Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 888 · 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 25 children, 14 like cricket, 13 like football and 8 like both. How many like at least one of the two? (a) 19 (b) 11 (c) 27 (d) 25
2. 2.Using (a − b)² = a² − 2ab + b², what is 87²? (a) 8091 (b) 8649 (c) 7579 (d) 7569
3. 3.What is the smallest prime factor of 21? (a) 1 (b) 3 (c) 7 (d) 2
4. 4.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 20 (b) 22 (c) 28 (d) 21
5. 5.What is the 29th term of the AP 1, 8, 15, 22, …? (a) 204 (b) 197 (c) 196 (d) 203
6. 6.What is the smallest prime factor of 319? (a) 11 (b) 1 (c) 2 (d) 29
7. 7.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
8. 8.In a class of 34 children, 28 like cricket, 12 like football and 9 like both. How many like neither? (a) 4 (b) 9 (c) 3 (d) 12
9. 9.How many factors does 105 have? (a) 7 (b) 6 (c) 9 (d) 8
10. 10.A bag has 4 black balls and 5 red 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) 9 (c) 6 (d) 2
11. 11.What is the midpoint of the line joining (1, 7) and (9, 13)? (a) (4, 3) (b) (10, 5) (c) (10, 20) (d) (5, 10)
12. 12.What is the 35th term of the AP 17, 25, 33, 41, …? (a) 297 (b) 272 (c) 289 (d) 280
13. 13.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
14. 14.A bag has 3 blue, 8 white and 8 red balls. One ball is taken out without looking. What is the probability that it is blue? (a) 3/16 (b) 3/19 (c) 16/19 (d) 1/3
15. 15.How many factors does 32 have? (a) 5 (b) 6 (c) 7 (d) 4
16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 5 (b) 3 (c) 4 (d) 6
17. 17.Two angles of a triangle are 65° and 40°. What is the exterior angle at the third corner? (a) 75° (b) 140° (c) 105° (d) 115°
18. 18.In a class of 39 children, 16 like tea, 26 like coffee and 7 like both. How many like only tea? (a) 16 (b) 19 (c) 13 (d) 9
19. 19.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 182 (c) 105 (d) 91
20. 20.A cuboid is 6 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 16 cu cm (b) 150 cu cm (c) 30 cu cm (d) 170 cu cm
21. 21.How many factors does 58 have? (a) 2 (b) 4 (c) 5 (d) 3
22. 22.In a class of 28 children, 17 like dance, 10 like music and 4 like both. How many like only dance? (a) 13 (b) 17 (c) 6 (d) 18
23. 23.What is the distance between the points (4, 4) and (19, 12)? (a) 23 (b) 289 (c) 18 (d) 17
24. 24.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 1232 sq cm
25. 25.Two angles of a triangle are 30° and 140°. What is the third angle? (a) 10° (b) 40° (c) 170° (d) 150°
26. 26.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 125° (b) 110° (c) 56° (d) 55°
27. 27.In a class of 23 children, 11 like cricket, 10 like football and 3 like both. How many like at least one of the two? (a) 15 (b) 18 (c) 21 (d) 23
28. 28.What is the distance between the points (8, 2) and (20, 11)? (a) 21 (b) 15 (c) 16 (d) 225
29. 29.What is the sum of the first 11 terms of the AP 9, 10, 11, …? (a) 154 (b) 155 (c) 19 (d) 308
30. 30.What is the midpoint of the line joining (5, 8) and (9, 12)? (a) (2, 2) (b) (14, 20) (c) (10, 7) (d) (7, 10)
31. 31.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
32. 32.A cube has edges of 6 cm. What is its total surface area? (a) 36 sq cm (b) 216 sq cm (c) 217 sq cm (d) 144 sq cm
33. 33.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
34. 34.How many factors does 50 have? (a) 4 (b) 5 (c) 7 (d) 6
35. 35.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 58 (c) 67 (d) 68
36. 36.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 15 (d) 30
37. 37.What is the smallest prime factor of 143? (a) 1 (b) 13 (c) 11 (d) 2
38. 38.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 28 (c) 56 (d) 32
39. 39.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) 39 (b) 12 (c) 36 (d) 108
40. 40.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 196 sq cm (c) 294 sq cm (d) 49 sq cm

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