Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 442 · 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 book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 402 (c) 486 (d) 496
2. 2.What is the missing term in the AP 9, 12, 15, ?, 21? (a) 21 (b) 17 (c) 19 (d) 18
3. 3.In a class of 38 children, 21 like tea, 27 like coffee and 12 like both. How many like neither? (a) 12 (b) 2 (c) 3 (d) 14
4. 4.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
5. 5.A drawer has lots of red, blue, black and green 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) 8 (c) 5 (d) 2
6. 6.A bag has 4 blue balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 6 (b) 13 (c) 2 (d) 5
7. 7.Two angles of a triangle are 25° and 120°. What is the exterior angle at the third corner? (a) 145° (b) 60° (c) 35° (d) 155°
8. 8.How many prime numbers are there between 90 and 120? (a) 7 (b) 8 (c) 5 (d) 6
9. 9.A bag has 8 yellow balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 17 (b) 10 (c) 9 (d) 2
10. 10.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 16 (c) 24 (d) 12
11. 11.What is the midpoint of the line joining (4, 8) and (10, 0)? (a) (7, 4) (b) (4, 7) (c) (14, 8) (d) (3, 4)
12. 12.In a class of 36 children, 17 like cricket, 23 like football and 5 like both. How many like neither? (a) 6 (b) 2 (c) 5 (d) 1
13. 13.What is the prime factorisation of 45? (a) 3 × 5² (b) 3 × 5 (c) 3² × 5 (d) 3³ × 5
14. 14.How many prime numbers are there between 70 and 100? (a) 6 (b) 7 (c) 5 (d) 8
15. 15.In a class of 43 children, 23 like tea, 22 like coffee and 4 like both. How many like only tea? (a) 23 (b) 18 (c) 21 (d) 19
16. 16.The mean of 5 numbers is 21. When the number 39 is added to them, what is the new mean? (a) 30 (b) 25 (c) 21 (d) 24
17. 17.In a class of 33 children, 15 like cricket, 24 like football and 12 like both. How many like neither? (a) 12 (b) 7 (c) 6 (d) 18
18. 18.In a class of 46 children, 19 like dance, 28 like music and 10 like both. How many like only dance? (a) 9 (b) 19 (c) 10 (d) 18
19. 19.A bag has 8 blue balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 9 (c) 2 (d) 11
20. 20.In which quadrant does the point (−2, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
21. 21.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2³ × 3 × 7
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/12 (c) 1/11 (d) 1/36
23. 23.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
24. 24.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
25. 25.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
26. 26.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 3/4 (c) 1/8 (d) 1/4
27. 27.In which quadrant does the point (8, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
28. 28.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
29. 29.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 15 (c) 21 (d) 36
30. 30.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 631 (c) 492 (d) 630
31. 31.Using (a − b)² = a² − 2ab + b², what is 87²? (a) 8091 (b) 7579 (c) 8649 (d) 7569
32. 32.In a class of 19 children, 8 like maths, 10 like science and 3 like both. How many like at least one of the two? (a) 18 (b) 12 (c) 15 (d) 19
33. 33.Using (a − b)² = a² − 2ab + b², what is 68²? (a) 4896 (b) 4624 (c) 4634 (d) 5184
34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 15 (d) 30
35. 35.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 150 cu cm (c) 100 cu cm (d) 125 cu cm
36. 36.In a class of 48 children, 27 like mangoes, 26 like bananas and 10 like both. How many like neither? (a) 10 (b) 15 (c) 5 (d) 6
37. 37.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
38. 38.How many factors does 81 have? (a) 4 (b) 3 (c) 5 (d) 6
39. 39.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 48 (c) 135 (d) 45
40. 40.Two angles of a triangle are 50° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 60° (c) 120° (d) 130°

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