Đề thi FMO vòng chung kết quốc tế 2022 Khối 8 (Kèm đáp án)

 FMO – Grade 8 
 A. Warm-up (3 points per question / No points deducted for wrong answers) 
1. A bike travels at a constant speed of 12km/h. A car starts 16km behind the bike and 
 catches up to the bike in half an hour. What is the average speed of the car in km/h? 
 A) 56 km/h B) 40 km/h C) 20 km/h D) 28 km/h E) 44km/h 
2. Given a function f( x ) x2 (2 m 1) x m and f (2) 21. Find the value of f (1). 
 A) 5 B) -1 C) -3 D) 7 E) 3 
3. Given a quadrilateral ABCD with BAD BDC90o , AB 3, AD 4 and BC 13. 
 Find the perimeter of . 
 A) 30 B) 34 C) 25 D) 37 E) 32 
4. When the number 15 is reversed to form the number 51, it is increased by 36. How 
 many 2-digit numbers which are increased by 36 when their digits are reversed? 
 A) 5 B) 10 C) 4 D) 6 E) 8 
5. Henry draws a zigzag line inside a rectangle and measures some of the angles as 
 below. Find the measure of the missing angle. 
 A) 12o B) 13o C) 14o D) 15o E) 16o 
 1 
FERMAT Mathematical Olympiad Summer 2022 
All materials on the test are copyrighted and owned by Fermat Education 
B. Speed-up (4 points per question / No points deducted for wrong answers) 
11. Find the value of F + M + S + C + O given that they are different digits. 
 F M O 
 F S O 
 + F C O 
 2 0 2 4 
 A) 34 B) 36 C) 38 D) 32 E) 30 
12. Find the area of the triangle ABC given the coordinates ABC(0,3); (6,4); (4,0) . 
 A) 8 B) 9 C) 10 D) 11 E) 12 
13. How many 3-digit numbers divisible by 6 but not divisible by 8 are there? 
 A) 38 B) 132 C) 225 D) 75 E) 113 
14. Bob cuts a quarter of a circle to make a fan as follows. He measures the perimeter of 
 the fan and gets 84cm. Assume that 3, find the area of the fan in cm2. 
 A) 432 B) 2352 C) 588 D) 147 E) 363 
15. A bag of 8 apples costs 12 dollars and a box of 5 mangoes costs 8 dollars. Customers 
 can buy only a whole number of bags and boxes. One day, Henry buys exactly 100 
 fruits in total, including apples and mangoes. At least how much money did he spend? 
 A) $132 B) $136 C) $160 D) $156 E) $152 
 3 
FERMAT Mathematical Olympiad Summer 2022 
All materials on the test are copyrighted and owned by Fermat Education 
 D. Star of hope (10 points per question/ 10 points deducted for wrong answer) 
 In this part, you must write your answer on the answer sheet. 
21. A group of 50 nurses had to do at least one of three shifts including the morning shift, 
 the afternoon shift and the night shift. The results are listed below: 
 The number of nurses 
 The morning shift 37 
 The afternoon shift 42 
 The night shift 30 
 At most how many nurses did all 3 shifts in that day? 
 Congratulations! 
 This is the end of the test. Please review the answers carefully before submission. 
 5 
FERMAT Mathematical Olympiad Summer 2022 
All materials on the test are copyrighted and owned by Fermat Education