Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 793 · 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) 4 times (b) 8 times (c) 64 times (d) 16 times
2. 2.What is the mode of 12, 13, 5, 12, 20, 13 and 13? (a) 20 (b) 5 (c) 13 (d) 12
3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
4. 4.What is the 35th term of the AP 7, 16, 25, 34, …? (a) 306 (b) 322 (c) 313 (d) 315
5. 5.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
6. 6.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 48 (c) 16 (d) 144
7. 7.Two angles of a triangle are 25° and 80°. What is the third angle? (a) 75° (b) 105° (c) 100° (d) 155°
8. 8.What is the prime factorisation of 504? (a) 2⁴ × 3² × 7 (b) 2² × 3² × 7 (c) 2 × 3² × 7³ (d) 2³ × 3² × 7
9. 9.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/2 (c) 3/4 (d) 1/4
10. 10.The mean of 4 numbers is 19. When the number 24 is added to them, what is the new mean? (a) 19 (b) 20 (c) 21 (d) 22
11. 11.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
12. 12.In a class of 47 children, 27 like mangoes, 26 like bananas and 9 like both. How many like neither? (a) 12 (b) 4 (c) 3 (d) 9
13. 13.A bag has 3 white balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 4 (b) 10 (c) 2 (d) 5
14. 14.A drawer has lots of black, red, blue and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 5 (c) 8 (d) 4
15. 15.In a class of 48 children, 21 like dance, 30 like music and 10 like both. How many like neither? (a) 17 (b) 8 (c) 10 (d) 7
16. 16.What is the 40th term of the AP 8, 14, 20, 26, …? (a) 240 (b) 248 (c) 234 (d) 242
17. 17.A drawer has lots of blue, white 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) 6 (b) 2 (c) 4 (d) 3
18. 18.What is the distance between the points (8, 4) and (23, 12)? (a) 23 (b) 18 (c) 17 (d) 289
19. 19.In a class of 35 children, 16 like maths, 16 like science and 7 like both. How many like neither? (a) 7 (b) 17 (c) 3 (d) 10
20. 20.A bag has 3 black balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 10 (b) 5 (c) 2 (d) 4
21. 21.A bag has 3 green balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 14 (b) 2 (c) 4 (d) 12
22. 22.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 140° (b) 160° (c) 120° (d) 60°
23. 23.What is the smallest prime factor of 341? (a) 1 (b) 11 (c) 31 (d) 2
24. 24.How many factors does 101 have? (a) 1 (b) 2 (c) 4 (d) 3
25. 25.Using (a + b)² = a² + 2ab + b², what is 74²? (a) 4356 (b) 5476 (c) 5486 (d) 4916
26. 26.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 10° (c) 100° (d) 50°
27. 27.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 16 (c) 10 (d) 24
28. 28.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 55 (c) 22 (d) 110
29. 29.If a + b = 19 and ab = 90, what is a² + b²? (a) 541 (b) 361 (c) 181 (d) 271
30. 30.A drawer has lots of white, black, yellow, red and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 5 (c) 6 (d) 10
31. 31.A drawer has lots of blue, red, black, yellow and white 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) 6 (c) 5 (d) 2
32. 32.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) 22 (b) 14 (c) 21 (d) 15
33. 33.What is the prime factorisation of 180? (a) 2 × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5² (d) 2² × 3² × 5
34. 34.What is the mean of 4, 10, 14, 20, 8 and 16? (a) 12 (b) 13 (c) 11 (d) 14
35. 35.A bag has 10 black balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 11 (b) 13 (c) 12 (d) 2
36. 36.Which is the correct factorisation of x² + 14x + 45? (a) (x + 1)(x + 45) (b) (x + 1)(x + 13) (c) (x − 5)(x − 9) (d) (x + 5)(x + 9)
37. 37.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 532 (c) 531 (d) 522
38. 38.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 300 (c) 278 (d) 309
39. 39.In a class of 41 children, 18 like mangoes, 23 like bananas and 7 like neither. How many like both? (a) 6 (b) 7 (c) 8 (d) 34
40. 40.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 115 (c) 116 (d) 106

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