Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 918 · 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 sum of all the whole numbers from 1 to 53? (a) 1378 (b) 1432 (c) 2862 (d) 1431
2. 2.How many factors does 88 have? (a) 7 (b) 6 (c) 8 (d) 9
3. 3.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/8 (c) 3/4 (d) 3/8
4. 4.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 339 (c) 304 (d) 349
5. 5.Two angles of a triangle are 20° and 95°. What is the exterior angle at the third corner? (a) 160° (b) 85° (c) 115° (d) 65°
6. 6.In a class of 43 children, 21 like maths, 22 like science and 7 like both. How many like at least one of the two? (a) 29 (b) 37 (c) 36 (d) 43
7. 7.In a class of 27 children, 21 like cricket, 10 like football and 6 like both. How many like only cricket? (a) 17 (b) 21 (c) 4 (d) 15
8. 8.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
9. 9.What is the mode of 20, 20, 4, 18, 13, 20 and 18? (a) 13 (b) 18 (c) 4 (d) 20
10. 10.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 80° (b) 100° (c) 200° (d) 20°
11. 11.In a class of 38 children, 21 like tea, 22 like coffee and 11 like both. How many like only tea? (a) 11 (b) 10 (c) 16 (d) 21
12. 12.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
13. 13.How many factors does 120 have? (a) 14 (b) 17 (c) 15 (d) 16
14. 14.In a class of 28 children, 7 like maths, 22 like science and 3 like both. How many like only maths? (a) 4 (b) 7 (c) 6 (d) 19
15. 15.A drawer has lots of green, 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) 6 (b) 3 (c) 2 (d) 4
16. 16.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 45 (c) 48 (d) 135
17. 17.How many factors does 47 have? (a) 2 (b) 1 (c) 3 (d) 4
18. 18.What is the mode of 10, 6, 10, 13, 6, 19 and 6? (a) 19 (b) 13 (c) 6 (d) 10
19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/18 (c) 1/12 (d) 1/36
20. 20.What is the smallest prime factor of 33? (a) 2 (b) 3 (c) 1 (d) 11
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 5/36 (b) 1/9 (c) 4/11 (d) 1/11
22. 22.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 50° (c) 35° (d) 130°
23. 23.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 80° (d) 100°
24. 24.A bag has 9 yellow balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 10 (c) 15 (d) 2
25. 25.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 72 (c) 207 (d) 23
26. 26.If a + b = 18 and ab = 80, what is (a − b)²? (a) 2 (b) 4 (c) 164 (d) 324
27. 27.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 135° (b) 115° (c) 65° (d) 160°
28. 28.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
29. 29.What is the smallest prime factor of 247? (a) 19 (b) 13 (c) 1 (d) 2
30. 30.What is the 10th term of the AP 4, 9, 14, 19, …? (a) 50 (b) 54 (c) 45 (d) 49
31. 31.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 100° (d) 80°
32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 7 (b) 17 (c) 18 (d) 19
33. 33.What are the roots of x² − 15x + 54 = 0? (a) 1 and 54 (b) 2 and 27 (c) 1 and 14 (d) 6 and 9
34. 34.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/4 (b) 5/6 (c) 1/3 (d) 2/3
35. 35.The mean of 5 numbers is 29. When the number 17 is added to them, what is the new mean? (a) 27 (b) 29 (c) 23 (d) 28
36. 36.What is the smallest prime factor of 119? (a) 7 (b) 17 (c) 1 (d) 2
37. 37.A bag has 11 yellow balls and 3 black 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) 4 (c) 12 (d) 2
38. 38.What is the prime factorisation of 56? (a) 2³ × 7 (b) 2² × 7 (c) 2 × 7³ (d) 2⁴ × 7
39. 39.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 110 (c) 22 (d) 55
40. 40.A bag has 8 green balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 10 (b) 2 (c) 12 (d) 9

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