Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 849 · 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.Using (a − b)² = a² − 2ab + b², what is 18²? (a) 484 (b) 324 (c) 334 (d) 396
2. 2.A bag has 7 green balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 13 (d) 8
3. 3.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 475 (c) 465 (d) 474
4. 4.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 102 (b) 27 (c) 174 (d) 87
5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 20 (b) 9 (c) 19 (d) 18
6. 6.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) 15 (b) 10 (c) 20 (d) 7
7. 7.A bag has 8 yellow balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 8 (c) 2 (d) 9
8. 8.What is the median of 23, 1, 18, 39 and 33? (a) 24 (b) 33 (c) 18 (d) 23
9. 9.The mean of 4 numbers is 34. When the number 29 is added to them, what is the new mean? (a) 35 (b) 32 (c) 34 (d) 33
10. 10.In a class of 23 children, 13 like cricket, 13 like football and 6 like both. How many like neither? (a) 6 (b) 9 (c) 4 (d) 3
11. 11.What is the median of 10, 23, 28, 36 and 31? (a) 28 (b) 31 (c) 29 (d) 23
12. 12.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 16 (c) 64 (d) 56
13. 13.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 cm
14. 14.What is the 23rd term of the AP 9, 12, 15, 18, …? (a) 69 (b) 66 (c) 75 (d) 78
15. 15.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 120 (c) 210 (d) 105
16. 16.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/2 (c) 1/3 (d) 1/4
17. 17.Which term of the AP 18, 21, 24, 27, … is 90? (a) 25th (b) 26th (c) 24th (d) 30th
18. 18.A drawer has lots of red, black, yellow, green 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
19. 19.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 7 (b) 54 (c) 30 (d) 27
20. 20.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 125° (b) 150° (c) 55° (d) 155°
21. 21.What is the median of 18, 39, 9, 26 and 16? (a) 26 (b) 18 (c) 9 (d) 16
22. 22.A drawer has lots of black, green 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) 3 (b) 4 (c) 6 (d) 2
23. 23.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 75° (c) 30° (d) 105°
24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 7 (b) 16 (c) 17 (d) 15
25. 25.A drawer has lots of 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) 6 (b) 3 (c) 4 (d) 2
26. 26.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
27. 27.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 3 (d) 16
28. 28.What is the mean of 5, 20, 16 and 15? (a) 13 (b) 16 (c) 15 (d) 14
29. 29.Using (a + b)² = a² + 2ab + b², what is 22²? (a) 404 (b) 324 (c) 494 (d) 484
30. 30.In a class of 24 children, 17 like maths, 13 like science and 10 like both. How many like only maths? (a) 7 (b) 3 (c) 11 (d) 17
31. 31.In which quadrant does the point (1, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
32. 32.What is the sum of the first 5 terms of the AP 7, 12, 17, …? (a) 170 (b) 27 (c) 85 (d) 90
33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 4 (d) 15
34. 34.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 120 (d) 20
35. 35.Using (a + b)² = a² + 2ab + b², what is 62²? (a) 3854 (b) 3604 (c) 3364 (d) 3844
36. 36.There are 7 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 14 (b) 56 (c) 98 (d) 49
37. 37.A drawer has lots of yellow, blue, red, black and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 2 (c) 5 (d) 6
38. 38.In a class of 23 children, 9 like cricket, 17 like football and 4 like both. How many like at least one of the two? (a) 23 (b) 26 (c) 22 (d) 18
39. 39.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2⁴ × 3 × 5 (c) 2⁵ × 3 × 5 (d) 2 × 3 × 5⁴
40. 40.The mean of 5 numbers is 25. When the number 49 is added to them, what is the new mean? (a) 25 (b) 29 (c) 30 (d) 37

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