Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 971 · 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 many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
2. 2.A bag has 6 white balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 12 (b) 8 (c) 2 (d) 7
3. 3.What is the median of 30, 36, 24, 27 and 3? (a) 24 (b) 30 (c) 28 (d) 27
4. 4.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 15 (d) 30
5. 5.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 96 (c) 105 (d) 106
6. 6.In a class of 26 children, 8 like mangoes, 18 like bananas and 5 like both. How many like at least one of the two? (a) 22 (b) 26 (c) 21 (d) 16
7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 19 (b) 8 (c) 18 (d) 20
8. 8.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) 24 (b) 16 (c) 7 (d) 12
9. 9.What is the prime factorisation of 36? (a) 2³ × 3² (b) 2 × 3² (c) 2² × 3² (d) 2² × 3³
10. 10.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 120° (c) 60° (d) 240°
11. 11.There are 4 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 20 (c) 40 (d) 9
12. 12.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 61°
13. 13.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
14. 14.What is the smallest prime factor of 121? (a) 3 (b) 2 (c) 1 (d) 11
15. 15.In which quadrant does the point (−1, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
16. 16.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 21 (c) 42 (d) 49
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/11 (c) 1/6 (d) 5/36
18. 18.What is the 11th term of the AP 7, 11, 15, 19, …? (a) 44 (b) 47 (c) 51 (d) 40
19. 19.In a class of 30 children, 19 like cricket, 15 like football and 12 like both. How many like only cricket? (a) 3 (b) 15 (c) 7 (d) 19
20. 20.A drawer has lots of red, white, blue 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) 4 (b) 2 (c) 5 (d) 8
21. 21.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 55 (d) 110
22. 22.What is the sum of all the whole numbers from 1 to 15? (a) 240 (b) 120 (c) 105 (d) 121
23. 23.How many prime numbers are there between 70 and 100? (a) 5 (b) 7 (c) 6 (d) 8
24. 24.How many factors does 105 have? (a) 6 (b) 9 (c) 8 (d) 7
25. 25.A bag has 8 black balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 9 (c) 6 (d) 2
26. 26.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 406 (c) 435 (d) 436
27. 27.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 24 (c) 48 (d) 12
28. 28.In a class of 50 children, 28 like tea, 24 like coffee and 9 like both. How many like only tea? (a) 26 (b) 15 (c) 19 (d) 28
29. 29.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 100 (c) 110 (d) 19
30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 18 (b) 19 (c) 17 (d) 8
31. 31.In a class of 34 children, 19 like maths, 11 like science and 3 like both. How many like only maths? (a) 23 (b) 16 (c) 8 (d) 19
32. 32.What is the median of 31, 12, 40, 4 and 6? (a) 40 (b) 12 (c) 6 (d) 31
33. 33.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 50° (c) 130° (d) 80°
34. 34.What is the 14th term of the AP 7, 11, 15, 19, …? (a) 56 (b) 63 (c) 52 (d) 59
35. 35.Using (a − b)² = a² − 2ab + b², what is 18²? (a) 484 (b) 324 (c) 396 (d) 334
36. 36.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times
37. 37.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 80 (c) 40 (d) 13
38. 38.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 54 (c) 17 (d) 51
39. 39.How many prime numbers are there between 20 and 50? (a) 8 (b) 7 (c) 9 (d) 6
40. 40.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 36 (c) 21 (d) 15

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