Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 782 · 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.A bag has 4 yellow balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 6 (b) 2 (c) 10 (d) 5
2. 2.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/3 (b) 1/4 (c) 5/6 (d) 2/3
3. 3.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 386 (b) 471 (c) 462 (d) 472
4. 4.How many factors does 15 have? (a) 2 (b) 4 (c) 3 (d) 5
5. 5.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
6. 6.In a class of 35 children, 22 like maths, 15 like science and 3 like neither. How many like both? (a) 2 (b) 3 (c) 5 (d) 32
7. 7.A bag has 8 yellow, 7 blue and 2 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 15/17 (b) 16/17 (c) 1/3 (d) 2/17
8. 8.In a class of 41 children, 19 like cricket, 20 like football and 7 like neither. How many like both? (a) 7 (b) 6 (c) 5 (d) 34
9. 9.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
10. 10.In a class of 39 children, 19 like cricket, 25 like football and 2 like neither. How many like both? (a) 5 (b) 37 (c) 2 (d) 7
11. 11.The mean of 9 numbers is 14. When the number 34 is added to them, what is the new mean? (a) 24 (b) 16 (c) 17 (d) 14
12. 12.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
13. 13.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 121 sq cm (c) 484 sq cm (d) 1331 sq cm
14. 14.In a class of 36 children, 12 like cricket, 23 like football and 8 like both. How many like at least one of the two? (a) 36 (b) 19 (c) 35 (d) 27
15. 15.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 145° (d) 160°
16. 16.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 240 (c) 120 (d) 29
17. 17.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 364 (c) 429 (d) 439
18. 18.How many factors does 40 have? (a) 9 (b) 7 (c) 8 (d) 6
19. 19.In a class of 30 children, 11 like mangoes, 15 like bananas and 6 like both. How many like neither? (a) 6 (b) 16 (c) 10 (d) 4
20. 20.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 256 (d) 272
21. 21.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 100° (b) 130° (c) 150° (d) 80°
22. 22.What is the mean of 9, 10, 17 and 4? (a) 8 (b) 9 (c) 10 (d) 11
23. 23.What is the prime factorisation of 360? (a) 2³ × 3² × 5 (b) 2² × 3² × 5 (c) 2⁴ × 3² × 5 (d) 2 × 3² × 5³
24. 24.A bag has 5 black balls and 7 blue 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) 8 (c) 12 (d) 2
25. 25.What is the mean of 10, 8, 2, 4, 7 and 17? (a) 9 (b) 10 (c) 7 (d) 8
26. 26.In a class of 35 children, 18 like maths, 22 like science and 7 like both. How many like neither? (a) 2 (b) 7 (c) 9 (d) 3
27. 27.What is the 16th term of the AP 13, 22, 31, 40, …? (a) 157 (b) 144 (c) 148 (d) 135
28. 28.In a class of 31 children, 22 like tea, 19 like coffee and 11 like both. How many like at least one of the two? (a) 41 (b) 31 (c) 19 (d) 30
29. 29.A drawer has lots of red, yellow, white, blue 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) 6 (b) 5 (c) 10 (d) 2
30. 30.A drawer has lots of blue and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 5 (c) 3 (d) 4
31. 31.What is the 22nd term of the AP 14, 18, 22, 26, …? (a) 98 (b) 102 (c) 88 (d) 84
32. 32.What is the product of the roots of x² − 9x + 14 = 0? (a) 13 (b) 15 (c) 9 (d) 14
33. 33.The mean of 4 numbers is 17. When the number 2 is added to them, what is the new mean? (a) 14 (b) 13 (c) 17 (d) 15
34. 34.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 37 (c) 24 (d) 25
35. 35.In which quadrant does the point (−8, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
36. 36.A drawer has lots of red, white, black 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) 8 (b) 4 (c) 2 (d) 5
37. 37.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 444 (b) 414 (c) 62 (d) 828
38. 38.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 150° (b) 30° (c) 210° (d) 31°
39. 39.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 5544 sq cm (d) 132 sq cm
40. 40.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) 24 (b) 25 (c) 12 (d) 13

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