Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 463 · 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.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
2. 2.In a class of 28 children, 16 like cricket, 17 like football and 12 like both. How many like neither? (a) 7 (b) 12 (c) 19 (d) 8
3. 3.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2² × 3² × 7 (c) 2 × 3² × 7 (d) 2³ × 3² × 7
4. 4.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 24 (b) 12 (c) 13 (d) 25
5. 5.A bag has 9 red balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 8 (c) 2 (d) 10
6. 6.What is the 14th term of the AP 10, 12, 14, 16, …? (a) 26 (b) 36 (c) 38 (d) 28
7. 7.Which is the correct factorisation of x² + 15x + 56? (a) (x + 7)(x + 8) (b) (x + 1)(x + 14) (c) (x + 1)(x + 56) (d) (x − 7)(x − 8)
8. 8.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2² × 3² (c) 2³ × 3² (d) 2 × 3²
9. 9.What is the prime factorisation of 70? (a) 2 × 5 × 7² (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7
10. 10.In a class of 32 children, 26 like dance, 10 like music and 6 like both. How many like at least one of the two? (a) 30 (b) 24 (c) 32 (d) 36
11. 11.Which is the correct factorisation of x² + 8x + 12? (a) (x + 1)(x + 7) (b) (x + 1)(x + 12) (c) (x − 2)(x − 6) (d) (x + 2)(x + 6)
12. 12.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
13. 13.A bag has 4 red balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 5 (c) 6 (d) 10
14. 14.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 56 sq cm (b) 112 sq cm (c) 224 sq cm (d) 60 sq cm
15. 15.A bag has 2 green, 9 yellow and 4 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 2/5 (b) 3/5 (c) 2/3 (d) 1/3
16. 16.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 21 (b) 9 (c) 20 (d) 19
18. 18.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 72 (c) 36 (d) 18
19. 19.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
20. 20.What is the mode of 4, 9, 10, 7, 7, 9 and 9? (a) 7 (b) 9 (c) 4 (d) 10
21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 1 (b) 4 (c) 2 (d) 3
22. 22.6 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) 36 (c) 72 (d) 12
23. 23.In a class of 37 children, 20 like tea, 20 like coffee and 9 like both. How many like at least one of the two? (a) 22 (b) 31 (c) 40 (d) 37
24. 24.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
25. 25.What is the midpoint of the line joining (2, 9) and (12, 15)? (a) (5, 3) (b) (7, 12) (c) (14, 24) (d) (12, 7)
26. 26.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 144 (c) 78 (d) 132
27. 27.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 45 (c) 100 (d) 90
28. 28.A bag has 3 blue balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 4 (c) 5 (d) 6
29. 29.The mean of 6 numbers is 20. When the number 41 is added to them, what is the new mean? (a) 20 (b) 24 (c) 22 (d) 23
30. 30.If a + b = 5 and ab = 6, what is a² + b²? (a) 19 (b) 13 (c) 37 (d) 25
31. 31.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 3/11 (c) 1/12 (d) 1/11
32. 32.What is the mean of 8, 9, 7, 17, 7 and 24? (a) 13 (b) 11 (c) 12 (d) 14
33. 33.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
34. 34.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) 22 (b) 28 (c) 29 (d) 21
35. 35.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/5 (c) 1/4 (d) 3/8
36. 36.A cube has edges of 5 cm. What is its volume? (a) 150 cu cm (b) 15 cu cm (c) 100 cu cm (d) 125 cu cm
37. 37.In a class of 35 children, 20 like cricket, 17 like football and 9 like both. How many like at least one of the two? (a) 35 (b) 28 (c) 19 (d) 37
38. 38.In a class of 29 children, 24 like cricket, 13 like football and 10 like both. How many like neither? (a) 3 (b) 12 (c) 2 (d) 10
39. 39.What is the prime factorisation of 35? (a) 5³ × 7 (b) 5 × 7² (c) 5 × 7 (d) 5² × 7
40. 40.What is the 31st term of the AP 4, 10, 16, 22, …? (a) 184 (b) 180 (c) 190 (d) 186

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