Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 875 · 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.What is the prime factorisation of 35? (a) 5 × 7² (b) 5³ × 7 (c) 5² × 7 (d) 5 × 7
2. 2.What is the 28th term of the AP 19, 25, 31, 37, …? (a) 181 (b) 162 (c) 168 (d) 187
3. 3.A drawer has lots of black, green, blue 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) 5 (b) 2 (c) 4 (d) 8
4. 4.A bag has 12 black balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 20 (c) 13 (d) 14
5. 5.What is the 40th term of the AP 12, 19, 26, 33, …? (a) 273 (b) 292 (c) 280 (d) 285
6. 6.What is the smallest prime factor of 39? (a) 2 (b) 3 (c) 13 (d) 1
7. 7.What is the mode of 16, 17, 16, 17, 15, 17 and 18? (a) 16 (b) 18 (c) 17 (d) 15
8. 8.In which quadrant does the point (−1, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
9. 9.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) 22 (d) 21
10. 10.A bag has 5 red, 7 green and 3 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 11/15 (b) 2/3 (c) 1/15 (d) 1/3
11. 11.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 19 (b) 18 (c) 9 (d) 20
13. 13.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) 22 (c) 28 (d) 21
14. 14.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 cm
15. 15.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 24 (c) 48 (d) 16
16. 16.How many factors does 62 have? (a) 3 (b) 4 (c) 2 (d) 5
17. 17.In a class of 38 children, 24 like cricket, 22 like football and 11 like both. How many like at least one of the two? (a) 38 (b) 24 (c) 46 (d) 35
18. 18.A bag has 10 white balls and 9 black 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) 10 (c) 11 (d) 19
19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 19 (b) 18 (c) 17 (d) 7
20. 20.A drawer has lots of 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) 4 (b) 5 (c) 2 (d) 8
21. 21.In a class of 35 children, 6 like mangoes, 21 like bananas and 10 like neither. How many like both? (a) 10 (b) 2 (c) 3 (d) 25
22. 22.The mean of 8 numbers is 33. When the number 60 is added to them, what is the new mean? (a) 33 (b) 36 (c) 37 (d) 35
23. 23.A drawer has lots of blue, black, yellow and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 2 (c) 4 (d) 5
24. 24.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 110 (c) 121 (d) 55
25. 25.The mean of 7 numbers is 40. When the number 72 is added to them, what is the new mean? (a) 56 (b) 45 (c) 40 (d) 44
26. 26.What is the sum of all the whole numbers from 1 to 54? (a) 2970 (b) 1485 (c) 1431 (d) 1458
27. 27.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 7 (b) 19 (c) 18 (d) 17
29. 29.A bag has 11 blue balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 7 (c) 17 (d) 2
30. 30.In a class of 37 children, 22 like tea, 16 like coffee and 7 like both. How many like only tea? (a) 21 (b) 15 (c) 22 (d) 9
31. 31.A drawer has lots of black 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) 4 (c) 5 (d) 3
32. 32.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 7 (d) 6
33. 33.Two angles of a triangle are 20° and 115°. What is the third angle? (a) 160° (b) 45° (c) 135° (d) 65°
34. 34.How many factors does 97 have? (a) 4 (b) 3 (c) 2 (d) 1
35. 35.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
36. 36.A bag has 4 red balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 5 (b) 6 (c) 2 (d) 8
37. 37.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 55 (c) 90 (d) 45
38. 38.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 210° (c) 75° (d) 30°
39. 39.8 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 15 (b) 64 (c) 112 (d) 56
40. 40.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 225 (c) 210 (d) 120

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