Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 990 · 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 missing term in the AP 10, 13, 16, ?, 22? (a) 19 (b) 22 (c) 20 (d) 18
2. 2.In a class of 22 children, 7 like cricket, 9 like football and 3 like both. How many like neither? (a) 6 (b) 9 (c) 3 (d) 12
3. 3.In a class of 41 children, 17 like tea, 23 like coffee and 8 like both. How many like only tea? (a) 15 (b) 18 (c) 17 (d) 9
4. 4.A bag has 3 red, 8 green and 4 yellow balls. One ball is taken out without looking. What is the probability that it is green? (a) 3/5 (b) 1/3 (c) 7/15 (d) 8/15
5. 5.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 45 (c) 36 (d) 72
6. 6.What is the mode of 5, 5, 14, 18, 5, 18 and 7? (a) 7 (b) 14 (c) 18 (d) 5
7. 7.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 28 (c) 42 (d) 21
8. 8.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 15) (b) (x − 7)(x − 9) (c) (x + 1)(x + 63) (d) (x + 7)(x + 9)
9. 9.What is the sum of the first 5 terms of the AP 5, 9, 13, …? (a) 75 (b) 65 (c) 21 (d) 130
10. 10.What are the roots of x² − 7x + 10 = 0? (a) 1 and 10 (b) 1 and 6 (c) 2 and 5 (d) 3 and 4
11. 11.Using (a + b)² = a² + 2ab + b², what is 73²? (a) 5339 (b) 5329 (c) 4909 (d) 4489
12. 12.A bag has 2 blue, 7 red and 8 green balls. One ball is taken out without looking. What is the probability that it is red? (a) 7/10 (b) 1/3 (c) 7/17 (d) 10/17
13. 13.A cuboid is 11 cm long, 9 cm wide and 4 cm high. What is its volume? (a) 99 cu cm (b) 396 cu cm (c) 24 cu cm (d) 358 cu cm
14. 14.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/2 (c) 1/4 (d) 1/3
15. 15.How many prime numbers are there between 20 and 40? (a) 3 (b) 6 (c) 5 (d) 4
16. 16.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 3/4 (c) 1/4 (d) 1/2
17. 17.6 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 12 (b) 36 (c) 72 (d) 42
18. 18.In a class of 28 children, 12 like cricket, 17 like football and 9 like both. How many like at least one of the two? (a) 11 (b) 29 (c) 28 (d) 20
19. 19.Using (a − b)² = a² − 2ab + b², what is 65²? (a) 4875 (b) 4235 (c) 5625 (d) 4225
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) 14 (b) 7 (c) 15 (d) 8
21. 21.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 870 (b) 57 (c) 841 (d) 435
22. 22.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 65 (b) 770 (c) 418 (d) 385
23. 23.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
24. 24.How many prime numbers are there between 80 and 110? (a) 9 (b) 6 (c) 8 (d) 7
25. 25.A bag has 6 green balls and 10 red 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) 16 (c) 2 (d) 11
26. 26.Using (a + b)² = a² + 2ab + b², what is 64²? (a) 4096 (b) 3616 (c) 3136 (d) 4106
27. 27.What is the midpoint of the line joining (8, 3) and (12, 15)? (a) (20, 18) (b) (10, 9) (c) (2, 6) (d) (9, 10)
28. 28.What is the midpoint of the line joining (0, 4) and (10, 6)? (a) (5, 1) (b) (6, 5) (c) (5, 5) (d) (10, 10)
29. 29.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/2 (c) 1/4 (d) 1/3
30. 30.In a class of 16 children, 10 like mangoes, 7 like bananas and 4 like both. How many like at least one of the two? (a) 13 (b) 17 (c) 9 (d) 16
31. 31.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
32. 32.Two angles of a triangle are 20° and 50°. What is the exterior angle at the third corner? (a) 160° (b) 130° (c) 70° (d) 110°
33. 33.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
34. 34.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 64 (c) 56 (d) 55
35. 35.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 28 (c) 64 (d) 56
36. 36.Two angles of a triangle are 40° and 85°. What is the third angle? (a) 95° (b) 140° (c) 55° (d) 125°
37. 37.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 24 (c) 132 (d) 66
38. 38.In a class of 37 children, 22 like cricket, 9 like football and 2 like both. How many like neither? (a) 10 (b) 6 (c) 8 (d) 2
39. 39.What are the roots of x² − 14x + 45 = 0? (a) 5 and 9 (b) 3 and 15 (c) 1 and 13 (d) 1 and 45
40. 40.A bag has 7 red balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 19 (c) 2 (d) 13

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