Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 723 · 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 prime factor of 21? (a) 3 (b) 2 (c) 7 (d) 1
2. 2.What is the distance between the points (1, 6) and (25, 13)? (a) 25 (b) 625 (c) 26 (d) 31
3. 3.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 42 (c) 28 (d) 21
4. 4.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 19 (c) 60 (d) 171
5. 5.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 25 times (d) 10 times
6. 6.What is the distance between the points (2, 9) and (7, 21)? (a) 17 (b) 169 (c) 14 (d) 13
7. 7.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 125 (c) 126 (d) 134
8. 8.What is the sum of all the whole numbers from 1 to 99? (a) 9900 (b) 4951 (c) 4851 (d) 4950
9. 9.What is the distance between the points (8, 5) and (15, 29)? (a) 31 (b) 25 (c) 625 (d) 26
10. 10.A bag has 7 yellow balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 18 (b) 8 (c) 9 (d) 2
11. 11.In a class of 35 children, 13 like maths, 19 like science and 5 like both. How many like neither? (a) 5 (b) 3 (c) 8 (d) 13
12. 12.What is the 20th term of the AP 19, 25, 31, 37, …? (a) 139 (b) 120 (c) 114 (d) 133
13. 13.A bag has 3 yellow, 4 blue and 9 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 7/9 (b) 1/3 (c) 7/16 (d) 9/16
14. 14.What is the sum of all the whole numbers from 1 to 96? (a) 4656 (b) 4608 (c) 4560 (d) 9312
15. 15.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm
16. 16.Using (a + b)² = a² + 2ab + b², what is 103²? (a) 10619 (b) 9409 (c) 10609 (d) 10009
17. 17.Which is the correct factorisation of x² + 11x + 30? (a) (x + 5)(x + 6) (b) (x − 5)(x − 6) (c) (x + 1)(x + 30) (d) (x + 1)(x + 10)
18. 18.What is the mode of 16, 2, 15, 2, 11, 11 and 11? (a) 15 (b) 2 (c) 16 (d) 11
19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
20. 20.What is the distance between the points (1, 2) and (4, 6)? (a) 25 (b) 5 (c) 6 (d) 7
21. 21.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
22. 22.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 100° (c) 80° (d) 280°
23. 23.A bag has 9 yellow balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 13 (c) 10 (d) 11
24. 24.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
25. 25.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
26. 26.What is the mode of 12, 7, 20, 20, 20, 5 and 7? (a) 20 (b) 12 (c) 5 (d) 7
27. 27.How many prime numbers are there between 10 and 20? (a) 4 (b) 3 (c) 5 (d) 6
28. 28.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 325 (c) 324 (d) 315
29. 29.What is the mode of 6, 7, 7, 6, 13, 10 and 7? (a) 10 (b) 6 (c) 7 (d) 13
30. 30.A drawer has lots of red, green, 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) 6 (b) 2 (c) 10 (d) 5
31. 31.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 30° (c) 75° (d) 105°
32. 32.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 120° (d) 155°
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/18 (c) 1/12 (d) 1/11
34. 34.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 135° (b) 100° (c) 45° (d) 125°
35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 2 (b) 4 (c) 1 (d) 3
36. 36.How many factors does 32 have? (a) 7 (b) 4 (c) 5 (d) 6
37. 37.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 309 (c) 310 (d) 278
38. 38.Which term of the AP 14, 23, 32, 41, … is 356? (a) 38th (b) 39th (c) 41st (d) 40th
39. 39.A bag has 8 yellow balls and 12 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 20 (b) 2 (c) 9 (d) 10
40. 40.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 6 (d) 3

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