Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 594 · 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 angles of a triangle are 55° and 20°. What is the third angle? (a) 75° (b) 105° (c) 160° (d) 125°
2. 2.A drawer has lots of red and blue 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) 4 (c) 3 (d) 2
3. 3.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 5 (c) 45 (d) 15
4. 4.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 65° (b) 335° (c) 25° (d) 155°
5. 5.A bag has 4 blue, 2 white and 5 red balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 7/11 (b) 4/11 (c) 1/3 (d) 8/11
6. 6.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 75 (c) 72 (d) 216
7. 7.A cuboid is 6 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 18 cu cm (b) 12 cu cm (c) 90 cu cm (d) 54 cu cm
8. 8.5 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 30 (b) 50 (c) 10 (d) 25
9. 9.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 198 (c) 66 (d) 69
10. 10.How many prime numbers are there between 40 and 70? (a) 6 (b) 8 (c) 7 (d) 9
11. 11.A drawer has lots of red, yellow, blue, green 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) 2 (b) 5 (c) 6 (d) 10
12. 12.6 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 24 (c) 48 (d) 30
13. 13.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 25 (d) 240
14. 14.What is the mean of 12, 20, 3, 6 and 19? (a) 10 (b) 13 (c) 12 (d) 15
15. 15.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 121 (c) 66 (d) 55
16. 16.What is the mode of 1, 9, 5, 1, 14, 14 and 1? (a) 9 (b) 14 (c) 1 (d) 5
17. 17.What is the prime factorisation of 15? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5² (d) 3 × 5
18. 18.If a + b = 16 and ab = 60, what is a² + b²? (a) 196 (b) 376 (c) 136 (d) 256
19. 19.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 45 (c) 90 (d) 100
20. 20.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 30 (c) 36 (d) 15
21. 21.The mean of 5 numbers is 36. When the number 30 is added to them, what is the new mean? (a) 36 (b) 35 (c) 34 (d) 33
22. 22.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 14 (b) 126 (c) 42 (d) 45
23. 23.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 5 (d) 4
24. 24.What is the distance between the points (9, 15) and (24, 7)? (a) 23 (b) 18 (c) 17 (d) 289
25. 25.What is the mode of 4, 7, 4, 4, 8, 3 and 8? (a) 8 (b) 4 (c) 7 (d) 3
26. 26.What is the median of 23, 26, 18, 28, 22, 16 and 34? (a) 28 (b) 23 (c) 26 (d) 22
27. 27.Which term of the AP 7, 13, 19, 25, … is 193? (a) 31st (b) 32nd (c) 33rd (d) 34th
28. 28.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 160° (d) 145°
29. 29.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 20° (c) 70° (d) 340°
30. 30.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 135° (c) 91° (d) 90°
31. 31.What is the 29th term of the AP 15, 21, 27, 33, …? (a) 174 (b) 168 (c) 183 (d) 189
32. 32.If a + b = 20 and ab = 99, what is a² + b²? (a) 202 (b) 400 (c) 301 (d) 598
33. 33.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 72 (c) 36 (d) 45
34. 34.There are 5 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 40 (b) 35 (c) 12 (d) 70
35. 35.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 43 (c) 253 (d) 484
36. 36.What is the median of 6, 29, 21, 1 and 9? (a) 10 (b) 9 (c) 6 (d) 21
37. 37.In a class of 42 children, 18 like cricket, 27 like football and 11 like both. How many like only cricket? (a) 15 (b) 7 (c) 18 (d) 16
38. 38.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
39. 39.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 16 (c) 24 (d) 12
40. 40.In a class of 50 children, 21 like dance, 23 like music and 4 like both. How many like at least one of the two? (a) 40 (b) 36 (c) 44 (d) 50

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