Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 273 · 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.Using (a + b)² = a² + 2ab + b², what is 61²? (a) 3721 (b) 3731 (c) 3481 (d) 3601
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
3. 3.What is the prime factorisation of 90? (a) 2³ × 3² × 5 (b) 2 × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5²
4. 4.What is the prime factorisation of 210? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
5. 5.What is the sum of the first 6 terms of the AP 3, 8, 13, …? (a) 186 (b) 108 (c) 28 (d) 93
6. 6.A drawer has lots of blue, green 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) 3 (b) 6 (c) 4 (d) 2
7. 7.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 36 (c) 56 (d) 28
8. 8.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2³ × 3² (c) 2² × 3² (d) 2 × 3²
9. 9.Two angles of a triangle are 35° and 60°. What is the third angle? (a) 85° (b) 95° (c) 120° (d) 145°
10. 10.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/36 (b) 1/6 (c) 5/11 (d) 1/11
12. 12.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 87 (b) 78 (c) 96 (d) 88
13. 13.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) 24 (c) 72 (d) 27
14. 14.What is the mode of 6, 6, 6, 17, 4, 17 and 20? (a) 20 (b) 4 (c) 6 (d) 17
15. 15.What is the median of 14, 4, 22, 12 and 19? (a) 22 (b) 19 (c) 14 (d) 12
16. 16.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 45° (b) 115° (c) 110° (d) 135°
17. 17.What is the distance between the points (0, 9) and (15, 1)? (a) 289 (b) 23 (c) 17 (d) 18
18. 18.A drawer has lots of red, blue, white 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) 8 (b) 4 (c) 2 (d) 5
19. 19.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 24 (d) 16
20. 20.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 444 (c) 374 (d) 454
21. 21.If a + b = 13 and ab = 42, what is a² + b²? (a) 85 (b) 253 (c) 127 (d) 169
22. 22.What is the 24th term of the AP 20, 22, 24, 26, …? (a) 68 (b) 46 (c) 48 (d) 66
23. 23.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
24. 24.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 230° (b) 65° (c) 50° (d) 115°
25. 25.What is the missing term in the AP 5, 11, 17, ?, 29? (a) 23 (b) 29 (c) 24 (d) 22
26. 26.What is the distance between the points (1, 14) and (25, 7)? (a) 25 (b) 26 (c) 31 (d) 625
27. 27.What is the smallest prime factor of 69? (a) 2 (b) 23 (c) 3 (d) 1
28. 28.What is the smallest prime factor of 91? (a) 7 (b) 13 (c) 1 (d) 2
29. 29.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
30. 30.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
31. 31.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 313 (c) 312 (d) 280
32. 32.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/18 (c) 1/12 (d) 1/36
34. 34.What is the mean of 3, 5, 13, 5 and 4? (a) 8 (b) 7 (c) 5 (d) 6
35. 35.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 15 (d) 5
36. 36.In a class of 25 children, 17 like tea, 19 like coffee and 12 like both. How many like neither? (a) 12 (b) 13 (c) 1 (d) 2
37. 37.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 511 (b) 510 (c) 412 (d) 501
38. 38.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 96 (c) 114 (d) 105
39. 39.Which is the correct factorisation of x² + 15x + 56? (a) (x − 7)(x − 8) (b) (x + 7)(x + 8) (c) (x + 1)(x + 56) (d) (x + 1)(x + 14)
40. 40.What is the median of 25, 29, 4, 36 and 3? (a) 26 (b) 25 (c) 4 (d) 29

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