Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 387 · 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 45 children, 23 like maths, 26 like science and 6 like both. How many like only maths? (a) 23 (b) 20 (c) 19 (d) 17
2. 2.In a class of 31 children, 15 like maths, 15 like science and 3 like both. How many like only maths? (a) 3 (b) 16 (c) 12 (d) 15
3. 3.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
4. 4.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 50° (c) 40° (d) 140°
5. 5.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 48 (d) 24
6. 6.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 20 (c) 25 (d) 240
7. 7.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
8. 8.A bag has 11 black balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 17 (b) 12 (c) 13 (d) 2
9. 9.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 225 (c) 120 (d) 105
10. 10.What is the 17th term of the AP 8, 12, 16, 20, …? (a) 68 (b) 76 (c) 64 (d) 72
11. 11.What is the sum of all the whole numbers from 1 to 48? (a) 1152 (b) 2352 (c) 1176 (d) 1128
12. 12.A bag has 9 green, 2 yellow and 7 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 8/9 (b) 1/3 (c) 1/8 (d) 1/9
13. 13.What is the smallest prime factor of 209? (a) 19 (b) 1 (c) 2 (d) 11
14. 14.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 10 (c) 20 (d) 15
15. 15.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 5/8 (c) 3/8 (d) 3/5
16. 16.How many factors does 101 have? (a) 2 (b) 4 (c) 1 (d) 3
17. 17.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 2/3 (d) 5/6
18. 18.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 32 (b) 185 (c) 200 (d) 370
19. 19.In a class of 30 children, 21 like cricket, 8 like football and 5 like both. How many like at least one of the two? (a) 19 (b) 29 (c) 30 (d) 24
20. 20.Two straight lines cross. Two vertically opposite angles add up to 340°. What is each of the other two angles? (a) 11° (b) 10° (c) 170° (d) 20°
21. 21.What is the distance between the points (0, 12) and (12, 7)? (a) 169 (b) 14 (c) 17 (d) 13
22. 22.What is the mode of 4, 16, 16, 15, 10, 16 and 10? (a) 4 (b) 16 (c) 15 (d) 10
23. 23.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
24. 24.In which quadrant does the point (−2, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
25. 25.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
26. 26.A drawer has lots of red, black, green, 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) 6 (c) 5 (d) 10
27. 27.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 40° (b) 100° (c) 280° (d) 140°
28. 28.In a class of 48 children, 27 like maths, 25 like science and 9 like both. How many like at least one of the two? (a) 34 (b) 52 (c) 43 (d) 48
29. 29.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 70° (b) 135° (c) 110° (d) 155°
30. 30.In a class of 33 children, 20 like maths, 14 like science and 3 like both. How many like at least one of the two? (a) 34 (b) 28 (c) 33 (d) 31
31. 31.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
32. 32.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 24 (c) 144 (d) 132
33. 33.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 2 times (d) 8 times
34. 34.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
35. 35.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
36. 36.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 150° (d) 30°
37. 37.A bag has 8 blue, 4 green and 4 white balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 9/16 (c) 1/16 (d) 1/2
38. 38.What is the smallest prime factor of 49? (a) 7 (b) 3 (c) 2 (d) 1
39. 39.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 240 (c) 20 (d) 120
40. 40.What is the midpoint of the line joining (0, 3) and (8, 9)? (a) (4, 3) (b) (4, 6) (c) (6, 4) (d) (8, 12)

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