Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 431 · 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.In a class of 45 children, 23 like cricket, 25 like football and 8 like both. How many like neither? (a) 8 (b) 5 (c) 6 (d) 13
2. 2.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
3. 3.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 2/3 (c) 1/4 (d) 1/3
4. 4.In a class of 39 children, 27 like dance, 19 like music and 5 like neither. How many like both? (a) 12 (b) 5 (c) 7 (d) 34
5. 5.In a class of 32 children, 10 like dance, 24 like music and 5 like both. How many like only dance? (a) 5 (b) 19 (c) 8 (d) 10
6. 6.What is the midpoint of the line joining (7, 8) and (11, 2)? (a) (18, 10) (b) (5, 9) (c) (9, 5) (d) (2, 3)
7. 7.How many prime numbers are there between 20 and 50? (a) 9 (b) 7 (c) 8 (d) 6
8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 7 (b) 6 (c) 8 (d) 5
9. 9.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 16 (c) 12 (d) 48
10. 10.What is the prime factorisation of 90? (a) 2³ × 3² × 5 (b) 2 × 3² × 5² (c) 2 × 3² × 5 (d) 2² × 3² × 5
11. 11.The mean of 4 numbers is 40. When the number 30 is added to them, what is the new mean? (a) 35 (b) 38 (c) 40 (d) 39
12. 12.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
13. 13.Using (a − b)² = a² − 2ab + b², what is 48²? (a) 2314 (b) 2304 (c) 2704 (d) 2496
14. 14.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 21 (b) 14 (c) 15 (d) 22
15. 15.A cube has edges of 10 cm. What is its total surface area? (a) 1000 sq cm (b) 600 sq cm (c) 400 sq cm (d) 100 sq cm
16. 16.Which is the correct factorisation of x² + 11x + 24? (a) (x + 1)(x + 24) (b) (x + 3)(x + 8) (c) (x + 1)(x + 10) (d) (x − 3)(x − 8)
17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 17 (b) 16 (c) 15 (d) 6
18. 18.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 373 (b) 372 (c) 363 (d) 320
19. 19.In a class of 29 children, 23 like tea, 9 like coffee and 4 like both. How many like only tea? (a) 5 (b) 19 (c) 20 (d) 23
20. 20.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 3/4 (c) 1/3 (d) 1/4
21. 21.What is the distance between the points (7, 8) and (12, 20)? (a) 13 (b) 169 (c) 17 (d) 14
22. 22.What is the median of 34, 38, 32, 3, 19, 23 and 12? (a) 23 (b) 3 (c) 32 (d) 19
23. 23.Using (a − b)² = a² − 2ab + b², what is 39²? (a) 1681 (b) 1599 (c) 1531 (d) 1521
24. 24.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) 37 (c) 36 (d) 24
25. 25.In which quadrant does the point (2, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
26. 26.What is the median of 2, 16, 36, 32, 29, 28 and 27? (a) 28 (b) 29 (c) 27 (d) 32
27. 27.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
28. 28.What is the smallest prime factor of 51? (a) 2 (b) 17 (c) 1 (d) 3
29. 29.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
30. 30.What is the product of the roots of x² − 11x + 24 = 0? (a) 11 (b) 24 (c) 23 (d) 25
31. 31.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
32. 32.Which term of the AP 1, 5, 9, 13, … is 93? (a) 26th (b) 25th (c) 23rd (d) 24th
33. 33.A drawer has lots of black, white 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) 4 (b) 2 (c) 6 (d) 3
34. 34.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 15 (c) 20 (d) 25
35. 35.What is the mean of 16, 15, 19 and 10? (a) 20 (b) 12 (c) 15 (d) 16
36. 36.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 42 (c) 49 (d) 28
37. 37.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 120° (c) 150° (d) 30°
38. 38.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
39. 39.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/6 (b) 1/5 (c) 1/3 (d) 5/6
40. 40.How many factors does 98 have? (a) 6 (b) 7 (c) 4 (d) 5

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