Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 825 · 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 distance between the points (4, 0) and (7, 4)? (a) 25 (b) 7 (c) 5 (d) 6
2. 2.A drawer has lots of green, yellow, red, 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) 10 (b) 6 (c) 5 (d) 2
3. 3.A canteen sells 6 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 42 (c) 84 (d) 13
4. 4.In a class of 31 children, 17 like mangoes, 15 like bananas and 4 like both. How many like at least one of the two? (a) 31 (b) 24 (c) 32 (d) 28
5. 5.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 130° (d) 65°
6. 6.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 50° (c) 130° (d) 40°
7. 7.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 27 (c) 105 (d) 196
8. 8.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 80° (d) 140°
9. 9.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 18 (c) 81 (d) 36
10. 10.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2415 (c) 2485 (d) 4970
11. 11.In a class of 28 children, 10 like cricket, 19 like football and 4 like both. How many like at least one of the two? (a) 25 (b) 21 (c) 29 (d) 28
12. 12.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
13. 13.If a + b = 19 and ab = 90, what is (a − b)²? (a) 361 (b) 181 (c) 1 (d) 271
14. 14.Which term of the AP 2, 4, 6, 8, … is 80? (a) 41st (b) 42nd (c) 39th (d) 40th
15. 15.What is the sum of the roots of x² − 7x + 10 = 0? (a) 7 (b) 10 (c) 6 (d) 8
16. 16.A bag has 4 white balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 5 (c) 16 (d) 6
17. 17.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
18. 18.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 105° (b) 110° (c) 35° (d) 145°
19. 19.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 48 (c) 16 (d) 12
20. 20.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 22 (b) 15 (c) 21 (d) 14
21. 21.In a class of 55 children, 30 like tea, 29 like coffee and 11 like both. How many like at least one of the two? (a) 37 (b) 59 (c) 55 (d) 48
22. 22.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 20 (c) 90 (d) 45
23. 23.What is the midpoint of the line joining (8, 13) and (18, 1)? (a) (7, 13) (b) (5, 6) (c) (13, 7) (d) (26, 14)
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/11 (c) 1/12 (d) 1/18
25. 25.4 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 28 (b) 24 (c) 48 (d) 10
26. 26.What is the midpoint of the line joining (5, 12) and (9, 0)? (a) (2, 6) (b) (7, 6) (c) (6, 7) (d) (14, 12)
27. 27.What is the median of 11, 6, 12, 34, 10, 24 and 4? (a) 10 (b) 12 (c) 34 (d) 11
28. 28.What are the roots of x² − 14x + 45 = 0? (a) 1 and 45 (b) 1 and 13 (c) 5 and 9 (d) 3 and 15
29. 29.If a + b = 12 and ab = 20, what is (a − b)²? (a) 64 (b) 8 (c) 104 (d) 144
30. 30.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 110° (c) 70° (d) 130°
31. 31.The mean of 4 numbers is 32. When the number 17 is added to them, what is the new mean? (a) 29 (b) 28 (c) 30 (d) 32
32. 32.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 145 (c) 154 (d) 136
33. 33.What is the median of 34, 15, 13, 9 and 14? (a) 13 (b) 15 (c) 14 (d) 17
34. 34.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 91 (c) 156 (d) 78
35. 35.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 3/8 (c) 3/4 (d) 1/4
36. 36.A bag has 7 green balls and 8 black 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) 8 (c) 2 (d) 15
37. 37.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 25 (c) 20 (d) 10
38. 38.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 340° (c) 20° (d) 160°
39. 39.Which term of the AP 13, 22, 31, 40, … is 112? (a) 12th (b) 13th (c) 14th (d) 11th
40. 40.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 11° (b) 10° (c) 170° (d) 190°

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