Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 772 · 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 sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 210 (c) 420 (d) 39
2. 2.A bag has 6 green, 9 blue and 7 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 7/22 (c) 8/11 (d) 15/22
3. 3.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 20 (d) 240
4. 4.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 140° (b) 320° (c) 40° (d) 50°
5. 5.What is the sum of all the whole numbers from 1 to 21? (a) 231 (b) 232 (c) 210 (d) 462
6. 6.A bag has 8 green 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) 17 (b) 2 (c) 9 (d) 10
7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 19 (b) 18 (c) 7 (d) 17
8. 8.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 120° (b) 300° (c) 30° (d) 150°
9. 9.If a + b = 15 and ab = 44, what is a² + b²? (a) 181 (b) 313 (c) 137 (d) 225
10. 10.A bag has 7 red balls and 3 blue 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) 8 (d) 4
11. 11.What is the sum of all the whole numbers from 1 to 40? (a) 780 (b) 820 (c) 1640 (d) 800
12. 12.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 27 cu cm (c) 36 cu cm (d) 54 cu cm
13. 13.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 812 (b) 55 (c) 784 (d) 406
14. 14.How many prime numbers are there between 10 and 30? (a) 5 (b) 6 (c) 8 (d) 7
15. 15.What is the median of 13, 29, 1, 26, 31, 30 and 15? (a) 15 (b) 27 (c) 29 (d) 26
16. 16.In a class of 31 children, 13 like maths, 17 like science and 5 like both. How many like only maths? (a) 13 (b) 14 (c) 12 (d) 8
17. 17.A bag has 10 green balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 12 (c) 16 (d) 11
18. 18.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 16 (c) 48 (d) 12
19. 19.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 80° (c) 50° (d) 260°
20. 20.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 135° (c) 315° (d) 136°
21. 21.In a class of 44 children, 30 like cricket, 14 like football and 10 like neither. How many like both? (a) 11 (b) 10 (c) 34 (d) 9
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/18 (c) 1/12 (d) 1/11
23. 23.How many prime numbers are there between 70 and 100? (a) 8 (b) 7 (c) 6 (d) 5
24. 24.A drawer has lots of white, red, blue 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) 8 (b) 5 (c) 2 (d) 4
25. 25.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 130° (c) 155° (d) 50°
26. 26.In a class of 35 children, 14 like mangoes, 16 like bananas and 5 like both. How many like neither? (a) 5 (b) 15 (c) 10 (d) 11
27. 27.What is the median of 6, 3, 2, 15 and 23? (a) 15 (b) 3 (c) 6 (d) 2
28. 28.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 49 (c) 21 (d) 42
29. 29.In a class of 43 children, 15 like tea, 31 like coffee and 11 like both. How many like at least one of the two? (a) 35 (b) 43 (c) 46 (d) 24
30. 30.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
31. 31.What is the sum of all the whole numbers from 1 to 74? (a) 2701 (b) 2738 (c) 2775 (d) 5550
32. 32.A bag has 7 red balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 8 (c) 9 (d) 16
33. 33.A bag has 8 yellow, 7 red and 7 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 7/11 (b) 4/7 (c) 1/3 (d) 4/11
34. 34.In a class of 26 children, 11 like tea, 9 like coffee and 4 like both. How many like at least one of the two? (a) 12 (b) 16 (c) 20 (d) 26
35. 35.6 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) 10 (b) 48 (c) 24 (d) 30
36. 36.What is the missing term in the AP 8, 16, ?, 32, 40? (a) 32 (b) 25 (c) 23 (d) 24
37. 37.If a + b = 8 and ab = 7, what is a² + b²? (a) 50 (b) 57 (c) 78 (d) 64
38. 38.If a + b = 18 and ab = 72, what is a² + b²? (a) 252 (b) 180 (c) 468 (d) 324
39. 39.What is the midpoint of the line joining (0, 2) and (4, 4)? (a) (3, 2) (b) (2, 1) (c) (2, 3) (d) (4, 6)
40. 40.What is the smallest prime factor of 133? (a) 1 (b) 19 (c) 7 (d) 2

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