Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 608 · 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 circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
2. 2.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 3/4 (c) 1/2 (d) 1/4
3. 3.Two angles of a triangle are 40° and 65°. What is the third angle? (a) 140° (b) 105° (c) 115° (d) 75°
4. 4.In a class of 43 children, 17 like cricket, 30 like football and 10 like both. How many like neither? (a) 7 (b) 10 (c) 6 (d) 16
5. 5.If a + b = 21 and ab = 108, what is (a − b)²? (a) 441 (b) 9 (c) 3 (d) 225
6. 6.How many factors does 20 have? (a) 6 (b) 5 (c) 4 (d) 7
7. 7.A bag has 11 black balls and 12 yellow 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) 12 (c) 23 (d) 13
8. 8.If a + b = 6 and ab = 8, what is (a − b)²? (a) 2 (b) 36 (c) 4 (d) 20
9. 9.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
10. 10.What is the mode of 9, 4, 4, 9, 7, 4 and 8? (a) 7 (b) 8 (c) 9 (d) 4
11. 11.What is the smallest prime factor of 85? (a) 5 (b) 2 (c) 17 (d) 1
12. 12.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 17 (c) 81 (d) 90
13. 13.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 15 (b) 21 (c) 14 (d) 22
14. 14.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm
15. 15.What is the sum of all the whole numbers from 1 to 51? (a) 1326 (b) 1327 (c) 1275 (d) 2652
16. 16.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
17. 17.Using (a + b)² = a² + 2ab + b², what is 22²? (a) 494 (b) 484 (c) 324 (d) 404
18. 18.How many factors does 29 have? (a) 4 (b) 3 (c) 2 (d) 1
19. 19.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
20. 20.What is the mean of 9, 2, 2 and 7? (a) 4 (b) 5 (c) 7 (d) 6
21. 21.What is the prime factorisation of 45? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5 (d) 3 × 5²
22. 22.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 24 (c) 12 (d) 16
23. 23.Two angles of a triangle are 30° and 45°. What is the third angle? (a) 75° (b) 135° (c) 150° (d) 105°
24. 24.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2 × 3 × 5 (c) 2³ × 3 × 5 (d) 2² × 3 × 5
25. 25.What is the mean of 4, 2, 17, 17, 7 and 13? (a) 11 (b) 9 (c) 10 (d) 12
26. 26.A bag has 8 green, 4 yellow and 2 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 4/7 (b) 9/14 (c) 3/7 (d) 1/3
27. 27.What is the mode of 16, 10, 16, 15, 16, 10 and 17? (a) 10 (b) 16 (c) 15 (d) 17
28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 2 (b) 1 (c) 3 (d) 4
29. 29.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
30. 30.In a class of 31 children, 11 like tea, 17 like coffee and 3 like both. How many like neither? (a) 3 (b) 7 (c) 6 (d) 9
31. 31.What is the 29th term of the AP 2, 9, 16, 23, …? (a) 203 (b) 198 (c) 205 (d) 196
32. 32.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
33. 33.A drawer has lots of white, yellow and red 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) 2 (d) 4
34. 34.What is the missing term in the AP 4, ?, 18, 25, 32? (a) 12 (b) 18 (c) 10 (d) 11
35. 35.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) 22 (b) 21 (c) 29 (d) 28
36. 36.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 24 sq cm (c) 8 sq cm (d) 4 sq cm
37. 37.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 18 (b) 127 (c) 252 (d) 126
38. 38.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 140° (c) 280° (d) 100°
39. 39.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
40. 40.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 27 (c) 24 (d) 72

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