Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 511 · 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 33 children, 23 like mangoes, 18 like bananas and 12 like both. How many like at least one of the two? (a) 17 (b) 33 (c) 41 (d) 29
2. 2.The mean of 3 numbers is 31. When the number 23 is added to them, what is the new mean? (a) 31 (b) 29 (c) 27 (d) 30
3. 3.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 213 (c) 223 (d) 220
4. 4.A cube has edges of 2 cm. What is its total surface area? (a) 24 sq cm (b) 16 sq cm (c) 4 sq cm (d) 8 sq cm
5. 5.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 63 (c) 60 (d) 20
6. 6.A bag has 7 green, 3 blue and 7 yellow balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 3/14 (c) 3/17 (d) 14/17
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 5/11 (c) 1/6 (d) 1/11
8. 8.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 170° (b) 190° (c) 11° (d) 10°
9. 9.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 225° (d) 90°
10. 10.In a class of 16 children, 10 like maths, 7 like science and 4 like both. How many like only maths? (a) 6 (b) 10 (c) 9 (d) 3
11. 11.How many prime numbers are there between 80 and 100? (a) 2 (b) 5 (c) 4 (d) 3
12. 12.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
13. 13.If a + b = 14 and ab = 45, what is a² + b²? (a) 106 (b) 151 (c) 196 (d) 286
14. 14.What is the mean of 3, 7, 12 and 10? (a) 8 (b) 9 (c) 10 (d) 7
15. 15.In a class of 43 children, 28 like cricket, 20 like football and 9 like both. How many like at least one of the two? (a) 43 (b) 39 (c) 30 (d) 48
16. 16.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 100° (b) 260° (c) 160° (d) 80°
17. 17.In a class of 38 children, 21 like tea, 20 like coffee and 4 like both. How many like at least one of the two? (a) 38 (b) 37 (c) 33 (d) 41
18. 18.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 4095 (c) 4186 (d) 8372
19. 19.A cuboid is 12 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 52 sq cm (b) 104 sq cm (c) 208 sq cm (d) 48 sq cm
20. 20.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 100 (c) 45 (d) 55
21. 21.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 210 (c) 105 (d) 120
22. 22.In a class of 34 children, 21 like cricket, 15 like football and 10 like both. How many like neither? (a) 10 (b) 18 (c) 9 (d) 8
23. 23.A drawer has lots of white, red 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) 2 (b) 6 (c) 3 (d) 4
24. 24.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x − 8)(x − 9) (c) (x + 1)(x + 72) (d) (x + 1)(x + 16)
25. 25.A bag has 3 yellow balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 4 (d) 14
26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 6 (b) 5 (c) 8 (d) 7
27. 27.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 20 (c) 100 (d) 45
28. 28.In a class of 24 children, 7 like mangoes, 15 like bananas and 2 like both. How many like at least one of the two? (a) 20 (b) 24 (c) 18 (d) 22
29. 29.In a class of 26 children, 17 like maths, 11 like science and 8 like both. How many like at least one of the two? (a) 28 (b) 20 (c) 12 (d) 26
30. 30.Using (a − b)² = a² − 2ab + b², what is 69²? (a) 4899 (b) 5041 (c) 4771 (d) 4761
31. 31.In which quadrant does the point (2, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
32. 32.A bag has 11 red 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) 12 (b) 14 (c) 4 (d) 2
33. 33.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
34. 34.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 16 (d) 24
35. 35.In a class of 27 children, 14 like tea, 13 like coffee and 10 like both. How many like at least one of the two? (a) 27 (b) 18 (c) 17 (d) 7
36. 36.In a class of 25 children, 19 like tea, 11 like coffee and 6 like both. How many like at least one of the two? (a) 24 (b) 25 (c) 18 (d) 30
37. 37.In a class of 39 children, 27 like mangoes, 20 like bananas and 3 like neither. How many like both? (a) 36 (b) 11 (c) 3 (d) 8
38. 38.A bag has 9 white balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 4 (c) 2 (d) 10
39. 39.How many factors does 40 have? (a) 6 (b) 8 (c) 9 (d) 7
40. 40.4 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 16 (b) 8 (c) 6 (d) 12

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