Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 296 · 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 mean of 14, 17, 20, 11 and 18? (a) 16 (b) 20 (c) 17 (d) 15
2. 2.A bag has 5 blue balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 6 (c) 7 (d) 12
3. 3.Using (a − b)² = a² − 2ab + b², what is 25²? (a) 875 (b) 1225 (c) 635 (d) 625
4. 4.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
5. 5.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 21 (c) 15 (d) 22
6. 6.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 120° (c) 60° (d) 160°
7. 7.A cuboid is 12 cm long, 10 cm wide and 5 cm high. What is its volume? (a) 460 cu cm (b) 120 cu cm (c) 27 cu cm (d) 600 cu cm
8. 8.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 255° (b) 150° (c) 105° (d) 75°
9. 9.What is the sum of the first 12 terms of the AP 3, 9, 15, …? (a) 432 (b) 468 (c) 69 (d) 864
10. 10.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 144 (b) 23 (c) 78 (d) 156
11. 11.How many prime numbers are there between 20 and 40? (a) 3 (b) 6 (c) 4 (d) 5
12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
13. 13.Which is the correct factorisation of x² + 12x + 35? (a) (x − 5)(x − 7) (b) (x + 5)(x + 7) (c) (x + 1)(x + 35) (d) (x + 1)(x + 11)
14. 14.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 70° (c) 140° (d) 40°
15. 15.What is the sum of the first 8 terms of the AP 1, 5, 9, …? (a) 240 (b) 136 (c) 120 (d) 29
16. 16.A cuboid is 7 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 112 cu cm (b) 15 cu cm (c) 144 cu cm (d) 28 cu cm
17. 17.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 24 (d) 12
18. 18.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
19. 19.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 4 (b) 1 (c) 2 (d) 3
21. 21.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 15 (c) 20 (d) 25
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 2/11 (c) 1/12 (d) 1/18
23. 23.In a class of 33 children, 22 like cricket, 20 like football and 11 like both. How many like neither? (a) 11 (b) 13 (c) 3 (d) 2
24. 24.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 64 (c) 56 (d) 16
25. 25.What is the sum of the first 9 terms of the AP 8, 12, 16, …? (a) 40 (b) 216 (c) 432 (d) 234
26. 26.What is the midpoint of the line joining (7, 10) and (11, 6)? (a) (9, 8) (b) (2, 2) (c) (18, 16) (d) (8, 9)
27. 27.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 150° (b) 270° (c) 90° (d) 120°
28. 28.What is the distance between the points (2, 0) and (8, 8)? (a) 100 (b) 11 (c) 14 (d) 10
29. 29.How many prime numbers are there between 30 and 40? (a) 3 (b) 4 (c) 1 (d) 2
30. 30.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 24 (c) 12 (d) 16
31. 31.In a class of 27 children, 10 like mangoes, 14 like bananas and 6 like both. How many like at least one of the two? (a) 18 (b) 12 (c) 27 (d) 24
32. 32.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3655 (c) 7482 (d) 3741
33. 33.There are 6 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) 24 (b) 30 (c) 10 (d) 48
34. 34.What is the prime factorisation of 15? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5² (d) 3 × 5
35. 35.In a class of 32 children, 20 like cricket, 17 like football and 7 like neither. How many like both? (a) 25 (b) 12 (c) 5 (d) 7
36. 36.What is the smallest prime factor of 253? (a) 2 (b) 1 (c) 23 (d) 11
37. 37.In a class of 23 children, 11 like cricket, 14 like football and 2 like neither. How many like both? (a) 4 (b) 5 (c) 2 (d) 21
38. 38.What is the missing term in the AP 5, 7, ?, 11, 13? (a) 10 (b) 11 (c) 9 (d) 8
39. 39.What is the distance between the points (7, 6) and (15, 21)? (a) 289 (b) 23 (c) 18 (d) 17
40. 40.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10

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