Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 847 · 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 an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 50° (d) 70°
2. 2.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 8 (c) 7 (d) 9
3. 3.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2 × 3 × 5
4. 4.Using (a − b)² = a² − 2ab + b², what is 66²? (a) 4356 (b) 5476 (c) 4884 (d) 4366
5. 5.Using (a − b)² = a² − 2ab + b², what is 96²? (a) 9216 (b) 9226 (c) 9984 (d) 10816
6. 6.A bag has 7 black 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) 2 (b) 10 (c) 4 (d) 8
7. 7.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 3/4 (c) 1/3 (d) 1/4
8. 8.The mean of 6 numbers is 21. When the number 49 is added to them, what is the new mean? (a) 21 (b) 26 (c) 35 (d) 25
9. 9.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 360 (c) 433 (d) 423
10. 10.Two angles of a triangle are 30° and 85°. What is the exterior angle at the third corner? (a) 115° (b) 150° (c) 65° (d) 95°
11. 11.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
12. 12.6 T-shirts and 3 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) 18 (c) 36 (d) 24
13. 13.In a class of 38 children, 15 like tea, 21 like coffee and 3 like both. How many like at least one of the two? (a) 33 (b) 36 (c) 38 (d) 30
14. 14.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
15. 15.In a class of 32 children, 18 like cricket, 11 like football and 7 like both. How many like only cricket? (a) 4 (b) 11 (c) 18 (d) 21
16. 16.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 15 (c) 30 (d) 9
17. 17.What is the distance between the points (2, 8) and (10, 23)? (a) 289 (b) 23 (c) 18 (d) 17
18. 18.In a class of 26 children, 11 like dance, 10 like music and 2 like both. How many like only dance? (a) 16 (b) 9 (c) 11 (d) 8
19. 19.8 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) 64 (b) 32 (c) 12 (d) 40
20. 20.Which is the correct factorisation of x² + 14x + 48? (a) (x + 1)(x + 13) (b) (x + 1)(x + 48) (c) (x − 6)(x − 8) (d) (x + 6)(x + 8)
21. 21.In a class of 21 children, 8 like cricket, 12 like football and 5 like both. How many like only cricket? (a) 9 (b) 8 (c) 7 (d) 3
22. 22.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 37 (b) 48 (c) 36 (d) 49
23. 23.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
24. 24.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 253 (c) 43 (d) 506
25. 25.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 50° (c) 65° (d) 40°
26. 26.What is the median of 12, 22, 15, 29 and 1? (a) 15 (b) 22 (c) 12 (d) 16
27. 27.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 125° (b) 75° (c) 130° (d) 105°
28. 28.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) 5 times (d) 2 times
29. 29.How many factors does 117 have? (a) 7 (b) 4 (c) 5 (d) 6
30. 30.The mean of 8 numbers is 13. When the number 22 is added to them, what is the new mean? (a) 14 (b) 13 (c) 16 (d) 15
31. 31.In a class of 47 children, 19 like cricket, 30 like football and 10 like neither. How many like both? (a) 10 (b) 2 (c) 37 (d) 12
32. 32.A bag has 8 yellow balls and 9 red 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) 17 (c) 10 (d) 2
33. 33.What is the 24th term of the AP 20, 27, 34, 41, …? (a) 181 (b) 188 (c) 168 (d) 161
34. 34.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 24 (c) 48 (d) 12
35. 35.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) 29 (c) 22 (d) 21
36. 36.In a class of 32 children, 28 like tea, 13 like coffee and 10 like both. How many like only tea? (a) 28 (b) 19 (c) 18 (d) 3
37. 37.A drawer has lots of black and blue 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) 5 (c) 3 (d) 4
38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 19 (d) 20
39. 39.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 85° (b) 5° (c) 95° (d) 275°
40. 40.In a class of 29 children, 11 like cricket, 25 like football and 8 like both. How many like neither? (a) 8 (b) 2 (c) 9 (d) 1

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