Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 167 · 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 many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 1 (b) 4 (c) 2 (d) 3
2. 2.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
3. 3.What is the prime factorisation of 84? (a) 2 × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7² (d) 2² × 3 × 7
4. 4.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 10 (c) 15 (d) 20
5. 5.How many factors does 77 have? (a) 3 (b) 5 (c) 4 (d) 2
6. 6.A bag has 9 red, 9 yellow and 8 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 17/26 (b) 9/26 (c) 9/17 (d) 1/3
7. 7.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 15 (c) 36 (d) 21
8. 8.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 20 (c) 10 (d) 11
9. 9.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/2 (c) 1/3 (d) 2/3
10. 10.A bag has 11 red balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 12 (b) 13 (c) 2 (d) 21
11. 11.What are the roots of x² − 9x + 20 = 0? (a) 1 and 8 (b) 4 and 5 (c) 2 and 10 (d) 1 and 20
12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 1/11 (c) 4/11 (d) 5/36
13. 13.How many prime numbers are there between 40 and 60? (a) 5 (b) 4 (c) 6 (d) 7
14. 14.How many factors does 87 have? (a) 4 (b) 2 (c) 5 (d) 3
15. 15.4 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 7 (b) 24 (c) 16 (d) 12
16. 16.A bag has 12 green balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 19 (c) 13 (d) 2
17. 17.3 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 6 (b) 12 (c) 9 (d) 5
18. 18.There are 8 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 64 (b) 40 (c) 12 (d) 32
19. 19.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/4 (c) 3/4 (d) 1/2
20. 20.What is the mode of 5, 5, 2, 8, 5, 17 and 17? (a) 17 (b) 8 (c) 5 (d) 2
21. 21.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
22. 22.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 420 (c) 39 (d) 210
23. 23.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
24. 24.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
25. 25.A bag has 8 yellow balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 10 (b) 9 (c) 2 (d) 17
26. 26.The mean of 7 numbers is 36. When the number 52 is added to them, what is the new mean? (a) 38 (b) 36 (c) 39 (d) 44
27. 27.In a class of 45 children, 22 like dance, 25 like music and 6 like both. How many like only dance? (a) 16 (b) 19 (c) 22 (d) 20
28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 16 (b) 14 (c) 15 (d) 4
29. 29.The mean of 6 numbers is 29. When the number 57 is added to them, what is the new mean? (a) 33 (b) 34 (c) 43 (d) 29
30. 30.What is the mode of 20, 8, 19, 8, 13, 20 and 8? (a) 8 (b) 13 (c) 20 (d) 19
31. 31.A drawer has lots of blue, white, black and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 5 (c) 2 (d) 4
32. 32.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2⁴ × 7 (c) 2⁵ × 7 (d) 2 × 7⁴
33. 33.Using (a + b)² = a² + 2ab + b², what is 92²? (a) 8104 (b) 8464 (c) 8474 (d) 7744
34. 34.A drawer has lots of blue, white, black, green 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) 10 (b) 6 (c) 5 (d) 2
35. 35.What is the missing term in the AP 15, 17, 19, ?, 23? (a) 23 (b) 20 (c) 22 (d) 21
36. 36.In a class of 31 children, 14 like dance, 22 like music and 1 like neither. How many like both? (a) 5 (b) 6 (c) 1 (d) 30
37. 37.What is the median of 4, 27, 12, 24, 3, 26 and 5? (a) 24 (b) 5 (c) 13 (d) 12
38. 38.In a class of 22 children, 15 like maths, 5 like science and 2 like both. How many like neither? (a) 4 (b) 6 (c) 5 (d) 2
39. 39.What is the sum of all the whole numbers from 1 to 24? (a) 276 (b) 288 (c) 600 (d) 300
40. 40.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 240 (d) 20

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