Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 430 · 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.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
2. 2.A bag has 4 red, 3 white and 9 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 3/16 (b) 7/8 (c) 13/16 (d) 1/3
3. 3.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
4. 4.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 1000 sq cm (c) 600 sq cm (d) 100 sq cm
5. 5.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2 × 3 × 5 (c) 2³ × 3 × 5 (d) 2² × 3 × 5
6. 6.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
7. 7.What is the mode of 7, 2, 16, 7, 11, 7 and 16? (a) 7 (b) 2 (c) 11 (d) 16
8. 8.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 156 (b) 23 (c) 78 (d) 90
9. 9.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 89 (c) 80 (d) 98
10. 10.If a + b = 4 and ab = 3, what is a² + b²? (a) 16 (b) 10 (c) 13 (d) 22
11. 11.In a class of 44 children, 20 like cricket, 22 like football and 4 like both. How many like only cricket? (a) 16 (b) 18 (c) 20 (d) 22
12. 12.A drawer has lots of yellow, black, white, green 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) 10 (b) 2 (c) 6 (d) 5
13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 6 (b) 16 (c) 18 (d) 17
14. 14.In a class of 17 children, 8 like cricket, 8 like football and 2 like both. How many like at least one of the two? (a) 17 (b) 14 (c) 16 (d) 12
15. 15.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 110° (d) 70°
16. 16.If a + b = 19 and ab = 88, what is a² + b²? (a) 537 (b) 185 (c) 361 (d) 273
17. 17.What is the distance between the points (3, 3) and (8, 15)? (a) 17 (b) 14 (c) 13 (d) 169
18. 18.In a class of 38 children, 27 like mangoes, 13 like bananas and 7 like both. How many like only mangoes? (a) 6 (b) 27 (c) 25 (d) 20
19. 19.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 2 times (d) 5 times
20. 20.In a class of 20 children, 10 like maths, 14 like science and 2 like neither. How many like both? (a) 4 (b) 6 (c) 2 (d) 18
21. 21.What is the smallest prime factor of 319? (a) 29 (b) 2 (c) 11 (d) 1
22. 22.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
23. 23.What is the sum of the first 5 terms of the AP 3, 7, 11, …? (a) 19 (b) 110 (c) 55 (d) 65
24. 24.What is the missing term in the AP 17, 26, ?, 44, 53? (a) 36 (b) 34 (c) 35 (d) 44
25. 25.The mean of 8 numbers is 23. When the number 41 is added to them, what is the new mean? (a) 25 (b) 26 (c) 23 (d) 32
26. 26.A bag has 10 white balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 14 (b) 12 (c) 11 (d) 2
27. 27.What is the mode of 6, 20, 5, 4, 4, 4 and 6? (a) 5 (b) 4 (c) 20 (d) 6
28. 28.What is the mode of 19, 8, 19, 3, 1, 3 and 19? (a) 3 (b) 8 (c) 1 (d) 19
29. 29.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 36 (c) 72 (d) 81
30. 30.How many factors does 119 have? (a) 2 (b) 3 (c) 5 (d) 4
31. 31.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 30° (b) 55° (c) 150° (d) 155°
32. 32.In a class of 41 children, 25 like cricket, 20 like football and 9 like both. How many like only cricket? (a) 11 (b) 25 (c) 21 (d) 16
33. 33.In a class of 34 children, 14 like cricket, 12 like football and 2 like both. How many like at least one of the two? (a) 34 (b) 24 (c) 26 (d) 22
34. 34.If a + b = 12 and ab = 20, what is a² + b²? (a) 124 (b) 104 (c) 184 (d) 144
35. 35.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 30° (c) 15° (d) 150°
36. 36.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 10° (b) 140° (c) 170° (d) 50°
37. 37.What is the smallest prime factor of 115? (a) 1 (b) 23 (c) 2 (d) 5
38. 38.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 78 (c) 156 (d) 169
39. 39.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 19 (c) 171 (d) 60
40. 40.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 2/3 (c) 1/2 (d) 1/3

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