Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 137 · 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 an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 70° (d) 40°
2. 2.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 562 (b) 561 (c) 446 (d) 552
3. 3.Two angles of a triangle are 25° and 115°. What is the third angle? (a) 65° (b) 140° (c) 40° (d) 155°
4. 4.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 20 (d) 15
5. 5.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1176 (c) 1128 (d) 1152
6. 6.How many factors does 36 have? (a) 10 (b) 8 (c) 9 (d) 7
7. 7.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
8. 8.A bag has 11 green balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 14 (b) 2 (c) 12 (d) 13
9. 9.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 145° (b) 55° (c) 325° (d) 35°
10. 10.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/12 (c) 1/18 (d) 1/36
12. 12.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 60 (b) 11 (c) 36 (d) 30
13. 13.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
14. 14.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 440 cm (c) 110 cm (d) 3850 cm
15. 15.What is the mode of 13, 5, 9, 6, 13, 13 and 6? (a) 5 (b) 9 (c) 13 (d) 6
16. 16.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 190 (b) 110 (c) 31 (d) 95
17. 17.A cuboid is 11 cm long, 5 cm wide and 6 cm high. What is its total surface area? (a) 302 sq cm (b) 151 sq cm (c) 330 sq cm (d) 604 sq cm
18. 18.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
19. 19.What is the distance between the points (2, 6) and (17, 14)? (a) 18 (b) 23 (c) 289 (d) 17
20. 20.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 90 (d) 81
21. 21.In a class of 36 children, 12 like dance, 26 like music and 7 like both. How many like at least one of the two? (a) 24 (b) 38 (c) 36 (d) 31
22. 22.Using (a − b)² = a² − 2ab + b², what is 66²? (a) 4884 (b) 5476 (c) 4366 (d) 4356
23. 23.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 496 (c) 497 (d) 992
24. 24.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
25. 25.What is the mean of 11, 3, 12 and 6? (a) 9 (b) 8 (c) 10 (d) 7
26. 26.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 208 (c) 207 (d) 210
27. 27.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
28. 28.A cuboid is 4 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 64 cu cm (b) 32 cu cm (c) 8 cu cm (d) 10 cu cm
29. 29.A bag has 10 white balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 15 (b) 2 (c) 11 (d) 12
30. 30.What is the prime factorisation of 560? (a) 2³ × 5 × 7 (b) 2 × 5 × 7⁴ (c) 2⁵ × 5 × 7 (d) 2⁴ × 5 × 7
31. 31.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
32. 32.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 100 (c) 55 (d) 90
33. 33.What is the sum of the first 8 terms of the AP 4, 6, 8, …? (a) 18 (b) 176 (c) 96 (d) 88
34. 34.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 49 (c) 21 (d) 28
35. 35.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) 35 (c) 60 (d) 11
36. 36.What is the smallest prime factor of 91? (a) 2 (b) 13 (c) 1 (d) 7
37. 37.In a class of 18 children, 8 like dance, 10 like music and 4 like neither. How many like both? (a) 4 (b) 5 (c) 14 (d) 3
38. 38.In a class of 35 children, 19 like dance, 15 like music and 3 like both. How many like only dance? (a) 16 (b) 20 (c) 12 (d) 19
39. 39.Two angles of a triangle are 45° and 65°. What is the exterior angle at the third corner? (a) 70° (b) 115° (c) 110° (d) 135°
40. 40.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 45 (c) 54 (d) 36

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