Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 327 · 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 3 green, 9 red and 2 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 13/14 (b) 6/7 (c) 1/7 (d) 1/3
2. 2.What is the missing term in the AP 12, ?, 18, 21, 24? (a) 16 (b) 15 (c) 14 (d) 18
3. 3.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
4. 4.What is the smallest prime factor of 77? (a) 1 (b) 2 (c) 7 (d) 11
5. 5.A bag has 4 red, 8 yellow and 5 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 14/17 (b) 4/17 (c) 1/3 (d) 13/17
6. 6.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 2/3 (c) 1/3 (d) 1/2
7. 7.What is the 23rd term of the AP 3, 8, 13, 18, …? (a) 118 (b) 113 (c) 115 (d) 110
8. 8.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 9 (c) 14 (d) 21
9. 9.If a + b = 16 and ab = 63, what is a² + b²? (a) 256 (b) 382 (c) 193 (d) 130
10. 10.Two angles of a triangle are 55° and 30°. What is the exterior angle at the third corner? (a) 125° (b) 95° (c) 85° (d) 150°
11. 11.What is the prime factorisation of 21? (a) 3 × 7² (b) 3 × 7 (c) 3² × 7 (d) 3³ × 7
12. 12.Using (a − b)² = a² − 2ab + b², what is 35²? (a) 1225 (b) 2025 (c) 1235 (d) 1575
13. 13.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 132 (c) 66 (d) 144
14. 14.A drawer has lots of blue, red and white 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) 3 (c) 2 (d) 6
15. 15.How many prime numbers are there between 40 and 60? (a) 7 (b) 4 (c) 6 (d) 5
16. 16.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 18 (c) 72 (d) 81
17. 17.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/3 (c) 1/4 (d) 2/3
18. 18.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) 21 (b) 29 (c) 22 (d) 28
19. 19.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 25 (c) 20 (d) 240
20. 20.How many prime numbers are there between 80 and 110? (a) 7 (b) 8 (c) 9 (d) 6
21. 21.A bag has 11 black balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 12 (c) 20 (d) 2
22. 22.What is the mode of 20, 9, 17, 9, 20, 9 and 4? (a) 4 (b) 20 (c) 17 (d) 9
23. 23.What is the distance between the points (8, 8) and (13, 20)? (a) 169 (b) 17 (c) 13 (d) 14
24. 24.A bag has 4 white, 3 red and 8 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 13/15 (b) 4/5 (c) 1/5 (d) 1/3
25. 25.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 3 (d) 2
26. 26.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
27. 27.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
28. 28.A drawer has lots of green, white 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) 6 (b) 2 (c) 3 (d) 4
29. 29.What is the sum of the first 5 terms of the AP 10, 11, 12, …? (a) 14 (b) 61 (c) 60 (d) 120
30. 30.In a class of 32 children, 16 like dance, 25 like music and 1 like neither. How many like both? (a) 1 (b) 10 (c) 9 (d) 31
31. 31.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 517 (b) 507 (c) 516 (d) 416
32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 5 (b) 3 (c) 4 (d) 2
33. 33.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
34. 34.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
35. 35.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
36. 36.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/3 (c) 1/2 (d) 1/4
37. 37.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2 × 3⁴ (c) 2⁴ × 3 (d) 2⁵ × 3
38. 38.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 109 (b) 110 (c) 100 (d) 118
39. 39.In a class of 31 children, 12 like maths, 19 like science and 6 like both. How many like only maths? (a) 7 (b) 13 (c) 6 (d) 12
40. 40.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 45 (c) 36 (d) 72

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