Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 472 · 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.The mean of 6 numbers is 26. When the number 5 is added to them, what is the new mean? (a) 26 (b) 22 (c) 24 (d) 23
2. 2.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
3. 3.A drawer has lots of red, yellow, green, 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) 6 (b) 10 (c) 5 (d) 2
4. 4.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 25° (b) 145° (c) 155° (d) 60°
5. 5.What is the distance between the points (0, 3) and (9, 15)? (a) 225 (b) 21 (c) 15 (d) 16
6. 6.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 132 (c) 21 (d) 66
7. 7.What is the mode of 17, 17, 17, 6, 6, 5 and 1? (a) 6 (b) 1 (c) 5 (d) 17
8. 8.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
9. 9.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 3/8 (c) 1/8 (d) 1/4
10. 10.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 12 (c) 30 (d) 36
11. 11.What is the sum of the roots of x² − 10x + 21 = 0? (a) 21 (b) 11 (c) 9 (d) 10
12. 12.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/3 (c) 1/2 (d) 3/4
13. 13.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) 40 (b) 32 (c) 12 (d) 64
14. 14.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 55 (d) 66
15. 15.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 3 (c) 12 (d) 9
16. 16.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
17. 17.A bag has 12 red balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 17 (b) 14 (c) 13 (d) 2
18. 18.Which is the correct factorisation of x² + 12x + 27? (a) (x + 3)(x + 9) (b) (x − 3)(x − 9) (c) (x + 1)(x + 11) (d) (x + 1)(x + 27)
19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
20. 20.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 55 (c) 121 (d) 110
21. 21.Two angles of a triangle are 65° and 85°. What is the third angle? (a) 115° (b) 150° (c) 30° (d) 95°
22. 22.What is the mode of 17, 18, 17, 17, 18, 1 and 2? (a) 2 (b) 18 (c) 1 (d) 17
23. 23.What is the 27th term of the AP 12, 17, 22, 27, …? (a) 135 (b) 142 (c) 147 (d) 130
24. 24.A drawer has lots of yellow, black, white and red 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) 8 (c) 5 (d) 2
25. 25.In which quadrant does the point (7, 4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
26. 26.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2⁵ × 5 (c) 2 × 5⁴ (d) 2³ × 5
27. 27.There are 7 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) 14 (b) 56 (c) 49 (d) 98
28. 28.What is the distance between the points (2, 6) and (10, 21)? (a) 289 (b) 18 (c) 17 (d) 23
29. 29.What is the midpoint of the line joining (5, 9) and (9, 11)? (a) (10, 7) (b) (14, 20) (c) (7, 10) (d) (2, 1)
30. 30.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 105 (c) 120 (d) 210
31. 31.A bag has 5 white balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 6 (b) 9 (c) 7 (d) 2
32. 32.What is the midpoint of the line joining (5, 10) and (9, 6)? (a) (14, 16) (b) (7, 8) (c) (2, 2) (d) (8, 7)
33. 33.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
34. 34.A bag has 5 white balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 16 (c) 12 (d) 2
35. 35.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 2/3 (b) 1/4 (c) 1/3 (d) 5/6
36. 36.In a class of 40 children, 30 like mangoes, 18 like bananas and 3 like neither. How many like both? (a) 8 (b) 37 (c) 3 (d) 11
37. 37.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
38. 38.How many factors does 86 have? (a) 2 (b) 3 (c) 5 (d) 4
39. 39.What is the mode of 13, 14, 13, 14, 10, 20 and 13? (a) 13 (b) 20 (c) 14 (d) 10
40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 17 (b) 16 (c) 15 (d) 5

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