Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 880 · 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.How many prime numbers are there between 80 and 100? (a) 5 (b) 3 (c) 2 (d) 4
2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 4 (b) 3 (c) 1 (d) 2
3. 3.7 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 13 (b) 49 (c) 42 (d) 84
4. 4.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 37 (c) 49 (d) 36
5. 5.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 5° (d) 95°
6. 6.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7
7. 7.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 20° (c) 11° (d) 10°
8. 8.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 67 (b) 814 (c) 407 (d) 440
9. 9.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 28 (c) 16 (d) 56
10. 10.What is the mode of 11, 2, 5, 17, 2, 5 and 2? (a) 11 (b) 17 (c) 2 (d) 5
11. 11.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
12. 12.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 155° (b) 105° (c) 25° (d) 100°
13. 13.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
14. 14.How many factors does 30 have? (a) 9 (b) 7 (c) 6 (d) 8
15. 15.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
16. 16.In a class of 44 children, 21 like maths, 19 like science and 2 like both. How many like only maths? (a) 19 (b) 21 (c) 25 (d) 17
17. 17.There are 5 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 15 (b) 8 (c) 30 (d) 20
18. 18.A bag has 12 red balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 13 (b) 2 (c) 18 (d) 14
19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
20. 20.A bag has 6 blue balls and 4 yellow 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) 2 (c) 10 (d) 5
21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 5/36 (c) 1/11 (d) 1/6
22. 22.A bag has 8 black balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 15 (b) 9 (c) 2 (d) 10
23. 23.What is the median of 20, 39, 16, 6, 36, 3 and 15? (a) 20 (b) 16 (c) 15 (d) 6
24. 24.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 501 (c) 406 (d) 502
25. 25.What is the distance between the points (0, 12) and (3, 8)? (a) 7 (b) 25 (c) 6 (d) 5
26. 26.A drawer has lots of green, black, red, 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) 10 (b) 5 (c) 6 (d) 2
27. 27.A cuboid is 4 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 9 cu cm (b) 52 cu cm (c) 24 cu cm (d) 8 cu cm
28. 28.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 307 (c) 276 (d) 297
29. 29.What is the product of the roots of x² − 16x + 63 = 0? (a) 63 (b) 16 (c) 64 (d) 62
30. 30.Two angles of a triangle are 25° and 70°. What is the third angle? (a) 110° (b) 155° (c) 85° (d) 95°
31. 31.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
32. 32.If a + b = 10 and ab = 24, what is a² + b²? (a) 148 (b) 100 (c) 52 (d) 76
33. 33.What is the prime factorisation of 45? (a) 3 × 5 (b) 3³ × 5 (c) 3² × 5 (d) 3 × 5²
34. 34.Two angles of a triangle are 70° and 20°. What is the third angle? (a) 90° (b) 110° (c) 160° (d) 270°
35. 35.In how many different ways can the letters of the word TIGER be arranged? (a) 20 (b) 240 (c) 120 (d) 25
36. 36.What is the median of 32, 34, 2, 22 and 39? (a) 2 (b) 22 (c) 34 (d) 32
37. 37.What are the roots of x² − 9x + 20 = 0? (a) 1 and 8 (b) 1 and 20 (c) 2 and 10 (d) 4 and 5
38. 38.What is the distance between the points (6, 2) and (9, 6)? (a) 25 (b) 7 (c) 6 (d) 5
39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 9 (b) 19 (c) 21 (d) 20
40. 40.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 41 (c) 32 (d) 42

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad