Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 191 · 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 2 white, 4 red and 5 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 9/11 (b) 2/11 (c) 1/3 (d) 2/9
2. 2.Using (a − b)² = a² − 2ab + b², what is 26²? (a) 686 (b) 884 (c) 1156 (d) 676
3. 3.In which quadrant does the point (7, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
4. 4.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
5. 5.What is the sum of the roots of x² − 13x + 42 = 0? (a) 42 (b) 14 (c) 13 (d) 12
6. 6.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
7. 7.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 150 sq cm (c) 125 sq cm (d) 100 sq cm
8. 8.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
9. 9.What is the distance between the points (8, 4) and (23, 12)? (a) 23 (b) 289 (c) 17 (d) 18
10. 10.There are 7 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) 21 (b) 14 (c) 9 (d) 28
11. 11.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 48 (c) 16 (d) 12
12. 12.What is the mode of 20, 2, 20, 2, 11, 1 and 2? (a) 1 (b) 2 (c) 20 (d) 11
13. 13.What is the mean of 6, 14, 16, 15 and 14? (a) 12 (b) 14 (c) 15 (d) 13
14. 14.How many prime numbers are there between 90 and 120? (a) 6 (b) 8 (c) 5 (d) 7
15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 16 (b) 15 (c) 17 (d) 5
16. 16.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 100 (c) 55 (d) 90
17. 17.What is the smallest prime factor of 85? (a) 5 (b) 17 (c) 2 (d) 1
18. 18.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 15 (c) 30 (d) 25
19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 6 (b) 8 (c) 7 (d) 9
20. 20.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 350 (c) 418 (d) 417
21. 21.How many prime numbers are there between 50 and 80? (a) 6 (b) 9 (c) 8 (d) 7
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/36 (b) 1/11 (c) 5/11 (d) 1/6
23. 23.In a class of 33 children, 6 like tea, 20 like coffee and 2 like both. How many like at least one of the two? (a) 22 (b) 26 (c) 33 (d) 24
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 2/11 (c) 1/18 (d) 1/12
25. 25.A bag has 5 yellow balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 2 (c) 13 (d) 9
26. 26.What is the median of 21, 17, 38, 37 and 39? (a) 36 (b) 21 (c) 38 (d) 37
27. 27.What is the mode of 12, 15, 15, 8, 15, 5 and 12? (a) 12 (b) 15 (c) 5 (d) 8
28. 28.Using (a + b)² = a² + 2ab + b², what is 23²? (a) 529 (b) 409 (c) 539 (d) 289
29. 29.In a class of 50 children, 23 like dance, 28 like music and 9 like both. How many like only dance? (a) 23 (b) 14 (c) 22 (d) 19
30. 30.In a class of 30 children, 9 like mangoes, 15 like bananas and 3 like both. How many like neither? (a) 12 (b) 6 (c) 9 (d) 3
31. 31.A bag has 4 white, 8 blue and 2 yellow balls. One ball is taken out without looking. What is the probability that it is white? (a) 5/7 (b) 2/5 (c) 2/7 (d) 1/3
32. 32.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/8 (c) 5/8 (d) 3/5
33. 33.A drawer has lots of black 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) 5 (b) 2 (c) 3 (d) 4
34. 34.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
35. 35.Using (a − b)² = a² − 2ab + b², what is 27²? (a) 1089 (b) 739 (c) 729 (d) 891
36. 36.In a class of 40 children, 26 like tea, 13 like coffee and 9 like both. How many like only tea? (a) 26 (b) 17 (c) 4 (d) 27
37. 37.What is the distance between the points (1, 3) and (8, 27)? (a) 31 (b) 26 (c) 625 (d) 25
38. 38.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 3 (c) 6 (d) 12
39. 39.Using (a − b)² = a² − 2ab + b², what is 77²? (a) 6391 (b) 5929 (c) 5939 (d) 6889
40. 40.In a class of 33 children, 14 like mangoes, 28 like bananas and 11 like both. How many like neither? (a) 11 (b) 3 (c) 13 (d) 2

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