Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 297 · 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.The mean of 4 numbers is 18. When the number 28 is added to them, what is the new mean? (a) 23 (b) 21 (c) 20 (d) 18
2. 2.A drawer has lots of blue, black, green, red and yellow 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) 6 (d) 5
3. 3.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) 29 (b) 28 (c) 21 (d) 22
4. 4.What is the smallest prime factor of 169? (a) 2 (b) 1 (c) 3 (d) 13
5. 5.In a class of 33 children, 14 like cricket, 15 like football and 3 like both. How many like at least one of the two? (a) 23 (b) 33 (c) 29 (d) 26
6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
7. 7.A cube has edges of 9 cm. What is its volume? (a) 486 cu cm (b) 729 cu cm (c) 27 cu cm (d) 324 cu cm
8. 8.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 32 (b) 190 (c) 374 (d) 187
9. 9.A bag has 8 yellow balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 9 (b) 19 (c) 10 (d) 2
10. 10.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 42 (c) 49 (d) 14
11. 11.What is the prime factorisation of 504? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7³ (d) 2⁴ × 3² × 7
12. 12.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 160° (c) 135° (d) 45°
13. 13.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
14. 14.A drawer has lots of green and yellow 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) 5 (c) 2 (d) 4
15. 15.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 76 (c) 58 (d) 67
16. 16.What is the mode of 8, 9, 1, 15, 9, 8 and 9? (a) 15 (b) 1 (c) 9 (d) 8
17. 17.If a + b = 18 and ab = 80, what is a² + b²? (a) 324 (b) 244 (c) 164 (d) 484
18. 18.A bag has 3 black balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 10 (c) 4 (d) 5
19. 19.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 139 (b) 140 (c) 130 (d) 148
20. 20.How many factors does 23 have? (a) 2 (b) 4 (c) 3 (d) 1
21. 21.What is the median of 14, 6, 3, 24 and 36? (a) 3 (b) 6 (c) 24 (d) 14
22. 22.8 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 48 (b) 13 (c) 80 (d) 40
23. 23.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) 36 (c) 49 (d) 37
24. 24.A bag has 3 red balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 11 (c) 4 (d) 2
25. 25.There are 8 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 14 (b) 96 (c) 56 (d) 48
26. 26.What is the distance between the points (6, 13) and (22, 1)? (a) 21 (b) 28 (c) 20 (d) 400
27. 27.A bag has 9 black balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 10 (b) 11 (c) 2 (d) 12
28. 28.In a class of 36 children, 29 like dance, 15 like music and 9 like both. How many like only dance? (a) 6 (b) 20 (c) 29 (d) 21
29. 29.A bag has 10 black balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 12 (c) 11 (d) 22
30. 30.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 20 (c) 120 (d) 25
31. 31.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 61° (c) 30° (d) 60°
32. 32.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
33. 33.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2³ × 7 (c) 2 × 7⁴ (d) 2⁴ × 7
34. 34.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 70° (c) 40° (d) 140°
35. 35.What is the missing term in the AP 13, 18, 23, ?, 33? (a) 27 (b) 29 (c) 28 (d) 33
36. 36.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 523 (c) 522 (d) 513
37. 37.How many prime numbers are there between 30 and 50? (a) 7 (b) 4 (c) 5 (d) 6
38. 38.What is the median of 21, 11, 37, 10 and 14? (a) 14 (b) 11 (c) 37 (d) 21
39. 39.What is the distance between the points (2, 22) and (14, 6)? (a) 20 (b) 21 (c) 28 (d) 400
40. 40.In a class of 26 children, 16 like maths, 13 like science and 6 like both. How many like at least one of the two? (a) 26 (b) 17 (c) 29 (d) 23

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