Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 147 · 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.What is the median of 1, 13, 2, 20, 18, 16 and 33? (a) 18 (b) 20 (c) 16 (d) 13
2. 2.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
3. 3.Two angles of a triangle are 55° and 65°. What is the exterior angle at the third corner? (a) 60° (b) 115° (c) 120° (d) 125°
4. 4.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/5 (b) 1/3 (c) 5/6 (d) 1/6
5. 5.A drawer has lots of green, white, black, 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) 5 (b) 6 (c) 10 (d) 2
6. 6.A bag has 8 blue balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 19 (b) 9 (c) 2 (d) 10
7. 7.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 8 (c) 24 (d) 72
8. 8.6 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) 11 (b) 30 (c) 60 (d) 36
9. 9.The mean of 9 numbers is 36. When the number 76 is added to them, what is the new mean? (a) 56 (b) 36 (c) 40 (d) 41
10. 10.What is the distance between the points (5, 2) and (10, 14)? (a) 14 (b) 17 (c) 13 (d) 169
11. 11.A bag has 4 black balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 9 (c) 5 (d) 6
12. 12.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 10 (c) 20 (d) 21
13. 13.Using (a − b)² = a² − 2ab + b², what is 29²? (a) 899 (b) 851 (c) 961 (d) 841
14. 14.In a class of 31 children, 8 like mangoes, 18 like bananas and 4 like both. How many like at least one of the two? (a) 18 (b) 22 (c) 26 (d) 31
15. 15.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 50° (d) 100°
16. 16.A bag has 4 yellow, 3 red and 8 white balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 4/5 (c) 4/15 (d) 11/15
17. 17.Using (a − b)² = a² − 2ab + b², what is 45²? (a) 3025 (b) 2475 (c) 2035 (d) 2025
18. 18.In a class of 42 children, 21 like cricket, 24 like football and 5 like both. How many like only cricket? (a) 16 (b) 21 (c) 19 (d) 18
19. 19.How many prime numbers are there between 80 and 90? (a) 1 (b) 3 (c) 2 (d) 4
20. 20.In a class of 50 children, 28 like cricket, 28 like football and 11 like both. How many like at least one of the two? (a) 56 (b) 34 (c) 50 (d) 45
21. 21.What is the midpoint of the line joining (1, 2) and (11, 8)? (a) (6, 5) (b) (5, 3) (c) (12, 10) (d) (5, 6)
22. 22.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 48 (c) 37 (d) 49
23. 23.Using (a + b)² = a² + 2ab + b², what is 92²? (a) 7744 (b) 8464 (c) 8104 (d) 8474
24. 24.A drawer has lots of red, yellow, black 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) 8 (b) 5 (c) 2 (d) 4
25. 25.What is the 23rd term of the AP 4, 11, 18, 25, …? (a) 154 (b) 165 (c) 158 (d) 161
26. 26.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/12 (c) 1/11 (d) 1/18
27. 27.What is the distance between the points (1, 30) and (8, 6)? (a) 26 (b) 25 (c) 31 (d) 625
28. 28.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 693 sq cm
29. 29.What is the 15th term of the AP 2, 6, 10, 14, …? (a) 56 (b) 62 (c) 60 (d) 58
30. 30.In a class of 39 children, 18 like mangoes, 24 like bananas and 4 like both. How many like at least one of the two? (a) 39 (b) 42 (c) 38 (d) 34
31. 31.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 10 (d) 8
32. 32.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 40° (c) 65° (d) 130°
33. 33.What is the median of 38, 11, 10, 24, 21, 18 and 17? (a) 21 (b) 18 (c) 17 (d) 24
34. 34.Two angles of a triangle are 20° and 125°. What is the exterior angle at the third corner? (a) 55° (b) 35° (c) 145° (d) 160°
35. 35.What is the smallest prime factor of 55? (a) 11 (b) 1 (c) 5 (d) 2
36. 36.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
37. 37.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 30° (c) 120° (d) 60°
38. 38.What is the midpoint of the line joining (2, 3) and (8, 5)? (a) (4, 5) (b) (10, 8) (c) (5, 4) (d) (3, 1)
39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 17 (d) 18
40. 40.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 176 sq cm

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