Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 662 · 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 9, 7, 5, 10, 2 and 21? (a) 10 (b) 8 (c) 11 (d) 9
2. 2.A bag has 9 red, 2 blue and 9 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 11/20 (b) 9/20 (c) 9/11 (d) 1/3
3. 3.What is the smallest prime factor of 143? (a) 2 (b) 13 (c) 1 (d) 11
4. 4.What is the sum of all the whole numbers from 1 to 29? (a) 870 (b) 436 (c) 406 (d) 435
5. 5.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 135° (b) 70° (c) 115° (d) 110°
6. 6.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 145° (b) 120° (c) 95° (d) 85°
7. 7.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 66 (c) 69 (d) 22
8. 8.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 3/8 (c) 1/4 (d) 1/8
9. 9.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
10. 10.What is the distance between the points (8, 1) and (11, 5)? (a) 7 (b) 25 (c) 6 (d) 5
11. 11.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 60° (d) 30°
12. 12.What is the midpoint of the line joining (2, 5) and (14, 3)? (a) (8, 4) (b) (16, 8) (c) (6, 1) (d) (4, 8)
13. 13.What is the 32nd term of the AP 16, 18, 20, 22, …? (a) 64 (b) 62 (c) 78 (d) 80
14. 14.In a class of 29 children, 9 like cricket, 17 like football and 6 like both. How many like at least one of the two? (a) 26 (b) 14 (c) 29 (d) 20
15. 15.Which term of the AP 11, 17, 23, 29, … is 215? (a) 34th (b) 36th (c) 37th (d) 35th
16. 16.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 22 (c) 29 (d) 28
17. 17.What is the mode of 6, 4, 6, 13, 15, 13 and 13? (a) 15 (b) 13 (c) 6 (d) 4
18. 18.In a class of 39 children, 23 like cricket, 23 like football and 12 like both. How many like only cricket? (a) 11 (b) 23 (c) 12 (d) 16
19. 19.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) 25 (b) 36 (c) 37 (d) 24
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) 8 (b) 15 (c) 14 (d) 7
21. 21.In a league, 14 teams each play every other team once. How many matches are played? (a) 105 (b) 182 (c) 196 (d) 91
22. 22.Using (a − b)² = a² − 2ab + b², what is 49²? (a) 2601 (b) 2411 (c) 2401 (d) 2499
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 5/36 (b) 1/11 (c) 1/9 (d) 4/11
24. 24.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
25. 25.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 42 (d) 21
26. 26.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 252 (c) 246 (d) 262
27. 27.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 57 (c) 19 (d) 171
28. 28.If a + b = 8 and ab = 12, what is a² + b²? (a) 88 (b) 52 (c) 40 (d) 64
29. 29.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 30 (c) 12 (d) 36
30. 30.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 36 (c) 81 (d) 72
31. 31.How many factors does 44 have? (a) 4 (b) 7 (c) 6 (d) 5
32. 32.If a + b = 13 and ab = 36, what is a² + b²? (a) 97 (b) 241 (c) 133 (d) 169
33. 33.What is the distance between the points (1, 19) and (13, 3)? (a) 400 (b) 28 (c) 20 (d) 21
34. 34.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 21 (c) 30 (d) 15
35. 35.Two angles of a triangle are 50° and 110°. What is the third angle? (a) 130° (b) 160° (c) 20° (d) 70°
36. 36.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 50° (c) 40° (d) 130°
37. 37.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
38. 38.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
39. 39.What are the roots of x² − 16x + 63 = 0? (a) 1 and 63 (b) 1 and 15 (c) 7 and 9 (d) 3 and 21
40. 40.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 86° (c) 265° (d) 95°

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