奧 冠 教 育 中心
OLYMPIAD CHAMPION EDUCATION CENTRE
Room 309-310, 8 Jordan Road, Yau Ma Tei, Kowloon, Hong Kong SAR, CHINA
Tel (852) 3153 2028 / 9310 1240
Website: www.olympiadchampion.com
Fax (852) 3153 2074
Email: olympiadchampion@gmail.com
泰國國際數學競賽晉級賽 2022 - 2023（香港賽區）
THAILAND INTERNATIONAL
MATHEMATICAL OLYMPIAD
SEMI FINAL 2022 - 2023 (HONG KONG REGION)
中學一年級 Secondary 1
時限：90 分鐘
Time allowed:
90
minutes
試題
Question Paper
考生須知：
Instructions to Contestants:
1.
本卷包括 試題 乙份，試題紙不可取走。
Each contestant should have ONE Question-Answer Book which CANNOT be taken away.
2.
本卷共 5 個範疇，每範疇有 5 題，共 25 題，每題 4 分，總分 100 分，答錯不扣分。
There are 5 exam areas and 5 questions in each exam area. There are a total of 25 questions in this
Question-Answer Book. Each carries 4 marks. Total score is 100 marks. No points are deducted for
incorrect answers.
3.
請將答案寫在 答題紙 上。
All answers should be written on ANSWER SHEET.
4.
比賽期間，不得使用計算工具。
NO calculators can be used during the contest.
5.
本卷中所有圖形不一定依比例繪成。
All figures in the paper are not necessarily drawn to scale.
6.
比賽完畢時，本試題會被收回。
This Question-Answer Book will be collected at the end of the contest.
請以最簡形式填寫答案，若計算結果是分數，請確保為真分數或帶分數，或將計算結果寫成小數。錯誤單位將不給予任何分數。
Write down the answer in the simplest form. If the calculation result is a fraction, please write down the answer as a proper or mixed fraction,
decimal figure is also accepted. Marks will NOT be given for incorrect unit.
請將答案寫在 答題紙 上。
All answers should be written on the ANSWER SHEET.
本試題不可取走。
THIS Question-Answer Book CANNOT BE TAKEN AWAY.
未得監考官同意，切勿翻閱試題，否則參賽者將有可能被取消資格。
DO NOT turn over this Question-Answer Book without approval of the examiner.
Otherwise, contestant may be DISQUALIFIED.
請以最簡形式填寫答案，若計算結果是分數，請確保為真分數或帶分數，或將計算結果寫成小數。錯誤單位將不給予任何分數。
Write down the answer in the simplest form. If the calculation result is a fraction, please write down the answer as a proper or mixed fraction,
decimal figure is also accepted. Marks will NOT be given for incorrect unit.
請將答案寫在 答題紙 上。
All answers should be written on the ANSWER SHEET.
填空題（第 1 至 25 題）（每題 4 分，答錯及空題不扣分）
Open-Ended Questions (1st ~25th) (4 points for correct answer, no penalty point for wrong answer)
Logical Thinking
邏輯思維
1.
There are some giraffes and ants in a room. The number of ants is 7 times the number of giraffes. The
total number of legs of giraffes is 570 less than that of ants. How many ant(s) is / are there? (An ant has
six legs.)
Tinilah beberapajerapahdansemutdi sebuahkamar. Jumlahsemutadalah7kali jumlahjerapah. Jumlah
seluruhnyajumlahkaki darijerapahadalah570 lebih sedikitdaripada itusemut. Berapa banyaksemut(s) ada /
ada?(Semut memiliki enam kaki.)
2.
2.
According to the pattern shown below, what should be the number filled in the blank?
Menurut pola yang ditunjukkan di bawah ini, apaseharusnyanomordipenuhidi kosong?
3 、 4 、 9 、 34 、 159、 __ 、…
3.
Find the average of the selling prices of the following 10 electrical appliances listed below.
3. Temukan rata-rata harga jual 10 peralatan listrik berikut yang tercantum di bawah ini.
$ 5466、$ 5523、$ 5534、$ 5497、$ 5489、$ 5509、$ 5511、$ 5585、$ 5445、$ 5481
4.
Given that A : B = 4 : 7 , B : C = 3: 2 , C : D = 7 :8 and A + B + C + D = 1014 . What is the value of B?
4. Mengingat bahwa A : B = 4 : 7 , B : C = 3: 2 , C : D = 7 :8 dan A + B + C + D = 1014 . Berapakah nilai
B?
5.
A railway company laid 20 kilometers of track from station A to the east to station B, and then laid 21
kilometers of track to the north to station C. Now the railway company plans to open a new railway to
connect stations A and C directly. How many kilometers of track is needed for the new railway?
5.
Sebuah perusahaan kereta api meletakkan 20 kilometer rel dari stasiun A ke timur ke stasiun B, dan
kemudian meletakkan 21 kilometer rel ke utara ke stasiun C. Sekarang perusahaan kereta api berencana
untuk membuka kereta api baru untuk menghubungkan stasiun A dan Csecara langsung. Berapa
kilometer lintasandiperlukan untuk kereta api baru?
Algebra
代數
請以最簡形式填寫答案，若計算結果是分數，請確保為真分數或帶分數，或將計算結果寫成小數。錯誤單位將不給予任何分數。
Write down the answer in the simplest form. If the calculation result is a fraction, please write down the answer as a proper or mixed fraction,
decimal figure is also accepted. Marks will NOT be given for incorrect unit.
請將答案寫在 答題紙 上。
All answers should be written on the ANSWER SHEET.
6.
 x + 2 y = 25
Find the value of xy if 
.
3x − y = 26
6.
 x + 2 y = 25
Carilah nilai dari xy jika 
.
3x − y = 26
7.
7.
Factorise 7 x 2 + 28 x − 84 .
2
Faktorkan 7 x + 28 x − 84 .
8.
Find the value of 5 + 15 + 45 + 135 +
8.
Carilah nilai dari 5 + 15 + 45 + 135 +
9.
Find the value of x if 3 ( 4 x − 5) − ( 9 x + 31) + 17 = 30 .
9.
Tentukan nilai x jika 3 ( 4 x − 5) − ( 9 x + 31) + 17 = 30 .
+ 3645 .
+ 3645 .
10. Given a is an integer and a + 4 + 8 + a = 6 , find the product of all possible value of a.
10. Diketahui a adalah bilangan bulat dan a + 4 + 8 + a = 6 , temukanprodukdari semua kemungkinan nilai a.
Number Theory
數論
11. If 8-digit number 2022616A is divisible by 36, find the value of A.
11. Jika8-nomor digit 2022616A habis dibagi 36, tentukan nilai A
12. It is known that x is rational, x  0 and x = 30 − 30 − 30 − 30 −
12. Diketahui bahwaxrasional, x  0 dan x = 30 − 30 − 30 − 30 −
. Find the value of x.
. Cari nilai x.
13. A 4-digit number has a remainder 4 when divided by 5, has a remainder 5 when divided by 6 and has a
remainder 6 when divided by 7. What is the smallest possible value of this 4-digit number?
13. Bilangan 4 digit memiliki sisa 4 jika dibagi 5, memiliki sisa 5 jika dibagi dengan 6 dan memiliki sisa 6
jika dibagi 7. Berapakah?yang kecilEstnilai yang mungkin dari iniangka 4 angka?
14. Find the unit digit of 1 + 52 + 93 + 114 + 155 + 196 + + 4113 + 4514 + 4915 .
2
3
4
5
6
13
14
15
14. Temukan angka satuan dari 1 + 5 + 9 + 11 + 15 + 19 + + 41 + 45 + 49 .
1
1
15. Given x  0 and ( x + ) − 5 = 9 , find the value of x 2 + 2 .
x
x
請以最簡形式填寫答案，若計算結果是分數，請確保為真分數或帶分數，或將計算結果寫成小數。錯誤單位將不給予任何分數。
Write down the answer in the simplest form. If the calculation result is a fraction, please write down the answer as a proper or mixed fraction,
decimal figure is also accepted. Marks will NOT be given for incorrect unit.
請將答案寫在 答題紙 上。
All answers should be written on the ANSWER SHEET.
1
1
15. Diberikan x  0 dan ( x + ) − 5 = 9 , tentukan nilai x 2 + 2 .
x
x
Geometry
幾何
16. There are 14 points on a circle. How many different nonagon(s) can we draw with those points as its
vertices?
16. Ada14titik pada lingkaran. Berapa banyak nonagon berbeda yang dapat kita gambar dengan titik-titik
tersebut sebagaisudut?
17. A solid cuboid is formed by merging 480 cubes with side length 1cm. Find the minimum value of the
total surface area of the cuboid.
17. Sebuah balok padat dibentuk dengan menggabungkan 480 buah kubus dengan panjang rusuk 1 cm.
Tentukan nilai minimum luas permukaan total balok tersebut.
18. Six of the interior angles of an irregular heptagon are 127 , 265 , 151 , 112 , 101 and 75 . What
is the size of the seventh interior angle?
18. Enam daridisudut luar tidak beraturansegi tujuhadalah127 , 265 , 151 , 112 , 101 dan 75 .Berapa
ukurantujuhthdisudut luar?
19. It is given that the perimeter of a rectangle is 60 and the width and length of that rectangle are even
numbers. Find the largest possible value of its area.
19. Diketahui keliling persegi panjang adalah60 danlebar dan panjangpersegi panjang ituadalah bilangan
genap. Temukan yang terbesarmungkinNilai dari-nyadaerah.
20. The lengths of sides of a triangle are 7, 25 and 24. Find the area of the triangle.
20. Panjang sisi segitiga adalah7, 25 dan 24. Temukan luas segitiga.
Combinatorics
組合數學
21. Choose 4 digits, without repetition, from 1, 2, 9, 8, 3 to construct 4-digit numbers. Of these 4-digit
numbers, how many of them are divisible by 3?
請以最簡形式填寫答案，若計算結果是分數，請確保為真分數或帶分數，或將計算結果寫成小數。錯誤單位將不給予任何分數。
Write down the answer in the simplest form. If the calculation result is a fraction, please write down the answer as a proper or mixed fraction,
decimal figure is also accepted. Marks will NOT be given for incorrect unit.
請將答案寫在 答題紙 上。
All answers should be written on the ANSWER SHEET.
21. Pilih 4 digit,tanpapengulangan,dari 1, 2, 9, 8, 3 untuk menyusun angka 4 digit. Dari 4 angka tersebut,
berapa banyak yang habis dibagi? 3?
22. One set of poker have 52 cards, which have four suits (Black spades, red hearts, red diamonds, and black
clubs, and thirteen values (A, two to ten, jack, queen and king) .Find the probability that four cards drawn
are of same suit or same color.(Assume that cards drawn will not be drawn again.)
22. HAIsatu set poker memiliki 52 kartu, yang memiliki empatsetelan(Sekop hitam, hati merah, berlian
merah, dan tongkat hitam, dan tiga belasnilai-nilai(Duasampai sepuluh, jack, ratu dan raja) .Temukan
peluang terambilnya empat kartudarisamasetelanatausamawarna. (Asumsikan bahwa kartu yang ditarik
tidak akan ditarik lagi.)
23. There are nine oranges and four mangoes. If we choose 4 fruits at random, find the probability that three
oranges and one mango are chosen from those fruits.
23. Ada sembilan jeruk dan empat mangga.Jika kita memilih 4 buah secara acak, tentukanpeluang
terambilnya tiga jeruk dan satu mangga dari buah-buahan tersebut.
24. Two fair 6-face dice are thrown. Find the probability that the sum of numbers obtained is a multiple of 3.
24. Dua di 6-wajah yang adilce dibuang. Tentukan peluang bahwa jumlah bilangan yang diperoleh adalah
kelipatan 3.
25. In how many different way(s) can Terry walk from point A to point B following the paths outlined in the
figure below such that he can only move down or move right?
25. Dalam berapa banyak cara yang berbeda dapatTerryberjalan dari titik A ke titik B mengikuti jalur yang
digariskan pada gambar di bawah sehingga dia hanya bisa bergerak ke bawah atau bergerak ke kanan?
A
請以最簡形式填寫答案，若計算結果是分數，請確保為真分數或帶分數，或將計算結果寫成小數。錯誤單位將不給予任何分數。
Write down the answer in the simplest form. If the calculation result is a fraction, please write down the answer as a proper or mixed fraction,
decimal figure is also accepted. Marks will NOT be given for incorrect unit.
請將答案寫在 答題紙 上。
All answers should be written on the ANSWER SHEET.
B
Question 25
第 25 題
~ 全卷完 ~
~ End of Paper ~
請以最簡形式填寫答案，若計算結果是分數，請確保為真分數或帶分數，或將計算結果寫成小數。錯誤單位將不給予任何分數。
Write down the answer in the simplest form. If the calculation result is a fraction, please write down the answer as a proper or mixed fraction,
decimal figure is also accepted. Marks will NOT be given for incorrect unit.