Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 81 · 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 drawer has lots of green, white 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) 3 (b) 6 (c) 4 (d) 2
2. 2.What is the prime factorisation of 35? (a) 5² × 7 (b) 5 × 7 (c) 5 × 7² (d) 5³ × 7
3. 3.Which term of the AP 1, 8, 15, 22, … is 120? (a) 20th (b) 17th (c) 19th (d) 18th
4. 4.Using (a + b)² = a² + 2ab + b², what is 23²? (a) 409 (b) 289 (c) 539 (d) 529
5. 5.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
6. 6.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
7. 7.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
8. 8.What is the sum of all the whole numbers from 1 to 18? (a) 162 (b) 153 (c) 342 (d) 171
9. 9.Which is the correct factorisation of x² + 7x + 12? (a) (x − 3)(x − 4) (b) (x + 3)(x + 4) (c) (x + 1)(x + 12) (d) (x + 1)(x + 6)
10. 10.In a class of 41 children, 18 like mangoes, 21 like bananas and 6 like neither. How many like both? (a) 5 (b) 35 (c) 6 (d) 4
11. 11.What is the median of 17, 39, 12, 30 and 4? (a) 12 (b) 18 (c) 30 (d) 17
12. 12.Using (a − b)² = a² − 2ab + b², what is 57²? (a) 3591 (b) 3259 (c) 3969 (d) 3249
13. 13.Two angles of a triangle are 75° and 30°. What is the exterior angle at the third corner? (a) 255° (b) 75° (c) 105° (d) 150°
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/6 (b) 1/11 (c) 7/36 (d) 6/11
15. 15.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 13 (b) 24 (c) 25 (d) 12
16. 16.What is the mode of 19, 4, 3, 3, 4, 3 and 16? (a) 3 (b) 4 (c) 19 (d) 16
17. 17.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 266 (c) 292 (d) 291
18. 18.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 24 (c) 48 (d) 12
19. 19.There are 6 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 84 (b) 13 (c) 48 (d) 42
20. 20.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 25 sq cm (c) 100 sq cm (d) 125 sq cm
21. 21.What is the distance between the points (3, 12) and (8, 0)? (a) 14 (b) 169 (c) 17 (d) 13
22. 22.How many factors does 93 have? (a) 4 (b) 2 (c) 5 (d) 3
23. 23.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 99 (c) 11 (d) 33
24. 24.What is the missing term in the AP 6, ?, 22, 30, 38? (a) 13 (b) 22 (c) 14 (d) 15
25. 25.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 36 (c) 37 (d) 49
26. 26.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 65° (b) 50° (c) 115° (d) 230°
27. 27.In a class of 33 children, 15 like dance, 20 like music and 5 like both. How many like at least one of the two? (a) 25 (b) 35 (c) 30 (d) 33
28. 28.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 150° (c) 30° (d) 60°
29. 29.What is the smallest prime factor of 155? (a) 1 (b) 2 (c) 31 (d) 5
30. 30.In a class of 44 children, 16 like cricket, 24 like football and 9 like neither. How many like both? (a) 6 (b) 35 (c) 5 (d) 9
31. 31.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
32. 32.There are 8 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) 10 (b) 24 (c) 16 (d) 32
33. 33.Using (a − b)² = a² − 2ab + b², what is 19²? (a) 441 (b) 361 (c) 399 (d) 371
34. 34.What is the smallest prime factor of 203? (a) 29 (b) 7 (c) 2 (d) 1
35. 35.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 1/4 (c) 7/8 (d) 1/7
36. 36.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
37. 37.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 64 (b) 40 (c) 12 (d) 32
38. 38.What are the roots of x² − 11x + 18 = 0? (a) 2 and 9 (b) 1 and 18 (c) 1 and 10 (d) 3 and 6
39. 39.In a class of 19 children, 12 like mangoes, 12 like bananas and 8 like both. How many like at least one of the two? (a) 24 (b) 16 (c) 19 (d) 8
40. 40.A bag has 9 white balls and 5 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) 6 (c) 2 (d) 10

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