Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 393 · 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.In a class of 39 children, 28 like maths, 18 like science and 9 like both. How many like neither? (a) 9 (b) 3 (c) 11 (d) 2
2. 2.A bag has 4 red balls and 9 yellow 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) 13 (c) 5 (d) 10
3. 3.How many prime numbers are there between 60 and 70? (a) 4 (b) 1 (c) 2 (d) 3
4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 15 (b) 16 (c) 5 (d) 17
5. 5.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 70° (c) 40° (d) 50°
6. 6.How many prime numbers are there between 40 and 70? (a) 6 (b) 7 (c) 8 (d) 9
7. 7.How many prime numbers are there between 30 and 40? (a) 3 (b) 4 (c) 1 (d) 2
8. 8.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 78 (d) 144
9. 9.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 210 (c) 120 (d) 225
10. 10.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 150° (c) 15° (d) 30°
11. 11.Which is the correct factorisation of x² + 11x + 30? (a) (x − 5)(x − 6) (b) (x + 5)(x + 6) (c) (x + 1)(x + 30) (d) (x + 1)(x + 10)
12. 12.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
13. 13.A bag has 11 yellow balls and 6 red 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) 7 (c) 12 (d) 2
14. 14.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 15 (d) 30
15. 15.What is the median of 19, 25, 22, 3 and 10? (a) 20 (b) 19 (c) 10 (d) 22
16. 16.There are 5 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 25 (b) 20 (c) 9 (d) 40
17. 17.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
18. 18.A drawer has lots of red, green, white, 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) 5 (b) 10 (c) 2 (d) 6
19. 19.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
20. 20.What is the mode of 12, 20, 1, 12, 1, 1 and 19? (a) 12 (b) 1 (c) 20 (d) 19
21. 21.What is the smallest prime factor of 57? (a) 2 (b) 1 (c) 19 (d) 3
22. 22.A bag has 12 black balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 13 (c) 24 (d) 14
23. 23.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
24. 24.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 7/8 (c) 1/4 (d) 3/8
25. 25.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 63) (b) (x − 7)(x − 9) (c) (x + 7)(x + 9) (d) (x + 1)(x + 15)
26. 26.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 145° (b) 90° (c) 125° (d) 270°
27. 27.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 110° (b) 145° (c) 105° (d) 35°
28. 28.In a class of 39 children, 20 like tea, 18 like coffee and 3 like both. How many like neither? (a) 1 (b) 7 (c) 3 (d) 4
29. 29.A bag has 4 white, 4 yellow and 5 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 5/13 (b) 9/13 (c) 1/3 (d) 8/13
30. 30.Using (a + b)² = a² + 2ab + b², what is 41²? (a) 1521 (b) 1691 (c) 1681 (d) 1601
31. 31.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 318 (c) 369 (d) 360
32. 32.In a class of 55 children, 26 like tea, 31 like coffee and 12 like both. How many like only tea? (a) 19 (b) 26 (c) 14 (d) 24
33. 33.In a class of 45 children, 27 like maths, 29 like science and 12 like both. How many like neither? (a) 13 (b) 2 (c) 12 (d) 1
34. 34.The mean of 3 numbers is 13. When the number 29 is added to them, what is the new mean? (a) 13 (b) 17 (c) 18 (d) 21
35. 35.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 8 (b) 19 (c) 20 (d) 18
37. 37.What is the midpoint of the line joining (1, 9) and (11, 21)? (a) (15, 6) (b) (5, 6) (c) (12, 30) (d) (6, 15)
38. 38.What is the distance between the points (8, 6) and (13, 18)? (a) 169 (b) 17 (c) 14 (d) 13
39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 1/6 (c) 1/11 (d) 5/11
40. 40.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 120 (d) 240

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