Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 788 · 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 mode of 19, 2, 11, 13, 2, 19 and 2? (a) 19 (b) 11 (c) 2 (d) 13
2. 2.A drawer has lots of white, 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) 6 (b) 4 (c) 3 (d) 2
3. 3.The mean of 3 numbers is 10. When the number 6 is added to them, what is the new mean? (a) 11 (b) 10 (c) 9 (d) 8
4. 4.A bag has 11 red balls and 4 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) 2 (c) 12 (d) 5
5. 5.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 225 (c) 210 (d) 120
6. 6.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
7. 7.7 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 21 (b) 9 (c) 28 (d) 14
8. 8.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 3/11 (c) 1/11 (d) 1/12
9. 9.The mean of 3 numbers is 17. When the number 21 is added to them, what is the new mean? (a) 18 (b) 19 (c) 17 (d) 20
10. 10.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 24 (c) 66 (d) 144
11. 11.A bag has 3 blue, 2 yellow and 6 red balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 9/11 (b) 2/9 (c) 2/11 (d) 1/3
12. 12.How many factors does 108 have? (a) 12 (b) 11 (c) 13 (d) 10
13. 13.What is the mean of 17, 19, 5, 6 and 13? (a) 10 (b) 12 (c) 13 (d) 15
14. 14.What is the smallest prime factor of 145? (a) 5 (b) 1 (c) 2 (d) 29
15. 15.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 48 (c) 30 (d) 10
16. 16.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) 20 (c) 30 (d) 15
17. 17.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 16 (d) 24
18. 18.In which quadrant does the point (−6, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
19. 19.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
20. 20.In a class of 52 children, 23 like tea, 28 like coffee and 9 like neither. How many like both? (a) 8 (b) 9 (c) 7 (d) 43
21. 21.In a class of 17 children, 12 like maths, 11 like science and 7 like both. How many like neither? (a) 1 (b) 8 (c) 7 (d) 2
22. 22.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2³ × 3 × 7 (c) 2 × 3 × 7 (d) 2² × 3 × 7
23. 23.Which term of the AP 3, 5, 7, 9, … is 35? (a) 17th (b) 19th (c) 16th (d) 18th
24. 24.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) 36 (b) 37 (c) 49 (d) 48
25. 25.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 15) (b) (x − 7)(x − 9) (c) (x + 1)(x + 63) (d) (x + 7)(x + 9)
26. 26.Two angles of a triangle are 30° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 50° (c) 150° (d) 130°
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/9 (d) 1/12
28. 28.What is the distance between the points (8, 6) and (16, 12)? (a) 10 (b) 11 (c) 14 (d) 100
29. 29.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm
30. 30.In a class of 21 children, 9 like tea, 12 like coffee and 6 like both. How many like neither? (a) 0 (b) 12 (c) 6 (d) 7
31. 31.The mean of 6 numbers is 19. When the number 33 is added to them, what is the new mean? (a) 19 (b) 22 (c) 26 (d) 21
32. 32.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 56 (c) 16 (d) 28
33. 33.What is the missing term in the AP 19, 24, ?, 34, 39? (a) 30 (b) 29 (c) 28 (d) 34
34. 34.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 49 (c) 14 (d) 21
35. 35.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 16 (c) 12 (d) 48
36. 36.In a class of 33 children, 17 like cricket, 18 like football and 11 like both. How many like at least one of the two? (a) 35 (b) 24 (c) 13 (d) 33
37. 37.A bag has 3 blue, 2 green and 2 white balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 6/7 (c) 2/7 (d) 5/7
38. 38.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
39. 39.What are the roots of x² − 10x + 21 = 0? (a) 1 and 21 (b) 2 and 8 (c) 1 and 9 (d) 3 and 7
40. 40.In a class of 38 children, 19 like mangoes, 20 like bananas and 3 like neither. How many like both? (a) 3 (b) 35 (c) 4 (d) 1

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