Tag: Singapore math

Posted in Assessment, Math research

Student Achievement in Mathematics – TIMSS Ranking

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East Asian countries continue to lead the world in student achievement in mathematics. Singapore, Korea, and Hong Kong SAR, followed by Chinese Taipei and Japan, were the top-performing countries in TIMSS 2011 at the fourth grade. Similarly, at the eighth grade, Korea, Singapore, and Chinese Taipei outperformed all countries, followed by Hong Kong SAR and Japan. Here’s the result for 4th Grade and 8th grade achievement for 2011 released last December 2012.  The number enclosed in the parenthesis is the average scale score of the country. The average scale centrepoint is 500 for both grade levels. TIMSS stands for Trends in Mathematics and Science Study.

You can access the full report in International Student Achievement in Mathematics.

8th Grade TIMSS 2011 4th Grade TIMSS 2011
  1. South Korea (613)
  2. Singapore (611)
  3. Chinese Taipei (609)
  4. Hong Kong SAR (586)
  5. Japan (570)
  6. Russian Federation (539)
  7. Israel (516)
  8. Finland (514)
  9. United States (509)
  10. England (507)
  11. Hungary (505)
  12. Australia (505)
  13. Slovenia (505)
  14. Lithuania (502)
  15. Italy (498)
  16. New Zealand (488)
  17. Kazakhstan (487)
  18. Sweden (484)
  19. Ukraine (479)
  20. Norway (475)
  21. Armenia (467)
  22. Romania (458)
  23. United Arab Emirates (456)
  24. Turkey (452)
  25. Lebanon (449)
  26. Malaysia (440)
  27. Georgia (431)
  28. Thailand (427)
  29. Macedonia (426)
  30. Tunisia (425)
  31. Chile (416)
  32. Iran (415)
  33. Qatar (410)
  34. Bahrain (409)
  35. Jordan (406)
  36. Palestinian Nat’l Auth (404)
  37. Saudi Arabia (394)
  38. Indonesia (386)
  39. Syrian Arab Rep (380)
  40. Morocco (371)
  41. Oman (366)
  42. Ghana (331)
  1. Singapore (606)
  2. South Korea (605)
  3. Hong Kong SAR (602)
  4. Chinese Taipei (591)
  5. Japan (585)
  6. Northern Ireland (562)
  7. Belgium (549)
  8. Finland (545)
  9. England (542)
  10. Russian Federation (542)
  11. United States (541)
  12. Netherlands (540)
  13. Denmark (537)
  14. Lithuania (534)
  15. Portugal (532)
  16. Germany (528)
  17. Ireland (527)
  18. Serbia (516)
  19. Australia (516)
  20. Hungary (515)
  21. Slovenia (513)
  22. Czech Republic (511)
  23. Austria (508)
  24. Italy (508)
  25. Slovak Republic (507)
  26. Sweden (504)
  27. Kazakhstan (501)
  28. Malta (496)
  29. Norway (495)
  30. Croatia (490)
  31. New Zealand (486)
  32. Spain (482)
  33. Romania (482)
  34. Poland (481)
  35. Turkey (469)
  36. Azerbaijan (463)
  37. Chile (462)
  38. Thailand (458)
  39. Armenia (452)
  40. Georgia (450)
  41. Bahrain (436)
  42. United Arab Emirates (434)
  43. Iran (431)
  44. Qatar (413)
  45. Saudi Arabia (410)
  46. Oman (385)
  47. Tunisia (359)
  48. Kuwait (342)
  49. Morocco (335)
  50. Yemen (248)

 

Posted in Algebra

A challenging complex number problem with solution

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This complex number problem was selected on the basis of its uniqueness in terms of phrasing things within the Argand diagram/locus context. While my proposed solutions might be short, bear in mind this question truly demands/challenges the student to think unconventionally in order to formulate a viable solving approach.

 

Problem

A complex number z=x+iy is represented by the point P in an Argand diagram. If the complex number w where w = \frac{z-8i}{z+6}, (z\neq-6) has its real part zero, show that the locus of P in the Argand diagram is a circle and find the radius and the coordinates of the centre of this circle. If, however, w is real, find the locus of P in this case.

Solution

complex number problem

The author of this post is Mr. Frederick Koh. He is a teacher residing in Singapore who specialises in teaching the A level maths curriculum. He has accumulated more than a decade of tutoring experience and loves to share his passion for mathematics on his personal site www.whitegroupmaths.com.

If you love this problem, I’m sure you will also enjoy the two other challenging problems shared by Mr. Koh in this site:

  1. Differentiation in parametric context
  2. Working with summation problems
Posted in Calculus

Differentiation problem in parametric context with solution

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This is hot off the press-a question taken from the recently concluded 2011 September Preliminary Examinations of a school in Singapore. It deals with applications  of differentiation in the parametric context. Extensive trigonometry is employed here together with the manipulation of surd forms. I have personally worked out everything for your (the student’s) reference.

If you want a real calculus challenge, the problem below should satisfy your appetite. Peace.

QUESTION :

The parametric equations of a curve  are

x = sin2t and y= a cos t

where is a positive constant \frac{-\pi}{2} \le t \le\frac{\pi}{2}

(i) Find the equation of the tangent to the curve at the point P  where t= \frac{\pi}{4}.

(ii) The normal to the curve at the point Q where t = \frac {\pi}{3} intersects the axis at R. Find the coordinates of R and hence show that the area enclosed by the normal at Q , the tangent P and the x-axis is

differentiation

Author

Frederick Koh is a teacher residing in Singapore who specialises in teaching the A level maths curriculum. He has accumulated more than a decade of tutoring experience and loves to share his passion for mathematics on his personal site www.whitegroupmaths.com.

Mr Koh is also the author of the post Working with summation.

I have created a GeoGebra applet to visualize Question 1 above.