Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 507 · 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 book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 466 (c) 592 (d) 582
2. 2.What is the 40th term of the AP 7, 11, 15, 19, …? (a) 160 (b) 163 (c) 167 (d) 156
3. 3.In a class of 34 children, 11 like cricket, 22 like football and 4 like both. How many like only cricket? (a) 7 (b) 11 (c) 12 (d) 18
4. 4.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 640 (b) 498 (c) 630 (d) 639
5. 5.What is the median of 16, 28, 7, 27 and 39? (a) 7 (b) 27 (c) 16 (d) 28
6. 6.In a class of 36 children, 23 like maths, 13 like science and 6 like both. How many like neither? (a) 12 (b) 0 (c) 7 (d) 6
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/12 (c) 1/18 (d) 2/11
8. 8.How many factors does 27 have? (a) 2 (b) 3 (c) 5 (d) 4
9. 9.A bag has 11 yellow balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 13 (b) 22 (c) 2 (d) 12
10. 10.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
11. 11.What is the mean of 9, 5, 10, 16 and 10? (a) 12 (b) 9 (c) 11 (d) 10
12. 12.What is the sum of the first 6 terms of the AP 4, 9, 14, …? (a) 198 (b) 114 (c) 99 (d) 29
13. 13.If a + b = 18 and ab = 72, what is a² + b²? (a) 468 (b) 252 (c) 324 (d) 180
14. 14.In a class of 43 children, 18 like mangoes, 19 like bananas and 4 like both. How many like neither? (a) 6 (b) 4 (c) 14 (d) 10
15. 15.What is the median of 25, 32, 15, 21 and 40? (a) 32 (b) 25 (c) 21 (d) 15
16. 16.What is the prime factorisation of 168? (a) 2⁴ × 3 × 7 (b) 2 × 3 × 7³ (c) 2³ × 3 × 7 (d) 2² × 3 × 7
17. 17.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 170° (b) 10° (c) 130° (d) 60°
18. 18.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 90° (b) 135° (c) 225° (d) 45°
19. 19.A drawer has lots of blue, black, white, red 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) 5 (b) 10 (c) 6 (d) 2
20. 20.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 60 (c) 11 (d) 35
21. 21.If a + b = 20 and ab = 96, what is a² + b²? (a) 400 (b) 304 (c) 208 (d) 592
22. 22.In a class of 23 children, 17 like tea, 16 like coffee and 11 like both. How many like at least one of the two? (a) 33 (b) 11 (c) 23 (d) 22
23. 23.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 70° (b) 150° (c) 140° (d) 110°
24. 24.A drawer has lots of green and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 2 (c) 5 (d) 3
25. 25.A bag has 9 red balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 11 (b) 12 (c) 10 (d) 2
26. 26.A bag has 7 green, 9 yellow and 3 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 16/19 (b) 3/19 (c) 3/16 (d) 1/3
27. 27.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) 75 (b) 216 (c) 24 (d) 72
28. 28.A cuboid is 11 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 66 sq cm (b) 244 sq cm (c) 61 sq cm (d) 122 sq cm
29. 29.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
30. 30.Two angles of a triangle are 40° and 100°. What is the third angle? (a) 80° (b) 40° (c) 140° (d) 220°
31. 31.What is the sum of all the whole numbers from 1 to 68? (a) 4692 (b) 2312 (c) 2278 (d) 2346
32. 32.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 88 cm (d) 154 cm
33. 33.The mean of 7 numbers is 31. When the number 23 is added to them, what is the new mean? (a) 29 (b) 31 (c) 27 (d) 30
34. 34.A bag has 4 white balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 6 (c) 2 (d) 9
35. 35.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 55 (d) 110
36. 36.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x − 6)(x − 7) (c) (x + 6)(x + 7) (d) (x + 1)(x + 12)
37. 37.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
38. 38.7 T-shirts and 2 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) 14 (c) 21 (d) 9
39. 39.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 110 (c) 22 (d) 121
40. 40.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 65° (b) 100° (c) 145° (d) 115°

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