Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 566 · 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 prime factorisation of 112? (a) 2³ × 7 (b) 2⁴ × 7 (c) 2 × 7⁴ (d) 2⁵ × 7
2. 2.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) 21 (b) 14 (c) 22 (d) 15
3. 3.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
4. 4.How many prime numbers are there between 20 and 40? (a) 6 (b) 5 (c) 3 (d) 4
5. 5.What is the midpoint of the line joining (3, 9) and (11, 13)? (a) (14, 22) (b) (7, 11) (c) (4, 2) (d) (11, 7)
6. 6.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 144 (c) 132 (d) 66
7. 7.How many prime numbers are there between 50 and 80? (a) 6 (b) 9 (c) 7 (d) 8
8. 8.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 55 (c) 45 (d) 90
9. 9.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 20 (c) 10 (d) 25
10. 10.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 105° (b) 210° (c) 75° (d) 30°
11. 11.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 1/3 (c) 1/4 (d) 2/3
12. 12.What is the smallest prime factor of 91? (a) 7 (b) 2 (c) 13 (d) 1
13. 13.What is the mode of 12, 11, 6, 17, 6, 12 and 12? (a) 6 (b) 12 (c) 17 (d) 11
14. 14.Two angles of a triangle are 30° and 105°. What is the exterior angle at the third corner? (a) 45° (b) 150° (c) 135° (d) 75°
15. 15.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 120° (b) 60° (c) 300° (d) 30°
16. 16.A cuboid is 7 cm long, 5 cm wide and 2 cm high. What is its total surface area? (a) 236 sq cm (b) 59 sq cm (c) 118 sq cm (d) 70 sq cm
17. 17.How many prime numbers are there between 50 and 60? (a) 3 (b) 4 (c) 1 (d) 2
18. 18.A bag has 7 black balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 9 (b) 2 (c) 8 (d) 10
19. 19.What is the midpoint of the line joining (3, 3) and (15, 1)? (a) (2, 9) (b) (18, 4) (c) (6, 1) (d) (9, 2)
20. 20.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 231 (d) 441
21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 18 (b) 9 (c) 20 (d) 19
22. 22.How many prime numbers are there between 30 and 50? (a) 4 (b) 6 (c) 7 (d) 5
23. 23.What is the distance between the points (5, 17) and (10, 5)? (a) 17 (b) 169 (c) 14 (d) 13
24. 24.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
25. 25.What is the prime factorisation of 168? (a) 2³ × 3 × 7 (b) 2 × 3 × 7³ (c) 2⁴ × 3 × 7 (d) 2² × 3 × 7
26. 26.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
27. 27.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 453 (c) 374 (d) 454
28. 28.What is the mode of 14, 19, 19, 12, 10, 14 and 19? (a) 14 (b) 12 (c) 10 (d) 19
29. 29.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
30. 30.In a class of 14 children, 5 like cricket, 9 like football and 2 like both. How many like only cricket? (a) 5 (b) 7 (c) 2 (d) 3
31. 31.In a class of 38 children, 20 like maths, 17 like science and 6 like both. How many like only maths? (a) 20 (b) 11 (c) 14 (d) 21
32. 32.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 11 (d) 10
33. 33.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/4 (c) 2/3 (d) 1/3
34. 34.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 100° (c) 40° (d) 80°
35. 35.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
36. 36.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 220 (b) 110 (c) 120 (d) 20
37. 37.Two straight lines cross. Two vertically opposite angles add up to 70°. What is each of the other two angles? (a) 110° (b) 290° (c) 35° (d) 145°
38. 38.A bag has 3 green balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 15 (b) 4 (c) 2 (d) 5
39. 39.In a class of 26 children, 6 like cricket, 18 like football and 3 like both. How many like at least one of the two? (a) 24 (b) 18 (c) 26 (d) 21
40. 40.In a class of 40 children, 12 like mangoes, 21 like bananas and 2 like both. How many like at least one of the two? (a) 29 (b) 40 (c) 31 (d) 33

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