Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 661 · 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 36th term of the AP 13, 22, 31, 40, …? (a) 324 (b) 315 (c) 328 (d) 337
2. 2.In a class of 38 children, 19 like cricket, 27 like football and 10 like both. How many like only cricket? (a) 19 (b) 17 (c) 9 (d) 11
3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 13 (b) 15 (c) 14 (d) 3
4. 4.What is the midpoint of the line joining (8, 0) and (10, 2)? (a) (9, 1) (b) (1, 9) (c) (1, 1) (d) (18, 2)
5. 5.A bag has 3 green, 3 yellow and 9 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 4/5 (c) 1/4 (d) 1/5
6. 6.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 14) (b) (x + 1)(x + 56) (c) (x + 7)(x + 8) (d) (x − 7)(x − 8)
7. 7.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 49 (d) 21
8. 8.How many factors does 119 have? (a) 2 (b) 3 (c) 5 (d) 4
9. 9.A bag has 2 blue, 7 white and 5 red balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/6 (b) 6/7 (c) 1/3 (d) 1/7
10. 10.What is the sum of all the whole numbers from 1 to 86? (a) 3741 (b) 3655 (c) 7482 (d) 3698
11. 11.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
12. 12.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 190 (b) 380 (c) 361 (d) 37
13. 13.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 60° (c) 61° (d) 30°
14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/11 (c) 1/12 (d) 1/36
15. 15.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) 28 (b) 29 (c) 21 (d) 22
16. 16.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 52 (c) 70 (d) 61
17. 17.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
18. 18.How many prime numbers are there between 10 and 40? (a) 9 (b) 7 (c) 8 (d) 10
19. 19.What is the mean of 10, 16, 20, 12 and 22? (a) 17 (b) 20 (c) 16 (d) 15
20. 20.What is the missing term in the AP 2, ?, 8, 11, 14? (a) 6 (b) 8 (c) 4 (d) 5
21. 21.A bag has 5 red, 6 green and 2 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 6/13 (b) 7/13 (c) 1/3 (d) 6/7
22. 22.A cuboid is 11 cm long, 7 cm wide and 4 cm high. What is its volume? (a) 298 cu cm (b) 22 cu cm (c) 308 cu cm (d) 77 cu cm
23. 23.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 90° (c) 45° (d) 135°
24. 24.The mean of 4 numbers is 16. When the number 6 is added to them, what is the new mean? (a) 11 (b) 16 (c) 14 (d) 15
25. 25.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
26. 26.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 201 (b) 33 (c) 198 (d) 396
27. 27.A cuboid is 9 cm long, 4 cm wide and 8 cm high. What is its volume? (a) 280 cu cm (b) 36 cu cm (c) 288 cu cm (d) 21 cu cm
28. 28.Using (a − b)² = a² − 2ab + b², what is 39²? (a) 1521 (b) 1531 (c) 1681 (d) 1599
29. 29.A bag has 3 white, 7 blue and 6 green balls. One ball is taken out without looking. What is the probability that it is white? (a) 3/16 (b) 3/13 (c) 13/16 (d) 1/3
30. 30.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 27 (c) 24 (d) 72
31. 31.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 69 (c) 198 (d) 22
32. 32.A drawer has lots of yellow, green 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) 6 (b) 2 (c) 3 (d) 4
33. 33.A cuboid is 11 cm long, 3 cm wide and 3 cm high. What is its total surface area? (a) 99 sq cm (b) 150 sq cm (c) 75 sq cm (d) 300 sq cm
34. 34.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) 24 (b) 13 (c) 25 (d) 12
35. 35.In a class of 32 children, 16 like cricket, 22 like football and 9 like both. How many like neither? (a) 12 (b) 9 (c) 4 (d) 3
36. 36.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
37. 37.What is the distance between the points (2, 3) and (6, 6)? (a) 7 (b) 6 (c) 5 (d) 25
38. 38.In a class of 25 children, 7 like mangoes, 12 like bananas and 3 like both. How many like only mangoes? (a) 7 (b) 13 (c) 9 (d) 4
39. 39.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 60° (c) 30° (d) 150°
40. 40.What is the median of 29, 23, 22, 13, 10, 25 and 11? (a) 13 (b) 22 (c) 23 (d) 19

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