Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 237 · 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 prime factorisation of 36? (a) 2² × 3³ (b) 2 × 3² (c) 2² × 3² (d) 2³ × 3²
2. 2.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 20 (d) 10
3. 3.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 25 (b) 36 (c) 24 (d) 37
4. 4.In which quadrant does the point (−9, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
5. 5.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
6. 6.Which is the correct factorisation of x² + 13x + 36? (a) (x − 4)(x − 9) (b) (x + 1)(x + 12) (c) (x + 1)(x + 36) (d) (x + 4)(x + 9)
7. 7.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 78 (d) 169
8. 8.If a + b = 12 and ab = 20, what is a² + b²? (a) 144 (b) 124 (c) 104 (d) 184
9. 9.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 75° (b) 145° (c) 105° (d) 140°
10. 10.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
11. 11.What is the smallest prime factor of 155? (a) 31 (b) 2 (c) 5 (d) 1
12. 12.How many factors does 52 have? (a) 6 (b) 5 (c) 7 (d) 4
13. 13.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 49 (c) 28 (d) 21
14. 14.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
15. 15.What is the sum of all the whole numbers from 1 to 78? (a) 3081 (b) 3042 (c) 3003 (d) 6162
16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/11 (c) 1/36 (d) 1/18
17. 17.A cuboid is 11 cm long, 3 cm wide and 7 cm high. What is its total surface area? (a) 131 sq cm (b) 231 sq cm (c) 524 sq cm (d) 262 sq cm
18. 18.If a + b = 17 and ab = 72, what is a² + b²? (a) 217 (b) 433 (c) 289 (d) 145
19. 19.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 1/4 (b) 2/3 (c) 5/6 (d) 1/3
20. 20.In a class of 26 children, 7 like dance, 17 like music and 5 like neither. How many like both? (a) 4 (b) 3 (c) 5 (d) 21
21. 21.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
22. 22.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
23. 23.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 240 (b) 480 (c) 260 (d) 42
24. 24.In a class of 61 children, 32 like tea, 32 like coffee and 12 like both. How many like at least one of the two? (a) 40 (b) 64 (c) 61 (d) 52
25. 25.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 15 (c) 45 (d) 5
26. 26.The mean of 8 numbers is 40. When the number 76 is added to them, what is the new mean? (a) 45 (b) 44 (c) 40 (d) 58
27. 27.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
28. 28.If a + b = 19 and ab = 90, what is a² + b²? (a) 271 (b) 361 (c) 541 (d) 181
29. 29.The mean of 6 numbers is 36. When the number 15 is added to them, what is the new mean? (a) 36 (b) 32 (c) 34 (d) 33
30. 30.How many factors does 66 have? (a) 6 (b) 8 (c) 9 (d) 7
31. 31.If a + b = 6 and ab = 8, what is a² + b²? (a) 36 (b) 28 (c) 20 (d) 52
32. 32.In a league, 11 teams each play every other team once. How many matches are played? (a) 110 (b) 55 (c) 121 (d) 66
33. 33.A drawer has lots of white, black 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) 3 (b) 2 (c) 6 (d) 4
34. 34.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 165° (b) 40° (c) 155° (d) 15°
35. 35.A bag has 8 blue balls and 11 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) 9 (c) 12 (d) 19
36. 36.What is the distance between the points (3, 1) and (9, 9)? (a) 100 (b) 14 (c) 10 (d) 11
37. 37.A bag has 3 blue, 9 red and 2 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 6/7 (c) 13/14 (d) 1/7
38. 38.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
39. 39.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 162 (b) 18 (c) 57 (d) 54
40. 40.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 144 (c) 78 (d) 66

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