Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 498 · 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 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) 8 (b) 15 (c) 7 (d) 14
2. 2.A bag has 12 blue balls and 3 green 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) 15 (c) 4 (d) 13
3. 3.A bag has 3 blue balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 4 (b) 15 (c) 2 (d) 5
4. 4.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
5. 5.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
6. 6.Using (a + b)² = a² + 2ab + b², what is 25²? (a) 425 (b) 225 (c) 635 (d) 625
7. 7.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 120 (c) 20 (d) 240
8. 8.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 20 (d) 25
9. 9.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
10. 10.What is the distance between the points (8, 8) and (13, 20)? (a) 17 (b) 14 (c) 13 (d) 169
11. 11.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 70° (d) 340°
12. 12.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 22 (b) 21 (c) 29 (d) 28
13. 13.What is the 20th term of the AP 3, 5, 7, 9, …? (a) 41 (b) 38 (c) 40 (d) 43
14. 14.In a class of 43 children, 30 like tea, 18 like coffee and 12 like both. How many like neither? (a) 8 (b) 12 (c) 7 (d) 19
15. 15.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 15 (d) 30
16. 16.What is the distance between the points (2, 0) and (10, 6)? (a) 11 (b) 100 (c) 14 (d) 10
17. 17.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 66 (b) 11 (c) 132 (d) 67
18. 18.What is the 35th term of the AP 1, 8, 15, 22, …? (a) 246 (b) 238 (c) 239 (d) 245
19. 19.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 12 (c) 5 (d) 6
20. 20.Using (a − b)² = a² − 2ab + b², what is 98²? (a) 9614 (b) 9604 (c) 10404 (d) 9996
21. 21.The mean of 5 numbers is 40. When the number 58 is added to them, what is the new mean? (a) 43 (b) 44 (c) 40 (d) 49
22. 22.If a + b = 12 and ab = 27, what is a² + b²? (a) 198 (b) 144 (c) 117 (d) 90
23. 23.What is the sum of the first 9 terms of the AP 9, 11, 13, …? (a) 153 (b) 306 (c) 162 (d) 25
24. 24.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
25. 25.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
26. 26.What is the midpoint of the line joining (9, 6) and (15, 10)? (a) (24, 16) (b) (12, 8) (c) (8, 12) (d) (3, 2)
27. 27.What is the mode of 6, 9, 11, 9, 13, 11 and 11? (a) 11 (b) 9 (c) 13 (d) 6
28. 28.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 36 (c) 21 (d) 30
29. 29.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
30. 30.In a class of 36 children, 14 like cricket, 27 like football and 9 like both. How many like at least one of the two? (a) 23 (b) 36 (c) 32 (d) 41
31. 31.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
32. 32.If a + b = 13 and ab = 12, what is a² + b²? (a) 169 (b) 193 (c) 145 (d) 157
33. 33.What is the 16th term of the AP 3, 11, 19, 27, …? (a) 123 (b) 120 (c) 128 (d) 131
34. 34.In a class of 42 children, 14 like maths, 29 like science and 11 like both. How many like neither? (a) 9 (b) 21 (c) 10 (d) 11
35. 35.A bag has 3 red balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 4 (b) 2 (c) 12 (d) 5
36. 36.In a class of 33 children, 15 like tea, 27 like coffee and 10 like both. How many like only tea? (a) 17 (b) 5 (c) 6 (d) 15
37. 37.In a class of 26 children, 8 like maths, 11 like science and 3 like both. How many like only maths? (a) 8 (b) 3 (c) 5 (d) 15
38. 38.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
39. 39.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 562 (c) 1122 (d) 528
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 5/36 (c) 1/9 (d) 1/11

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