Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 843 · 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. 1.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 81 (c) 36 (d) 72
2. 2.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 25 (d) 20
3. 3.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
4. 4.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 64 (c) 36 (d) 56
5. 5.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
6. 6.In a class of 30 children, 11 like mangoes, 24 like bananas and 6 like both. How many like only mangoes? (a) 11 (b) 6 (c) 18 (d) 5
7. 7.What is the mean of 6, 13, 20, 18 and 8? (a) 14 (b) 12 (c) 15 (d) 13
8. 8.In a class of 22 children, 7 like tea, 15 like coffee and 3 like neither. How many like both? (a) 3 (b) 2 (c) 19 (d) 4
9. 9.Which term of the AP 6, 15, 24, 33, … is 177? (a) 20th (b) 21st (c) 22nd (d) 19th
10. 10.Using (a − b)² = a² − 2ab + b², what is 68²? (a) 5184 (b) 4896 (c) 4624 (d) 4634
11. 11.Which is the correct factorisation of x² + 13x + 36? (a) (x + 1)(x + 12) (b) (x + 4)(x + 9) (c) (x − 4)(x − 9) (d) (x + 1)(x + 36)
12. 12.A drawer has lots of yellow, blue, green and white 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) 4 (c) 2 (d) 8
13. 13.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
14. 14.What is the mode of 20, 3, 12, 3, 20, 20 and 17? (a) 17 (b) 3 (c) 20 (d) 12
15. 15.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
16. 16.Which is the correct factorisation of x² + 15x + 54? (a) (x + 1)(x + 14) (b) (x + 1)(x + 54) (c) (x − 6)(x − 9) (d) (x + 6)(x + 9)
17. 17.What is the smallest prime factor of 85? (a) 2 (b) 17 (c) 5 (d) 1
18. 18.What is the sum of the roots of x² − 6x + 8 = 0? (a) 6 (b) 7 (c) 5 (d) 8
19. 19.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 30° (c) 75° (d) 105°
20. 20.How many factors does 79 have? (a) 4 (b) 3 (c) 2 (d) 1
21. 21.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 88 sq cm (d) 2464 sq cm
22. 22.What is the 37th term of the AP 13, 20, 27, 34, …? (a) 252 (b) 259 (c) 272 (d) 265
23. 23.A bag has 4 blue balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 6 (c) 5 (d) 14
24. 24.A drawer has lots of green, blue 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) 6 (b) 4 (c) 2 (d) 3
25. 25.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 60 (b) 11 (c) 36 (d) 30
26. 26.A bag has 6 white, 6 blue and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not white? (a) 4/7 (b) 1/3 (c) 9/14 (d) 3/7
27. 27.Two angles of a triangle are 55° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 125° (c) 95° (d) 85°
28. 28.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 55° (b) 105° (c) 130° (d) 125°
29. 29.In a class of 32 children, 19 like maths, 12 like science and 3 like both. How many like neither? (a) 3 (b) 7 (c) 1 (d) 4
30. 30.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 2 times (c) 4 times (d) 8 times
31. 31.What is the 21st term of the AP 5, 9, 13, 17, …? (a) 84 (b) 89 (c) 85 (d) 80
32. 32.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
33. 33.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/2 (c) 1/4 (d) 1/3
34. 34.In a class of 38 children, 28 like maths, 15 like science and 9 like both. How many like at least one of the two? (a) 34 (b) 38 (c) 25 (d) 43
35. 35.If a + b = 13 and ab = 36, what is a² + b²? (a) 169 (b) 241 (c) 97 (d) 133
36. 36.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
37. 37.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 37 (c) 25 (d) 24
38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/12 (b) 2/11 (c) 1/18 (d) 1/11
39. 39.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 53 (b) 54 (c) 44 (d) 62
40. 40.What is the midpoint of the line joining (9, 11) and (11, 7)? (a) (20, 18) (b) (9, 10) (c) (10, 9) (d) (1, 2)

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