Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 725 · 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.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) 40 (b) 20 (c) 24 (d) 9
2. 2.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 15 (c) 20 (d) 30
3. 3.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 28 (b) 266 (c) 136 (d) 133
4. 4.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
5. 5.What is the smallest prime factor of 247? (a) 2 (b) 13 (c) 1 (d) 19
6. 6.What is the prime factorisation of 36? (a) 2 × 3² (b) 2² × 3² (c) 2² × 3³ (d) 2³ × 3²
7. 7.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 125 sq cm (c) 150 sq cm (d) 100 sq cm
8. 8.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 90 (c) 100 (d) 45
9. 9.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
10. 10.In a class of 33 children, 15 like tea, 20 like coffee and 10 like both. How many like neither? (a) 18 (b) 8 (c) 10 (d) 9
11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 9 (b) 20 (c) 18 (d) 19
12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 4/11 (c) 5/36 (d) 1/9
13. 13.In a class of 44 children, 31 like cricket, 22 like football and 2 like neither. How many like both? (a) 9 (b) 2 (c) 42 (d) 11
14. 14.How many prime numbers are there between 60 and 70? (a) 1 (b) 4 (c) 3 (d) 2
15. 15.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 529 (c) 45 (d) 276
16. 16.A drawer has lots of red, yellow, black, blue 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) 5 (c) 10 (d) 6
17. 17.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 4 times (d) 8 times
18. 18.What is the sum of the roots of x² − 17x + 72 = 0? (a) 16 (b) 18 (c) 17 (d) 72
19. 19.Two angles of a triangle are 35° and 105°. What is the third angle? (a) 145° (b) 40° (c) 140° (d) 75°
20. 20.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 66 (c) 144 (d) 132
21. 21.Two angles of a triangle are 25° and 120°. What is the exterior angle at the third corner? (a) 155° (b) 145° (c) 60° (d) 35°
22. 22.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 135° (b) 125° (c) 100° (d) 45°
23. 23.Using (a − b)² = a² − 2ab + b², what is 75²? (a) 6375 (b) 5635 (c) 5625 (d) 7225
24. 24.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 150° (c) 75° (d) 30°
25. 25.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 48 (c) 24 (d) 32
26. 26.What is the smallest prime factor of 121? (a) 11 (b) 3 (c) 1 (d) 2
27. 27.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 160° (b) 270° (c) 90° (d) 110°
28. 28.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
29. 29.What is the 22nd term of the AP 6, 10, 14, 18, …? (a) 90 (b) 84 (c) 94 (d) 88
30. 30.What is the mean of 12, 5, 2, 10, 13 and 12? (a) 8 (b) 11 (c) 9 (d) 10
31. 31.What is the sum of the roots of x² − 9x + 20 = 0? (a) 9 (b) 8 (c) 20 (d) 10
32. 32.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
33. 33.A bag has 10 green balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 12 (c) 11 (d) 13
34. 34.A bag has 11 yellow balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 13 (b) 20 (c) 2 (d) 12
35. 35.What is the mean of 19, 5, 15 and 5? (a) 13 (b) 10 (c) 12 (d) 11
36. 36.What is the median of 8, 10, 2, 9, 15, 35 and 29? (a) 15 (b) 9 (c) 10 (d) 11
37. 37.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
38. 38.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 100 (c) 90 (d) 55
39. 39.What is the smallest prime factor of 87? (a) 2 (b) 3 (c) 1 (d) 29
40. 40.How many factors does 111 have? (a) 2 (b) 5 (c) 3 (d) 4

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