Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 29 · 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.In a class of 46 children, 26 like tea, 21 like coffee and 6 like both. How many like at least one of the two? (a) 46 (b) 35 (c) 41 (d) 47
2. 2.Which term of the AP 19, 21, 23, 25, … is 81? (a) 34th (b) 33rd (c) 31st (d) 32nd
3. 3.A bag has 11 white balls and 12 yellow 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) 12 (c) 23 (d) 13
4. 4.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 120 (d) 240
5. 5.A cube has edges of 4 cm. What is its volume? (a) 64 cu cm (b) 12 cu cm (c) 96 cu cm (d) 65 cu cm
6. 6.What is the smallest prime factor of 299? (a) 1 (b) 2 (c) 23 (d) 13
7. 7.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 130° (d) 160°
8. 8.In a class of 48 children, 29 like tea, 25 like coffee and 10 like both. How many like only tea? (a) 15 (b) 19 (c) 29 (d) 23
9. 9.In a class of 37 children, 25 like maths, 15 like science and 7 like both. How many like only maths? (a) 25 (b) 8 (c) 22 (d) 18
10. 10.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 93 (b) 102 (c) 84 (d) 94
11. 11.What is the distance between the points (4, 1) and (12, 7)? (a) 10 (b) 14 (c) 11 (d) 100
12. 12.A bag has 6 red balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 9 (c) 2 (d) 7
13. 13.What is the median of 28, 23, 21, 37, 33, 18 and 32? (a) 23 (b) 32 (c) 37 (d) 28
14. 14.Which term of the AP 20, 22, 24, 26, … is 88? (a) 36th (b) 35th (c) 34th (d) 44th
15. 15.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 240 (b) 225 (c) 29 (d) 120
16. 16.3 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) 6 (b) 12 (c) 9 (d) 5
17. 17.Two angles of a triangle are 55° and 60°. What is the third angle? (a) 125° (b) 65° (c) 115° (d) 120°
18. 18.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
19. 19.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 15 (d) 30
20. 20.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
21. 21.In a class of 35 children, 12 like dance, 24 like music and 6 like both. How many like neither? (a) 6 (b) 4 (c) 11 (d) 5
22. 22.In a class of 27 children, 10 like cricket, 18 like football and 4 like both. How many like only cricket? (a) 9 (b) 14 (c) 10 (d) 6
23. 23.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 1/8 (c) 1/4 (d) 3/4
24. 24.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 60° (c) 30° (d) 150°
25. 25.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 26 (b) 44 (c) 36 (d) 35
26. 26.If a + b = 19 and ab = 90, what is (a − b)²? (a) 271 (b) 361 (c) 1 (d) 181
27. 27.How many prime numbers are there between 60 and 70? (a) 4 (b) 1 (c) 3 (d) 2
28. 28.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 51 (c) 153 (d) 54
29. 29.What is the distance between the points (9, 6) and (16, 30)? (a) 25 (b) 625 (c) 26 (d) 31
30. 30.Using (a − b)² = a² − 2ab + b², what is 27²? (a) 891 (b) 729 (c) 739 (d) 1089
31. 31.A bag has 5 blue balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 12 (c) 7 (d) 6
32. 32.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
33. 33.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/3 (c) 1/4 (d) 3/4
34. 34.What is the distance between the points (3, 14) and (8, 2)? (a) 14 (b) 13 (c) 169 (d) 17
35. 35.What is the sum of all the whole numbers from 1 to 48? (a) 1176 (b) 1128 (c) 2352 (d) 1152
36. 36.A bag has 7 green, 9 red and 3 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 17/19 (b) 3/19 (c) 1/3 (d) 16/19
37. 37.What is the prime factorisation of 35? (a) 5³ × 7 (b) 5² × 7 (c) 5 × 7² (d) 5 × 7
38. 38.How many prime numbers are there between 20 and 40? (a) 3 (b) 4 (c) 6 (d) 5
39. 39.A bag has 3 red balls and 8 white 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) 4 (c) 11 (d) 2
40. 40.In which quadrant does the point (−8, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant

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