Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 545 · 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.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 145° (b) 75° (c) 110° (d) 105°
2. 2.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x + 8)(x + 9) (c) (x − 8)(x − 9) (d) (x + 1)(x + 72)
3. 3.How many prime numbers are there between 40 and 50? (a) 3 (b) 2 (c) 5 (d) 4
4. 4.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 29 (c) 21 (d) 22
5. 5.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 42 (c) 10 (d) 28
6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/18 (c) 1/36 (d) 1/11
7. 7.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 5° (c) 85° (d) 95°
8. 8.In a class of 21 children, 8 like maths, 12 like science and 2 like both. How many like neither? (a) 2 (b) 5 (c) 3 (d) 1
9. 9.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) 25 (c) 24 (d) 37
10. 10.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 65° (b) 245° (c) 66° (d) 115°
11. 11.What is the distance between the points (7, 6) and (11, 3)? (a) 5 (b) 25 (c) 6 (d) 7
12. 12.In a class of 34 children, 15 like tea, 25 like coffee and 1 like neither. How many like both? (a) 33 (b) 7 (c) 6 (d) 1
13. 13.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 20° (c) 160° (d) 21°
14. 14.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 567 (c) 558 (d) 450
15. 15.What is the distance between the points (9, 3) and (21, 8)? (a) 17 (b) 14 (c) 13 (d) 169
16. 16.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 294 (c) 304 (d) 303
17. 17.In a class of 37 children, 13 like cricket, 21 like football and 7 like both. How many like at least one of the two? (a) 20 (b) 37 (c) 27 (d) 34
18. 18.What is the prime factorisation of 504? (a) 2 × 3² × 7³ (b) 2² × 3² × 7 (c) 2⁴ × 3² × 7 (d) 2³ × 3² × 7
19. 19.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 300 (c) 291 (d) 272
20. 20.A bag has 3 blue balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 12 (b) 2 (c) 5 (d) 4
21. 21.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
22. 22.What is the missing term in the AP 15, 18, ?, 24, 27? (a) 24 (b) 21 (c) 22 (d) 20
23. 23.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 155° (b) 160° (c) 135° (d) 45°
24. 24.A bag has 5 white, 3 blue and 5 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 8/13 (b) 1/3 (c) 5/13 (d) 9/13
25. 25.What is the median of 12, 25, 17, 38, 14, 23 and 3? (a) 38 (b) 14 (c) 17 (d) 23
26. 26.A bag has 12 red balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 13 (b) 15 (c) 2 (d) 14
27. 27.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 76° (c) 75° (d) 105°
28. 28.A cube has edges of 2 cm. What is its volume? (a) 8 cu cm (b) 6 cu cm (c) 16 cu cm (d) 24 cu cm
29. 29.How many factors does 106 have? (a) 4 (b) 3 (c) 5 (d) 2
30. 30.In a class of 48 children, 20 like cricket, 30 like football and 10 like both. How many like only cricket? (a) 20 (b) 10 (c) 11 (d) 18
31. 31.If a + b = 20 and ab = 99, what is a² + b²? (a) 301 (b) 202 (c) 400 (d) 598
32. 32.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 55 (c) 121 (d) 110
33. 33.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2⁴ × 5 (c) 2³ × 5 (d) 2⁵ × 5
34. 34.What is the smallest prime factor of 253? (a) 2 (b) 11 (c) 23 (d) 1
35. 35.A bag has 7 yellow, 3 red and 2 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 5/12 (b) 7/12 (c) 2/3 (d) 1/3
36. 36.A drawer has lots of 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) 4 (c) 2 (d) 3
37. 37.A bag has 10 green balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 11 (b) 21 (c) 2 (d) 12
38. 38.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 7/8 (b) 1/8 (c) 1/7 (d) 1/4
39. 39.How many factors does 113 have? (a) 2 (b) 3 (c) 4 (d) 1
40. 40.What is the mean of 3, 20, 16 and 5? (a) 11 (b) 12 (c) 10 (d) 13

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