Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 278 · 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 straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 325° (b) 55° (c) 35° (d) 145°
2. 2.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) 22 (b) 29 (c) 21 (d) 28
3. 3.In a class of 24 children, 16 like dance, 8 like music and 2 like both. How many like only dance? (a) 6 (b) 16 (c) 2 (d) 14
4. 4.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
5. 5.In a class of 17 children, 12 like cricket, 11 like football and 8 like both. How many like only cricket? (a) 3 (b) 4 (c) 6 (d) 12
6. 6.In a class of 34 children, 14 like cricket, 17 like football and 6 like both. How many like at least one of the two? (a) 19 (b) 25 (c) 34 (d) 31
7. 7.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 6 cu cm (c) 8 cu cm (d) 16 cu cm
8. 8.How many prime numbers are there between 30 and 50? (a) 4 (b) 5 (c) 7 (d) 6
9. 9.How many factors does 61 have? (a) 3 (b) 4 (c) 1 (d) 2
10. 10.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 484 cu cm (c) 726 cu cm (d) 33 cu cm
11. 11.Two angles of a triangle are 70° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 135° (c) 110° (d) 45°
12. 12.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
13. 13.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
14. 14.A drawer has lots of white 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) 3 (c) 5 (d) 4
15. 15.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 145° (b) 120° (c) 85° (d) 95°
16. 16.In which quadrant does the point (6, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
17. 17.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 75° (b) 30° (c) 60° (d) 150°
18. 18.If a + b = 3 and ab = 2, what is (a − b)²? (a) 7 (b) 5 (c) 9 (d) 1
19. 19.A cube has edges of 12 cm. What is its volume? (a) 36 cu cm (b) 1728 cu cm (c) 864 cu cm (d) 576 cu cm
20. 20.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 96 cu cm (d) 64 cu cm
21. 21.Two angles of a triangle are 65° and 50°. What is the third angle? (a) 245° (b) 115° (c) 130° (d) 65°
22. 22.In a class of 31 children, 11 like dance, 23 like music and 8 like both. How many like only dance? (a) 3 (b) 15 (c) 11 (d) 8
23. 23.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 105° (d) 160°
24. 24.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
25. 25.What is the distance between the points (8, 9) and (20, 25)? (a) 20 (b) 21 (c) 28 (d) 400
26. 26.Using (a − b)² = a² − 2ab + b², what is 28²? (a) 1024 (b) 896 (c) 784 (d) 794
27. 27.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/4 (c) 1/2 (d) 2/3
28. 28.Using (a − b)² = a² − 2ab + b², what is 55²? (a) 3035 (b) 3575 (c) 4225 (d) 3025
29. 29.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 12 (b) 25 (c) 24 (d) 13
30. 30.A bag has 12 black balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 14 (b) 13 (c) 2 (d) 21
31. 31.Using (a − b)² = a² − 2ab + b², what is 16²? (a) 266 (b) 256 (c) 576 (d) 384
32. 32.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 156 (c) 91 (d) 169
33. 33.A bag has 7 green balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 8 (b) 13 (c) 2 (d) 9
34. 34.A bag has 6 green, 4 yellow and 7 red balls. One ball is taken out without looking. What is the probability that it is green? (a) 11/17 (b) 6/17 (c) 6/11 (d) 1/3
35. 35.What is the smallest prime factor of 49? (a) 2 (b) 3 (c) 7 (d) 1
36. 36.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
37. 37.In a class of 37 children, 18 like tea, 20 like coffee and 9 like both. How many like only tea? (a) 18 (b) 17 (c) 9 (d) 11
38. 38.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 16 (d) 24
39. 39.What is the smallest prime factor of 145? (a) 1 (b) 2 (c) 5 (d) 29
40. 40.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 125 times (c) 25 times (d) 5 times

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