Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 859 · 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 canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 11 (c) 24 (d) 32
2. 2.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/3 (c) 3/4 (d) 1/2
3. 3.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 25° (d) 50°
4. 4.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 10° (c) 50° (d) 80°
5. 5.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 42 (c) 49 (d) 21
6. 6.Using (a + b)² = a² + 2ab + b², what is 52²? (a) 2304 (b) 2704 (c) 2714 (d) 2504
7. 7.In a league, 8 teams each play every other team once. How many matches are played? (a) 64 (b) 56 (c) 28 (d) 36
8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 18 (d) 17
9. 9.What is the mean of 6, 10, 6 and 2? (a) 6 (b) 8 (c) 5 (d) 7
10. 10.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/3 (c) 2/3 (d) 1/2
11. 11.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 1/4 (c) 3/5 (d) 3/8
12. 12.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 9 (d) 12
13. 13.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) 37 (b) 48 (c) 49 (d) 36
14. 14.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 162 (c) 18 (d) 57
15. 15.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 50° (b) 40° (c) 140° (d) 320°
16. 16.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
17. 17.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) 8 (d) 14
18. 18.A drawer has lots of white, blue, black, yellow 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) 6 (b) 10 (c) 2 (d) 5
19. 19.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 48 (d) 24
20. 20.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 140° (b) 155° (c) 65° (d) 115°
21. 21.A bag has 6 green, 3 red and 7 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 13/16 (b) 3/13 (c) 3/16 (d) 1/3
22. 22.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 18 (d) 36
23. 23.The mean of 3 numbers is 15. When the number 23 is added to them, what is the new mean? (a) 19 (b) 15 (c) 17 (d) 18
24. 24.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 20 (d) 11
25. 25.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
26. 26.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 30° (b) 210° (c) 105° (d) 150°
27. 27.A cuboid is 3 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 54 sq cm (b) 51 sq cm (c) 102 sq cm (d) 204 sq cm
28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 4 (b) 3 (c) 2 (d) 1
29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 8 (b) 19 (c) 18 (d) 17
30. 30.What is the mean of 4, 15, 11, 18 and 12? (a) 15 (b) 12 (c) 13 (d) 10
31. 31.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 24 (c) 12 (d) 48
32. 32.A bag has 3 white, 3 blue and 7 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 3/13 (b) 3/10 (c) 1/3 (d) 10/13
33. 33.In which quadrant does the point (9, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
34. 34.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 110 (c) 55 (d) 121
35. 35.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 304 (c) 303 (d) 294
36. 36.What is the sum of the first 10 terms of the AP 3, 8, 13, …? (a) 280 (b) 255 (c) 48 (d) 510
37. 37.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
38. 38.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
39. 39.In which quadrant does the point (−9, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
40. 40.In a class of 39 children, 15 like dance, 22 like music and 5 like both. How many like neither? (a) 2 (b) 5 (c) 12 (d) 7

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