Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 652 · 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.If a + b = 5 and ab = 6, what is a² + b²? (a) 25 (b) 19 (c) 37 (d) 13
2. 2.What is the sum of the first 9 terms of the AP 7, 11, 15, …? (a) 225 (b) 207 (c) 39 (d) 414
3. 3.In a class of 32 children, 10 like cricket, 19 like football and 4 like both. How many like neither? (a) 7 (b) 3 (c) 4 (d) 11
4. 4.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 24 (c) 144 (d) 132
5. 5.What is the midpoint of the line joining (8, 5) and (12, 7)? (a) (20, 12) (b) (2, 1) (c) (10, 6) (d) (6, 10)
6. 6.In a class of 44 children, 27 like mangoes, 23 like bananas and 7 like both. How many like only mangoes? (a) 21 (b) 27 (c) 16 (d) 20
7. 7.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) 22 (b) 29 (c) 21 (d) 28
8. 8.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 42 (c) 13 (d) 39
9. 9.The mean of 7 numbers is 32. When the number 40 is added to them, what is the new mean? (a) 36 (b) 32 (c) 34 (d) 33
10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
11. 11.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 250° (b) 140° (c) 70° (d) 110°
12. 12.In a class of 49 children, 23 like dance, 27 like music and 11 like both. How many like at least one of the two? (a) 49 (b) 39 (c) 50 (d) 28
13. 13.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 155° (b) 55° (c) 150° (d) 30°
14. 14.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 120 (d) 20
15. 15.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 28 (c) 35 (d) 11
16. 16.What is the mean of 9, 20, 20, 10, 2 and 23? (a) 14 (b) 13 (c) 15 (d) 12
17. 17.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 120 (c) 105 (d) 210
18. 18.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7
19. 19.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 110 (c) 55 (d) 22
20. 20.In a class of 38 children, 20 like tea, 20 like coffee and 12 like both. How many like at least one of the two? (a) 38 (b) 16 (c) 28 (d) 40
21. 21.In a class of 30 children, 15 like tea, 18 like coffee and 4 like both. How many like at least one of the two? (a) 30 (b) 29 (c) 25 (d) 33
22. 22.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 150° (c) 60° (d) 75°
23. 23.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 21 (c) 42 (d) 14
24. 24.What is the median of 3, 39, 1, 29 and 5? (a) 29 (b) 5 (c) 1 (d) 3
25. 25.A bag has 6 green, 2 white and 9 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 6/17 (b) 11/17 (c) 1/3 (d) 12/17
26. 26.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 228 (b) 432 (c) 216 (d) 29
27. 27.There are 6 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 12 (c) 8 (d) 18
28. 28.What is the median of 4, 37, 20, 22 and 10? (a) 21 (b) 22 (c) 20 (d) 10
29. 29.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) 3 (b) 2 (c) 4 (d) 5
30. 30.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 75° (b) 105° (c) 135° (d) 150°
31. 31.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 3/8 (c) 1/8 (d) 3/4
32. 32.In a class of 34 children, 15 like cricket, 20 like football and 3 like both. How many like neither? (a) 3 (b) 1 (c) 5 (d) 2
33. 33.What is the missing term in the AP 17, ?, 31, 38, 45? (a) 25 (b) 31 (c) 24 (d) 23
34. 34.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) 49 (b) 48 (c) 37 (d) 36
35. 35.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 28 (c) 38 (d) 37
36. 36.Two angles of a triangle are 25° and 65°. What is the third angle? (a) 115° (b) 90° (c) 270° (d) 155°
37. 37.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/3 (c) 1/2 (d) 3/4
38. 38.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
39. 39.What is the distance between the points (3, 0) and (6, 4)? (a) 25 (b) 7 (c) 5 (d) 6
40. 40.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 7 (b) 21 (c) 24 (d) 63

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