Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 155 · 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 distance between the points (4, 20) and (16, 4)? (a) 20 (b) 21 (c) 400 (d) 28
2. 2.In a class of 44 children, 23 like mangoes, 21 like bananas and 5 like neither. How many like both? (a) 4 (b) 39 (c) 5 (d) 6
3. 3.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 4 (b) 2 (c) 3 (d) 5
5. 5.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 42 (c) 41 (d) 50
6. 6.In a class of 29 children, 22 like mangoes, 11 like bananas and 6 like both. How many like only mangoes? (a) 22 (b) 5 (c) 16 (d) 18
7. 7.What is the prime factorisation of 504? (a) 2⁴ × 3² × 7 (b) 2³ × 3² × 7 (c) 2² × 3² × 7 (d) 2 × 3² × 7³
8. 8.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 84 (c) 94 (d) 93
9. 9.What is the smallest prime factor of 221? (a) 17 (b) 13 (c) 1 (d) 2
10. 10.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 40° (c) 50° (d) 140°
11. 11.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
12. 12.What is the product of the roots of x² − 7x + 10 = 0? (a) 9 (b) 10 (c) 7 (d) 11
13. 13.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
14. 14.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 130° (c) 40° (d) 80°
15. 15.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 78 (c) 132 (d) 66
16. 16.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/2 (c) 1/3 (d) 1/4
17. 17.A bag has 3 white balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 12 (b) 4 (c) 5 (d) 2
18. 18.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 36 (c) 64 (d) 28
19. 19.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 18 (c) 36 (d) 81
20. 20.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 25 (c) 37 (d) 24
21. 21.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
22. 22.How many factors does 27 have? (a) 2 (b) 4 (c) 3 (d) 5
23. 23.A bag has 6 white balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 8 (b) 7 (c) 2 (d) 13
24. 24.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
25. 25.In a class of 23 children, 6 like mangoes, 19 like bananas and 1 like neither. How many like both? (a) 3 (b) 22 (c) 1 (d) 2
26. 26.In a class of 31 children, 7 like dance, 18 like music and 4 like both. How many like only dance? (a) 13 (b) 3 (c) 14 (d) 7
27. 27.What is the distance between the points (4, 21) and (9, 9)? (a) 17 (b) 169 (c) 14 (d) 13
28. 28.In a class of 36 children, 16 like mangoes, 14 like bananas and 4 like both. How many like at least one of the two? (a) 30 (b) 26 (c) 36 (d) 22
29. 29.How many prime numbers are there between 20 and 30? (a) 1 (b) 4 (c) 3 (d) 2
30. 30.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
31. 31.What is the product of the roots of x² − 6x + 8 = 0? (a) 8 (b) 6 (c) 9 (d) 7
32. 32.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) 22 (c) 14 (d) 15
33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 14 (b) 15 (c) 3 (d) 13
34. 34.If a + b = 11 and ab = 30, what is a² + b²? (a) 91 (b) 181 (c) 61 (d) 121
35. 35.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
36. 36.If a + b = 21 and ab = 108, what is a² + b²? (a) 333 (b) 657 (c) 441 (d) 225
37. 37.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 19 (c) 171 (d) 60
38. 38.What is the 26th term of the AP 2, 6, 10, 14, …? (a) 104 (b) 106 (c) 100 (d) 102
39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/11 (b) 1/12 (c) 3/11 (d) 1/9
40. 40.A bag has 9 blue balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 18 (b) 10 (c) 11 (d) 2

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