Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 57 · 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 league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 55 (c) 121 (d) 110
2. 2.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 7/8 (c) 1/4 (d) 1/8
3. 3.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 15 (c) 21 (d) 30
4. 4.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 144 (c) 48 (d) 16
5. 5.In a class of 28 children, 11 like maths, 13 like science and 4 like both. How many like only maths? (a) 15 (b) 11 (c) 9 (d) 7
6. 6.A bag has 8 white balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 9 (c) 2 (d) 8
7. 7.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 35° (b) 145° (c) 100° (d) 115°
8. 8.In which quadrant does the point (−9, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
9. 9.What is the mode of 3, 2, 1, 2, 3, 17 and 2? (a) 1 (b) 17 (c) 3 (d) 2
10. 10.What is the midpoint of the line joining (4, 0) and (12, 4)? (a) (8, 2) (b) (16, 4) (c) (4, 2) (d) (2, 8)
11. 11.How many prime numbers are there between 60 and 90? (a) 8 (b) 6 (c) 7 (d) 9
12. 12.What is the missing term in the AP 9, ?, 27, 36, 45? (a) 18 (b) 27 (c) 17 (d) 19
13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/11 (c) 1/12 (d) 1/18
14. 14.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
15. 15.How many factors does 81 have? (a) 4 (b) 3 (c) 6 (d) 5
16. 16.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 20 (c) 25 (d) 10
17. 17.What is the sum of the first 10 terms of the AP 5, 11, 17, …? (a) 320 (b) 59 (c) 350 (d) 640
18. 18.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
19. 19.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 48 (c) 12 (d) 24
20. 20.A cuboid is 9 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 84 sq cm (b) 108 sq cm (c) 168 sq cm (d) 336 sq cm
21. 21.What is the distance between the points (5, 9) and (17, 18)? (a) 16 (b) 15 (c) 225 (d) 21
22. 22.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 65° (c) 130° (d) 40°
23. 23.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) 48 (b) 37 (c) 36 (d) 49
24. 24.What is the 13th term of the AP 9, 15, 21, 27, …? (a) 81 (b) 72 (c) 78 (d) 87
25. 25.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 100 (c) 20 (d) 90
26. 26.Using (a − b)² = a² − 2ab + b², what is 47²? (a) 2219 (b) 2491 (c) 2809 (d) 2209
27. 27.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 65° (b) 135° (c) 115° (d) 160°
28. 28.In a class of 33 children, 16 like maths, 16 like science and 5 like both. How many like neither? (a) 5 (b) 6 (c) 11 (d) 1
29. 29.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 24 (c) 25 (d) 36
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/11 (c) 1/18 (d) 1/36
31. 31.If a + b = 8 and ab = 15, what is a² + b²? (a) 64 (b) 34 (c) 49 (d) 94
32. 32.If a + b = 7 and ab = 10, what is (a − b)²? (a) 49 (b) 29 (c) 9 (d) 3
33. 33.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/4 (c) 1/8 (d) 3/8
34. 34.In a class of 36 children, 19 like cricket, 21 like football and 12 like both. How many like neither? (a) 9 (b) 12 (c) 8 (d) 20
35. 35.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 145° (d) 70°
36. 36.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
37. 37.In a class of 29 children, 10 like dance, 19 like music and 3 like both. How many like only dance? (a) 3 (b) 7 (c) 10 (d) 16
38. 38.How many prime numbers are there between 30 and 60? (a) 6 (b) 7 (c) 8 (d) 9
39. 39.What is the mode of 4, 4, 17, 4, 17, 2 and 15? (a) 17 (b) 2 (c) 4 (d) 15
40. 40.A bag has 5 green balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 6 (c) 8 (d) 4

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