Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 750 · 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. 1.5 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) 35 (b) 11 (c) 60 (d) 30
2. 2.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 63 (c) 20 (d) 180
3. 3.In a class of 24 children, 10 like dance, 14 like music and 2 like both. How many like at least one of the two? (a) 22 (b) 24 (c) 20 (d) 23
4. 4.In a class of 47 children, 21 like mangoes, 25 like bananas and 8 like both. How many like neither? (a) 9 (b) 17 (c) 1 (d) 8
5. 5.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/8 (c) 3/4 (d) 3/8
6. 6.Using (a + b)² = a² + 2ab + b², what is 53²? (a) 2809 (b) 2819 (c) 2509 (d) 2209
7. 7.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 40 (b) 45 (c) 80 (d) 12
8. 8.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
9. 9.What is the median of 33, 12, 22, 26, 19, 25 and 7? (a) 22 (b) 19 (c) 25 (d) 26
10. 10.In a class of 47 children, 23 like mangoes, 23 like bananas and 7 like both. How many like only mangoes? (a) 16 (b) 7 (c) 24 (d) 23
11. 11.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
12. 12.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 60° (c) 120° (d) 40°
13. 13.A bag has 8 green balls and 9 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) 17 (d) 9
14. 14.How many prime numbers are there between 60 and 80? (a) 5 (b) 6 (c) 4 (d) 7
15. 15.Using (a + b)² = a² + 2ab + b², what is 35²? (a) 625 (b) 925 (c) 1225 (d) 1235
16. 16.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) 36 (b) 37 (c) 49 (d) 48
17. 17.A bag has 11 green balls and 12 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 23 (c) 2 (d) 12
18. 18.Using (a + b)² = a² + 2ab + b², what is 33²? (a) 1089 (b) 909 (c) 1099 (d) 729
19. 19.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 39 (c) 36 (d) 12
20. 20.Using (a + b)² = a² + 2ab + b², what is 45²? (a) 1625 (b) 2025 (c) 1225 (d) 2035
21. 21.Two angles of a triangle are 25° and 50°. What is the third angle? (a) 130° (b) 75° (c) 105° (d) 155°
22. 22.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 16 (c) 24 (d) 12
23. 23.A drawer has lots of yellow, white 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) 6 (b) 3 (c) 2 (d) 4
24. 24.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 64 (c) 28 (d) 56
25. 25.In a class of 29 children, 14 like dance, 14 like music and 3 like both. How many like only dance? (a) 11 (b) 15 (c) 3 (d) 14
26. 26.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 55° (b) 105° (c) 125° (d) 130°
27. 27.If a + b = 15 and ab = 50, what is (a − b)²? (a) 5 (b) 25 (c) 225 (d) 125
28. 28.In a class of 29 children, 19 like mangoes, 20 like bananas and 11 like both. How many like neither? (a) 1 (b) 2 (c) 11 (d) 12
29. 29.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3
30. 30.What is the distance between the points (4, 5) and (16, 14)? (a) 16 (b) 15 (c) 225 (d) 21
31. 31.3 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) 9 (b) 18 (c) 21 (d) 36
32. 32.In a class of 36 children, 22 like maths, 16 like science and 4 like neither. How many like both? (a) 2 (b) 4 (c) 32 (d) 6
33. 33.In a class of 45 children, 25 like mangoes, 18 like bananas and 7 like both. How many like neither? (a) 2 (b) 16 (c) 9 (d) 7
34. 34.What is the mean of 2, 3, 12, 15, 11 and 11? (a) 10 (b) 8 (c) 9 (d) 11
35. 35.If a + b = 14 and ab = 48, what is a² + b²? (a) 292 (b) 100 (c) 196 (d) 148
36. 36.A bag has 8 blue, 8 white and 6 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 7/11 (b) 4/11 (c) 15/22 (d) 1/3
37. 37.What is the sum of the first 9 terms of the AP 3, 6, 9, …? (a) 270 (b) 138 (c) 27 (d) 135
38. 38.6 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) 42 (b) 72 (c) 12 (d) 36
39. 39.In which quadrant does the point (6, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
40. 40.A bag has 7 blue balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 14 (b) 2 (c) 8 (d) 9

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