Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 495 · 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.What is the smallest prime factor of 121? (a) 2 (b) 3 (c) 1 (d) 11
2. 2.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 1/8 (c) 1/4 (d) 7/8
3. 3.Which is the correct factorisation of x² + 7x + 12? (a) (x + 1)(x + 6) (b) (x + 1)(x + 12) (c) (x + 3)(x + 4) (d) (x − 3)(x − 4)
4. 4.What is the 18th term of the AP 7, 12, 17, 22, …? (a) 90 (b) 92 (c) 97 (d) 85
5. 5.What is the smallest prime factor of 49? (a) 2 (b) 1 (c) 7 (d) 3
6. 6.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 100° (d) 155°
7. 7.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 110° (b) 70° (c) 145° (d) 105°
8. 8.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 42 (c) 21 (d) 28
9. 9.What is the mode of 3, 7, 15, 15, 5, 7 and 7? (a) 3 (b) 7 (c) 5 (d) 15
10. 10.What is the 18th term of the AP 2, 8, 14, 20, …? (a) 108 (b) 104 (c) 110 (d) 102
11. 11.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 70° (d) 60°
12. 12.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/4
13. 13.A bag has 5 white balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 6 (b) 2 (c) 7 (d) 8
14. 14.What is the mean of 18, 6, 19, 20 and 17? (a) 20 (b) 17 (c) 16 (d) 15
15. 15.What is the missing term in the AP 18, ?, 30, 36, 42? (a) 24 (b) 25 (c) 30 (d) 23
16. 16.How many prime numbers are there between 40 and 60? (a) 4 (b) 6 (c) 5 (d) 7
17. 17.There are 3 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 21 (c) 10 (d) 42
18. 18.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 12 (b) 10 (c) 11 (d) 13
19. 19.In a class of 42 children, 26 like tea, 16 like coffee and 10 like both. How many like only tea? (a) 10 (b) 6 (c) 16 (d) 26
20. 20.What is the missing term in the AP 6, 12, ?, 24, 30? (a) 18 (b) 19 (c) 24 (d) 17
21. 21.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
22. 22.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
23. 23.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/18 (c) 1/36 (d) 1/11
25. 25.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 15 (d) 36
26. 26.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 15 (c) 10 (d) 20
27. 27.How many prime numbers are there between 50 and 70? (a) 3 (b) 6 (c) 5 (d) 4
28. 28.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 78 (c) 132 (d) 144
29. 29.What is the mean of 3, 4, 16, 7 and 5? (a) 7 (b) 6 (c) 8 (d) 9
30. 30.Which term of the AP 15, 17, 19, 21, … is 39? (a) 15th (b) 14th (c) 12th (d) 13th
31. 31.What is the median of 20, 30, 1, 31 and 40? (a) 31 (b) 1 (c) 20 (d) 30
32. 32.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 75° (d) 30°
33. 33.A bag has 6 red balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 10 (c) 15 (d) 2
34. 34.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
35. 35.The mean of 6 numbers is 30. When the number 2 is added to them, what is the new mean? (a) 27 (b) 26 (c) 30 (d) 16
36. 36.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 7/8 (c) 1/8 (d) 1/4
37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 16 (b) 15 (c) 17 (d) 5
38. 38.A bag has 8 white balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 10 (c) 14 (d) 9
39. 39.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) 21 (b) 28 (c) 22 (d) 29
40. 40.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18

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