Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 638 · 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.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
2. 2.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 50° (b) 160° (c) 150° (d) 130°
3. 3.A bag has 3 blue balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 5 (c) 4 (d) 7
4. 4.What is the 31st term of the AP 15, 22, 29, 36, …? (a) 217 (b) 225 (c) 210 (d) 232
5. 5.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 20° (c) 100° (d) 80°
6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/18 (c) 1/11 (d) 1/36
7. 7.What is the mode of 3, 2, 4, 12, 12, 12 and 4? (a) 12 (b) 4 (c) 3 (d) 2
8. 8.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 70° (d) 40°
9. 9.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 16 (c) 56 (d) 64
10. 10.In which quadrant does the point (1, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
11. 11.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
12. 12.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 125° (c) 55° (d) 70°
13. 13.Which term of the AP 19, 21, 23, 25, … is 59? (a) 22nd (b) 23rd (c) 21st (d) 20th
14. 14.How many factors does 75 have? (a) 5 (b) 4 (c) 6 (d) 7
15. 15.In a class of 43 children, 16 like dance, 22 like music and 10 like neither. How many like both? (a) 33 (b) 6 (c) 5 (d) 10
16. 16.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
17. 17.Which term of the AP 9, 14, 19, 24, … is 44? (a) 7th (b) 9th (c) 8th (d) 10th
18. 18.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 45 (c) 100 (d) 20
19. 19.In a class of 31 children, 16 like tea, 18 like coffee and 6 like neither. How many like both? (a) 3 (b) 9 (c) 25 (d) 6
20. 20.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 140° (b) 110° (c) 220° (d) 40°
21. 21.How many factors does 86 have? (a) 2 (b) 5 (c) 3 (d) 4
22. 22.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 5/6 (c) 1/4 (d) 1/3
23. 23.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 5/8 (c) 1/4 (d) 3/5
24. 24.In a class of 48 children, 18 like tea, 26 like coffee and 6 like both. How many like only tea? (a) 12 (b) 20 (c) 18 (d) 22
25. 25.How many prime numbers are there between 70 and 100? (a) 5 (b) 7 (c) 8 (d) 6
26. 26.Using (a − b)² = a² − 2ab + b², what is 49²? (a) 2499 (b) 2411 (c) 2601 (d) 2401
27. 27.In a class of 38 children, 21 like tea, 20 like coffee and 4 like both. How many like neither? (a) 2 (b) 4 (c) 1 (d) 5
28. 28.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 81 (c) 72 (d) 18
29. 29.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
30. 30.A bag has 10 blue balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 19 (b) 10 (c) 11 (d) 2
31. 31.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 48 (d) 16
32. 32.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 20 (c) 120 (d) 25
33. 33.Two angles of a triangle are 20° and 65°. What is the third angle? (a) 160° (b) 95° (c) 85° (d) 115°
34. 34.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 81 (d) 36
35. 35.A bag has 4 yellow, 5 white and 6 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 11/15 (b) 1/3 (c) 1/15 (d) 2/3
36. 36.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 28 (c) 42 (d) 49
37. 37.In a class of 32 children, 16 like maths, 22 like science and 3 like neither. How many like both? (a) 3 (b) 6 (c) 29 (d) 9
38. 38.A bag has 7 green, 9 blue and 4 yellow balls. One ball is taken out without looking. What is the probability that it is blue? (a) 9/11 (b) 9/20 (c) 11/20 (d) 1/3
39. 39.In a class of 19 children, 11 like maths, 10 like science and 3 like both. How many like at least one of the two? (a) 15 (b) 19 (c) 21 (d) 18
40. 40.A bag has 3 green balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 2 (c) 12 (d) 4

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