http://www.schoolworkout.co.uk/a_level.htm

The A level maths pages on schoolworkout contain a wide variety of revision material to help students prepare for their AS and A2 mathematics examinations. Resources cover modules in Core Maths, Statistics, Decision Maths and Further Pure Mathematics.

 

 
MATHS PAGES FOR STUDENTS
KS3
GCSE
A LEVEL
MATHS PAGES FOR TEACHERS
KS3 RESOURCES
GCSE RESOURCES
A LEVEL
Home

 

Revision material Links Past paper solutions

If you are about to start on an A level maths course, this Induction booklet revises key topics from GCSE, such as factorising, rearranging formulae and indices.  It will help you to make the best possible start to your course.

The Word documents given in the table below were designed to support OCR's A level mathematics and further mathematics courses.

I offer Maths tuition to people living in the Maidstone area of Kent.  Please email me for more information:  maths@schoolworkout.co.uk

 

Core Mathematics Statistics Further Mathematics
C1 and C2 S1 FP1

Applications of differentiation

Coordinate geometry

Differentiation revision

Factor and remainder theorems

Binomial theorem

Integration

Trigonometry

TOPIC NOTES

Standard deviation (doc or pdf)

Introduction to probability (doc or pdf)

Conditional probability (doc or pdf)

Further conditional probability (doc or pdf)

Product-moment correlation coefficient (docor pdf)

Spearman's Rank Correlation Coeff (doc orpdf)

Regression  (.doc or pdf)

 

REVISION NOTES

Descriptive & numerical stats (doc or pdf)

Probability (.doc or pdf)

Combinations/ permutations (.doc or pdf)

Discrete random variables (.doc or pdf)

Binomial and geometric (.doc or pdf)

Correlation coefficients (.doc or pdf)

Regression (.docx or pdf)

S1 mindmap (.doc or pdf)

Complex numbers

Introduction to matrices

Proof by induction

Roots of quadratic and cubic equations

Series

Matrices and transformations

3 by 3 matrices and systems of equations

 

FP1 (revision summary sheets)

Complex numbers

C3 and C4 S2 FP3

Functions

Exponential functions and logarithms

Chain, product and quotient rules

Integration (including volumes of revolution)

Trigonometry 1 (inverse functions)

Trigonometry 2 (identities and equations)

Numerical methods

Partial fractions

Binomial expansions and parametric functions

Differentiation (implicit, parametric and trigonometric)

Vectors

Integration  (trigonometric and use of substitution)

Integration by parts

Differential equations

Which method of integration should you use?

Summary of differentiation results

Summary of integration results

Revision documents for S2 coming soon!!

Introduction to groups

Differential equations

Complex numbers (de Moivre's theorem)

Vectors

 

FP3 (past examination questions)

Groups

Differential equations

Complex numbers

Vectors

Useful Links:

Mathsnet resources for C1-C4 as well as applied modules and further maths.

waldomaths:  interactive resources for maths.  The site includes a comprehensive set of links to other maths sites.

Milford Haven School: past examination questions for Mechanics organised into topics.

Kent Further Maths Centre: this website has particularly good resources for Decision Mathematics (D1), Mechanics and Further Mathematics.

Metric Maths at Imperial College London: 

Links to useful A level websites can be found here:  http://wanadoomaths.mysite.wanadoo-members.co.uk/page4.html

Mathcentre  - this website has excellent video tutorials.

Home ] GCSE ] Key Stage 3 ] Key Stage 4 ] [ A level ]

Past Paper Solutions (OCR)
Core Modules Statistics Modules Further Pure Modules

C1 - New OCR syllabus

January 2008  [pdf]  [word doc]

January 2007  [pdf]  [word doc]

(click here for the Jan 2007 question paper)

 

C2 - New OCR syllabus

January 2008  [pdf]  [word doc]

January 2007  [pdf]  [word doc]

(click here for the Jan 07 question paper)

June 2006  [pdf] [word doc]

(click here for June 06 exam paper)

 

C3 - New OCR syllabus

Specimen paper

June 2005

January 2006

 

C4 - New OCR syllabus

Specimen paper

June 2005

January 2006

 

S1 - Old OCR Syllabus

January 2001  ~  June 2001

January 2002  ~  June 2002

November 2002  ~  January 2003

June 2003  ~  November 2003

June 2004  ~  November 2004

January 2005  ~June 2005

 

S1 - New OCR syllabus

June 2005 [pdf] [word]

(click here for June 05 exam paper)

January 2006

(click here for Jan 06 exam paper)

May 2006

(click here for May 2006 exam paper)

January 2007 [pdf] [word]

(click here for Jan 07 exam paper)

June 2007 [pdf] [word]

(click here for June 07 exam paper)

 

S2 - Old OCR syllabus

June 2001    January 2003

June 2003   January 2004

June 2004   January 2005

June 2005

 

S2 - New OCR syllabus

January 2006

FP1 - New OCR syllabus

Specimen paper

June 2005 [pdf] [word doc]

(click here for the June 2005 FP1 question paper)

January 2006 [pdf]  [word doc]

(click here for the Jan 2006 FP1 question paper)

June 2006 [pdf]  [word doc]

(click here for the June 2006 FP1 question paper)

January 2007 [pdf] [word doc]

(click here for the Jan 2007 FP1 question paper)

June 2007 [pdf] [word doc]

(click here for June 2007 FP1 question paper)

 

 

Home ] GCSE ] Key Stage 3 ] Key Stage 4 ] [ A level ]

Apr 7, 2011

Singapore Mathematical Olympiad questions


  1. [PDF]
     

    Singapore International Mathematical Olympiad National Team ...

    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad. National Team Selection Tests 1994/95 - 2003/2004. 1994/95. 1.1.* Let N = {1,2,3, . ...
    sms.math.nus.edu.sg/Simo/199567890123.pdf
  2. [PDF] 

    Singapore International Mathematical Olympiad Committee 22-9-2001 ...

    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad Committee. 22-9-2001. 1. Consider the set of integers A = {2a3b5c : 0 ≤ a, b, c ≤ 5}. ...
    sms.math.nus.edu.sg/Simo/training2001.pdf
  3. [PDF] 

    Singapore International Mathematical Olympiad National Team ...

    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad. National Team Selection Test I 2006. Time allowed: 4.5 hours. 12 May 2006. No calculator is allowed ...
    sms.math.nus.edu.sg/Simo/selection_test_2006.pdf
  4. [PDF] 

    Competition corner

    File Format: PDF/Adobe Acrobat - Quick View
    Competition corner. All communications about this column should be sent to Dr. Tay Tiong. Seng, Department of Mathematics, National University of Singapore, ...
    sms.math.nus.edu.sg/simo/med022.pdf
  5. [PDF] 

    Training problems 10 April 2003 14. Let A be a set with 8 elements ...

    File Format: PDF/Adobe Acrobat - Quick View
    Training problems 10 April 2003. 14. Let A be a set with 8 elements. Find the maximum number of distinct 3-element subsets of A such that the intersection ...
    sms.math.nus.edu.sg/Simo/training2003/trainging_3q.pdf
  6. [PDF] 

    1 April - Training problems 1 April 2003 8. In a group of ...

    File Format: PDF/Adobe Acrobat - Quick View
    Training problems 1 April 2003. 8. In a group of interpreters each one speaks one or several languages, 24 of them speak ...
    sms.math.nus.edu.sg/Simo/training2003/training_2q.pdf
  7. [PDF] 

    Singapore International Mathematical Olympiad 2009 Senior Team ...

     - 4:35pm
    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad 2009. Senior Team Training. Take Home Test Solutions. 1. For any positive integer k, let f(k) be the number of ...
    sms.math.nus.edu.sg/Simo/2009/2009SeniorTestSoln.pdf
  8. [PDF] 

    200e +FilE#fi+Fffi[Ufrffi#-

    File Format: PDF/Adobe Acrobat - View as HTML
    200e +FilE#fi+Fffi[Ufrffi#- ffi-x r. ft u E_--+ *r:*WRn *-f$€'FE4'lLREt+#tJffiF-A. ffqE, xf{tffiiE. #W. n, #$#f:. n lY*fr.*,.flx), ]tfr1F- flx)fr\FfrH 6W. ...
    sms.math.nus.edu.sg/Simo/CWMO/cwmo2009_questions.pdf
  9. [PDF] 

    44th International Mathematical Olympiad

    File Format: PDF/Adobe Acrobat - Quick View
    44th International Mathematical Olympiad. Tokyo, Japan, July 2003. 1. Let A be a 101-element subset of the set S = {1,2,3,...,1000000}. Prove that there ...
    sms.math.nus.edu.sg/Simo/IMO_Problems/03.pdf
  10. [PDF] 

    Singapore International Mathematical Olympiad 2009 Senior Team ...

    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad 2009. Senior Team Training. Quiz. 1. Let p and q be distinct odd primes. Prove that. ∑. 0<j<p/2 ...
    sms.math.nus.edu.sg/Simo/2009/2009SeniorQuizSoln.pdf
  11. [PDF] 

    45th International Mathematical Olympiad

     - 4:22pm
    File Format: PDF/Adobe Acrobat - Quick View
    45th International Mathematical Olympiad. Athens, Greece, July 2004. 1. Let ABC be an acute-angled triangle with AB = AC. The circle with diameter BC ...
    sms.math.nus.edu.sg/Simo/IMO_Problems/04.pdf
  12. [PDF] 

    Selection Procedure of IMO participants

    File Format: PDF/Adobe Acrobat - Quick View
    Selection Procedure of IMO participants. SIMO Committee. SIMO Team to participate in IMO. Participate in. SMO(Junior). Junior Training Team. Final Selection ...
    sms.math.nus.edu.sg/Simo/Selection_Flowchart.pdf
  13. [PDF] 

    Singapore International Mathematical Olympiad 2003 National Team ...

    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad 2003. National Team Training. Geometry. (8) Let P and Q be the feet of the perpendiculars from the orthocenter ...
    sms.math.nus.edu.sg/Simo/training2003/training20_03_2003.pdf
  14. [PDF] 

    41st International Mathematical Olympiad

    File Format: PDF/Adobe Acrobat - Quick View
    41st International Mathematical Olympiad. Taejon, Korea, July 2000. 1. Two circles Γ1 and Γ2 intersect at M and N. Let l be the common tangent to Γ1 and Γ2 ...
    sms.math.nus.edu.sg/Simo/IMO_Problems%5C00.pdf
  15. [PDF] 

    2002 - 43rd International Mathematical Olympiad

    File Format: PDF/Adobe Acrobat - Quick View
    43rd International Mathematical Olympiad. Glasgow, United Kingdom, July 2002. 1. Let n be a positive integer. let T be the set of points (x, y) in the plane ...
    sms.math.nus.edu.sg/Simo/IMO_Problems%5C02.pdf
  16. [PDF] 

    40th International Mathematical Olympiad

    File Format: PDF/Adobe Acrobat - Quick View
    40th International Mathematical Olympiad. Bucharest, Romania, July 1999. 1. Determine all finite sets S of at least three points in the plane which satisfy ...
    sms.math.nus.edu.sg/Simo/IMO_Problems%5C99.pdf
  17. [PDF] 

    38th International Mathematical Olympiad

    File Format: PDF/Adobe Acrobat - Quick View
    38th International Mathematical Olympiad. Argentina, July 1997. 1. In the plane the points with integer coordinates are the vertices of unit squares. The ...
    sms.math.nus.edu.sg/Simo/IMO_Problems%5C97.pdf
  18. [PDF] 

    37th International Mathematical Olympiad

    File Format: PDF/Adobe Acrobat - Quick View
    37th International Mathematical Olympiad. India, July 1996. 1. Let ABCD be a rectangular board with |AB| = 20, |BC| = 12. The board is divided ...
    sms.math.nus.edu.sg/Simo/IMO_Problems%5C96.pdf
  19. [PDF] 

    42nd International Mathematical Olympiad

     - 4:22pm
    File Format: PDF/Adobe Acrobat - Quick View
    42nd International Mathematical Olympiad. Washington DC, United States of America, July 2001. 1. Let ABC be an acute-angled triangle with circumcentre O. ...
    sms.math.nus.edu.sg/Simo/IMO_Problems%5C01.pdf
  20. [PDF] 

    35th International Mathematical Olympiad

    File Format: PDF/Adobe Acrobat - Quick View
    35th International Mathematical Olympiad. Hong Kong, July 1994. 1. Let m and n be positive integers. let a1, a2, ..., am be distinct elements of {1,2,...,n} ...
    sms.math.nus.edu.sg/Simo/IMO_Problems%5C94.pdf
  21. [PDF] 

    39th International Mathematical Olympiad

     - 4:22pm
    File Format: PDF/Adobe Acrobat - Quick View
    39th International Mathematical Olympiad. Taiwan, July 1998. 1. In the convex quadrilateral ABCD, the diagonals AC and BD are perpendicular and ...
    sms.math.nus.edu.sg/Simo/IMO_Problems%5C98.pdf - Similar
  22. [PDF] 

    33th International Mathematical Olympiad

    File Format: PDF/Adobe Acrobat - Quick View
    33th International Mathematical Olympiad. Russia, July 1992. 1. Find all integers a, b, c with 1 <a<b<c such that (a − 1)(b − 1(c − 1) is a divisor of ...
    sms.math.nus.edu.sg/Simo/IMO_Problems%5C92.pdf
  23. [PDF] 

    36th International Mathematical Olympiad

    File Format: PDF/Adobe Acrobat - Quick View
    36th International Mathematical Olympiad. Canada, July 1995. 1. Let A, B, C, D be distinct points on a line, in that order. The circles with diameters ...
    sms.math.nus.edu.sg/Simo/IMO_Problems%5C95.pdf
  24. [PDF] 

    34th International Mathematical Olympiad

    File Format: PDF/Adobe Acrobat - Quick View
    34th International Mathematical Olympiad. Turkey, July 1993. 1. Let f(x) = xn + 5xn−1 + 3 where n > 1 is an integer. Prove that f(x) cannot be ...
    sms.math.nus.edu.sg/Simo/IMO_Problems%5C93.pdf - Similar
  25. [PDF] 

    12 July 2006 Problem 1. Let ABC be a triangle with incentre I. A ...

    File Format: PDF/Adobe Acrobat - Quick View
    12 Jul 2006 ... 12 July 2006. Problem 1. Let ABC be a triangle with incentre I. A point P in the interior of the triangle satisfies. PBA + PCA = PBC + PCB. ...
    sms.math.nus.edu.sg/SIMO/IMO_Participation/imo47/day1.pdf - Similar
  26. [PDF] 

    International Competitions IMO 2007

    File Format: PDF/Adobe Acrobat - Quick View
    Ha Noi, Vietnam. Day 2 - 26 July 2007. 4 In triangle ABC the bisector of angle BCA intersects the circumcircle again at R, the per- ...
    sms.math.nus.edu.sg/SIMO/IMO_Participation/imo48/day2.pdf
  27. [PDF] 

    46th International Mathematical Olympiad

    File Format: PDF/Adobe Acrobat - Quick View
    46th International Mathematical Olympiad. Second Day. Merida, Mexico, Thursday 14 July 2005. Language: English. Problem 4. Consider the sequence a1,a2,... ...
    sms.math.nus.edu.sg/SIMO/IMO_Participation/imo46/day2.pdf - Similar
  28. [PDF] 

    13 July 2006 Problem 4. Determine all pairs (x, y) of integers ...

    File Format: PDF/Adobe Acrobat - Quick View
    13 July 2006. Problem 4. Determine all pairs (x, y) of integers such that. 1+2x + 22x+1 = y2. Problem 5. Let P(x) be a polynomial of degree n > 1 with ...
    sms.math.nus.edu.sg/SIMO/IMO_Participation/imo47/day2.pdf - Similar
  29. [PDF] 

    46th International Mathematical Olympiad

    File Format: PDF/Adobe Acrobat - Quick View
    46th International Mathematical Olympiad. First Day. Merida, Mexico, Wednesday 13 July 2005. Language: English. Problem 1. Six points are chosen on the ...
    sms.math.nus.edu.sg/SIMO/IMO_Participation/imo46/day1.pdf - Similar
  30. [PDF] 

    Singapore International Mathematical Olympiad Training Problems

    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad. Training Problems. 18 January 2003. 1. Let M be a point on the segment AB. Squares AMCD and MBEF are erected ...
    sms.math.nus.edu.sg/Simo/training2003/training18_01_2003.pdf
  31. [PDF] 

    Singapore International Mathematical Olympiad Training Problems

     - 2 visits - 4:35pm
    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad. Training Problems. 25 January 2003. 1. In a quadrilateral ACGE, H is the intersection of AG and CE, ...
    sms.math.nus.edu.sg/Simo/training2003/training25_01_2003.pdf
  32. [PDF] 

    Training problems 27 March 2003 1. Find all integer solutions in x ...

    File Format: PDF/Adobe Acrobat - Quick View
    27 Mar 2003 ... Training problems 27 March 2003. 1. Find all integer solutions in x and y of the equation x3 + 27xy + 2009 = y3. Solution. Let y = x + a. ...
    sms.math.nus.edu.sg/Simo/training2003/training27_03_2003.pdf
  33. [PDF] 

    Singapore International Mathematical Olympiad Training Problems

    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad. Training Problems. 08 March 2003. 1. Let p be a prime number congruent to 1 modulo 4. Define the set ...
    sms.math.nus.edu.sg/Simo/training2003/training08_03_2003.pdf
  34. [PDF] 

    Singapore International Mathematical Olympiad Training Problems

    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad. Training Problems. 15 February 2003. 1. Let n be an odd integer which is not a multiple of 5. ...
    sms.math.nus.edu.sg/Simo/training2003/training15_02_2003.pdf
  35. [PDF] 

    Singapore International Mathematical Olympiad Training Problems

     - 4:33pm
    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad. Training Problems. 8 February 2003. 1. Determine whether there exist an integer polynomial f(x) together with ...
    sms.math.nus.edu.sg/Simo/training2003/training08_02_2003.pdf
  36. [PDF] 

    International Mathematical Olympiad

     - 4:33pm
    File Format: PDF/Adobe Acrobat - Quick View
    Thursday, July 16, 2009. Problem 4. Let ABC be a triangle with AB = AC. The angle bisectors of CAB and ABC meet the sides BC and CA at D and E, respectively ...
    sms.math.nus.edu.sg/Simo/IMO_Participation/imo50/Day2.pdf
  37. [PDF] 

    Language: English Day: 2 51st INTERNATIONAL MATHEMATICAL OLYMPIAD ...

    File Format: PDF/Adobe Acrobat - Quick View
    Language: English. Day: 2. 51st INTERNATIONAL MATHEMATICAL OLYMPIAD. ASTANA (KAZAKHSTAN), JULY 2-14, 2010. Thursday, July 8, 2010. Problem 4. ...
    sms.math.nus.edu.sg/Simo/IMO_Participation/imo51/Day_2.pdf
  38. [PDF] 

    Language: English Day: 1 51st INTERNATIONAL MATHEMATICAL OLYMPIAD ...

    File Format: PDF/Adobe Acrobat - Quick View
    Language: English. Day: 1. 51st INTERNATIONAL MATHEMATICAL OLYMPIAD. ASTANA (KAZAKHSTAN), JULY 2-14, 2010. Wednesday, July 7, 2010. Problem 1. ...
    sms.math.nus.edu.sg/Simo/IMO_Participation/imo51/Day_1.pdf
  39. [PDF] 

    International Mathematical Olympiad

    File Format: PDF/Adobe Acrobat - Quick View
    Thursday, July 17, 2008. Problem 4. Find all functions f : (0, ∞) → (0, ∞) (so, f is a function from the positive real ...
    sms.math.nus.edu.sg/Simo/IMO_Participation/imo49/Day2.pdf
  40. [PDF] 

    International Mathematical Olympiad

    File Format: PDF/Adobe Acrobat - Quick View
    Wednesday, July 16, 2008. Problem 1. An acute-angled triangle ABC has orthocentre H. The circle passing through H with centre the midpoint of BC intersects ...
    sms.math.nus.edu.sg/Simo/IMO_Participation/imo49/Day1.pdf
  41. [PDF] 

    International Mathematical Olympiad

     - 4:33pm
    File Format: PDF/Adobe Acrobat - Quick View
    Wednesday, July 15, 2009. Problem 1. Let n be a positive integer and let a1,...,ak (k ≥ 2) be distinct integers in the set ...
    sms.math.nus.edu.sg/Simo/IMO_Participation/imo50/Day1.pdf
  42. [PDF] 

    International Competitions IMO 2007

    File Format: PDF/Adobe Acrobat - Quick View
    Ha Noi, Vietnam. Day 1 - 25 July 2007. 1 Real numbers a1, a2, :::, an are given. For each i, (1 i n), define di = maxfaj j 1 ...
    sms.math.nus.edu.sg/SIMO/IMO_Participation/imo48/day1.pdf
  43. [PDF] 

    Singapore International Mathematical Olympiad Junior Group Test

    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad Junior. Group Test. Take Home Test - Number Theory. 13-8-2005. 1. Suppose a, b are integers satisfying 24a2 +1 ...
    sms.math.nus.edu.sg/Simo/Junior_test2005.pdf
  44. [PDF] 

    Singapore International Mathematical Olympiad National Team ...

    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad. National Team Selection Test I 2008. Time allowed: 4.5 hours. 26 April 2008. No calculator is allowed ...
    sms.math.nus.edu.sg/simo/selection_test_2008.pdf
  45. Singapore International Mathematical Olympiad Committee (SIMO ...

    Singapore International Mathematical. Olympiad Committee (SIMO). Annual Training Camp. Programme for. Senior Group. 8 – 13 June 2007 ...
    sms.math.nus.edu.sg/simo/smocamp_2007.pdf
  46. [PDF] 

    Graph Theory Problems/Solns

    File Format: PDF/Adobe Acrobat - Quick View
    Graph Theory Problems/Solns. 1. There are n participants in a meeting. Among any group of 4 participants, there is one who knows the other three members of ...
    sms.math.nus.edu.sg/simo/training2003/smograph.pdf
  47. [PDF] 

    Singapore International Mathematical Olympiad 2008 Senior Team ...

     - 4:25pm
    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad 2008. Senior Team Training. Take Home Test Solutions. 1. Show that the equation 15x2 − 7y2 = 9 has no ...
    sms.math.nus.edu.sg/simo/2008/2008SeniorTestSoln.pdf
  48. [PDF] 

    Singapore International Mathematical Olympiad 2005 Senior Team ...

     - 4:25pm
    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad 2005. Senior Team Training. Take Home Test Solutions. 1. Determine which of the numbers. 20011111 + 1 ...
    sms.math.nus.edu.sg/simo/training2005/2005-th.pdf
  49. [PDF] 

    Singapore International Mathematical Olympiad 2008 Senior Team ...

     - 4:25pm
    File Format: PDF/Adobe Acrobat - Quick View
    Singapore International Mathematical Olympiad 2008. Senior Team Training. Take Home Test. Submit written solutions by 12 April 2008. ...
    sms.math.nus.edu.sg/SIMO/2008/2008SeniorTest.pdf