Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 655 · 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.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 121 (c) 110 (d) 66
2. 2.Two angles of a triangle are 30° and 30°. What is the third angle? (a) 120° (b) 300° (c) 60° (d) 150°
3. 3.The mean of 9 numbers is 14. When the number 34 is added to them, what is the new mean? (a) 24 (b) 17 (c) 14 (d) 16
4. 4.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
5. 5.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/9 (c) 1/12 (d) 1/11
7. 7.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 25 (b) 30 (c) 9 (d) 15
8. 8.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 25 (d) 20
9. 9.If a + b = 12 and ab = 35, what is (a − b)²? (a) 74 (b) 144 (c) 4 (d) 2
10. 10.A bag has 6 red balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 14 (b) 8 (c) 7 (d) 2
11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 3 (b) 2 (c) 4 (d) 1
12. 12.What is the mode of 2, 3, 12, 2, 3, 6 and 3? (a) 2 (b) 12 (c) 6 (d) 3
13. 13.What is the distance between the points (1, 4) and (4, 8)? (a) 7 (b) 5 (c) 25 (d) 6
14. 14.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
15. 15.Using (a − b)² = a² − 2ab + b², what is 59²? (a) 3721 (b) 3599 (c) 3481 (d) 3491
16. 16.What is the product of the roots of x² − 11x + 30 = 0? (a) 31 (b) 29 (c) 30 (d) 11
17. 17.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 10° (c) 11° (d) 160°
18. 18.A bag has 12 blue balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 13 (b) 2 (c) 14 (d) 20
19. 19.A bag has 3 white balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 4 (c) 9 (d) 7
20. 20.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 110° (d) 55°
21. 21.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 9 times (c) 6 times (d) 3 times
22. 22.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
23. 23.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 72 (b) 8 (c) 40 (d) 36
24. 24.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 100° (c) 10° (d) 80°
25. 25.Using (a + b)² = a² + 2ab + b², what is 61²? (a) 3481 (b) 3721 (c) 3731 (d) 3601
26. 26.What is the midpoint of the line joining (0, 2) and (4, 4)? (a) (2, 1) (b) (3, 2) (c) (4, 6) (d) (2, 3)
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/11 (c) 1/12 (d) 1/18
28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 3 (b) 2 (c) 5 (d) 4
29. 29.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 267 (c) 250 (d) 268
30. 30.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 45 (c) 90 (d) 55
31. 31.A bag has 8 blue balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 9 (b) 10 (c) 2 (d) 16
32. 32.Using (a + b)² = a² + 2ab + b², what is 55²? (a) 2025 (b) 3025 (c) 3035 (d) 2525
33. 33.In a class of 24 children, 10 like tea, 10 like coffee and 3 like both. How many like only tea? (a) 14 (b) 3 (c) 10 (d) 7
34. 34.In a class of 32 children, 8 like mangoes, 21 like bananas and 5 like both. How many like at least one of the two? (a) 32 (b) 24 (c) 29 (d) 19
35. 35.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x + 1)(x + 16) (c) (x + 8)(x + 9) (d) (x − 8)(x − 9)
36. 36.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 140° (c) 115° (d) 65°
37. 37.What is the 16th term of the AP 8, 14, 20, 26, …? (a) 96 (b) 104 (c) 98 (d) 90
38. 38.Which is the correct factorisation of x² + 10x + 16? (a) (x + 2)(x + 8) (b) (x + 1)(x + 16) (c) (x + 1)(x + 9) (d) (x − 2)(x − 8)
39. 39.In a class of 21 children, 12 like dance, 12 like music and 2 like neither. How many like both? (a) 19 (b) 2 (c) 3 (d) 5
40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 7 (b) 6 (c) 5 (d) 4

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