Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 720 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.What is the smallest prime factor of 299? (a) 1 (b) 23 (c) 2 (d) 13
2. 2.What is the missing term in the AP 14, ?, 24, 29, 34? (a) 19 (b) 20 (c) 24 (d) 18
3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
4. 4.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 10 (c) 15 (d) 20
5. 5.6 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 18 (c) 36 (d) 9
6. 6.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 49 (c) 37 (d) 36
7. 7.Using (a − b)² = a² − 2ab + b², what is 26²? (a) 1156 (b) 884 (c) 686 (d) 676
8. 8.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 25 (c) 24 (d) 37
9. 9.What is the distance between the points (6, 15) and (18, 6)? (a) 16 (b) 21 (c) 15 (d) 225
10. 10.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 40° (c) 70° (d) 140°
11. 11.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 56 (c) 36 (d) 64
12. 12.In a class of 40 children, 30 like cricket, 17 like football and 5 like neither. How many like both? (a) 35 (b) 5 (c) 12 (d) 7
13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 7 (b) 6 (c) 4 (d) 5
14. 14.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
15. 15.There are 4 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 24 (c) 16 (d) 7
16. 16.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 30 (c) 15 (d) 36
17. 17.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
18. 18.What is the smallest prime factor of 35? (a) 7 (b) 1 (c) 2 (d) 5
19. 19.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 25 (c) 20 (d) 240
20. 20.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 130° (d) 65°
21. 21.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 28 (c) 29 (d) 22
22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 19 (b) 17 (c) 7 (d) 18
23. 23.A bag has 5 white balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 16 (d) 6
24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 19 (b) 20 (c) 9 (d) 18
25. 25.What is the mean of 15, 2, 19, 8, 16 and 18? (a) 13 (b) 14 (c) 12 (d) 15
26. 26.In a class of 50 children, 24 like mangoes, 21 like bananas and 10 like neither. How many like both? (a) 40 (b) 5 (c) 6 (d) 10
27. 27.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 85° (b) 155° (c) 95° (d) 120°
28. 28.Using (a + b)² = a² + 2ab + b², what is 63²? (a) 3609 (b) 3969 (c) 3249 (d) 3979
29. 29.Which term of the AP 3, 6, 9, 12, … is 114? (a) 39th (b) 38th (c) 40th (d) 37th
30. 30.What is the prime factorisation of 105? (a) 3² × 5 × 7 (b) 3 × 5 × 7² (c) 3 × 5 × 7 (d) 3³ × 5 × 7
31. 31.How many factors does 108 have? (a) 11 (b) 10 (c) 13 (d) 12
32. 32.Which is the correct factorisation of x² + 15x + 56? (a) (x − 7)(x − 8) (b) (x + 1)(x + 56) (c) (x + 1)(x + 14) (d) (x + 7)(x + 8)
33. 33.How many factors does 58 have? (a) 2 (b) 4 (c) 3 (d) 5
34. 34.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
35. 35.A bag has 8 white balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 9 (d) 18
36. 36.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 150° (c) 65° (d) 115°
37. 37.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 5/6 (b) 1/3 (c) 1/5 (d) 1/6
38. 38.What is the sum of all the whole numbers from 1 to 67? (a) 2211 (b) 2279 (c) 4556 (d) 2278
39. 39.In a class of 34 children, 23 like mangoes, 7 like bananas and 3 like both. How many like only mangoes? (a) 4 (b) 23 (c) 27 (d) 20
40. 40.A bag has 4 red balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 9 (c) 6 (d) 2

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