Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 678 · 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. 1.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 210 (c) 225 (d) 105
2. 2.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 615 (c) 488 (d) 625
3. 3.In a class of 50 children, 27 like dance, 26 like music and 9 like both. How many like only dance? (a) 18 (b) 24 (c) 27 (d) 17
4. 4.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 153 (c) 51 (d) 17
5. 5.In a class of 32 children, 17 like dance, 16 like music and 2 like neither. How many like both? (a) 1 (b) 2 (c) 3 (d) 30
6. 6.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 11 (b) 36 (c) 42 (d) 72
7. 7.The mean of 9 numbers is 34. When the number 14 is added to them, what is the new mean? (a) 34 (b) 24 (c) 33 (d) 32
8. 8.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 5 (c) 12 (d) 9
9. 9.What is the smallest prime factor of 55? (a) 11 (b) 1 (c) 2 (d) 5
10. 10.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 28 (c) 49 (d) 21
11. 11.What is the distance between the points (9, 6) and (21, 11)? (a) 14 (b) 169 (c) 13 (d) 17
12. 12.A drawer has lots of yellow, blue and red 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
13. 13.What is the median of 1, 13, 9, 29 and 12? (a) 11 (b) 12 (c) 9 (d) 13
14. 14.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
15. 15.Two angles of a triangle are 25° and 70°. What is the exterior angle at the third corner? (a) 95° (b) 155° (c) 110° (d) 85°
16. 16.What is the prime factorisation of 360? (a) 2⁴ × 3² × 5 (b) 2³ × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5³
17. 17.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 105 (c) 120 (d) 225
18. 18.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
19. 19.What is the midpoint of the line joining (7, 7) and (19, 1)? (a) (4, 13) (b) (6, 3) (c) (26, 8) (d) (13, 4)
20. 20.A cuboid is 3 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 12 sq cm (b) 32 sq cm (c) 64 sq cm (d) 16 sq cm
21. 21.A drawer has lots of red, green, blue, yellow 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) 2 (b) 5 (c) 6 (d) 10
22. 22.What is the distance between the points (6, 18) and (15, 6)? (a) 16 (b) 15 (c) 21 (d) 225
23. 23.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
24. 24.Two angles of a triangle are 70° and 45°. What is the exterior angle at the third corner? (a) 110° (b) 115° (c) 135° (d) 65°
25. 25.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
26. 26.How many prime numbers are there between 40 and 60? (a) 6 (b) 7 (c) 5 (d) 4
27. 27.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 504 (b) 264 (c) 32 (d) 252
28. 28.A cuboid is 7 cm long, 3 cm wide and 4 cm high. What is its total surface area? (a) 122 sq cm (b) 84 sq cm (c) 244 sq cm (d) 61 sq cm
29. 29.Which term of the AP 6, 8, 10, 12, … is 66? (a) 33rd (b) 31st (c) 30th (d) 32nd
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/12 (c) 3/11 (d) 1/11
31. 31.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 50° (b) 115° (c) 130° (d) 230°
32. 32.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 156 (c) 78 (d) 144
33. 33.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
34. 34.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2² × 5 (c) 2 × 5³ (d) 2³ × 5
35. 35.What is the midpoint of the line joining (10, 6) and (12, 12)? (a) (1, 3) (b) (22, 18) (c) (11, 9) (d) (9, 11)
36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 20 (d) 9
37. 37.A bag has 5 blue balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 6 (c) 7 (d) 8
38. 38.How many factors does 74 have? (a) 3 (b) 5 (c) 4 (d) 2
39. 39.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 15 cu cm (c) 150 cu cm (d) 125 cu cm
40. 40.In a class of 28 children, 15 like cricket, 18 like football and 2 like neither. How many like both? (a) 26 (b) 5 (c) 7 (d) 2

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