Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 528 · 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 how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 6 (d) 3
2. 2.What is the sum of the first 11 terms of the AP 8, 12, 16, …? (a) 616 (b) 48 (c) 308 (d) 330
3. 3.Which term of the AP 1, 8, 15, 22, … is 64? (a) 12th (b) 11th (c) 9th (d) 10th
4. 4.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 49 sq cm (c) 294 sq cm (d) 196 sq cm
5. 5.Which term of the AP 14, 20, 26, 32, … is 80? (a) 11th (b) 14th (c) 12th (d) 13th
6. 6.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 25 (c) 21 (d) 20
7. 7.What is the sum of the roots of x² − 10x + 16 = 0? (a) 9 (b) 11 (c) 10 (d) 16
8. 8.What is the median of 22, 7, 11, 30 and 19? (a) 19 (b) 11 (c) 22 (d) 20
9. 9.A bag has 6 yellow, 4 red and 6 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 3/4 (c) 1/4 (d) 13/16
10. 10.Using (a − b)² = a² − 2ab + b², what is 35²? (a) 1235 (b) 1575 (c) 1225 (d) 2025
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
12. 12.Using (a + b)² = a² + 2ab + b², what is 72²? (a) 5194 (b) 4624 (c) 4904 (d) 5184
13. 13.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 105 (c) 182 (d) 196
14. 14.How many factors does 66 have? (a) 9 (b) 6 (c) 7 (d) 8
15. 15.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 45 (c) 81 (d) 36
16. 16.A bag has 5 red, 8 blue and 7 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/4 (b) 1/3 (c) 3/4 (d) 3/10
17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 5 (b) 7 (c) 4 (d) 6
18. 18.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
19. 19.A bag has 7 red, 9 green and 2 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 8/9 (c) 1/9 (d) 1/8
20. 20.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) 22 (b) 14 (c) 15 (d) 21
21. 21.What is the 15th term of the AP 18, 27, 36, 45, …? (a) 144 (b) 135 (c) 153 (d) 126
22. 22.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 155° (b) 60° (c) 145° (d) 120°
23. 23.In a class of 35 children, 21 like mangoes, 15 like bananas and 6 like both. How many like only mangoes? (a) 21 (b) 9 (c) 20 (d) 15
24. 24.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
25. 25.A drawer has lots of blue, red 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) 6 (c) 4 (d) 3
26. 26.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 93 (c) 84 (d) 102
27. 27.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 14 (c) 21 (d) 49
28. 28.In a class of 33 children, 17 like dance, 17 like music and 6 like both. How many like only dance? (a) 6 (b) 11 (c) 16 (d) 17
29. 29.A cuboid is 4 cm long, 3 cm wide and 6 cm high. What is its volume? (a) 12 cu cm (b) 13 cu cm (c) 72 cu cm (d) 108 cu cm
30. 30.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 240 (c) 20 (d) 120
31. 31.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 65° (c) 115° (d) 125°
32. 32.What is the mean of 4, 11, 6 and 7? (a) 6 (b) 9 (c) 7 (d) 8
33. 33.In which quadrant does the point (1, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
34. 34.7 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) 35 (b) 56 (c) 28 (d) 11
35. 35.4 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) 24 (b) 9 (c) 20 (d) 40
36. 36.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 305° (c) 55° (d) 125°
37. 37.A drawer has lots of white, 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) 6 (c) 3 (d) 2
38. 38.What is the sum of all the whole numbers from 1 to 15? (a) 121 (b) 240 (c) 120 (d) 105
39. 39.In a class of 45 children, 18 like maths, 24 like science and 9 like neither. How many like both? (a) 9 (b) 36 (c) 6 (d) 7
40. 40.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 91° (c) 135° (d) 90°

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