Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 218 · 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 dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/11 (c) 3/11 (d) 1/12
2. 2.What is the prime factorisation of 36? (a) 2 × 3² (b) 2² × 3³ (c) 2³ × 3² (d) 2² × 3²
3. 3.How many factors does 72 have? (a) 13 (b) 10 (c) 11 (d) 12
4. 4.In a class of 47 children, 26 like cricket, 20 like football and 9 like both. How many like only cricket? (a) 26 (b) 11 (c) 27 (d) 17
5. 5.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
6. 6.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
7. 7.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 24 (d) 48
8. 8.What is the median of 25, 32, 34, 10 and 4? (a) 34 (b) 25 (c) 32 (d) 21
9. 9.In a class of 34 children, 16 like mangoes, 25 like bananas and 9 like both. How many like only mangoes? (a) 7 (b) 9 (c) 8 (d) 16
10. 10.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 61° (c) 120° (d) 60°
11. 11.In a class of 35 children, 28 like maths, 14 like science and 11 like both. How many like at least one of the two? (a) 35 (b) 42 (c) 20 (d) 31
12. 12.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
13. 13.A bag has 7 green, 7 yellow and 6 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 7/10 (b) 3/10 (c) 1/3 (d) 3/4
14. 14.What is the median of 23, 12, 6, 3 and 10? (a) 6 (b) 12 (c) 11 (d) 10
15. 15.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
16. 16.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 16 (c) 12 (d) 24
17. 17.What is the median of 21, 10, 34, 9, 30, 12 and 38? (a) 9 (b) 21 (c) 30 (d) 22
18. 18.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 3/4 (c) 3/8 (d) 1/8
19. 19.A bag has 11 white balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 2 (c) 12 (d) 16
20. 20.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 784 (c) 406 (d) 812
21. 21.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
22. 22.What is the mode of 1, 11, 11, 14, 1, 1 and 2? (a) 1 (b) 11 (c) 14 (d) 2
23. 23.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 66 (d) 24
24. 24.A cuboid is 11 cm long, 7 cm wide and 5 cm high. What is its total surface area? (a) 385 sq cm (b) 334 sq cm (c) 167 sq cm (d) 668 sq cm
25. 25.In a class of 36 children, 20 like maths, 10 like science and 4 like both. How many like only maths? (a) 26 (b) 20 (c) 6 (d) 16
26. 26.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 155° (b) 115° (c) 25° (d) 90°
27. 27.In a class of 51 children, 23 like dance, 25 like music and 10 like neither. How many like both? (a) 10 (b) 8 (c) 41 (d) 7
28. 28.If a + b = 17 and ab = 72, what is (a − b)²? (a) 145 (b) 1 (c) 289 (d) 217
29. 29.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 80 (b) 41 (c) 10 (d) 40
30. 30.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 12 (b) 13 (c) 25 (d) 24
31. 31.What is the distance between the points (6, 18) and (18, 2)? (a) 28 (b) 20 (c) 21 (d) 400
32. 32.How many factors does 33 have? (a) 5 (b) 2 (c) 3 (d) 4
33. 33.How many prime numbers are there between 50 and 80? (a) 9 (b) 8 (c) 6 (d) 7
34. 34.Using (a + b)² = a² + 2ab + b², what is 91²? (a) 8281 (b) 7921 (c) 8291 (d) 8101
35. 35.What is the smallest prime factor of 319? (a) 11 (b) 1 (c) 29 (d) 2
36. 36.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 155° (b) 100° (c) 105° (d) 75°
37. 37.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 55° (b) 110° (c) 235° (d) 125°
38. 38.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) 15 (c) 22 (d) 14
39. 39.What is the smallest prime factor of 91? (a) 7 (b) 13 (c) 2 (d) 1
40. 40.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 2/3 (b) 5/6 (c) 1/3 (d) 1/4

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