Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 607 · 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 mode of 16, 4, 1, 4, 2, 4 and 16? (a) 4 (b) 2 (c) 1 (d) 16
2. 2.What is the sum of the first 14 odd numbers (1 + 3 + 5 + …)? (a) 27 (b) 105 (c) 196 (d) 210
3. 3.What is the midpoint of the line joining (7, 5) and (15, 9)? (a) (4, 2) (b) (11, 7) (c) (22, 14) (d) (7, 11)
4. 4.A bag has 3 red, 2 green and 3 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 3/8 (b) 5/8 (c) 3/4 (d) 1/3
5. 5.Which is the correct factorisation of x² + 8x + 15? (a) (x + 1)(x + 7) (b) (x + 1)(x + 15) (c) (x − 3)(x − 5) (d) (x + 3)(x + 5)
6. 6.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 240 (c) 25 (d) 120
7. 7.What are the roots of x² − 8x + 12 = 0? (a) 2 and 6 (b) 1 and 7 (c) 1 and 12 (d) 3 and 4
8. 8.A drawer has lots of blue, 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) 6 (b) 3 (c) 2 (d) 4
9. 9.In a class of 33 children, 26 like tea, 12 like coffee and 6 like both. How many like only tea? (a) 20 (b) 26 (c) 21 (d) 6
10. 10.What is the mean of 8, 7, 9, 11, 13 and 6? (a) 11 (b) 10 (c) 9 (d) 8
11. 11.What is the product of the roots of x² − 9x + 14 = 0? (a) 14 (b) 15 (c) 13 (d) 9
12. 12.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 10° (c) 100° (d) 50°
13. 13.Which is the correct factorisation of x² + 15x + 54? (a) (x + 1)(x + 14) (b) (x − 6)(x − 9) (c) (x + 1)(x + 54) (d) (x + 6)(x + 9)
14. 14.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
15. 15.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
16. 16.What is the 16th term of the AP 12, 21, 30, 39, …? (a) 135 (b) 156 (c) 147 (d) 144
17. 17.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) 7 (b) 8 (c) 15 (d) 14
18. 18.3 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 5 (c) 12 (d) 6
19. 19.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 25° (c) 15° (d) 30°
20. 20.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 72 (b) 81 (c) 18 (d) 36
21. 21.In a class of 22 children, 15 like cricket, 13 like football and 7 like both. How many like neither? (a) 8 (b) 7 (c) 1 (d) 2
22. 22.Using (a − b)² = a² − 2ab + b², what is 37²? (a) 1849 (b) 1591 (c) 1379 (d) 1369
23. 23.The mean of 6 numbers is 27. When the number 20 is added to them, what is the new mean? (a) 28 (b) 27 (c) 26 (d) 25
24. 24.What is the mode of 10, 10, 4, 14, 4, 9 and 4? (a) 10 (b) 9 (c) 14 (d) 4
25. 25.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
26. 26.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 6/11 (c) 1/11 (d) 1/6
27. 27.A drawer has lots of red and black 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) 2 (d) 3
28. 28.What is the mean of 20, 11, 4 and 5? (a) 10 (b) 8 (c) 9 (d) 11
29. 29.What is the smallest prime factor of 33? (a) 1 (b) 11 (c) 3 (d) 2
30. 30.In a class of 33 children, 27 like cricket, 16 like football and 2 like neither. How many like both? (a) 2 (b) 10 (c) 31 (d) 12
31. 31.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
32. 32.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 155 (c) 156 (d) 146
33. 33.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 150° (b) 60° (c) 30° (d) 330°
34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/9 (c) 5/36 (d) 1/11
35. 35.5 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 35 (b) 70 (c) 40 (d) 12
36. 36.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
37. 37.In which quadrant does the point (4, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
38. 38.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 24 (d) 48
39. 39.In which quadrant does the point (−6, 6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
40. 40.What is the smallest prime factor of 155? (a) 2 (b) 5 (c) 1 (d) 31

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad