Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 122 · 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.A bag has 4 red balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 8 (c) 11 (d) 2
2. 2.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 125° (c) 145° (d) 35°
3. 3.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 145° (c) 55° (d) 110°
4. 4.What is the distance between the points (0, 19) and (8, 4)? (a) 23 (b) 18 (c) 17 (d) 289
5. 5.What is the midpoint of the line joining (4, 0) and (16, 2)? (a) (6, 1) (b) (20, 2) (c) (10, 1) (d) (1, 10)
6. 6.In a class of 29 children, 11 like maths, 18 like science and 7 like both. How many like at least one of the two? (a) 23 (b) 22 (c) 15 (d) 29
7. 7.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 155° (b) 140° (c) 65° (d) 25°
8. 8.In a class of 43 children, 27 like cricket, 21 like football and 7 like both. How many like neither? (a) 7 (b) 3 (c) 2 (d) 9
9. 9.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 438 (c) 439 (d) 364
10. 10.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 3 (c) 9 (d) 12
11. 11.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 294 sq cm (c) 343 sq cm (d) 49 sq cm
12. 12.The mean of 6 numbers is 27. When the number 20 is added to them, what is the new mean? (a) 25 (b) 28 (c) 27 (d) 26
13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 18 (b) 17 (c) 7 (d) 19
14. 14.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 121 (c) 55 (d) 22
15. 15.How many factors does 106 have? (a) 2 (b) 5 (c) 3 (d) 4
16. 16.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 145° (b) 115° (c) 35° (d) 100°
17. 17.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 278 (c) 310 (d) 309
18. 18.In a class of 56 children, 27 like dance, 28 like music and 8 like both. How many like neither? (a) 1 (b) 8 (c) 17 (d) 9
19. 19.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 680 (b) 61 (c) 340 (d) 370
20. 20.Which is the correct factorisation of x² + 8x + 15? (a) (x + 1)(x + 7) (b) (x + 1)(x + 15) (c) (x − 3)(x − 5) (d) (x + 3)(x + 5)
21. 21.Using (a + b)² = a² + 2ab + b², what is 41²? (a) 1601 (b) 1521 (c) 1691 (d) 1681
22. 22.In a class of 41 children, 22 like tea, 17 like coffee and 3 like both. How many like neither? (a) 8 (b) 5 (c) 2 (d) 3
23. 23.What is the distance between the points (9, 5) and (16, 29)? (a) 625 (b) 25 (c) 26 (d) 31
24. 24.How many prime numbers are there between 90 and 120? (a) 8 (b) 7 (c) 5 (d) 6
25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 4/11 (c) 1/9 (d) 5/36
26. 26.A bag has 4 green balls and 8 blue 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) 5 (c) 12 (d) 2
27. 27.What is the median of 36, 38, 3, 1 and 37? (a) 36 (b) 3 (c) 37 (d) 23
28. 28.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 90° (b) 150° (c) 270° (d) 120°
29. 29.A bag has 8 yellow balls and 12 black 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) 2 (c) 20 (d) 13
30. 30.What is the mode of 12, 9, 3, 3, 6, 12 and 3? (a) 12 (b) 9 (c) 6 (d) 3
31. 31.How many factors does 38 have? (a) 2 (b) 4 (c) 3 (d) 5
32. 32.Using (a − b)² = a² − 2ab + b², what is 29²? (a) 851 (b) 841 (c) 961 (d) 899
33. 33.What is the sum of the first 6 terms of the AP 4, 8, 12, …? (a) 24 (b) 96 (c) 168 (d) 84
34. 34.What is the distance between the points (3, 3) and (19, 15)? (a) 400 (b) 28 (c) 21 (d) 20
35. 35.There are 5 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 20 (b) 10 (c) 7 (d) 15
36. 36.What is the smallest prime factor of 143? (a) 11 (b) 13 (c) 1 (d) 2
37. 37.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
38. 38.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 270° (b) 90° (c) 110° (d) 160°
39. 39.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 156 (c) 23 (d) 78
40. 40.A bag has 12 black balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 13 (c) 2 (d) 16

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