Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 321 · 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.What is the distance between the points (0, 6) and (4, 3)? (a) 6 (b) 5 (c) 7 (d) 25
2. 2.How many prime numbers are there between 90 and 120? (a) 8 (b) 6 (c) 5 (d) 7
3. 3.A bag has 4 green, 5 blue and 6 yellow balls. One ball is taken out without looking. What is the probability that it is not green? (a) 4/15 (b) 11/15 (c) 4/5 (d) 1/3
4. 4.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 105 (c) 120 (d) 225
5. 5.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 64 (c) 56 (d) 55
6. 6.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 2/3 (c) 1/4 (d) 1/3
7. 7.What is the prime factorisation of 70? (a) 2³ × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7 (d) 2 × 5 × 7²
8. 8.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 9 (d) 7
9. 9.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 16 (c) 24 (d) 48
10. 10.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
11. 11.A bag has 5 red balls and 4 black 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) 9 (d) 5
12. 12.How many factors does 27 have? (a) 2 (b) 3 (c) 4 (d) 5
13. 13.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 145° (b) 125° (c) 270° (d) 90°
14. 14.A bag has 11 white balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 13 (c) 20 (d) 12
15. 15.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) 5 (b) 3 (c) 2 (d) 4
16. 16.What is the median of 26, 29, 11, 12, 16, 8 and 25? (a) 17 (b) 12 (c) 16 (d) 25
17. 17.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/4 (c) 1/3 (d) 1/2
18. 18.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 80° (c) 100° (d) 20°
19. 19.What is the distance between the points (0, 8) and (3, 12)? (a) 25 (b) 5 (c) 7 (d) 6
20. 20.What is the 37th term of the AP 5, 10, 15, 20, …? (a) 186 (b) 180 (c) 185 (d) 190
21. 21.In which quadrant does the point (4, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
22. 22.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 15 (c) 8 (d) 14
23. 23.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 24 (c) 34 (d) 33
24. 24.A bag has 4 green, 7 red and 5 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 5/16 (b) 3/4 (c) 1/3 (d) 11/16
25. 25.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 132 cm (d) 1386 cm
26. 26.What is the median of 11, 21, 15, 9 and 8? (a) 12 (b) 15 (c) 9 (d) 11
27. 27.A bag has 10 yellow 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) 17 (b) 8 (c) 2 (d) 11
28. 28.What is the smallest prime factor of 161? (a) 2 (b) 23 (c) 7 (d) 1
29. 29.In a class of 28 children, 18 like maths, 9 like science and 2 like both. How many like neither? (a) 3 (b) 5 (c) 2 (d) 1
30. 30.The mean of 3 numbers is 19. When the number 7 is added to them, what is the new mean? (a) 13 (b) 16 (c) 19 (d) 17
31. 31.How many prime numbers are there between 70 and 80? (a) 4 (b) 2 (c) 5 (d) 3
32. 32.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 72 (d) 36
33. 33.In a class of 22 children, 12 like maths, 13 like science and 5 like both. How many like at least one of the two? (a) 22 (b) 25 (c) 15 (d) 20
34. 34.What is the smallest prime factor of 77? (a) 2 (b) 11 (c) 1 (d) 7
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 1/6 (c) 5/36 (d) 5/11
36. 36.What is the missing term in the AP 1, ?, 19, 28, 37? (a) 19 (b) 11 (c) 10 (d) 9
37. 37.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 5/6 (b) 1/3 (c) 1/4 (d) 2/3
38. 38.How many factors does 46 have? (a) 5 (b) 2 (c) 3 (d) 4
39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 4 (b) 3 (c) 5 (d) 2
40. 40.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 50° (c) 40° (d) 130°

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