Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 640 · 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 two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
2. 2.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
3. 3.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 24 (c) 16 (d) 48
4. 4.In a class of 36 children, 14 like cricket, 18 like football and 10 like neither. How many like both? (a) 6 (b) 7 (c) 26 (d) 10
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/6 (b) 1/11 (c) 5/11 (d) 5/36
6. 6.What is the median of 1, 24, 33, 37, 7, 6 and 8? (a) 8 (b) 24 (c) 7 (d) 37
7. 7.What is the mean of 6, 10, 15 and 13? (a) 12 (b) 11 (c) 13 (d) 10
8. 8.A bag has 3 green, 9 yellow and 6 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/18 (b) 2/3 (c) 13/18 (d) 1/3
9. 9.How many prime numbers are there between 80 and 100? (a) 4 (b) 2 (c) 3 (d) 5
10. 10.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 110 (c) 121 (d) 66
11. 11.What is the mean of 17, 10, 14, 4 and 5? (a) 11 (b) 12 (c) 9 (d) 10
12. 12.In a class of 38 children, 29 like mangoes, 14 like bananas and 11 like both. How many like only mangoes? (a) 3 (b) 24 (c) 29 (d) 18
13. 13.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2³ × 3² (c) 2² × 3² (d) 2² × 3³
14. 14.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 105 (b) 196 (c) 210 (d) 27
15. 15.How many factors does 81 have? (a) 6 (b) 5 (c) 4 (d) 3
16. 16.A bag has 11 red balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 14 (b) 12 (c) 4 (d) 2
17. 17.The mean of 6 numbers is 33. When the number 5 is added to them, what is the new mean? (a) 33 (b) 30 (c) 19 (d) 29
18. 18.In which quadrant does the point (−8, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
19. 19.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 115° (b) 65° (c) 140° (d) 155°
20. 20.In a class of 30 children, 14 like dance, 9 like music and 2 like both. How many like only dance? (a) 7 (b) 21 (c) 14 (d) 12
21. 21.What is the distance between the points (7, 29) and (14, 5)? (a) 625 (b) 25 (c) 31 (d) 26
22. 22.A drawer has lots of white, green, black, blue 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) 10 (b) 5 (c) 2 (d) 6
23. 23.How many factors does 119 have? (a) 4 (b) 2 (c) 5 (d) 3
24. 24.In a class of 36 children, 23 like dance, 14 like music and 4 like both. How many like only dance? (a) 23 (b) 19 (c) 22 (d) 10
25. 25.How many factors does 108 have? (a) 11 (b) 10 (c) 13 (d) 12
26. 26.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) 14 (b) 7 (c) 15 (d) 8
27. 27.What is the mode of 11, 11, 17, 13, 13, 13 and 12? (a) 13 (b) 17 (c) 11 (d) 12
28. 28.Using (a + b)² = a² + 2ab + b², what is 93²? (a) 7569 (b) 8659 (c) 8109 (d) 8649
29. 29.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 115° (b) 95° (c) 150° (d) 85°
30. 30.A bag has 11 green balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 13 (c) 14 (d) 12
31. 31.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 19 (c) 171 (d) 60
32. 32.In a class of 16 children, 8 like mangoes, 9 like bananas and 4 like both. How many like at least one of the two? (a) 16 (b) 9 (c) 17 (d) 13
33. 33.What is the median of 9, 39, 36, 33 and 35? (a) 34 (b) 33 (c) 36 (d) 35
34. 34.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 240 (d) 120
35. 35.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
36. 36.Two angles of a triangle are 30° and 30°. What is the exterior angle at the third corner? (a) 120° (b) 300° (c) 150° (d) 60°
37. 37.What is the product of the roots of x² − 15x + 54 = 0? (a) 53 (b) 55 (c) 15 (d) 54
38. 38.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 5 times (d) 4 times
39. 39.Using (a − b)² = a² − 2ab + b², what is 66²? (a) 4366 (b) 5476 (c) 4356 (d) 4884
40. 40.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 30 (d) 12

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