Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 280 · 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.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 1/11 (c) 5/11 (d) 1/6
2. 2.A drawer has lots of 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) 4 (b) 5 (c) 3 (d) 2
3. 3.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 240 (d) 120
4. 4.What is the sum of the first 6 terms of the AP 10, 12, 14, …? (a) 90 (b) 20 (c) 180 (d) 96
5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 16 (b) 14 (c) 5 (d) 15
6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 3 (b) 2 (c) 4 (d) 5
7. 7.A bag has 3 red, 8 green and 8 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 8/19 (c) 8/11 (d) 11/19
8. 8.Two angles of a triangle are 40° and 105°. What is the exterior angle at the third corner? (a) 35° (b) 140° (c) 75° (d) 145°
9. 9.A bag has 12 red balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 22 (c) 13 (d) 14
10. 10.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 121 (c) 110 (d) 55
11. 11.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 14 (c) 42 (d) 21
12. 12.What is the mode of 2, 4, 9, 11, 9, 9 and 11? (a) 11 (b) 9 (c) 4 (d) 2
13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 5 (b) 3 (c) 4 (d) 6
14. 14.6 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 42 (b) 12 (c) 72 (d) 36
15. 15.What is the mode of 9, 18, 7, 2, 2, 18 and 18? (a) 7 (b) 9 (c) 2 (d) 18
16. 16.What is the prime factorisation of 90? (a) 2 × 3² × 5² (b) 2³ × 3² × 5 (c) 2 × 3² × 5 (d) 2² × 3² × 5
17. 17.A bag has 4 white balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 9 (d) 6
18. 18.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 115° (b) 65° (c) 66° (d) 245°
19. 19.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 100 (c) 90 (d) 55
20. 20.Which term of the AP 10, 16, 22, 28, … is 118? (a) 20th (b) 19th (c) 21st (d) 18th
21. 21.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 88 sq cm (c) 308 sq cm (d) 2464 sq cm
22. 22.A bag has 3 green, 8 yellow and 6 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 9/17 (b) 8/17 (c) 8/9 (d) 1/3
23. 23.A bag has 9 white balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 13 (c) 2 (d) 21
24. 24.What is the 16th term of the AP 11, 18, 25, 32, …? (a) 123 (b) 105 (c) 116 (d) 112
25. 25.What is the mode of 19, 9, 9, 9, 19, 17 and 16? (a) 9 (b) 16 (c) 17 (d) 19
26. 26.How many factors does 29 have? (a) 4 (b) 1 (c) 2 (d) 3
27. 27.In a class of 38 children, 11 like mangoes, 26 like bananas and 8 like both. How many like neither? (a) 17 (b) 8 (c) 9 (d) 1
28. 28.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/36 (c) 1/11 (d) 1/12
30. 30.What is the sum of the first 8 terms of the AP 4, 10, 16, …? (a) 200 (b) 46 (c) 224 (d) 400
31. 31.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
32. 32.In a class of 35 children, 23 like maths, 21 like science and 12 like both. How many like at least one of the two? (a) 44 (b) 35 (c) 32 (d) 20
33. 33.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 144 (b) 27 (c) 132 (d) 264
34. 34.A drawer has lots of white, red, yellow, black and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 6 (c) 2 (d) 10
35. 35.Which term of the AP 11, 15, 19, 23, … is 163? (a) 41st (b) 38th (c) 40th (d) 39th
36. 36.In a class of 29 children, 19 like dance, 12 like music and 3 like both. How many like at least one of the two? (a) 28 (b) 31 (c) 25 (d) 29
37. 37.There are 5 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 30 (b) 11 (c) 35 (d) 60
38. 38.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 1/4 (c) 1/2 (d) 3/4
39. 39.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
40. 40.What is the mode of 3, 3, 3, 8, 9, 18 and 8? (a) 8 (b) 3 (c) 18 (d) 9

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