Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 389 · 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 32 children, 17 like maths, 23 like science and 11 like both. How many like at least one of the two? (a) 40 (b) 29 (c) 32 (d) 18
2. 2.A bag has 6 black balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 8 (c) 7 (d) 14
3. 3.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 36 (c) 30 (d) 60
4. 4.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 196 (c) 105 (d) 91
5. 5.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/2 (c) 1/4 (d) 1/3
6. 6.How many factors does 32 have? (a) 4 (b) 5 (c) 6 (d) 7
7. 7.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 244 (c) 351 (d) 243
8. 8.In which quadrant does the point (4, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
9. 9.What is the sum of the first 9 terms of the AP 3, 7, 11, …? (a) 189 (b) 342 (c) 35 (d) 171
10. 10.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
11. 11.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 100 (c) 90 (d) 45
12. 12.What is the smallest prime factor of 93? (a) 2 (b) 3 (c) 31 (d) 1
13. 13.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 27 sq cm (c) 54 sq cm (d) 9 sq cm
14. 14.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 30° (c) 140° (d) 40°
15. 15.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 225 (c) 105 (d) 210
16. 16.What is the prime factorisation of 252? (a) 2² × 3² × 7 (b) 2 × 3² × 7² (c) 2 × 3² × 7 (d) 2³ × 3² × 7
17. 17.Using (a − b)² = a² − 2ab + b², what is 37²? (a) 1591 (b) 1849 (c) 1369 (d) 1379
18. 18.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 90 (c) 89 (d) 80
19. 19.What is the mean of 15, 16, 6 and 15? (a) 12 (b) 13 (c) 14 (d) 15
20. 20.In which quadrant does the point (−8, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
21. 21.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/11 (c) 1/12 (d) 1/9
23. 23.What is the mean of 3, 14, 14, 4 and 20? (a) 11 (b) 13 (c) 10 (d) 12
24. 24.In a class of 40 children, 17 like cricket, 25 like football and 3 like neither. How many like both? (a) 2 (b) 5 (c) 37 (d) 3
25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 2/11 (c) 1/11 (d) 1/18
26. 26.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 1/4 (c) 3/4 (d) 3/8
27. 27.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 5/8 (c) 3/5 (d) 3/8
28. 28.What is the distance between the points (5, 19) and (14, 7)? (a) 225 (b) 16 (c) 15 (d) 21
29. 29.If a + b = 7 and ab = 12, what is a² + b²? (a) 37 (b) 73 (c) 25 (d) 49
30. 30.In a class of 48 children, 27 like cricket, 24 like football and 7 like both. How many like at least one of the two? (a) 48 (b) 44 (c) 51 (d) 37
31. 31.A bag has 7 red balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 13 (b) 8 (c) 2 (d) 9
32. 32.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 70° (b) 115° (c) 135° (d) 110°
33. 33.A bag has 7 black balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 15 (c) 8 (d) 2
34. 34.In a class of 19 children, 7 like cricket, 12 like football and 2 like both. How many like only cricket? (a) 7 (b) 10 (c) 5 (d) 2
35. 35.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 45° (c) 135° (d) 90°
36. 36.How many prime numbers are there between 30 and 50? (a) 4 (b) 5 (c) 6 (d) 7
37. 37.In which quadrant does the point (3, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
38. 38.A cuboid is 7 cm long, 2 cm wide and 3 cm high. What is its volume? (a) 42 cu cm (b) 12 cu cm (c) 82 cu cm (d) 14 cu cm
39. 39.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 48 (c) 24 (d) 12
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/9 (b) 4/11 (c) 1/11 (d) 5/36

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