Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 47 · 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.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
2. 2.What is the sum of the first 8 terms of the AP 9, 13, 17, …? (a) 184 (b) 368 (c) 37 (d) 200
3. 3.What is the smallest prime factor of 299? (a) 23 (b) 1 (c) 2 (d) 13
4. 4.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 3 (c) 12 (d) 9
5. 5.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 574 (c) 564 (d) 573
6. 6.In a class of 43 children, 25 like tea, 19 like coffee and 9 like both. How many like only tea? (a) 10 (b) 25 (c) 24 (d) 16
7. 7.The mean of 7 numbers is 32. When the number 40 is added to them, what is the new mean? (a) 36 (b) 33 (c) 32 (d) 34
8. 8.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 225 (c) 105 (d) 210
9. 9.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 7 (b) 24 (c) 63 (d) 21
10. 10.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 9 sq cm (c) 27 sq cm (d) 36 sq cm
11. 11.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 24 (c) 40 (d) 20
12. 12.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 31° (c) 210° (d) 150°
13. 13.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 60° (c) 61° (d) 30°
14. 14.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
15. 15.A drawer has lots of black, yellow, white and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 8 (c) 5 (d) 4
16. 16.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 15 (c) 21 (d) 22
17. 17.How many prime numbers are there between 50 and 60? (a) 4 (b) 1 (c) 2 (d) 3
18. 18.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 105 (c) 91 (d) 196
19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 1/9 (c) 3/11 (d) 1/11
20. 20.Two angles of a triangle are 60° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 85° (c) 95° (d) 120°
21. 21.What is the mode of 3, 4, 9, 3, 19, 3 and 19? (a) 3 (b) 19 (c) 9 (d) 4
22. 22.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
23. 23.A drawer has lots of white, blue, green, red and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 10 (c) 5 (d) 6
24. 24.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 125° (c) 140° (d) 55°
25. 25.A drawer has lots of yellow, black, red and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 8 (c) 4 (d) 5
26. 26.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
27. 27.What is the midpoint of the line joining (0, 22) and (8, 10)? (a) (16, 4) (b) (4, 6) (c) (8, 32) (d) (4, 16)
28. 28.What is the median of 6, 36, 1, 25 and 8? (a) 1 (b) 6 (c) 8 (d) 25
29. 29.In a class of 35 children, 11 like cricket, 19 like football and 5 like both. How many like only cricket? (a) 6 (b) 11 (c) 16 (d) 14
30. 30.A bag has 4 green balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 5 (c) 15 (d) 12
31. 31.A drawer has lots of black, yellow and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 3 (c) 6 (d) 2
32. 32.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 241 (b) 231 (c) 232 (d) 240
33. 33.In a class of 21 children, 11 like maths, 12 like science and 7 like both. How many like at least one of the two? (a) 21 (b) 23 (c) 9 (d) 16
34. 34.The mean of 8 numbers is 14. When the number 41 is added to them, what is the new mean? (a) 14 (b) 18 (c) 17 (d) 16
35. 35.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 19 (b) 99 (c) 108 (d) 198
36. 36.The mean of 7 numbers is 17. When the number 41 is added to them, what is the new mean? (a) 29 (b) 21 (c) 17 (d) 20
37. 37.What is the midpoint of the line joining (6, 1) and (14, 3)? (a) (20, 4) (b) (2, 10) (c) (4, 1) (d) (10, 2)
38. 38.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 50° (c) 40° (d) 130°
39. 39.Using (a − b)² = a² − 2ab + b², what is 49²? (a) 2499 (b) 2411 (c) 2401 (d) 2601
40. 40.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 12 (d) 6

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