Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 307 · 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.In which quadrant does the point (2, 4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
2. 2.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
3. 3.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 105° (b) 10° (c) 85° (d) 170°
4. 4.A bag has 10 red balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 15 (c) 11 (d) 6
5. 5.In a class of 31 children, 9 like cricket, 17 like football and 9 like neither. How many like both? (a) 9 (b) 4 (c) 5 (d) 22
6. 6.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 501 (b) 492 (c) 502 (d) 406
7. 7.A bag has 3 red balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 4 (d) 15
8. 8.What is the product of the roots of x² − 11x + 30 = 0? (a) 30 (b) 11 (c) 31 (d) 29
9. 9.The mean of 7 numbers is 36. When the number 52 is added to them, what is the new mean? (a) 38 (b) 36 (c) 44 (d) 39
10. 10.The mean of 5 numbers is 15. When the number 27 is added to them, what is the new mean? (a) 15 (b) 17 (c) 18 (d) 21
11. 11.Which term of the AP 1, 6, 11, 16, … is 51? (a) 13th (b) 12th (c) 11th (d) 10th
12. 12.In which quadrant does the point (8, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 11 (b) 12 (c) 3 (d) 13
14. 14.A drawer has lots of yellow, green and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 4 (c) 2 (d) 3
15. 15.What is the 22nd term of the AP 20, 29, 38, 47, …? (a) 189 (b) 218 (c) 198 (d) 209
16. 16.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
17. 17.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 25 (c) 20 (d) 120
18. 18.What is the sum of the roots of x² − 10x + 16 = 0? (a) 11 (b) 9 (c) 16 (d) 10
19. 19.In a class of 40 children, 27 like maths, 19 like science and 12 like both. How many like neither? (a) 6 (b) 7 (c) 12 (d) 18
20. 20.Which is the correct factorisation of x² + 12x + 35? (a) (x + 5)(x + 7) (b) (x + 1)(x + 11) (c) (x − 5)(x − 7) (d) (x + 1)(x + 35)
21. 21.A drawer has lots of white and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 3 (d) 2
22. 22.8 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) 96 (b) 48 (c) 56 (d) 14
23. 23.In a class of 35 children, 19 like cricket, 18 like football and 4 like both. How many like only cricket? (a) 15 (b) 17 (c) 14 (d) 19
24. 24.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 5/6 (c) 1/3 (d) 1/4
25. 25.What is the mode of 3, 1, 17, 20, 20, 17 and 17? (a) 1 (b) 3 (c) 17 (d) 20
26. 26.What is the product of the roots of x² − 11x + 18 = 0? (a) 17 (b) 18 (c) 19 (d) 11
27. 27.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 176 cm (d) 2464 cm
28. 28.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 100° (b) 125° (c) 135° (d) 45°
29. 29.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
30. 30.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 25 (d) 240
31. 31.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 49 (c) 21 (d) 28
32. 32.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
33. 33.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
34. 34.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/4 (c) 1/3 (d) 3/4
35. 35.What is the prime factorisation of 280? (a) 2³ × 5 × 7 (b) 2 × 5 × 7³ (c) 2⁴ × 5 × 7 (d) 2² × 5 × 7
36. 36.In a class of 25 children, 11 like dance, 12 like music and 4 like both. How many like only dance? (a) 11 (b) 7 (c) 8 (d) 13
37. 37.What is the prime factorisation of 15? (a) 3² × 5 (b) 3 × 5² (c) 3³ × 5 (d) 3 × 5
38. 38.In a class of 20 children, 13 like cricket, 6 like football and 4 like neither. How many like both? (a) 2 (b) 16 (c) 4 (d) 3
39. 39.If a + b = 13 and ab = 22, what is a² + b²? (a) 125 (b) 147 (c) 213 (d) 169
40. 40.A bag has 8 red balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 8 (c) 15 (d) 9

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