Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 256 · 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.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
2. 2.What is the 15th term of the AP 4, 9, 14, 19, …? (a) 74 (b) 75 (c) 70 (d) 79
3. 3.If a + b = 13 and ab = 30, what is a² + b²? (a) 109 (b) 229 (c) 139 (d) 169
4. 4.There are 8 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 32 (b) 11 (c) 24 (d) 48
5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 43? (a) 3 (b) 2 (c) 5 (d) 4
6. 6.What is the mode of 16, 5, 18, 16, 11, 18 and 16? (a) 5 (b) 18 (c) 11 (d) 16
7. 7.What is the mean of 17, 3, 12, 7 and 6? (a) 10 (b) 11 (c) 8 (d) 9
8. 8.Two angles of a triangle are 25° and 55°. What is the exterior angle at the third corner? (a) 155° (b) 80° (c) 100° (d) 125°
9. 9.A drawer has lots of blue, green 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) 2 (b) 3 (c) 6 (d) 4
10. 10.How many prime numbers are there between 60 and 80? (a) 6 (b) 7 (c) 5 (d) 4
11. 11.Which is the correct factorisation of x² + 9x + 20? (a) (x + 4)(x + 5) (b) (x + 1)(x + 8) (c) (x − 4)(x − 5) (d) (x + 1)(x + 20)
12. 12.In a class of 26 children, 8 like dance, 18 like music and 4 like both. How many like at least one of the two? (a) 23 (b) 26 (c) 18 (d) 22
13. 13.Using (a − b)² = a² − 2ab + b², what is 48²? (a) 2314 (b) 2304 (c) 2704 (d) 2496
14. 14.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 2/3 (c) 1/2 (d) 1/3
15. 15.A drawer has lots of red, white, yellow, blue 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) 5 (b) 2 (c) 10 (d) 6
16. 16.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 216 cu cm (c) 217 cu cm (d) 144 cu cm
17. 17.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 70° (b) 130° (c) 160° (d) 110°
18. 18.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/4 (c) 1/2 (d) 1/3
19. 19.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
20. 20.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 7 (c) 15 (d) 8
21. 21.What is the distance between the points (0, 1) and (12, 17)? (a) 28 (b) 400 (c) 21 (d) 20
22. 22.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 2 times (d) 6 times
23. 23.What is the mean of 2, 17, 2, 8, 3 and 10? (a) 7 (b) 8 (c) 6 (d) 9
24. 24.What is the median of 35, 24, 15, 19 and 14? (a) 19 (b) 24 (c) 20 (d) 15
25. 25.What is the smallest prime factor of 93? (a) 31 (b) 2 (c) 3 (d) 1
26. 26.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2³ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2⁵ × 3 × 5
27. 27.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 95° (d) 115°
28. 28.In a class of 25 children, 10 like mangoes, 12 like bananas and 5 like both. How many like neither? (a) 3 (b) 13 (c) 5 (d) 8
29. 29.In a class of 43 children, 17 like cricket, 21 like football and 3 like both. How many like at least one of the two? (a) 38 (b) 43 (c) 35 (d) 32
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/36 (b) 1/11 (c) 1/18 (d) 1/12
31. 31.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
32. 32.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 15 (d) 30
33. 33.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) 37 (b) 25 (c) 36 (d) 24
34. 34.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 132 (c) 144 (d) 66
35. 35.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 169 (b) 182 (c) 25 (d) 91
36. 36.What is the 22nd term of the AP 10, 19, 28, 37, …? (a) 208 (b) 199 (c) 198 (d) 189
37. 37.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 24 (c) 10 (d) 21
38. 38.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
39. 39.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
40. 40.A bag has 8 yellow, 6 red and 8 white balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 4/11 (b) 7/11 (c) 1/3 (d) 15/22

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