Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 368 · 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.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 155° (c) 80° (d) 100°
2. 2.There are 8 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) 10 (b) 32 (c) 16 (d) 24
3. 3.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 29 (c) 22 (d) 21
4. 4.A drawer has lots of 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) 2 (b) 5 (c) 4 (d) 3
5. 5.What is the sum of the first 6 terms of the AP 4, 7, 10, …? (a) 138 (b) 78 (c) 69 (d) 19
6. 6.What is the smallest prime factor of 69? (a) 23 (b) 1 (c) 2 (d) 3
7. 7.A bag has 10 yellow balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 22 (b) 11 (c) 12 (d) 2
8. 8.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 99 (c) 100 (d) 108
9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 80? (a) 8 (b) 7 (c) 9 (d) 10
10. 10.Two angles of a triangle are 50° and 70°. What is the third angle? (a) 60° (b) 110° (c) 120° (d) 130°
11. 11.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2 × 3² × 5 (c) 2 × 3² × 5² (d) 2³ × 3² × 5
12. 12.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 110° (b) 235° (c) 55° (d) 125°
13. 13.In a class of 33 children, 16 like mangoes, 14 like bananas and 4 like both. How many like neither? (a) 11 (b) 7 (c) 4 (d) 3
14. 14.In which quadrant does the point (9, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
15. 15.Two angles of a triangle are 30° and 90°. What is the third angle? (a) 120° (b) 60° (c) 90° (d) 150°
16. 16.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 16 (d) 48
17. 17.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 80° (b) 160° (c) 100° (d) 260°
18. 18.A bag has 6 red balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 15 (c) 2 (d) 7
19. 19.In a class of 41 children, 16 like maths, 23 like science and 3 like both. How many like neither? (a) 2 (b) 8 (c) 5 (d) 3
20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 8 (b) 17 (c) 19 (d) 18
21. 21.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 50° (c) 80° (d) 100°
22. 22.If a + b = 8 and ab = 15, what is (a − b)²? (a) 34 (b) 4 (c) 2 (d) 64
23. 23.How many factors does 61 have? (a) 4 (b) 1 (c) 3 (d) 2
24. 24.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
25. 25.If a + b = 6 and ab = 8, what is a² + b²? (a) 20 (b) 36 (c) 28 (d) 52
26. 26.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
27. 27.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
28. 28.What is the mode of 12, 1, 2, 12, 19, 19 and 12? (a) 2 (b) 12 (c) 1 (d) 19
29. 29.What is the missing term in the AP 6, 9, 12, ?, 18? (a) 15 (b) 18 (c) 16 (d) 14
30. 30.What is the sum of the first 5 terms of the AP 3, 9, 15, …? (a) 90 (b) 27 (c) 150 (d) 75
31. 31.The mean of 5 numbers is 16. When the number 4 is added to them, what is the new mean? (a) 16 (b) 14 (c) 15 (d) 10
32. 32.A bag has 11 yellow balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 14 (c) 12 (d) 4
33. 33.Using (a − b)² = a² − 2ab + b², what is 47²? (a) 2209 (b) 2809 (c) 2219 (d) 2491
34. 34.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 60° (b) 30° (c) 75° (d) 150°
35. 35.A bag has 4 red balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 9 (c) 5 (d) 2
36. 36.What is the mean of 10, 3, 9 and 6? (a) 7 (b) 9 (c) 6 (d) 8
37. 37.A bag has 5 green balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 7 (b) 2 (c) 6 (d) 10
38. 38.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 90 (d) 81
39. 39.If a + b = 14 and ab = 45, what is a² + b²? (a) 151 (b) 286 (c) 106 (d) 196
40. 40.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/3 (c) 2/3 (d) 1/2

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