Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 3 · 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.A bag has 4 blue balls and 10 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) 2 (c) 11 (d) 14
2. 2.In a class of 30 children, 12 like mangoes, 16 like bananas and 8 like both. How many like at least one of the two? (a) 20 (b) 30 (c) 28 (d) 12
3. 3.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 225 (c) 105 (d) 120
4. 4.Using (a − b)² = a² − 2ab + b², what is 57²? (a) 3259 (b) 3969 (c) 3249 (d) 3591
5. 5.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
6. 6.What is the mean of 17, 13, 18, 8, 14 and 8? (a) 12 (b) 13 (c) 14 (d) 15
7. 7.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/5 (b) 1/3 (c) 5/6 (d) 1/6
8. 8.What is the distance between the points (0, 6) and (5, 18)? (a) 169 (b) 14 (c) 13 (d) 17
9. 9.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 25° (c) 130° (d) 155°
10. 10.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
11. 11.Which is the correct factorisation of x² + 15x + 54? (a) (x − 6)(x − 9) (b) (x + 1)(x + 14) (c) (x + 6)(x + 9) (d) (x + 1)(x + 54)
12. 12.What is the mode of 6, 10, 19, 7, 10, 10 and 7? (a) 6 (b) 19 (c) 7 (d) 10
13. 13.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 324 (b) 35 (c) 342 (d) 171
14. 14.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 45 (c) 81 (d) 72
15. 15.Using (a − b)² = a² − 2ab + b², what is 46²? (a) 2116 (b) 2126 (c) 2484 (d) 2916
16. 16.What is the smallest prime factor of 87? (a) 2 (b) 1 (c) 3 (d) 29
17. 17.In a class of 19 children, 11 like cricket, 13 like football and 6 like both. How many like at least one of the two? (a) 12 (b) 24 (c) 18 (d) 19
18. 18.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 44 cm (c) 154 cm (d) 88 cm
19. 19.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
20. 20.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
21. 21.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 7 (c) 10 (d) 15
22. 22.How many prime numbers are there between 30 and 60? (a) 9 (b) 7 (c) 8 (d) 6
23. 23.What is the midpoint of the line joining (8, 9) and (10, 19)? (a) (18, 28) (b) (1, 5) (c) (9, 14) (d) (14, 9)
24. 24.How many prime numbers are there between 50 and 60? (a) 4 (b) 2 (c) 1 (d) 3
25. 25.Using (a − b)² = a² − 2ab + b², what is 38²? (a) 1444 (b) 1454 (c) 1596 (d) 1764
26. 26.A bag has 9 yellow, 4 blue and 3 red balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 1/4 (c) 5/16 (d) 3/4
27. 27.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 1/4 (c) 1/2 (d) 2/3
28. 28.In a class of 38 children, 15 like tea, 22 like coffee and 6 like neither. How many like both? (a) 32 (b) 4 (c) 5 (d) 6
29. 29.A bag has 7 black balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 11 (b) 2 (c) 8 (d) 9
30. 30.There are 8 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 14 (b) 96 (c) 56 (d) 48
31. 31.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 155° (b) 45° (c) 135° (d) 70°
32. 32.How many prime numbers are there between 40 and 50? (a) 3 (b) 5 (c) 2 (d) 4
33. 33.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
34. 34.A cuboid is 6 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 192 sq cm (b) 416 sq cm (c) 104 sq cm (d) 208 sq cm
35. 35.In a class of 51 children, 28 like cricket, 28 like football and 9 like both. How many like at least one of the two? (a) 56 (b) 38 (c) 51 (d) 47
36. 36.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 14 (c) 126 (d) 45
37. 37.How many prime numbers are there between 40 and 70? (a) 7 (b) 9 (c) 8 (d) 6
38. 38.A cuboid is 12 cm long, 9 cm wide and 4 cm high. What is its volume? (a) 25 cu cm (b) 108 cu cm (c) 432 cu cm (d) 384 cu cm
39. 39.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) 22 (b) 29 (c) 21 (d) 28
40. 40.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 155° (d) 25°

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