Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 308 · 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 book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 410 (c) 508 (d) 498
2. 2.A bag has 12 red balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 13 (b) 14 (c) 17 (d) 2
3. 3.What is the 13th term of the AP 20, 24, 28, 32, …? (a) 72 (b) 52 (c) 68 (d) 48
4. 4.A bag has 8 blue, 2 red and 3 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 2/13 (c) 11/13 (d) 12/13
5. 5.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 56 (c) 28 (d) 16
6. 6.What is the sum of the roots of x² − 13x + 40 = 0? (a) 12 (b) 14 (c) 13 (d) 40
7. 7.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
8. 8.What is the distance between the points (6, 12) and (12, 4)? (a) 100 (b) 10 (c) 14 (d) 11
9. 9.How many prime numbers are there between 30 and 40? (a) 4 (b) 1 (c) 3 (d) 2
10. 10.How many factors does 89 have? (a) 3 (b) 1 (c) 4 (d) 2
11. 11.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 248 (c) 264 (d) 265
12. 12.What is the sum of all the whole numbers from 1 to 48? (a) 1128 (b) 1176 (c) 2352 (d) 1152
13. 13.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 140° (d) 100°
14. 14.In a class of 34 children, 12 like tea, 27 like coffee and 9 like both. How many like only tea? (a) 12 (b) 7 (c) 18 (d) 3
15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 92? (a) 18 (b) 9 (c) 19 (d) 20
16. 16.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 80° (c) 50° (d) 100°
17. 17.In a class of 38 children, 17 like maths, 24 like science and 6 like both. How many like neither? (a) 4 (b) 6 (c) 3 (d) 9
18. 18.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 240 (d) 120
19. 19.What is the distance between the points (2, 4) and (6, 1)? (a) 25 (b) 5 (c) 6 (d) 7
20. 20.What is the 11th term of the AP 20, 27, 34, 41, …? (a) 70 (b) 77 (c) 90 (d) 97
21. 21.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
22. 22.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 125° (b) 120° (c) 115° (d) 65°
23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 15 (b) 14 (c) 4 (d) 16
24. 24.What is the midpoint of the line joining (0, 16) and (2, 10)? (a) (1, 13) (b) (1, 3) (c) (2, 26) (d) (13, 1)
25. 25.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2³ × 5 (c) 2 × 5⁴ (d) 2⁵ × 5
26. 26.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 70° (d) 155°
27. 27.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 45 (b) 54 (c) 46 (d) 36
28. 28.What is the mean of 11, 4, 18, 5 and 22? (a) 10 (b) 15 (c) 13 (d) 12
29. 29.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 105 (c) 91 (d) 182
30. 30.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 155° (b) 100° (c) 80° (d) 125°
31. 31.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 314 (c) 354 (d) 364
32. 32.How many factors does 30 have? (a) 9 (b) 8 (c) 6 (d) 7
33. 33.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
34. 34.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
35. 35.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 81 (c) 72 (d) 18
36. 36.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
37. 37.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 16 (c) 28 (d) 56
38. 38.How many prime numbers are there between 10 and 20? (a) 3 (b) 6 (c) 5 (d) 4
39. 39.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 240 (d) 120
40. 40.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm

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