Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 727 · 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.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
2. 2.Using (a − b)² = a² − 2ab + b², what is 87²? (a) 8649 (b) 7579 (c) 8091 (d) 7569
3. 3.In a class of 34 children, 11 like cricket, 19 like football and 5 like both. How many like only cricket? (a) 15 (b) 6 (c) 11 (d) 14
4. 4.In which quadrant does the point (−1, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
5. 5.What is the sum of all the whole numbers from 1 to 63? (a) 1953 (b) 2017 (c) 2016 (d) 4032
6. 6.A bag has 7 yellow, 5 white and 4 red balls. One ball is taken out without looking. What is the probability that it is not white? (a) 3/4 (b) 1/3 (c) 11/16 (d) 5/16
7. 7.What is the sum of the first 5 terms of the AP 10, 12, 14, …? (a) 70 (b) 75 (c) 18 (d) 140
8. 8.In a class of 26 children, 13 like mangoes, 18 like bananas and 1 like neither. How many like both? (a) 25 (b) 1 (c) 6 (d) 5
9. 9.What is the missing term in the AP 16, 23, 30, ?, 44? (a) 36 (b) 44 (c) 38 (d) 37
10. 10.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 15 (c) 14 (d) 8
11. 11.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) 20 (c) 60 (d) 63
12. 12.What is the sum of all the whole numbers from 1 to 98? (a) 4802 (b) 4753 (c) 4851 (d) 9702
13. 13.What is the sum of all the whole numbers from 1 to 78? (a) 3042 (b) 3081 (c) 3003 (d) 6162
14. 14.A drawer has lots of green, yellow, blue, white 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) 5 (b) 6 (c) 2 (d) 10
15. 15.A drawer has lots of blue, black, yellow, 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) 10 (c) 5 (d) 6
16. 16.A cube has edges of 11 cm. What is its total surface area? (a) 726 sq cm (b) 1331 sq cm (c) 121 sq cm (d) 484 sq cm
17. 17.What is the smallest prime factor of 33? (a) 11 (b) 3 (c) 1 (d) 2
18. 18.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
19. 19.What is the prime factorisation of 48? (a) 2⁴ × 3 (b) 2 × 3⁴ (c) 2³ × 3 (d) 2⁵ × 3
20. 20.In which quadrant does the point (1, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
21. 21.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 60° (c) 30° (d) 120°
22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 6 (b) 5 (c) 4 (d) 7
23. 23.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
24. 24.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
25. 25.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 21 (c) 22 (d) 29
26. 26.In a class of 34 children, 19 like tea, 15 like coffee and 9 like both. How many like at least one of the two? (a) 26 (b) 16 (c) 25 (d) 34
27. 27.How many factors does 99 have? (a) 5 (b) 4 (c) 6 (d) 7
28. 28.A bag has 9 white balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 10 (c) 16 (d) 8
29. 29.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
30. 30.What is the mean of 12, 20, 7, 11 and 15? (a) 15 (b) 14 (c) 12 (d) 13
31. 31.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 135° (c) 45° (d) 90°
32. 32.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 46° (c) 45° (d) 90°
33. 33.In a class of 27 children, 18 like tea, 7 like coffee and 2 like both. How many like at least one of the two? (a) 27 (b) 25 (c) 23 (d) 21
34. 34.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 120 (c) 25 (d) 20
35. 35.There are 5 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 60 (b) 35 (c) 30 (d) 11
36. 36.In which quadrant does the point (−2, −5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
37. 37.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 55 (d) 110
38. 38.What is the prime factorisation of 45? (a) 3 × 5 (b) 3³ × 5 (c) 3² × 5 (d) 3 × 5²
39. 39.A drawer has lots of white, red, green, yellow 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) 2 (b) 5 (c) 10 (d) 6
40. 40.3 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 36 (c) 21 (d) 18

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