Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 200 · 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.A bag has 12 green balls and 3 yellow 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) 13 (c) 4 (d) 2
2. 2.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
3. 3.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 5 (c) 18 (d) 15
4. 4.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 55 (d) 19
5. 5.What is the sum of the first 8 terms of the AP 3, 6, 9, …? (a) 120 (b) 216 (c) 24 (d) 108
6. 6.What is the 18th term of the AP 7, 13, 19, 25, …? (a) 115 (b) 102 (c) 109 (d) 108
7. 7.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 589 (c) 464 (d) 588
8. 8.A bag has 8 red, 8 green and 9 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 16/25 (c) 9/16 (d) 9/25
9. 9.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 16 (c) 20 (d) 32
10. 10.In a class of 38 children, 18 like cricket, 23 like football and 9 like neither. How many like both? (a) 29 (b) 9 (c) 12 (d) 3
11. 11.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
12. 12.A drawer has lots of yellow 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) 4 (b) 2 (c) 5 (d) 3
13. 13.In a class of 42 children, 21 like mangoes, 22 like bananas and 10 like neither. How many like both? (a) 32 (b) 11 (c) 1 (d) 10
14. 14.How many factors does 35 have? (a) 2 (b) 5 (c) 3 (d) 4
15. 15.A bag has 4 blue balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 14 (b) 2 (c) 5 (d) 6
16. 16.What is the smallest prime factor of 169? (a) 1 (b) 13 (c) 2 (d) 3
17. 17.What is the distance between the points (6, 10) and (10, 7)? (a) 6 (b) 7 (c) 5 (d) 25
18. 18.The mean of 6 numbers is 35. When the number 7 is added to them, what is the new mean? (a) 32 (b) 35 (c) 21 (d) 31
19. 19.What is the smallest prime factor of 57? (a) 1 (b) 19 (c) 2 (d) 3
20. 20.What is the sum of all the whole numbers from 1 to 26? (a) 702 (b) 325 (c) 351 (d) 338
21. 21.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 30 (d) 15
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 1/12 (c) 1/11 (d) 2/11
23. 23.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 7 (c) 63 (d) 21
24. 24.In a class of 40 children, 26 like maths, 25 like science and 12 like both. How many like neither? (a) 2 (b) 13 (c) 1 (d) 12
25. 25.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 300° (d) 150°
26. 26.What is the mode of 19, 16, 7, 16, 19, 1 and 16? (a) 1 (b) 16 (c) 19 (d) 7
27. 27.In a class of 32 children, 23 like mangoes, 13 like bananas and 6 like both. How many like only mangoes? (a) 19 (b) 23 (c) 17 (d) 7
28. 28.In a class of 39 children, 13 like tea, 21 like coffee and 2 like both. How many like neither? (a) 5 (b) 7 (c) 2 (d) 9
29. 29.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 9 (d) 12
30. 30.In a class of 31 children, 9 like cricket, 14 like football and 10 like neither. How many like both? (a) 3 (b) 2 (c) 21 (d) 10
31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 12 (b) 9 (c) 11 (d) 6
32. 32.What is the median of 4, 33, 3, 15 and 6? (a) 6 (b) 15 (c) 4 (d) 3
33. 33.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
34. 34.In which quadrant does the point (−4, 7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
35. 35.5 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 40 (c) 25 (d) 20
36. 36.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 72) (c) (x + 1)(x + 16) (d) (x + 8)(x + 9)
37. 37.What is the midpoint of the line joining (5, 6) and (17, 18)? (a) (11, 12) (b) (22, 24) (c) (12, 11) (d) (6, 6)
38. 38.What is the distance between the points (5, 21) and (21, 9)? (a) 20 (b) 21 (c) 28 (d) 400
39. 39.What is the sum of the roots of x² − 9x + 18 = 0? (a) 18 (b) 9 (c) 8 (d) 10
40. 40.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) 10 (b) 48 (c) 30 (d) 24

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