Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 978 · 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 fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
2. 2.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 266 (c) 282 (d) 291
3. 3.A bag has 3 red balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 5 (b) 2 (c) 4 (d) 11
4. 4.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 24 (c) 12 (d) 13
5. 5.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 22 (c) 110 (d) 121
6. 6.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
7. 7.Using (a + b)² = a² + 2ab + b², what is 55²? (a) 3025 (b) 3035 (c) 2525 (d) 2025
8. 8.A bag has 6 blue, 7 yellow and 2 green balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 3/5 (b) 1/3 (c) 2/3 (d) 2/5
9. 9.In a class of 30 children, 22 like tea, 19 like coffee and 12 like both. How many like at least one of the two? (a) 30 (b) 29 (c) 41 (d) 17
10. 10.How many prime numbers are there between 80 and 110? (a) 6 (b) 7 (c) 8 (d) 9
11. 11.Which term of the AP 12, 18, 24, 30, … is 72? (a) 12th (b) 11th (c) 10th (d) 13th
12. 12.What is the median of 8, 21, 6, 3 and 31? (a) 8 (b) 21 (c) 6 (d) 9
13. 13.What is the missing term in the AP 1, 4, 7, ?, 13? (a) 10 (b) 9 (c) 13 (d) 11
14. 14.How many factors does 94 have? (a) 3 (b) 5 (c) 4 (d) 2
15. 15.A drawer has lots of white 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) 2 (b) 4 (c) 5 (d) 3
16. 16.In a class of 46 children, 28 like tea, 26 like coffee and 11 like both. How many like only tea? (a) 28 (b) 15 (c) 17 (d) 20
17. 17.What is the median of 39, 21, 20, 2 and 37? (a) 22 (b) 20 (c) 21 (d) 37
18. 18.A drawer has lots of blue, yellow 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) 3 (b) 4 (c) 6 (d) 2
19. 19.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 140 (b) 135 (c) 18 (d) 270
20. 20.What is the smallest prime factor of 161? (a) 1 (b) 7 (c) 23 (d) 2
21. 21.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 864 cu cm (c) 1728 cu cm (d) 576 cu cm
22. 22.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2³ × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5
23. 23.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
24. 24.A bag has 8 red balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 12 (b) 10 (c) 2 (d) 9
25. 25.What is the distance between the points (7, 5) and (19, 14)? (a) 16 (b) 225 (c) 21 (d) 15
26. 26.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 85° (c) 5° (d) 10°
27. 27.In a class of 27 children, 11 like mangoes, 21 like bananas and 8 like both. How many like only mangoes? (a) 13 (b) 3 (c) 11 (d) 6
28. 28.How many factors does 119 have? (a) 3 (b) 2 (c) 4 (d) 5
29. 29.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 80° (c) 20° (d) 100°
30. 30.What is the median of 13, 22, 15, 16, 20, 26 and 30? (a) 20 (b) 22 (c) 16 (d) 21
31. 31.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 16 (c) 12 (d) 48
32. 32.What is the sum of all the whole numbers from 1 to 34? (a) 561 (b) 1190 (c) 578 (d) 595
33. 33.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 36 (c) 9 (d) 18
34. 34.What is the sum of all the whole numbers from 1 to 97? (a) 9506 (b) 4754 (c) 4753 (d) 4656
35. 35.Two angles of a triangle are 40° and 70°. What is the exterior angle at the third corner? (a) 250° (b) 70° (c) 110° (d) 140°
36. 36.Using (a − b)² = a² − 2ab + b², what is 88²? (a) 8096 (b) 8464 (c) 7744 (d) 7754
37. 37.A bag has 7 red, 5 green and 7 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 13/19 (b) 12/19 (c) 7/19 (d) 1/3
38. 38.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 5 (b) 6 (c) 12 (d) 9
39. 39.How many factors does 42 have? (a) 6 (b) 7 (c) 9 (d) 8
40. 40.How many factors does 67 have? (a) 2 (b) 4 (c) 3 (d) 1

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