Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 522 · 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.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/9 (b) 4/11 (c) 5/36 (d) 1/11
2. 2.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/3 (c) 1/4 (d) 2/3
3. 3.Which is the correct factorisation of x² + 15x + 54? (a) (x + 1)(x + 54) (b) (x − 6)(x − 9) (c) (x + 1)(x + 14) (d) (x + 6)(x + 9)
4. 4.In a class of 44 children, 24 like maths, 19 like science and 6 like neither. How many like both? (a) 5 (b) 4 (c) 6 (d) 38
5. 5.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 25 (b) 36 (c) 37 (d) 24
6. 6.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁵ × 3² (c) 2² × 3⁴ (d) 2⁴ × 3²
7. 7.A drawer has lots of black, green, blue and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 4 (d) 8
8. 8.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
9. 9.What is the 11th term of the AP 17, 23, 29, 35, …? (a) 83 (b) 77 (c) 66 (d) 60
10. 10.If a + b = 7 and ab = 12, what is (a − b)²? (a) 1 (b) 49 (c) 25 (d) 37
11. 11.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) 49 (b) 37 (c) 48 (d) 36
12. 12.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
13. 13.What is the mode of 14, 18, 6, 6, 19, 6 and 19? (a) 18 (b) 6 (c) 19 (d) 14
14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 5 (b) 2 (c) 3 (d) 4
15. 15.In a class of 20 children, 13 like maths, 13 like science and 10 like both. How many like at least one of the two? (a) 26 (b) 20 (c) 6 (d) 16
16. 16.In a class of 28 children, 14 like mangoes, 11 like bananas and 3 like both. How many like only mangoes? (a) 17 (b) 11 (c) 8 (d) 14
17. 17.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 30 (c) 15 (d) 36
18. 18.What is the sum of all the whole numbers from 1 to 40? (a) 820 (b) 1640 (c) 800 (d) 780
19. 19.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
20. 20.What is the sum of all the whole numbers from 1 to 54? (a) 1485 (b) 1458 (c) 1431 (d) 2970
21. 21.A drawer has lots of 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) 4 (b) 3 (c) 5 (d) 2
22. 22.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 296 (c) 336 (d) 337
23. 23.What is the prime factorisation of 45? (a) 3 × 5 (b) 3² × 5 (c) 3³ × 5 (d) 3 × 5²
24. 24.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 478 (c) 600 (d) 609
25. 25.In a class of 24 children, 18 like tea, 6 like coffee and 2 like both. How many like at least one of the two? (a) 22 (b) 23 (c) 20 (d) 24
26. 26.In a class of 18 children, 8 like tea, 11 like coffee and 3 like both. How many like neither? (a) 3 (b) 2 (c) 5 (d) 1
27. 27.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 110° (c) 71° (d) 70°
28. 28.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
29. 29.Using (a + b)² = a² + 2ab + b², what is 22²? (a) 404 (b) 484 (c) 324 (d) 494
30. 30.What is the sum of the first 11 terms of the AP 9, 15, 21, …? (a) 858 (b) 462 (c) 69 (d) 429
31. 31.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 1000 cu cm (c) 30 cu cm (d) 400 cu cm
32. 32.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) 72 (b) 24 (c) 8 (d) 27
33. 33.Which term of the AP 18, 21, 24, 27, … is 120? (a) 36th (b) 40th (c) 34th (d) 35th
34. 34.In a class of 33 children, 18 like tea, 19 like coffee and 11 like both. How many like at least one of the two? (a) 33 (b) 15 (c) 37 (d) 26
35. 35.Using (a + b)² = a² + 2ab + b², what is 74²? (a) 4916 (b) 5476 (c) 5486 (d) 4356
36. 36.What is the smallest prime factor of 21? (a) 3 (b) 2 (c) 1 (d) 7
37. 37.What is the midpoint of the line joining (9, 4) and (15, 0)? (a) (3, 2) (b) (24, 4) (c) (12, 2) (d) (2, 12)
38. 38.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 70° (c) 20° (d) 40°
39. 39.Two angles of a triangle are 80° and 45°. What is the third angle? (a) 135° (b) 100° (c) 55° (d) 125°
40. 40.What is the sum of all the whole numbers from 1 to 93? (a) 4372 (b) 4278 (c) 8742 (d) 4371

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