Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 729 · 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.In a class of 42 children, 28 like cricket, 23 like football and 10 like both. How many like neither? (a) 2 (b) 10 (c) 11 (d) 1
2. 2.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
3. 3.What is the mean of 10, 16, 13, 4, 15 and 20? (a) 13 (b) 15 (c) 12 (d) 14
4. 4.What is the mode of 8, 6, 9, 8, 6, 6 and 14? (a) 14 (b) 8 (c) 9 (d) 6
5. 5.In a class of 41 children, 16 like dance, 23 like music and 7 like both. How many like only dance? (a) 16 (b) 18 (c) 9 (d) 7
6. 6.Two angles of a triangle are 30° and 110°. What is the third angle? (a) 70° (b) 140° (c) 150° (d) 40°
7. 7.What is the sum of all the whole numbers from 1 to 80? (a) 3200 (b) 3160 (c) 6480 (d) 3240
8. 8.Using (a − b)² = a² − 2ab + b², what is 15²? (a) 235 (b) 375 (c) 225 (d) 625
9. 9.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 78 (c) 91 (d) 156
10. 10.What is the median of 11, 3, 13, 35 and 17? (a) 17 (b) 11 (c) 14 (d) 13
11. 11.What is the mean of 9, 14, 2, 2 and 13? (a) 10 (b) 7 (c) 9 (d) 8
12. 12.In a class of 47 children, 25 like dance, 19 like music and 7 like both. How many like only dance? (a) 25 (b) 18 (c) 12 (d) 28
13. 13.What is the median of 23, 30, 17, 11 and 25? (a) 24 (b) 25 (c) 17 (d) 23
14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 19 (d) 8
15. 15.Two angles of a triangle are 35° and 125°. What is the third angle? (a) 20° (b) 55° (c) 160° (d) 145°
16. 16.Which term of the AP 2, 4, 6, 8, … is 64? (a) 34th (b) 33rd (c) 32nd (d) 31st
17. 17.8 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 15 (b) 64 (c) 56 (d) 112
18. 18.What is the 36th term of the AP 5, 11, 17, 23, …? (a) 215 (b) 221 (c) 216 (d) 210
19. 19.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) 24 (b) 25 (c) 36 (d) 37
20. 20.A drawer has lots of red, 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) 3 (b) 6 (c) 4 (d) 2
21. 21.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 125° (c) 80° (d) 155°
22. 22.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 525 (c) 428 (d) 535
23. 23.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 85° (b) 155° (c) 110° (d) 95°
24. 24.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 174 (c) 166 (d) 165
25. 25.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 150° (c) 160° (d) 50°
26. 26.What is the distance between the points (1, 6) and (5, 9)? (a) 5 (b) 25 (c) 6 (d) 7
27. 27.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/4
28. 28.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 18 (c) 15 (d) 30
29. 29.What is the prime factorisation of 168? (a) 2⁴ × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7³ (d) 2² × 3 × 7
30. 30.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 1458 (c) 1485 (d) 2970
31. 31.A bag has 12 red balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 16 (b) 2 (c) 13 (d) 14
32. 32.In a class of 34 children, 11 like dance, 23 like music and 7 like neither. How many like both? (a) 27 (b) 6 (c) 8 (d) 7
33. 33.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 25° (c) 155° (d) 130°
34. 34.A bag has 2 green, 7 blue and 7 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/7 (b) 1/3 (c) 7/8 (d) 1/8
35. 35.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
36. 36.In a class of 33 children, 28 like maths, 13 like science and 9 like both. How many like neither? (a) 1 (b) 9 (c) 10 (d) 2
37. 37.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 2 (b) 4 (c) 3 (d) 5
39. 39.A bag has 7 yellow balls and 9 black 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) 16 (c) 8 (d) 10
40. 40.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 30 (c) 25 (d) 9

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