Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 371 · 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.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 56° (b) 110° (c) 125° (d) 55°
2. 2.A bag has 6 black balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 13 (d) 8
3. 3.How many factors does 52 have? (a) 5 (b) 4 (c) 7 (d) 6
4. 4.In a class of 18 children, 8 like mangoes, 11 like bananas and 4 like both. How many like at least one of the two? (a) 11 (b) 19 (c) 18 (d) 15
5. 5.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
6. 6.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 57 (c) 58 (d) 48
7. 7.How many prime numbers are there between 80 and 110? (a) 6 (b) 9 (c) 8 (d) 7
8. 8.What is the product of the roots of x² − 15x + 56 = 0? (a) 15 (b) 56 (c) 57 (d) 55
9. 9.There are 7 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 35 (b) 12 (c) 70 (d) 42
10. 10.Using (a − b)² = a² − 2ab + b², what is 19²? (a) 371 (b) 399 (c) 441 (d) 361
11. 11.In a class of 26 children, 15 like mangoes, 6 like bananas and 8 like neither. How many like both? (a) 4 (b) 8 (c) 18 (d) 3
12. 12.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
13. 13.What is the midpoint of the line joining (6, 7) and (16, 9)? (a) (8, 11) (b) (5, 1) (c) (22, 16) (d) (11, 8)
14. 14.What is the mode of 2, 20, 13, 4, 20, 4 and 4? (a) 4 (b) 13 (c) 2 (d) 20
15. 15.Two angles of a triangle are 25° and 90°. What is the exterior angle at the third corner? (a) 155° (b) 115° (c) 65° (d) 90°
16. 16.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/4 (c) 1/3 (d) 2/3
17. 17.Two angles of a triangle are 20° and 115°. What is the third angle? (a) 160° (b) 135° (c) 65° (d) 45°
18. 18.Using (a − b)² = a² − 2ab + b², what is 38²? (a) 1764 (b) 1444 (c) 1596 (d) 1454
19. 19.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) 16 times (c) 4 times (d) 64 times
20. 20.In a class of 38 children, 15 like mangoes, 23 like bananas and 3 like both. How many like at least one of the two? (a) 38 (b) 36 (c) 35 (d) 32
21. 21.A bag has 10 white balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 14 (c) 2 (d) 11
22. 22.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 16 (d) 24
23. 23.A bag has 6 blue, 4 yellow and 9 white balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 6/19 (c) 14/19 (d) 13/19
24. 24.What is the smallest prime factor of 319? (a) 11 (b) 29 (c) 2 (d) 1
25. 25.In a class of 44 children, 22 like dance, 22 like music and 7 like both. How many like only dance? (a) 22 (b) 16 (c) 7 (d) 15
26. 26.A bag has 5 yellow, 7 green and 4 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 7/9 (b) 9/16 (c) 7/16 (d) 1/3
27. 27.In a class of 25 children, 13 like tea, 8 like coffee and 8 like neither. How many like both? (a) 17 (b) 4 (c) 5 (d) 8
28. 28.5 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 50 (c) 30 (d) 25
29. 29.What is the prime factorisation of 35? (a) 5³ × 7 (b) 5² × 7 (c) 5 × 7² (d) 5 × 7
30. 30.A bag has 9 green, 3 white and 2 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 13/14 (b) 1/7 (c) 6/7 (d) 1/3
31. 31.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 36 (c) 45 (d) 81
32. 32.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 9 (c) 27 (d) 30
33. 33.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 20 (c) 25 (d) 21
34. 34.In a class of 36 children, 19 like cricket, 21 like football and 8 like both. How many like only cricket? (a) 19 (b) 11 (c) 15 (d) 13
35. 35.Two angles of a triangle are 35° and 105°. What is the exterior angle at the third corner? (a) 40° (b) 145° (c) 75° (d) 140°
36. 36.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 50° (c) 40° (d) 65°
37. 37.What is the distance between the points (9, 20) and (17, 5)? (a) 23 (b) 289 (c) 18 (d) 17
38. 38.A bag has 8 blue balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 10 (c) 9 (d) 15
39. 39.How many prime numbers are there between 70 and 100? (a) 8 (b) 6 (c) 5 (d) 7
40. 40.If a + b = 14 and ab = 48, what is (a − b)²? (a) 100 (b) 2 (c) 196 (d) 4

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