IMO Class 6 Practice Questions Math Olympiad

 IMO Grade6 Math Olympiad Practice Questions 

Sample Paper 

Grade 6 Mathematics Olympiad Questions

Section 1: Arithmetic & Number Theory

1. What is the sum of the first 20 natural numbers?
2. Find the LCM of 36 and 48.
3. The product of two numbers is 504. If one number is 12, find the other.
4. A number is divisible by both 4 and 6. What is the smallest possible number greater than 10?
5. If 5x + 12 = 32, find the value of x.
6. A number is 4 times another number. Their sum is 50. Find the numbers.
7. Find the missing number in the pattern: 2, 6, 12, __, 30, 42.
8. A train travels at 60 km/h. How far will it travel in 2.5 hours?
9. A shopkeeper sells a pen for ₹45, earning a profit of ₹9. What was the cost price?
10. What is the HCF of 72, 96, and 120?

Section 2: Fractions & Decimals

11. Convert 3.75 into a fraction in its simplest form.
12. Divide 8/9 by 2/3 and simplify.
13. Find the value of .
14. A wire of length 4.5 meters is cut into 3 equal parts. What is the length of each part?
15. 4/7 of a number is 28. Find the number.

Section 3: Ratio & Proportion

16. The ratio of apples to oranges in a basket is 5:3. If there are 40 apples, how many oranges are there?
17. If ₹600 is divided between A and B in the ratio 2:3, how much does B get?
18. A map has a scale of 1 cm = 5 km. How many kilometers does 3.5 cm on the map represent?
19. Find the missing term in the proportion: 6:18 = ?:36.
20. The speed of a car is 90 km/h. If it travels for 2 hours 40 minutes, find the distance covered.

Section 4: Algebra

21. Solve for x: 3x+6=30
22. Find the next term in the sequence: 2, 5, 10, 17, 26, __.
23. if y is double of x and the of x is 1/2 then the value of y is?
24. Solve for z, 2(z-8)=10
25. 1,8,27,64,.... Find the next term

Section 5: Geometry

26. The perimeter of a square is 48 cm. Find its area.
27. Find the area of a triangle with base 10 cm and height 8 cm.
28. The sum of the angles in a quadrilateral is ____.
29. A circle has a radius of 7 cm. Find its circumference.
30. A rectangular field is 30 m long and 20 m wide. Find its perimeter.

Section 6: Data Handling & Probability

31. The mean of five numbers is 12. If four numbers are 10, 14, 8, and 16, find the fifth number.
32. A dice is rolled. What is the probability of getting an even number?
33. A class has 25 students. The heights (in cm) of some students are: 140, 145, 142, 143, 140. Find the mode.
34. In a survey, 40% of 200 students preferred mathematics. How many students preferred mathematics?
35. The bar graph shows the number of books read by students: A (8), B (10), C (12), and D (14). Find the total number of books read.

Section 7: Logical Reasoning

36. Find the missing number in the series: 4, 9, 16, __, 36, 49.
37. A is the brother of B, and B is the sister of C. How is A related to C?
38. Find the odd one out: 64, 125, 216, 343, 512.
39. A clock shows 2:30. What is the angle between the hour and minute hands?
40. If 5 cats can catch 5 mice in 5 minutes, how long will it take 10 cats to catch 10 mice?

Section 8: Mensuration

41. A cube has a side length of 6 cm. Find its volume.
42. A cylindrical water tank has a radius of 7 m and height of 10 m. Find its volume.
43. Convert 2.5 km into meters.
44. A rectangular prism has a length of 12 cm, width of 8 cm, and height of 5 cm. Find its total surface area.
45. A triangle has sides of length 7 cm, 24 cm, and 25 cm. Is it a right-angled triangle?

Section 9: Speed, Time, and Distance

46. A car travels at 80 km/h. How much time will it take to cover 320 km?
47. A cyclist travels 15 km in 50 minutes. Find his speed in km/h.
48. A train departs at 10:30 AM and reaches its destination at 3:15 PM. Find the travel time.
49. A bus travels 90 km in 1.5 hours. Find its speed.
50. A river flows at 5 km/h, and a boat rows at 15 km/h in still water. Find its speed against the current.

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