Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 82 · 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 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 206 (c) 192 (d) 202
2. 2.In which quadrant does the point (6, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
3. 3.A bag has 6 red balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 7 (c) 2 (d) 11
4. 4.What is the smallest prime factor of 145? (a) 1 (b) 29 (c) 5 (d) 2
5. 5.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 56 (c) 28 (d) 36
6. 6.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 24 (c) 132 (d) 144
7. 7.Using (a + b)² = a² + 2ab + b², what is 101²? (a) 10201 (b) 9801 (c) 10211 (d) 10001
8. 8.If a + b = 5 and ab = 4, what is (a − b)²? (a) 25 (b) 17 (c) 9 (d) 3
9. 9.In a class of 42 children, 25 like cricket, 24 like football and 2 like neither. How many like both? (a) 9 (b) 2 (c) 40 (d) 7
10. 10.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 11 (c) 24 (d) 32
11. 11.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
12. 12.In a class of 53 children, 28 like maths, 25 like science and 9 like both. How many like at least one of the two? (a) 53 (b) 44 (c) 45 (d) 35
13. 13.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 18 (c) 72 (d) 81
14. 14.In a class of 35 children, 24 like mangoes, 17 like bananas and 8 like both. How many like at least one of the two? (a) 25 (b) 41 (c) 33 (d) 35
15. 15.How many prime numbers are there between 20 and 30? (a) 3 (b) 2 (c) 1 (d) 4
16. 16.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 45 (c) 100 (d) 55
17. 17.How many prime numbers are there between 10 and 20? (a) 3 (b) 5 (c) 6 (d) 4
18. 18.In a class of 29 children, 8 like dance, 19 like music and 2 like both. How many like only dance? (a) 10 (b) 6 (c) 8 (d) 17
19. 19.In a class of 22 children, 9 like dance, 15 like music and 4 like neither. How many like both? (a) 4 (b) 2 (c) 18 (d) 6
20. 20.A drawer has lots of red and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 3 (d) 2
21. 21.What is the distance between the points (8, 5) and (16, 11)? (a) 100 (b) 14 (c) 10 (d) 11
22. 22.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 2464 sq cm
23. 23.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 182 (c) 91 (d) 196
24. 24.In a class of 33 children, 24 like dance, 9 like music and 4 like both. How many like neither? (a) 5 (b) 8 (c) 0 (d) 4
25. 25.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
26. 26.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 517 (b) 416 (c) 516 (d) 507
27. 27.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 23 (c) 69 (d) 207
28. 28.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 60° (b) 160° (c) 120° (d) 140°
29. 29.What is the sum of the first 12 terms of the AP 7, 13, 19, …? (a) 960 (b) 73 (c) 480 (d) 516
30. 30.A bag has 5 yellow balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 7 (c) 2 (d) 6
31. 31.3 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 18 (b) 12 (c) 9 (d) 6
32. 32.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
33. 33.What is the 33rd term of the AP 2, 7, 12, 17, …? (a) 165 (b) 160 (c) 162 (d) 167
34. 34.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2 × 5 × 7 (c) 2³ × 5 × 7 (d) 2² × 5 × 7
35. 35.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
36. 36.There are 7 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) 56 (b) 11 (c) 28 (d) 35
37. 37.A bag has 6 blue balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 7 (c) 2 (d) 8
38. 38.What is the mode of 13, 13, 1, 17, 17, 15 and 13? (a) 13 (b) 17 (c) 1 (d) 15
39. 39.What is the mode of 15, 10, 10, 12, 10, 17 and 15? (a) 15 (b) 12 (c) 17 (d) 10
40. 40.What is the mean of 18, 12, 18 and 4? (a) 12 (b) 15 (c) 14 (d) 13

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