Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 987 · 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 an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 115° (c) 65° (d) 25°
2. 2.A drawer has lots of white, green, black, red and blue 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) 5 (c) 2 (d) 6
3. 3.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 452 (b) 561 (c) 571 (d) 570
4. 4.A bag has 4 yellow balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 13 (c) 5 (d) 6
5. 5.In a class of 35 children, 18 like maths, 17 like science and 6 like neither. How many like both? (a) 7 (b) 5 (c) 29 (d) 6
6. 6.The mean of 4 numbers is 22. When the number 32 is added to them, what is the new mean? (a) 24 (b) 22 (c) 25 (d) 27
7. 7.In a class of 32 children, 23 like cricket, 12 like football and 8 like both. How many like only cricket? (a) 23 (b) 15 (c) 20 (d) 4
8. 8.What is the mean of 6, 16, 2, 18 and 18? (a) 15 (b) 12 (c) 13 (d) 10
9. 9.A bag has 7 green balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 13 (b) 2 (c) 8 (d) 9
10. 10.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 63 (b) 12 (c) 64 (d) 126
11. 11.What is the smallest prime factor of 187? (a) 2 (b) 11 (c) 17 (d) 1
12. 12.A bag has 5 blue, 8 red and 2 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 8/15 (b) 1/3 (c) 7/15 (d) 3/5
13. 13.Two angles of a triangle are 60° and 90°. What is the third angle? (a) 90° (b) 150° (c) 120° (d) 30°
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/36 (c) 1/6 (d) 5/11
15. 15.A drawer has lots of red, blue, green, white and yellow 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) 5 (c) 2 (d) 10
16. 16.What is the mode of 6, 16, 18, 16, 6, 16 and 1? (a) 6 (b) 18 (c) 1 (d) 16
17. 17.What is the prime factorisation of 36? (a) 2 × 3² (b) 2² × 3² (c) 2² × 3³ (d) 2³ × 3²
18. 18.A cuboid is 10 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 256 sq cm (b) 180 sq cm (c) 512 sq cm (d) 128 sq cm
19. 19.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 45 (c) 46 (d) 54
20. 20.What is the mean of 5, 19, 18 and 6? (a) 11 (b) 13 (c) 12 (d) 16
21. 21.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 3/8 (c) 5/8 (d) 1/4
22. 22.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 126 (c) 45 (d) 14
23. 23.What is the sum of all the whole numbers from 1 to 66? (a) 2178 (b) 4422 (c) 2145 (d) 2211
24. 24.A drawer has lots of white and blue 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) 4 (c) 2 (d) 5
25. 25.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 25 (c) 20 (d) 120
26. 26.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 12 (c) 8 (d) 24
27. 27.In a class of 28 children, 10 like mangoes, 15 like bananas and 7 like both. How many like at least one of the two? (a) 18 (b) 28 (c) 11 (d) 25
28. 28.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 153 (c) 162 (d) 154
29. 29.Using (a − b)² = a² − 2ab + b², what is 55²? (a) 3025 (b) 3035 (c) 4225 (d) 3575
30. 30.A drawer has lots of black, 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) 6 (b) 4 (c) 2 (d) 3
31. 31.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 63) (b) (x + 7)(x + 9) (c) (x − 7)(x − 9) (d) (x + 1)(x + 15)
32. 32.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 676 (c) 351 (d) 702
33. 33.Two angles of a triangle are 70° and 55°. What is the third angle? (a) 110° (b) 125° (c) 55° (d) 235°
34. 34.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 95° (b) 130° (c) 85° (d) 145°
35. 35.Which is the correct factorisation of x² + 6x + 8? (a) (x − 2)(x − 4) (b) (x + 1)(x + 5) (c) (x + 1)(x + 8) (d) (x + 2)(x + 4)
36. 36.A bag has 12 green balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 13 (c) 2 (d) 20
37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/11 (c) 1/9 (d) 1/12
38. 38.Which is the correct factorisation of x² + 13x + 40? (a) (x − 5)(x − 8) (b) (x + 1)(x + 12) (c) (x + 1)(x + 40) (d) (x + 5)(x + 8)
39. 39.A drawer has lots of yellow and blue 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) 5 (c) 4 (d) 2
40. 40.Which is the correct factorisation of x² + 9x + 20? (a) (x + 1)(x + 20) (b) (x + 4)(x + 5) (c) (x − 4)(x − 5) (d) (x + 1)(x + 8)

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