Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 193 · 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 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) 28 (b) 21 (c) 22 (d) 29
2. 2.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 56 (c) 28 (d) 36
3. 3.If a + b = 8 and ab = 7, what is a² + b²? (a) 78 (b) 64 (c) 57 (d) 50
4. 4.In a class of 48 children, 24 like mangoes, 30 like bananas and 10 like both. How many like at least one of the two? (a) 44 (b) 54 (c) 48 (d) 34
5. 5.What is the prime factorisation of 112? (a) 2⁴ × 7 (b) 2⁵ × 7 (c) 2 × 7⁴ (d) 2³ × 7
6. 6.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 120° (c) 30° (d) 60°
7. 7.How many factors does 88 have? (a) 8 (b) 9 (c) 6 (d) 7
8. 8.A bag has 4 blue balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 5 (b) 2 (c) 6 (d) 7
9. 9.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 95° (d) 60°
10. 10.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 253 (b) 43 (c) 506 (d) 484
11. 11.What is the distance between the points (8, 4) and (24, 16)? (a) 28 (b) 20 (c) 400 (d) 21
12. 12.How many factors does 25 have? (a) 4 (b) 1 (c) 2 (d) 3
13. 13.What is the mean of 19, 8, 16, 6, 9 and 20? (a) 14 (b) 13 (c) 12 (d) 15
14. 14.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2 × 3⁴ (c) 2⁴ × 3 (d) 2³ × 3
15. 15.What is the distance between the points (3, 0) and (27, 7)? (a) 26 (b) 25 (c) 625 (d) 31
16. 16.How many factors does 28 have? (a) 7 (b) 5 (c) 6 (d) 4
17. 17.A drawer has lots of red 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) 5 (c) 3 (d) 2
18. 18.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 110° (c) 120° (d) 60°
19. 19.What is the mean of 7, 17, 11, 17, 7 and 7? (a) 10 (b) 11 (c) 12 (d) 13
20. 20.In a class of 34 children, 20 like dance, 18 like music and 10 like both. How many like at least one of the two? (a) 34 (b) 28 (c) 38 (d) 18
21. 21.If a + b = 13 and ab = 40, what is a² + b²? (a) 129 (b) 249 (c) 169 (d) 89
22. 22.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 110° (b) 100° (c) 150° (d) 30°
23. 23.A drawer has lots of white, blue and red 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
24. 24.A bag has 5 red balls and 7 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) 6 (d) 8
25. 25.The mean of 5 numbers is 19. When the number 13 is added to them, what is the new mean? (a) 16 (b) 18 (c) 17 (d) 19
26. 26.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
27. 27.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 337 (c) 327 (d) 336
28. 28.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 10 (c) 25 (d) 20
29. 29.How many prime numbers are there between 50 and 60? (a) 3 (b) 1 (c) 2 (d) 4
30. 30.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 25 (d) 240
31. 31.Which is the correct factorisation of x² + 5x + 6? (a) (x + 2)(x + 3) (b) (x + 1)(x + 6) (c) (x + 1)(x + 4) (d) (x − 2)(x − 3)
32. 32.A bag has 11 yellow balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 14 (c) 13 (d) 12
33. 33.What is the smallest prime factor of 299? (a) 1 (b) 23 (c) 13 (d) 2
34. 34.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
35. 35.How many prime numbers are there between 80 and 100? (a) 2 (b) 3 (c) 4 (d) 5
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/36 (b) 1/6 (c) 5/11 (d) 1/11
37. 37.Which is the correct factorisation of x² + 16x + 63? (a) (x + 7)(x + 9) (b) (x + 1)(x + 63) (c) (x + 1)(x + 15) (d) (x − 7)(x − 9)
38. 38.Using (a + b)² = a² + 2ab + b², what is 65²? (a) 4235 (b) 4225 (c) 3025 (d) 3625
39. 39.How many prime numbers are there between 10 and 30? (a) 7 (b) 8 (c) 6 (d) 5
40. 40.A bag has 10 yellow balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 15 (c) 12 (d) 11

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