Olimpiad Matematik Kebangsaan (Bahagian 3)

Silibus OMK

Silibus soalan-soalan OMK tidak mengikut silibus KBSM. Walau bagaimanapun, panel penyediaan soalan OMK akan mengambilkira peringkat pengetahuan pelajar di setiap kategori, sama ada Bongsu, Muda dan Sulung.

Soalan OMK menguji keupayaan berfikir dan berhujah, bukan kebolehan mengira pantas atau kebolehan menghafal formula. Oleh itu, pelajar yang mempunyai pengetahuan matematik yang melebihi umurnya, tidak semestinya boleh menjawab soalan Olimpiad, jika pelajar itu tidak mempunyai keupayaan berfikir yang tinggi.

Beberapa topik yang tidak diuji dalam OMK ialah kalkulus (differentiation, integration, motion in a straight line, etc), statistik (mode-median-mean, normal distribution, dsb.), dan algebra linear (matrices).

Secara umumnya, silibus OMK terbahagi kepada empat kategori, iaitu Algebra, Combinatorics, Number Theory, dan Geometry.

1) Algebra
Soalan-soalan di dalam topik ini membabitkan operasi-operasi algebra.

Antara subtopik yang terbabit ialah:

  • Equations (linear, quadratic, system of simultaneous equations)
  • Arithmetic and geometric progressions
  • Algebraic identities
  • Polynomials and their roots
  • Inequalities
  • Functions

Contoh soalan:

  • (OMK 2008, Bongsu) Ali tore out several sheets from a book. The sheets are consecutive. The first page number that he tore is 365. It is known that the number of the last page torn can be written using exactly the same digits in different order. Find the number of sheets that Ali tore out.
  • (OMK 2008, Muda) Let a, b, c be positive real numbers. Show that a^2 + b^2 + c^2 + ab + bc + ca + 6 >= 4(a + b + c).
  • (OMK 2008, Sulung) Simplify the expression: square root of n(n+1)(n+2)(n+3) + 1.

2) Combinatorics
Soalan-soalan di dalam topik ini membabitkan kemahiran mengira objek-objek matematik.

Antara subtopik yang terbabit ialah:

  • Counting Principles
  • Permutations and Combinations
  • Enumerative Combinatorics
  • Pigeonhole Principle

Contoh soalan:

  • (OMK 2008, Bongsu) Find the number of positive integers less than 500, which is not divisible by 5 or 7.
  • Count the number of even integers between 400 and 900 with all digits different.
  • (OMK 2008, Sulung) Determine the number of four digit numbers which start with 3 and have exactly two identical digits. (e.g 3447, 3005 or 3243 but not 3388 or 3666).

3) Number Theory
Soalan-soalan di dalam topik ini membabitkan sifat-sifat nombor bulat (integers).

Antara subtopik yang terbabit ialah:

  • Primes and Composite Numbers
  • Divisibility
  • Divisibility Tests
  • Last Digit Analysis
  • Parity
  • Diophantine Equations

Contoh soalan:

  • (OMK 2008, Bongsu) Find the smallest positive integer N such that every digit of N is either 0 or 7, and N is divisible by 15.
  • (OMK 2008, Muda) Let n and k be two positive integers such that k is less than n. It is known that (1 + 2 + … + n) + k = 202.  Find k.
  • (OMK 2008, Sulung) Find positive integers p, q, n such that p and q are prime numbers, and 1/p + 1/q + 1/pq = 1/n.

4) Geometry
Soalan-soalan di dalam topik ini membabitkan objek-objek geometri.

Antara subtopik yang terbabit ialah:

  • Geometric Calculations (angles, length, areas)
  • Triangles
  • Quadrilaterals
  • Polygons
  • Trigonometric Identities

Contoh soalan:

  • (OMK 2008, Bongsu) An equilateral triangle with sides 2 units is inscribed in a circle. Find the area of the circle.
  • (OMK 2008, Muda) Given that ABC is an isosceles triangle with angle ABC = angle ACB = 80 degrees. Two points E and F are on AB and AC, respectively, such that angle ABF = 10 degrees and angle ACE = 20 degrees. Let line AM where M is the midpoint of BC intersects CE at the point N. Show that FN is parallel to AB.
  • (OMK 2008, Sulung) Let ABCD be a square. Let M be the midpoint of AB, and let N be the midpoint of BC. Lines AN and DM intersect at P, lines AN and CM intersect at Q, and lines CM and DN intersect at R. Show that (Area of AMP) + (Area of BMQN) + (Area of CNR) = (Area of DPQR).
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37 Responses to Olimpiad Matematik Kebangsaan (Bahagian 3)

  1. xoxo says:

    can u help me with the 2009 omk questions? =)

    1. An old man has a total of 258 children,grandchildren and great geandchildren.None of his great grandchildren has any children.All the others have an equal number of children.How many children does the old man have .

  2. suhaimiramly says:

    the easiest way is to perform trial and error with small numbers.

    suppose the number of children of the old man = 2

    then the number of grandchildren = 2 x 2 = 4
    and the number of great grandchildren = 2 x 2 x 2 = 8

    then the total is 2+4+8 = 14, which is too low. so we increase the number of children until we got the right total (258)

    hope this helps.

  3. flizzo says:

    I think a better question is why the heck is this old man has so many chrildren! Somebody needs to introduce this old foo to condoms!

  4. suhaimiramly says:

    actually when we were drafting the problems last year, we wanted to make the old man a rabbit. but we were not sure about the terms for rabbit grandchildren (grandoffspring?) so we used human instead.

    by the way this problem appeared in a Bulgarian National Olympiad few years back, we adapted it and changed the number.

  5. tcchuin says:

    is there any past year qeustion we can find for OMK?

  6. tcchuin says:

    can i buy that with 4 books you wrote together?><

  7. suhaimiramly says:

    the problem collection can only be obtained from PERSAMA.

  8. afiqah says:

    mathematics…
    the omk’s question are veryvery hard laa..
    its very hard for me to get the answer..
    sometimes the question just out of my mind..
    how can people makes such that hard???

  9. Question says:

    can i have any other OMK questions than the 2007 one?
    It is better if it comes with solution…….
    thx a lot…..

  10. Question says:

    Anyway……
    can i have the solution for the above four OMK 2008 bongsu question……
    Coz i am preparing for the tournament (2010)……
    any tips for this year’s OMK bongsu?
    Anyway,TQ for yur help…….

  11. Question says:

    I am interested with yur books….
    can i buy it on the tournament day (OMK2010)
    How much does the book cost?……

  12. suhaimiramly says:

    Afiqah,
    We have to make the problems hard because even at the current standard many students get more than 20 points (out of 30) on the paper. If we make it easier then we will have like 200 perfect scorers out of the 9000 contestants, which will make it impossible to select the winner :)

    Question,
    I have the past year papers but I am not authorized to share them. PERSAMA holds the copyright and they usually compile a book with past year problems and solutions.
    You can buy my books on OMK at several centers (UKM and UiTM for sure). If not, you can order from us at the “Books” link on top.

    Thanks for your interest.

  13. Siva says:

    do you publish any books? On olympiad mathematics..im looking for good books to train myself cuz im going for this competition. I need ur opinion on good books and wer can i get them?
    thanks!

  14. suhaimiramly says:

    Hello Siva,

    You can find the order form on the Books link:

    http://suhaimiramly.wordpress.com/books/

    The quickest way to order is to send us an email at info@ardentedu.com with all the information given in the order form. Fax would take a while to process.

  15. Dreaming of IMO says:

    May i know what are the criteria for getting sanjungan kehormat? Are there any cutoff points like IMO?

  16. suhaimiramly says:

    There is no cutoff point. SK is given to the top 50-60 contestants after the main prize (No 1,2,3 & Saguhati). Im not sure about the exact number of SK winners.

  17. Dreaming of IMO says:

    I see. May i know roughly how much do most of the SK winners score every year? 20+ maybe?

  18. suhaimiramly says:

    Depends on the level. Bongsu SK tends to be in high teens to low 20s. Muda and Sulung SK is around 12-20 range, but again, it depends on which year. I heard that in some years, some SK winners only scored 9.

    To be sure, aim for 20+.

  19. asker says:

    (OMK 2008, Muda) Let a, b, c be positive real numbers. Show that a^2 + b^2 + c^2 + ab + bc + ca + 6 >= 4(a + b + c). May i know how to prove?

    • How says:

      a^2+b^2+c^2+ab+bc+ca+6-4(a+b+c)
      =(a^2-2a+1)+(b^2-2b+1)+(c^2-2c+1)+(ab-a-b+1)+(ac-a-c+1)+(bc-b-c+1)
      =(a-1)^2+(b-1)^2+(c-1)^2+(a-1)(b-1)+(a-1)(c-1)+(b-1)(c-1)
      =(1/2){[(a-1)+(b-1)]^2+[(a-1)+(c-1)]^2+[(b-1)+(c-1)]^2}>=0
      Hence,a^2+b^2+c^2+ab+bc+ca+6>=4(a+b+c)
      (Proved.)

      • Wx Loh says:

        sir i dun understand =(1/2){[(a-1)+(b-1)]^2+[(a-1)+(c-1)]^2+[(b-1)+(c-1)]^2}>=0.. cn u do further explanation?? thx!

  20. Question says:

    can i know when will the results announced exactly for OMK 2010?

    thx

  21. Kanez says:

    Can u help me the value of ‘n’. 2^n+n^2=3

  22. a^2-b^2=(a+b)(a-b) says:

    can i know where to get the answers for 2008 OMK muda category questions? also what is the average mark in OMK

  23. Wamwa97 says:

    Apa jawapan untuk soalan ni?

    Ali tore out several sheets from a book. The sheets are consecutive. The first page number that he tore is 365. It is known that the number of the last page torn can be written using exactly the same digits in different order. Find the number of sheets that Ali tore out.

  24. summer says:

    may i know how to solve OMK 2008 bongsu, question 3? in triangle ABC, the lines AD, BE and CF meet at O, given that area of triangleAOF = 84, area triangle BOD = 40, area triangle COD = 30 and area triangle COE = 35, find the area of triangle ABC.

  25. amil says:

    may i know how to get the olympiad question booklet..?
    i entered this thing once in f2 and manage to get SK..
    but in f4, some teachers are very x adil.. they chose those from ex-mrsm only.. =.=” of course.. they would trust them more then the ‘ordinary’ ex government school student….
    anyway.. i really want to do this..

  26. fitrie says:

    can tou give some tips 4 answer OMK questions….

  27. wan k says:

    (OMK 2008, Sulung) Let ABCD be a square. Let M be the midpoint of AB, and let N be the midpoint of BC. Lines AN and DM intersect at P, lines AN and CM intersect at Q, and lines CM and DN intersect at R. Show that (Area of AMP) + (Area of BMQN) + (Area of CNR) = (Area of DPQR).

    saya dh selesaiknnya megunakn kalkulator… tp bgaimna nk selesaiknnya tnpa kalkulator..?

  28. Dest says:

    Mr Suhaimi Ramly, is it against the rules for a student of different nationality to represent Malaysia for IMO?

  29. jijul says:

    can teach me how to solve the question omk 2010. very hard laa.. this question will giving me high attack. haghgahag.. pleaseeeee.. i want now..

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