Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 101 · 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 6 terms of the AP 10, 11, 12, …? (a) 78 (b) 150 (c) 15 (d) 75
2. 2.In a class of 38 children, 25 like tea, 14 like coffee and 9 like both. How many like at least one of the two? (a) 30 (b) 39 (c) 38 (d) 21
3. 3.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
4. 4.A bag has 7 yellow balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 11 (c) 9 (d) 8
5. 5.What is the midpoint of the line joining (5, 7) and (17, 17)? (a) (6, 5) (b) (11, 12) (c) (12, 11) (d) (22, 24)
6. 6.In a class of 29 children, 22 like dance, 6 like music and 4 like neither. How many like both? (a) 3 (b) 25 (c) 2 (d) 4
7. 7.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 10 (c) 25 (d) 20
8. 8.A bag has 11 green balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 13 (c) 18 (d) 12
9. 9.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 24 (c) 75 (d) 72
10. 10.Which term of the AP 15, 20, 25, 30, … is 140? (a) 25th (b) 28th (c) 27th (d) 26th
11. 11.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 20 (c) 25 (d) 15
12. 12.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 20 (d) 120
13. 13.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 55° (c) 70° (d) 125°
14. 14.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
15. 15.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1
16. 16.What is the missing term in the AP 6, 15, 24, ?, 42? (a) 33 (b) 32 (c) 42 (d) 34
17. 17.A drawer has lots of blue, red, white, green 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) 6 (b) 10 (c) 5 (d) 2
18. 18.Which term of the AP 1, 5, 9, 13, … is 41? (a) 12th (b) 11th (c) 10th (d) 13th
19. 19.What is the median of 2, 39, 17, 8 and 12? (a) 13 (b) 17 (c) 8 (d) 12
20. 20.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
21. 21.What is the mode of 17, 7, 20, 7, 20, 20 and 2? (a) 2 (b) 20 (c) 17 (d) 7
22. 22.There are 8 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) 10 (b) 24 (c) 32 (d) 16
23. 23.A cuboid is 8 cm long, 7 cm wide and 10 cm high. What is its volume? (a) 56 cu cm (b) 25 cu cm (c) 412 cu cm (d) 560 cu cm
24. 24.What is the mean of 8, 20, 14, 2 and 21? (a) 14 (b) 15 (c) 13 (d) 12
25. 25.A cuboid is 7 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 136 sq cm (b) 84 sq cm (c) 68 sq cm (d) 272 sq cm
26. 26.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 452 (c) 571 (d) 570
27. 27.What is the 14th term of the AP 17, 20, 23, 26, …? (a) 59 (b) 42 (c) 39 (d) 56
28. 28.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
29. 29.What is the mean of 6, 8, 3, 10, 5 and 16? (a) 10 (b) 7 (c) 8 (d) 9
30. 30.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 13 (b) 24 (c) 12 (d) 25
31. 31.What is the distance between the points (4, 0) and (8, 3)? (a) 6 (b) 25 (c) 5 (d) 7
32. 32.There are 7 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 56 (b) 35 (c) 11 (d) 28
33. 33.A bag has 5 green balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 2 (c) 11 (d) 7
34. 34.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 195 (c) 208 (d) 205
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 month? (a) 48 (b) 37 (c) 36 (d) 49
36. 36.A bag has 12 green balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 18 (b) 13 (c) 7 (d) 2
37. 37.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
38. 38.What is the median of 21, 14, 2, 11, 29, 10 and 36? (a) 14 (b) 15 (c) 21 (d) 11
39. 39.What is the missing term in the AP 3, ?, 7, 9, 11? (a) 5 (b) 7 (c) 6 (d) 4
40. 40.What is the 17th term of the AP 1, 5, 9, 13, …? (a) 68 (b) 69 (c) 65 (d) 64

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