Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 305 · 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 median of 33, 10, 38, 25 and 17? (a) 17 (b) 33 (c) 38 (d) 25
2. 2.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 14 (c) 49 (d) 21
3. 3.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 130° (b) 110° (c) 60° (d) 120°
4. 4.What is the mean of 14, 11, 9 and 14? (a) 13 (b) 11 (c) 12 (d) 16
5. 5.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 39 (c) 36 (d) 12
6. 6.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
7. 7.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 9 cu cm (b) 52 cu cm (c) 24 cu cm (d) 6 cu cm
8. 8.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 135° (b) 136° (c) 315° (d) 45°
9. 9.A bag has 3 white balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 4 (b) 11 (c) 2 (d) 5
10. 10.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/3 (c) 1/4 (d) 1/2
11. 11.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
12. 12.What is the 16th term of the AP 3, 7, 11, 15, …? (a) 64 (b) 63 (c) 67 (d) 60
13. 13.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) 21 (b) 28 (c) 29 (d) 22
14. 14.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 580 (c) 570 (d) 579
15. 15.A bag has 4 black balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 14 (d) 5
16. 16.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 595 (c) 468 (d) 594
17. 17.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 265° (c) 85° (d) 86°
18. 18.In a class of 35 children, 10 like maths, 21 like science and 2 like both. How many like only maths? (a) 19 (b) 14 (c) 8 (d) 10
19. 19.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
20. 20.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 145° (c) 110° (d) 35°
21. 21.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 160° (c) 11° (d) 10°
22. 22.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 576 cu cm (c) 36 cu cm (d) 1728 cu cm
23. 23.In a class of 18 children, 12 like cricket, 7 like football and 4 like both. How many like only cricket? (a) 11 (b) 8 (c) 3 (d) 12
24. 24.How many prime numbers are there between 30 and 50? (a) 7 (b) 5 (c) 6 (d) 4
25. 25.What is the mean of 6, 5, 20, 9 and 5? (a) 8 (b) 10 (c) 11 (d) 9
26. 26.How many factors does 28 have? (a) 5 (b) 7 (c) 4 (d) 6
27. 27.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 8 (c) 14 (d) 7
28. 28.In a class of 43 children, 17 like mangoes, 28 like bananas and 7 like neither. How many like both? (a) 2 (b) 7 (c) 36 (d) 9
29. 29.What is the 16th term of the AP 4, 10, 16, 22, …? (a) 100 (b) 96 (c) 90 (d) 94
30. 30.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 160° (c) 80° (d) 81°
31. 31.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 55 (c) 110 (d) 66
32. 32.What is the 32nd term of the AP 2, 4, 6, 8, …? (a) 64 (b) 66 (c) 62 (d) 65
33. 33.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 12 (c) 48 (d) 24
34. 34.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 66 (c) 132 (d) 144
35. 35.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 65° (b) 160° (c) 115° (d) 135°
36. 36.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
37. 37.What is the sum of the first 12 terms of the AP 4, 9, 14, …? (a) 408 (b) 59 (c) 378 (d) 756
38. 38.What is the sum of the first 12 terms of the AP 4, 8, 12, …? (a) 624 (b) 312 (c) 336 (d) 48
39. 39.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
40. 40.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 1/4 (c) 3/4 (d) 1/2

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